work out the equation of the straight line that passes (5,6)and (8,21)
give answer in the form y=mx+c where m and c are intergers
Answers
Answer:
Text Answer
y = 5x -24
Picture Answer
A = -8
B = 4
C = -24
Text Step-by-Step
Find the equation of the straight line that passes through (5, 6) and (8, 21). Give answer in y-intercept form.
slope = \(\frac{21-6}{8-5} = \frac{15}{3} = 5\)
y = 5x + b
Substitute the first point into my equation with unknown y-intercept.
6 = 5(5) + b
6 = 30 + b
b = -24
Equation of the line is: y = 5x -24
Picture Step-by-Step
Find the y-value for each respective x-value.
y = -x³ - 5x² +4
A = y(-2)
= -(-2)³ - 5(-2)² + 4
= 8 - 20 + 4
= -8
B = y(0)
= -(0)³ - 5(0)² + 4
= 0 - 0 + 4
= 4
C = y(2)
= -(2)³ - 5(2)² + 4
= -8 - 20 + 4
= -24
Related Questions
Solve and graph –7 < w – 4 < 2
Answers
Answer:
solution: -3<w<6
interval notation: (-3,6)
Step-by-step explanation:
The coordinates are (-3,6) all you have to do is put them on a graph! Hope this helps!
What is the value of each of the following expressions? 8+10∗2= 8/2∗∗3= 2∗∗2∗(1+4)∗∗2= 6+10/2.0−12=
Answers
The values of the given expressions are:
8 + 10 * 2 = 28
8 / 2 ** 3 = 1
2 ** 2 * (1 + 4) ** 2 = 100
6 + 10 / 2.0 - 12 = -1.0
Let's evaluate each expression step by step:
8 + 10 * 2
Start by performing the multiplication: 10 * 2 = 20
Then, perform the addition: 8 + 20 = 28
The value of the expression is 28.
8 / 2 ** 3
In this expression, ** represents exponentiation.
Start by evaluating 2 ** 3: 2 ** 3 = 8
Then, perform the division: 8 / 8 = 1
The value of the expression is 1.
2 ** 2 * (1 + 4) ** 2
Start by evaluating the parentheses: (1 + 4) = 5
Then, perform the exponentiation: (1 + 4) ** 2 = 5 ** 2 = 25
Finally, perform the remaining multiplication: 2 ** 2 * 25 = 4 * 25 = 100
The value of the expression is 100.
6 + 10 / 2.0 - 12
Start by performing the division: 10 / 2.0 = 5.0
Then, perform the addition and subtraction: 6 + 5.0 - 12 = 11.0 - 12 = -1.0
The value of the expression is -1.0.
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Some one explain please
Answers
Answer:
The value of \(x\):
\(\boxed {x = \frac{3y}{4} - 6}\)
The value of \(y\):
\(\boxed {y = \frac{4x}{3} + 8}\)
Step-by-step explanation:
Solve for the value of \(x\):
\(-4x + 3y = 24\)
-Subtract \(3y\) to both sides:
\(-4x + 3y - 3y = 24 - 3y\)
\(-4x = 24 - 3y\)
-Divide both sides by \(-4\):
\(\frac{-4x}{-4} = \frac{24 - 3y}{-4}\)
\(\boxed {x = \frac{3y}{4} - 6}\)
-----------------------------------------------------------------------
Solve for the value of \(y\):
\(-4x + 3y = 24\)
-Add \(4x\) to both sides:
\(-4x + 4x + 3y = 24 + 4x\)
\(3y = 24 + 4x\)
-Remember that the equation is in Standard Form:
\(3y = 4x + 24\)
-Divide both sides by \(3\):
\(\frac{3y}{3} = \frac{4x + 24}{3}\)
\(\boxed {y = \frac{4x}{3} + 8}\)
Solve each double inequality and indicate any three solutions.
\(1\leq \frac{4-a}{3} \leq 5\)
Answers
The solution of the double inequality is -11 <= a <= 1 and the three solutions in the solutions are -11, -10 and -9
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to solve the double inequality and indicate any three solutions?The inequality expression is given as
1 <= (4 - a)/3 <= 5
Multiply through the inequality expression by 3
So, we have the following inequality expression
3 * 1 <= 3 * (4 - a)/3 <= 5 * 3
Evaluate the products in the above inequality expressions
So, we have
3 <= 4 - a <= 15
Subtract 4 from all sides of the inequality expression
So, we have
-1 <= - a <= 11
Multiply all sides of the inequality expression by 1
So, we have
1 >= a >= -11
Rewrite as
-11 <= a <= 1
The numbers in the above solution are -11, -10 and -9
Hence, the solution of the double inequality is -11 <= a <= 1 and the three solutions in the solutions are -11, -10 and -9
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pls help! question is on the picture
Answers
Answer:
Uhhh
Step-by-step explanation:
Answer:
9/40
Step-by-step explanation:
Tan of an angle equals the length of the side opposite the angle divided by the length of the leg adjacent to the angle. Thus, for angle C, AB is opposite it, which is 9, and although both CA and CB are adjacent, adjacent typically refers to the leg, not the hypotenuse, so we want CB, which is 40. Opposite/Adjacent = 9/40
Which is the correct quotient with a letter as the remainder?
Answers
Answer:
A
Step-by-step explanation:
876 divided by 43 = 20
and the remainder is 16
in the case of other options, the quotients are correct but the remainders are wrong.
Therefore, A is the option with both correct quotient and remainder.
Tina wrote the equations 3 x minus y = 9 and 4 x + y = 5. What can Tina conclude about the solution to this system of equations?
Answers
Answer:
(2, –3) is a solution to the system of linear equations.
Step-by-step explanation:
Given: Equations:
3x - y = 9 --------(1),
4x + y = 5 --------(2),
Add Equation (1) + Equation (2),
3x + 4x = 9 + 5
7x = 14 ( Combine like terms )
x = 2 ( Divide both sides by 7 ),
From equation 1:
3(2) - y = 9
6 - y = 9
-y = 9 - 6 ( Subtraction 6 on both sides )
-y = 3
y = - 3 ( Multiplying -1 on both sides )
Which of the following is a binomial with degree 4?
A. 4x4 − 5x3 + 2x2 − x + 1
B. 3x4 + 1
C. 4x − 3
D. A binomial cannot have degree 4.
Answers
Answer:
the answer is A
Step-by-step explanation:
hope it's help
NEED HELP FAST 50 POINTS FOR RIGHT ANSWER> Use the slider to change the value of k, and observe the effect on the graph. Equation 1, y = 2x, is the parent exponential function. Equation 2, y = akx, is a transformation of the parent function when a = 2, k ≠ 0, and k ≠ 1. Adjust the slider for k to observe what happens to the graph of the transformation.
Answers
The effect of the parameter k on the exponential function is given as follows:
If k < 0, the graph of the function is inverted due to the negative exponent.If 0 < k < 1, the graph of the function is horizontally stretched.If k > 1, the graph of the function is horizontally compressed.How to interpret the transformation?The parent function in this problem is defined as follows:
\(y = 2^x\)
The transformed function is given as follows:
\(y = 2^{kx}\)
Hence:
For negative values of k, the exponent is negative, hence the graph of the function is inverted.If k is non-negative, the graph of the function is either horizontally compressed or horizontally stretched.More can be learned about transformations at brainly.com/question/28687396
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4x^4+35x^2-9=0 solve by factoring
Answers
For each survey in Exercises 1-31, describe the target population, sampling frame, sampling unit, and observation unit. Discuss any possible sources of selection bias or inaccuracy of responses. 18. The U.S. National Intimate Partner and Sexual Violence Survey was launched in 2010 to assess sexual violence, stalking, and intimate partner violence victimization among adult men and women. The survey was conducted by telephone, and two sampling frames were used. The landline telephone frame consisted of hundred-banks of telephone numbers in which at least one of the numbers in the bank was known to be residential. (A hundredbank is the set of hundred numbers in which the area code and first five digits are fixed, and the last two digits take on any value between 00 and 99.) Numbers known to belong to businesses were excluded. The cellular telephone phone frame consisted of telephone banks known to be in use for cell phones. In 2010, of the 201,881 landline and cell telephone numbers sampled, approximately 31% were ineligible (for example, they belonged to a business or were nonworking numbers). Another 53% were of unknown eligibility (usually because no one answered the telephone). When someone from an eligible household answered, the adult with the most recent birthday was asked to take the survey. From the 31,241 households determined to be eligible, a total of 18,049 persons were interviewed, of whom 16,507 completed the survey (U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, 2014).
Answers
The target population of the survey is adult men and women in the United States, specifically aimed at assessing , stalking, and partner
Sampling frame: The survey utilized two sampling frames. The first frame was a landline telephone frame consisting of hundred-banks of residential telephone numbers. The second frame was a cellular telephone frame consisting of telephone banks known to be in use for cell phones.
Sampling unit: The sampling unit for this survey is the telephone number, both landline and cellular, that was included in the sampling frames.
Observation unit: The observation unit for this survey is the individual adult who answered the telephone in an eligible household and completed the survey.
Possible sources of selection bias or inaccuracy of responses: There are several potential sources of bias and inaccuracy in this survey. First, the exclusion of numbers known to belong to businesses may introduce bias by underrepresenting individuals who primarily use business phone lines. Second, the large proportion of unknown eligibility (53%) due to unanswered calls may introduce non-response bias if those who did not answer have different characteristics compared to those who did answer. Third, using the adult with the most recent birthday as the respondent introduces a potential bias if certain demographic groups are more likely to be selected based on this criterion.
. The survey used two sampling frames, landline and cellular telephone frames, with telephone numbers as the sampling unit. The observation unit was the individual adult who answered the telephone in eligible households. Possible sources of bias include the exclusion of business numbers, non-response due to unanswered calls, and the selection of respondents based on the most recent birthday.
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The sampling distribution of differences between means approximates a normal curve whose _____is zero.
Answers
The sampling distribution of difference between means approximates a normal curve whose mean is zero.
The sampling distribution means the probability distribution based on the large number of samples of size n from the given population
Mean is the average of the given numbers and it is calculated by dividing the sum of observation by the number of observation. Here the term observation represents the given data.
Here they used the normal curve, sot its mean value is zero
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You have 16 digs for your current volleyball season. There are 3 games left in the season. You want to break your previous record of 20 digs in a
season. Write and solve an inequality that represents the number 2 of digs you must get in the remaining 3 games to break your record
Answers
Answer: 16+d>20
d>4
Step-by-step explanation:
d=digs
16+d>20
16-16+d>20-16
d>4
a survey of 130 college graduates was conducted. students were asked whether they were employed and if they were looking for a job. the following table shows the results. job searching no job searching total employed 28 61 89 not employed 18 23 41 total 46 84 130 according to the table, what is the probability that a randomly chosen student is not employed given that they are job searching? give your answer as a fraction in simplest form.
Answers
The probability that a randomly chosen student is not employed given that they are job searching is 9/23.
What is the probability that a randomly chosen person is not employed despite job searching
The probability of a student not being employed given that they are job searching is given by the conditional probability:
P(not employed | job searching) = P(not employed and job searching) / P(job searching)
We can find the probabilities for the numerator and denominator from the table:
P(not employed and job searching) = 18
P(job searching) = 46
Therefore, the conditional probability is:
P(not employed | job searching) = 18 / 46
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
P(not employed | job searching) = 9 / 23
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Which set of ordered pairs is a function?
{(-21).(-4, 2), (0, 3), (4,1),(-2,5)}
{(-1,5), (-1,4),(-1,3), (-1,2), (-1,1)}
{(-6, -4), (-4,-2), (0,0).(-4, 2). (-6,4)}
{(-5,1). (-3, 2), (-1,3), (1,4), (3,5)}
Answers
step by step explanation
At the beginning of the month, Rachel's Used Car Dealership had 80 cars on
the lot. Today, there are 100 cars on thelot. What is the percent change in the
number of cars on the lot this month?"
Answers
Answer:
25%
Step-by-step explanation:
Evaluate 5m+4 when m=8.
Answers
Answer:
44 is the answer for the question
Answer:
44
Step-by-step explanation:
5x8= 40
40+4=44
Which FAR Part 77 imaginary surface has slopes that may range from 20:1 to 50:1?
The primary surface
The horizontal surface
The approach surface
The conical surface
Answers
The conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1. The FAR Part 77 imaginary surface that has slopes that may range from 20:1 to 50:1 is the conical surface.
The conical surface is a three-dimensional surface defined by a combination of horizontal and inclined planes. It extends upward and outward from the end of the primary surface and has varying slope requirements. The slope of the conical surface represents the ratio of the change in elevation to the horizontal distance. A slope of 20:1 indicates that for every 20 units of horizontal distance, there is a 1-unit increase in elevation.
Similarly, a slope of 50:1 means that for every 50 units of horizontal distance, there is a 1-unit increase in elevation. Therefore, the conical surface is the correct answer as it allows for slopes ranging from 20:1 to 50:1.
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please help asap!!
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Answers
19 points!!!!! Tyrone wants to know how much wrapping papers is needed to cover a box with the dimensions shown
Answers
Answer:
B. 54 square inches
Step-by-step explanation:
Surface Area
= 2(lb + bh + lh)
= 2(6 x 3 + 3 x 1 + 6 x 1)
= 2(18 + 3 + 6)
= 2(27)
= 54 square inches
The correct option is (B).
733 times 60 and work it out on your asnwcer plzz
Answers
Answer:
733 x 60 = 43,980.
Step-by-step explanation:
Another way to do this equation is by adding 733 by itself 60 times.
Solve for b.
3(b + 2) – 3 = 15
Answers
Answer:
b=4
Step-by-step explanation:
3(b + 2) - 3= 15
3b + 6 - 3 = 15
3b + 3 = 15
3b = 12
b = 4
6.5x-10=4.5x+6 can someone give a step by step answer plz
Answers
Collect like terms
6.5x-4.5x = 6+10
2x = 6+10
Divide both sides
2x = 16
X= 8
Answer:
\(\huge{\bold{\boxed{\sf{x = 8 }}}}\)
Step-by-step explanation:
\(6.5x - 10 = 4.5x + 6\)
Move 4.5x to left hand side and change its sign.
Similarly, move 10 to right hand side and change its sign.
⇒\(6.5x - 4.5x = 6 + 10\)
Subtract 4.5x from 6.5x
⇒\(2x = 6 + 10\)
Add the numbers: 6 and 10
⇒\(2x = 16\)
Divide both sides by 2
⇒\(\frac{2x}{2} = \frac{16}{2}\)
Calculate
⇒\(\boxed{\sf{ x = 8 }}\)
Hope I helped!
Best regards!
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Perimeter and area polynomials
Answers
The combined perimeter of
2b (14y - 12)
2c (18y + 4)
2d (14y - 16), is
\(P=14y-12+18y+4+14y-16\)Add the like terms
\(\begin{gathered} P=(14y+18y+14y)+(-12+4-16) \\ \\ P=46y+(-24) \\ \\ P=46y-24 \end{gathered}\)The combined perimeter is (46y - 24)
The combined area of
1b (10y^2 - 27y +5)
1c (20y^2 + 11y - 3)
1d (12y^2 -24y), is
\(A=10y^2-27y+5+20y^2+11y-3+12y^2-24y\)Add the like terms
\(\begin{gathered} A=(10y^2+20y^2+12y^2)+(-27y+11y-24y)+(5-3) \\ \\ A=42y^2+(-40y)+2 \\ \\ A=42y^2-40y+2 \end{gathered}\)The combined area is (42y^2 - 40y + 2)
On a cold February morning, Colton checked the temperature on his phone and saw that it was -3ºC. When he checked again after school, the temperature had dropped 3°C. What was the temperature after school? To solve the problem, Ellen subtracted -3 - (-3) and came up with an answer of 0°C. Is Ellen correct? Why or why not?
Answers
What is the value of x in the equation: 3x – 5x + 10 = 36
Answers
Answer:
-13
Step-by-step explanation:
3x-5x+10=35
-2x+10=36
-2x=36-10
-2x\-2=26\-2
x=-13
Question 3 Let X1, X2,..., Xn be independent random variables, each having a uniform distri- bution over (0,1). Let M = maximum (X₁, X₂,..., Xn). Show that the distribution function of M, FM(-), is given by FM(x)=x, 0≤x≤1 What is the probability density function of M?
Answers
The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.
The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.
In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.
For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).
The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).
To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.
The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.
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The graph of y=f(x) is shown below.Draw the graph of y= -f(x).N-22
Answers
To graph the function -f(x) you reflect f(x) across the x-axis:
Graph of f(x) in black
Graph of -f(x) in red
find the volume of a cube with the given sides length. 1/5b^3
Answers
Answer:
\(\sf \dfrac{b^9}{125}\)
Step-by-step explanation:
We need to find out the volume of cube with the given side length . The side of the cube is ,
\(\sf\longrightarrow Side =\dfrac{1}{5}b^3\)
Now as we know that the volume of cube is ,
\(\sf\longrightarrow Volume = side^3\)
Substitute the given value ,
\(\sf\longrightarrow Volume =\Bigg(\dfrac{1}{5}b^3\Bigg)^3\\\\\sf\longrightarrow \boxed{\red{\sf Volume = \dfrac{b^9}{125}}}\)
A hybrid car with a 9.80 gal tank consumes gasoline at a rate of 54.1 miles/gal. How many liters of gasoline will be consumed traveling 132 km
Answers
So, approximately 1.520 liters of gasoline will be consumed traveling 132 km in the hybrid car.
A hybrid car with a 9.80-gallon tank consumes gasoline at a rate of 54.1 miles/gallon. To determine how many liters of gasoline will be consumed traveling 132 km, we first need to convert the distance to miles and the fuel consumption rate to liters.
First, let's convert the 9.80 gallon tank to liters. One US gallon is equivalent to 3.78541 liters, so:
9.80 gal x 3.78541 L/gal = 37.09 L
This means that the hybrid car can hold up to 37.09 liters of gasoline in its tank.
Next, we need to determine how many gallons of gasoline will be consumed traveling 132 km. We know that the car has a fuel efficiency of 54.1 miles per gallon, but we need to convert that to kilometers per liter in order to make our calculation. One mile is equivalent to 1.60934 kilometers, and one gallon is equivalent to 3.78541 liters, so:
54.1 miles/gallon x 1.60934 km/mile = 86.905 km/liter
Now we can use this fuel efficiency to calculate how many liters of gasoline will be consumed traveling 132 km:
132 km / 86.905 km/liter = 1.520 liters
Therefore, the hybrid car will consume approximately 1.520 liters of gasoline traveling 132 km.
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