Determine the relationship between the point (1, –5) and the given system of inequalities.
y ≤ 3x + 2
y > –2x – 3
Explain your answer both algebraically and graphically.
Answers
Answer:
In terms of algebra, the point (1, -5) fulfills the first inequality, but not the second, since -5 is not bigger than -5. The point (1, -5) on the graph is in the shaded region of the first inequality, but it is on the dashed line of the second inequality, which is not inclusive.
The system of inequalities are solved and the solution is not ( 1 , -5 )
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
y ≤ 3x + 2 be equation (1)
y > -2x - 3 be equation (2)
Now , on simplifying , we get
when x = 1 and y = -5
-5 ≤ 3 ( 1 ) + 2
-5 ≤ 5
Therefore , the inequality is true
And , when x = 1 and y = -5
-5 > -2 ( 1 ) - 3
-5 > -5
The inequality is false
Therefore , we can see that the point (1, -5) falls within the shaded region of the first inequality (below the line) but outside the shaded region of the second inequality (above the line).
Hence , the point satisfies the first inequality but not the second inequality
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Related Questions
the smiths spend 6% of their budget on entertainment. their total budget this year is $1,000 more than last year, this year they plan to spend $2,820 on entertainment. what was their total budget last year?
Answers
Step-by-step explanation:
Given : The Smiths spend 6% of their budget on entertainment.
i.e. , The money they spend on entertainment = 0.06 x ( Total budget)
{ 6% is converted to 0.06 , when we divide it by 100 to remove percentage)
Since , this year they plan to spend $2,580 on entertainment.
i.e. 0.06 x ( Total budget ) = $2,580
On dividing both sides by 0.06 , we get
( Total budget ) = $2,580 ÷ 0.06
= $43,000
Thus , their total budget for this year = $43,000
Also, Their total budget this year is $3,000 more than last year.
Therefore , their last year total budget = ( Total budget this year ) - $3000
= $43,000 - $3000
= $40,000
Hence, their total budget last year was $40,000.
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sketch the region of integration for the integral z 3 0 z 9 9x2 z 9y 0 f(x, y, z) dz dy dx. rewrite this integral as an equivalent iterated integral in three of the five possible other orders
Answers
The integral that is an equivalent iterated integral in three of the five possible other orders is
I= \(\int\limits^9_0\) \(\int\limits^{9-z}_0\)\(\int\limits^3_{\sqrt{9-y}\) f(x, y, z)dzdydx
What is meant by integration?An integral in mathematics assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that come from merging infinitesimal data. The process of determining integrals is known as integration.
Consider the integral,
I= \(\int\limits^3_0\) \(\int\limits^9_{9-x^{2}}\) \(\int\limits^{9-y}_0\)f(x, y, z)dzdydx
This implies that the solid is bounded by
0≤z≤9-y
9-x²≤y≤9
0≤x≤3
Therefore, y+z=9, z=0
y=9-x², y=9
x=0, x=3
Now, the region is given by,
y=9-x², y=9, x=3, x=0
The shaded region is the required region of the figure region.
For the next integral,
√9-y≤x≤3
0≤y≤9
I= \(\int\limits^9_0\) \(\int\limits^3_{\sqrt{9-y}\) \(\int\limits^{9-y}_0\)f(x, y, z)dzdydx
Here we have,
y+z =9, z=0
y=9-x², y=9
x=0, x=3
So, √9-y≤x≤3
The projection on the yz plane is,
y+z=0, z=0
y=9
0≤z≤9-y
0≤y≤9
I= \(\int\limits^9_0\) \(\int\limits^{9-y}_0\)\(\int\limits^3_{\sqrt{9-y}\) f(x, y, z)dzdydx
Again, 0≤y≤9-z
0≤z≤9
I= \(\int\limits^9_0\) \(\int\limits^{9-z}_0\)\(\int\limits^3_{\sqrt{9-y}\) f(x, y, z)dzdydx
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Question 1
The diameter of a bike wheel is 27 inches. If the wheel makes 15 complete rotations, how far does the bike travel?
Answers
Answer:
The bike will travel approximately 1,272 inches or 106 feet.
Step-by-step explanation:
The diameter of a circle (wheel) can be used to find the circumference, which is the total perimeter around the wheel. The formula used to find circumference is: C = dπ, where 'd' is the diameter and π = 3.14. In this case C = 27 x 3.14 ≈ 84.78 inches. Since this measurement represents the perimeter of wheel, we would need to multiply this number by 15 in order to find the total distance after 15 complete rotations of the wheel: 84.78 x 15 ≈ 1,272 inches. 1,272 inches is a large measurement, so we can easily convert this to feet by dividing by the number of inches per foot, or 12: 1272/12 = 106 feet.
9. Sketch the following pair of inequalities on the same graph and indicate its solution region. 2x + 3 2 3y - x - 3 and 2 + y 24 - 2x (3mks)
Answers
To sketch the pair of inequalities 2x + 3 < 2 + 3y - x and 2 + y < 24 - 2x, we can start by graphing their corresponding boundary lines.
For the first inequality, 2x + 3 < 2 + 3y - x, we can rewrite it as 3y - x - 2x < 2 - 3. Simplifying further, we have 3y - 3x < -1.
To find the boundary line, we set this equation equal to 0: 3y - 3x = -1. Solving for y, we get y = x/3 - 1/3. The boundary line is a straight line with a slope of 1/3 and a y-intercept of -1/3.
For the second inequality, 2 + y < 24 - 2x, we can rewrite it as y < 22 - 2x. The boundary line is y = 22 - 2x. It is a straight line with a slope of -2 and a y-intercept of 22.
Now, let's plot these boundary lines on the same graph:
Choose a suitable range of x and y values for the graph.Draw the line y = x/3 - 1/3 with a slope of 1/3 and a y-intercept of -1/3.Draw the line y = 22 - 2x with a slope of -2 and a y-intercept of 22.Shade the region that satisfies both inequalities (below the line y = x/3 - 1/3 and below the line y = 22 - 2x).Learn more about inequalities here : brainly.com/question/20383699
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One year Terry had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 2.85 . Also, Karla had the lowest ERA of any female pitcher at the school with an ERA of 2.95 . For the males, the mean ERA was 4.893 and the standard deviation was 0.949 . For the females, the mean ERA was 4.348 and the standard deviation was 0.997 . Find their respective z-scores. Which player had the better year relative to their peers, Terry or Karla ? (Note: In general, the lower the ERA, the better the pitcher.)
Answers
Answer:
Their respective z-scores are:
Thomas : -2.15279
Karla : -1.40221
Which player had the better year relative to their peers, Terry or Karla ?
Terry had a better year because he had a lower Era and he was a better pitcher.
Step-by-step explanation:
The formula for calculating a z-score is is z = (x-μ)/σ,
where x is the raw score,
μ is the population mean
σ is the population standard deviation.
any male pitcher at his school,
For Thomas:
z = (x-μ)/σ
x = 2.85 μ = 4.893 σ = 0.949.
z = 2.85 - 4.893/0.949
z = -2.15279
For Karla
z = (x-μ)/σ
x = 2.95 μ = 4.348 σ = 0.997.
z = (2.95 - 4.348) /0
z = -1.40221
Their respective z-scores are:
Thomas : -2.15279
Karla : -1.40221
Which player had the better year relative to their peers, Terry or Karla ? (Note: In general, the lower the ERA, the better the pitcher.)
Terry had a better year because he had a lower Era and he was a better pitcher.
suppose we have four piles of coins - pennies, nickels, dimes, and quarters. assume there are an uncountable number of coins in each pile. how many ways are there to choose 20 coins given we want at least one dime and at most one penny and exactly 6 nickels?
Answers
There are probability 720 ways to choose 20 coins given the constraints of at least 1 dime, at most 1 penny, and exactly 6 nickels.
There are 720 different ways to choose 20 coins from the four piles given the constraints of at least 1 dime, at most 1 penny, and exactly 6 nickels. To understand why, let's start with the number of ways to choose 20 coins from the four piles with no constraints. The number of ways to choose 20 coins from the four piles is equal to the number of combinations of 20 objects taken 4 at a time, which can be calculated with the formula. Since this number is far too large to calculate, let's look at a simpler example. If we wanted to choose 5 coins with no constraints, the number of ways to do this would be equal to the number of combinations of 5 objects taken 4 at a time, which can be calculated with the formula (\(4^5\))/(5!*(4-5)!). This number is equal to 5,456. Now let's look at the number of ways to choose 20 coins given the constraints of at least 1 dime, at most 1 penny, and exactly 6 nickels.
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Joel bought a new baseball glove for $24.00. He received a discount of 20% off the original price. Which fraction or decimal is equivalent to 20%?
Answers
Answer:
20% = 0.2
Step-by-step explanation:
To find the decimal version of the percentage, we need to divide by a 100.
20 / 100 = 0.2
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identify a set of test cases that satisfies the all defs criterion, for variables x, k and y in method fun. use trace tables to show how the def-use pairs are covered.
Answers
Thus, the minimum time taken for a car from start to end of the assembly unit is 14.
Algorithm for assembly line scheduling using dynamic programming:-
1. We need following parameter:
· S[i,j]: The jth station on ith assembly line
· a[i,j]: Time required at station S[i,j], because every station has some dedicated job that needs to done. · e[i]: Entry time of product on assembly line i [here i= 1,2] · x[i]: Exit time from assembly line i· t[i,j]: Time required to transit from station S[i,j] to the other assembly line.
2. Further in dynamic programming we have to ways to do so:
· Reach station S1j from S1,j-1 (same assembly line).
· Reach station S1j from S2,j-1 (switch from second assembly line).
3. Calculate minimum time to leave.
4. After that find the minimum time to leave the previous two stations.
5. Then combining it with the time spent on station.
6. calculate the leaving time of previous stations.
7. Finally, we need two tables to store the partial results that are calculated for each station in an assembly line.
Example:- a = [[5,4,3], [2,3,7]], t = [[0,2,2], [0,1,1]]
e1 = 3, e2 = 2
x1 = 3, x2 = 4
T1[0] = e1 + a[0][0] = 3+5 = 8
T2[0] = e2 + a[0][1] = 2+2 = 4
T1 = [8, 0, 0]
T2 = [4, 0, 0]
i = 1
T1[1] = min(T1[1-1] + a[0][1], T2[1-1] + t[1][1] + a[0][1])
= min(8+4, 4+1+4) = min(12,9)
T1[1] = 9
T2[1] = min(T2[1-1] + a[1][1], T1[1-1] + t[0][1] + a[1][1])
= min(4+3, 8+2+3) = min(7,13)
T2[1] = 7
T1 = [8, 9, 0] T
2 = [4, 7, 0]
i = 2
T1[2] = min(T1[2-1] + a[0][2], T2[2-1] + t[1][2] + a[0][2])
= min(9+3, 7+1+3) = min(12,11)
T1[2] = 11
T2[2] = min(T2[2-1] + a[1][2], T1[2-1] + t[0][2] + a[1][2])
= min(7+7, 9+2+4) = min(14,15)
T2[2] = 14​
T1 = [8, 9, 11]
T2 = [4, 7, 14]
ans = min(T1[n-1]+x1, T2[n-1]+x2)
= min(11+3, 14+4) = min(14, 18)
ans = 14
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use pictures for the question 100 points to brainlyest
Answers
Answer:
Step-by-step explanation:
Population of X is {1, 1, 2, 2, 2, 3, 3, 3}
Based on that, X's expected value, variance and standard deviation can be calculated as follows:
Expected Value, μ = 2.125 or 2.13
Variance, σ2 = 0.609375 0r 0.61
Standard Deviation, σ = 0.78062475 or 0.78
A survey was done that asked people to indicate whether they preferred to ride a
street bike or a mountain bike. The results of the survey are shown in the two-way
table.
Amjed is making a relative frequency table from this data.
What operation should Amjed perform to determine the relative frequency of a
person over 30 years old who prefers to ride a mountain bike? 1) Subtract 25 from 462, then divide by 462. 2) Divide 25 by 462. 3) Add 180 to 462, then divide by 463. 4) Divide 180 by 462
Answers
The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:
2) Divide 25 by 462.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.
The total number of people is given as follows:
58 + 164 + 215 + 25 = 462.
Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:
25/462.
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You have two very special dice. One has the numbers 1, 3, and 5 on it (each equally likely). The other has the numbers 2, 4, and 6 on it (each equally likely). If you roll these dice and add the values, what is the expected value of this sum?
Answers
Let X be the number obtained on the first die and Y the number obtained on the second. Let Z be the sum of these numbers, then, Z = X + Y. Since X and Y are independent random variables, E(Z) = E(X + Y) = E(X) + E(Y).Expected value of this sum can be calculated as follows:
Given, two dice have the numbers 1, 3, and 5, and 2, 4, and 6, each equally likely respectively. Expected value of rolling the first die is,
E(X) = (1 × 1/3) + (3 × 1/3) + (5 × 1/3) = 3. So, E(X) = 3.
Expected value of rolling the second die is,
E(Y) = (2 × 1/3) + (4 × 1/3) + (6 × 1/3) = 4. So, E(Y) = 4. The expected value of sum of X and Y is, E(X + Y) = E(X) + E(Y) = 3 + 4 = 7.Therefore, the expected value of the sum of two dice is 7.
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write an equation in slope-intercept form of the line that bisects the angle formed by ba−→−ba→ and bc−→−bc→.
Answers
any point on the line formed by the given vectors, for example, the midpoint of the line segment ba→.
x₀ = (ba→.x + bc→.x) / 2
y₀ = (ba→.y + bc→.y) / 2
ba→ and bc→, we first need to determine the bisector vector. Let's assume the slope-intercept form of the line is y = mx + b, where m is the slope and b is the y-intercept.
Find the unit vectors for the given vectors:
ba^→ = ba→ / |ba→|
bc^→ = bc→ / |bc→|
Find the sum of the unit vectors:
bisector^→ = ba^→ + bc^→
Normalize the bisector vector:
bisector^→ = bisector^→ / |bisector^→|
Find the slope of the bisector line:
m = bisector^→.y / bisector^→.x (slope = y-component / x-component)
Find the point (x₀, y₀) through which the bisector line passes:
Choose any point on the line formed by the given vectors, for example, the midpoint of the line segment ba→.
x₀ = (ba→.x + bc→.x) / 2
y₀ = (ba→.y + bc→.y) / 2
Substitute the values of m and (x₀, y₀) into the slope-intercept form:
y = m(x - x₀) + y₀
Now you have the equation of the line that bisects the angle formed by ba→ and bc→ in slope-intercept form.
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a) To determine if b is in a1, a2, a3, we need more information about the vectors a1, a2, and a3. The number of vectors in a1, a2, a3 is also unspecified.
b) It is unclear whether b is in the set w, and the number of vectors in w is not provided.
c) To show that a1 is in w, we need additional information or conditions beyond row operations.
a) Without specific information about the vectors a1, a2, and a3, we cannot determine if b is in a1, a2, or a3. The question does not provide any details regarding the values or properties of these vectors. Additionally, the number of vectors in a1, a2, and a3 is not specified. Therefore, it is not possible to answer these questions without additional information.
b) The question does not provide enough information to determine whether b is in the set w. The set w could represent a subspace or a collection of vectors, but its characteristics are unknown. Similarly, the number of vectors in w is not given, making it impossible to ascertain whether b is a member of w.
c) To demonstrate that a1 is in w, we require more information or conditions beyond row operations. The question does not specify the nature of w or provide any criteria for inclusion. Without this information, it is not possible to show that a1 is in w. Additional details or constraints are needed to address this part of the question accurately.
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please help me this is due midnight
Answers
Answer:
Wait does it mean the actual real life distance or the distance on paper?
Step-by-step explanation:
If its real like just google it lol.
a tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. at the start of a weekend, her win ratio is exactly $0.500$. during the weekend, she plays four matches, winning three and losing one. at the end of the weekend, her win ratio is greater than $0.503$. what's the largest number of matches she could've won before the weekend began?
Answers
Using the ratio we know that before the weekend started, she could have won as many as 164 games.
What is the ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.
A proportion is an equation that sets two ratios at the same value.
For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
So, let n be the number of victories so that:
n/2n = 1/2 and n+3/2n+4 > 503/1000
Now, cross multiply as follows:
1000n + 3000 > 1006n + 2012
n < 988/6 = 164 4/6 = 164 2/3
Therefore, using the ratio we know that before the weekend started, she could have won as many as 164 games.
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A researcher describes the characteristics of three groups of subjects in a study. What statistics should the researcher use to analyze this demographic data
Answers
These statistical measures help the researcher summarize, describe, and understand the data collected from the study participants.
As the researcher is describing the characteristics of the subjects, the appropriate statistical analysis would be descriptive statistics.
Descriptive statistics is a method that summarizes and describes the data collected in a study. It includes measures such as mean, median, mode, standard deviation, range, and frequency distribution.
These measures can provide a clear picture of the demographic data of the three groups of subjects and help in drawing meaningful conclusions.
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Q.2. If the line y=x is reflected over the x - axis and made flatter(less steep) by a factor of ½ then write the equation of the new line
Answers
Using translation concepts, the equation of the new line is:
\(y = -\frac{1}{2}x\)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem:
The function is reflected over the x-axis, hence it is multiplied by -1.It is made flatter by a factor of 0.5, that is, it is multiplied by 1/2.Hence the equation of the new line is:
\(y = -1 \times \frac{1}{2} \times x = -\frac{1}{2}x\)
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Need a two column proof for this problem, can't use any parallelogram or quadrilateral theorems, only triangle related and equidistance, altitude, median, and perpendicular bisector related theorems. Thank you!
Answers
Therefore , We have proved AE ≅ CF in the given quadrilateral .
What is congruence ?Two figures or objects are said to be congruent in geometry if they are the same size and shape, or if one is the mirror image of the other.
Here,
Statement
1)AB≅CD , AB║CD ,BF⊥AC and
DE⊥AC
2)ABCD is a parallelogram
3) AD≅BE , AD║BE
4)ΔDAE≅ ΔBCF
5)ΔDAE≅ ΔBCF are right Δ's
6) ΔDEA≅ ΔBFC
7) ΔADE≅ ΔCBF
8)AE ≅ CF
Reasoning
1)Given
2)if a quadrilateral has 1 pair of opposite side both side ≅, ║, then it is a parallelogram
3)In a parallelogram opposite side are ≅, ║
4)Alternate interior angles Δ's are congruent.
5)⊥ segments forms right Δ's.
6)right Δ's. are ≅.
7)AAS congruency theorem
8)Cpetc
Therefore , We have proved AE ≅ CF in the given quadrilateral .
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state how the 2 triangles are congruent?? SSS and SAS HELP ASAPPP??
Answers
The two triangles are congruent by SAS criterion.
What is SAS criterion?According to this standard, two triangles are said to be congruent if their two sides are equal to the sides of another triangle and their respective angles are also equal. The "Side-Angle-Side" triangle congruence theorem is referred to as the SAS Criterion.According to the Side-Angle-Side theorem of congruency, two sides and the angle they produce are congruent if they are equivalent to two sides and the included angle of another triangle.Verification:
Let's carry out an exercise to demonstrate SAS's validity. AB=PQ, BC=QR, and ∠B=∠Q are given. To demonstrate: ΔABC≅ΔPQRPlacing the triangle ABC over the triangle PQR will cause B to fall on Q and the AB side to coincide with the PQ side.Point A falls on point P because AB=PQ.The side BC will fall along the side QR since ∠B=∠Q.Point C is in line with point R since BC=QR. As a result, BC and QR coincide, while AC and PR coincide.ΔABC will therefore match ΔPQR. Consequently, ΔABC ≅ ΔPQR. This exemplifies the SAS congruence criterion.To learn more about SAS criterion, refer to https://brainly.com/question/22472034
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A car has a full tank of gas, holding
15 gallons
. It drives
300 miles
, and then stops for gas. After
10 gallons
of gas are added, the tank is full again. What is the gas mileage of the car?
Answers
Answer:
The mileage of the car is 30 miles per gallon
Step-by-step explanation:
Here, we are interested in calculating the gas mileage of the car.
The gas mileage refers to the number of kilometers the car can travel on a particular amount of fuel.
The full capacity of the car tank is 15 gallon
Now after traveling 300 miles, it stops for gas and 10 gallons of fuel are added to make the car full again.
What this means is that the car used up a total of 10 gallons of fuel for the 300 miles
Thus, the gas mileage of the car is that it used 10 gallons to travel a total of 300 miles
Expressing this as a ratio, we have 300 miles/10 gallons = 30 miles/ gallon
This means that on a gallon of fuel, the car can travel 30 miles
A juice mixture is six parts, orange juice, and two parts peach juice for every pitcher of the mixture. What fraction of the pitcher each type of juice
Answers
The fraction of the pitcher each type of juice are 1/3 and 2/3
Calculation the fraction of the pitcher each type of juiceFrom the question, we have the following parameters that can be used in our computation:
Parts = 6
Orange juice = 1
Peach juice = 2
using the above as a guide, we have the following:
Orange juice : Peach juice = 1 : 2
Multiply by 2
So, we have
Orange juice : Peach juice = 2 : 4
When represented as a fraction, we have
Orange juice = 1/3
Peach juice = 2/3
Hence, the fractions are 1/3 and 2/3
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Darias bought 5 school binders that cost $8.00 per
binder. If a back-to-school discount of 40% was
applied to his purchase, and then a 6% sales tax was
added, what was the total cost of the binders?
Answers
Answer:
$25.44
Step-by-step explanation:
First, find the original cost of the binders:
5(8)
= $40
Find the cost with the 40% discount:
40(0.6)
= $24
Find the cost with the 6% sales tax:
24(1.06)
= $25.44
So, the total cost of the binders was $25.44
Tim wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 5 3 4 m by 3 1 2 m. Find the area the grass seed needs to cover. Solve on paper. Then check your work on Zearn
Answers
The area of the grass seed needs to cover is 38.625 m².
What is the area of the rectangle?
A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
Here, we have
Given: Tim wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 5 3/4 m by 3 1/2 m.
We have to find the area the grass seed needs to cover.
Let the area of the grass seed needs to cover be A
Now , the area of the lawn L = ( 11 3/4 ) x 5 m²
The area of the lawn L = 58.75 m²
where the length of the pool l= ( 5 3/4 ) m = 5.75 m
The width of the pool is w = ( 3 1/2 ) m = 3.5 m
Now, Area of Rectangle = Length x Width
On simplifying, we get
Area of the pool P = 5.75 x 3.5 = 20.125m²
Now, the area of the grass seed needs to cover A = L - P
The area of the grass seed needs to cover A = 58.75 m² - 20.125 m²
The area of the grass seed needs to cover A = 38.625 m²
Hence, the area of the grass seed needs to cover is 38.625 m².
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Factor 12+54. Write your answer in the form a(b+c) where a is the GCF of 12 and 54
Answers
For the answer of factors of expression (12 + 54), in the form of a(b + c), where a is the GCF of 12 and 54 is equals to 6( 2 + 9).
In math, to factor a number means to express it as a product of (other) whole numbers, called its factors. For example, if 7x5 = 35, 7 and 5 are both factors. The divisors that give the remainder to be 0 are the factors of the number. We have an expression of numbers, 12 + 54. We have to write this expression in form of a( b + c), where a is GCF of 12 and 54. Now, we can write the factors of 12 and 54 are 12 = 2×2×3
54 = 2×3 ×3×3
The greatest common factor, GCF of 12 and 54 is 2×3 = 6. So, 12 + 54 = 6× 2 + 6×9
Taking out the common factor 6 from above expression, 6( 2 + 9) which is required form a( b + c). Hence, required expression is 6( 2 + 9).
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A storage bin has the shape of a cylinder with a conical top. What is the volume of the storage bin if its radius is
r
=
5. 8
ft, the height of the cylindrical portion is
h
=
7. 9
ft, and the overall height is
H
=
16. 7
ft?
Answers
Total volume = (V_cylinder)+(V_cone)
= 827.64 + 305 .45
=1133.09 ft³
To calculate the volume of the storage bin with a cylindrical portion and a conical top, we need to find the volume of each part and add them together.
Given:
Radius (r) = 5.8 ft
Height of cylindrical portion (h) = 7.9 ft
Overall height (H) = 16.7 ft
First, find the height of the conical top by subtracting the height of the cylindrical portion from the overall height:
Height of conical top (h_cone) = H - h = 16.7 - 7.9 = 8.8 ft
Now, calculate the volume of each part:
1. Volume of cylindrical portion (V_cylinder) = π*r²h = π(5.8²)(7.9) ≈ 827.64 ft³
2. Volume of conical top. (V_cone) = (1/3)π*r²h. (V_cone) = (1/3)π(5.8²)(8.8) ≈ 305.45 ft³
Finally, add the volumes of both parts to find the total volume of the storage bin:
Total volume = V_cylinder + V_cone = 827.64 + 305.45 ≈ 1133.09 ft³
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Shelley is 15 and has a goal of saving $800 toward her prom and senior trip in 2 years; right now she has $20 total. She's planning to open a savings account to deposit money from each paycheck. Which factor should she be LEAST concerned with when choosing a savings account? * 1 point Is there a maintenance fee for this account? What is the minimum amount required to open the account? Do her friends have accounts at the same bank? Does the account allow for free automatic deposits from her checking account?
Answers
Answer:
The answer is "Do her friends have accounts at the same bank?"
Step-by-step explanation:
In this question, the above given-choice is correct because the account on the same bank has certainly, but when a retirement fund in a company is concerned, you could only have a savings account on their behalf, and the mutual funds must then be distributed, and these several savings accounts can be opened is by tracking the amount they need to save for every savings target.
Which of the following is equivalent to 5(4-m)-2(m+3)? *
don’t give me that link .
Answers
\(\longrightarrow{\green{Option\:1.\:(14\:-\:7m)}}\)
\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)
\(5 \: (4 - m) - 2 \: (m + 3) \\ \\ = 20 - 5m - 2m - 6\)
Combining like terms, we have
\( = 20 - 6 - 5m - 2m \\ \\ = 14 - 7m\)
\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}\)
Please help will give Brain liest
Answers
Answer:
Lauren will finish the race faster 7 seconds faster, and 14 meters ahead.
Step-by-step explanation:
To answer this question, I will use the strategy of finding the slope of each of the proportional relationships (y = 8x for Lauren's run and y = ?x for Amani's run). The slope represents the rate at which the distance changes for each unit of time, so the person with the greater slope will finish the race faster.
To find the slope of Amani's run, I will use the tool of point-slope form, which is y - y1 = m(x - x1). I will plug in the coordinates for the second point listed in the table for Amani's run (5 seconds and 30 meters) to get y - 30 = m(5 - x1). Since I don't know the value of x1, I will solve for it in terms of m. I get x1 = 5 - (30/m).
Next, I will plug in the coordinates for the first point listed in the table for Amani's run (3 seconds and 18 meters) into the equation y - 30 = m(5 - (30/m)). I get 18 - 30 = m(5 - (30/m)). Solving for m, I find that Amani's run has a slope of m = -6.
Since Lauren's run has a slope of 8 and Amani's run has a slope of -6, Lauren will finish the race faster. To find out by how much, I will use the tool of proportional reasoning. Since the slope represents the rate at which the distance changes for each unit of time, the difference in the slopes (8 - (-6)) represents the difference in the rate at which the distance changes for each unit of time between the two runs. The difference is 14, so Lauren will finish the race 14 meters ahead of Amani for each second that they run. Since the race is 100 meters long, Lauren will finish the race approximately 7 seconds faster than Amani.
OA) 30°
O B) 60°
D) 50°
OC) 90°
Answers
Answer:
A
Step-by-step explanation:
We know that the sum of interior angles in a triangle is 180°. Looking at ΔWYZ, we can write:
? + 75 + 75 = 180
? + 150 = 180
? = 30°
The three inside angles of a triangle need to equal 180 degrees.
You are given the bottom two angles.
75 + 75 = 150
WYZ = 180 - 150 = 30
The answer is 30 degrees.
Suppose that you were offered a lottery with a 0.50 probability of winning $500 and a 0.50 probability of winning nothing or a guaranteed payoff of $300. If you choose the lottery, you would be considered O a risk taker O a risk-neutral individual O a risk avoider O a risk-creator
Answers
If you choose the lottery, you would be considered a risk taker.
By opting for the lottery with a 0.50 probability of winning $500 and a 0.50 probability of winning nothing, you are demonstrating a willingness to take a chance and accept the uncertainty associated with the potential outcomes. A risk taker is someone who is willing to engage in risky or uncertain situations for the possibility of gaining a favorable outcome. In this case, you are accepting the risk of potentially winning nothing in exchange for the chance to win a larger amount.
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find the open intervals over which the function is increasing or decreasing. write the answers in interval notation.
Answers
Given a quadratic function y = 36 - x² , the intervals over which the function is increasing is: (-∞ , 0) and the intervals over which the function is decreasing is: (0, ∞).
The standard form of a quadratic function is given by:
f(x) = ax² + bx + c
If a > 0, the graph of the function opens upward and the extreme point is the minimum one.
If a < 0, the graph of the function opens downward and the extreme point is the maximum one.
In this case, the function is: y = 36 - x²
Since the coefficient of the quadratic term is negative, or a < 0, then the graph opens downward and has a maximum point.
y = 36 - x² is already in the form of perfect square, hence, we can immediately compute:
x-intercepts : (-6,0) and (6,0)
y-(intercept = maximum point = (0, 36)
Before the maximum point, the function is increasing, while after the maximum point, the function is decreasing.
Hence,
increasing interval = (-∞ , 0)
decreasing interval = (0, ∞)
Your question is incomplete, most likely, it was:
Find the open intervals over which the function is increasing or decreasing. write the answers in interval notation.
y = 36 - x²
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