The solution of the system of equations is equal to (3, 4).
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (3, 4).
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an air traffic controller is tracking two planes. to start plane A is at the altitude of 4000 feet and plane B is at an altitude of 3146 feet. plane A is gaining altitude at 33.5 feet per second and plane B is gaining altitude at 50.75 feet per second
the two planes will be at the same altitude of approximately 5675.48 feet after 49.45 seconds.
What is plane?A plane is a flat two-dimensional surface that extends infinitely in all directions. In geometry, a plane is defined as a surface that is completely flat and has no thickness. It is often represented as a coordinate system with two perpendicular axes, usually labeled as the x-axis and y-axis.
Assuming that the two planes maintain their rates of ascent, we can use the following equations to determine when the planes will be at the same altitude:
altitude of plane A = 4000 + 33.5t
altitude of plane B = 3146 + 50.75t
where t represents time in seconds.
To find the time at which the two planes will be at the same altitude, we can set the two equations equal to each other and solve for t:
4000 + 33.5t = 3146 + 50.75tSubtracting 3146 from both sides, we get:
854 + 33.5t = 50.75t
Subtracting 33.5t from both sides, we get:
854 = 17.25t
Dividing both sides by 17.25, we get:
t = 49.45 seconds
Therefore, it will take approximately 49.45 seconds for the two planes to be at the same altitude. To find the altitude at which they will meet, we can substitute this value of t into either equation. Using the equation for plane A, we get:
altitude of plane A = 4000 + 33.5(49.45) = 5645.08 feet
Using the equation for plane B, we get:
altitude of plane B = 3146 + 50.75(49.45) = 5675.48 feet
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What is the area of the square that measures 3.1 m on each side
The area of the square with a side length of 3.1 meters is 9.61 square meters.
To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.
Area of a square = side length × side length
Substituting the given side length into the formula:
Area = 3.1 m × 3.1 m
To perform the calculation:
Area = 9.61 m²
It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.
Remember, to find the area of any square, you simply need to multiply the length of one side by itself.
The area of the square with a side length of 3.1 meters is 9.61 square meters.
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A student measures the mass of a sample is 2.7 grams. What is the percent error, given that the correct mass is 2.58 grams? Round to the nearest hundredth of a percent.
Answer:
the percent error in the student's measurement is 4.65%.
Step-by-step explanation:
The percent error can be calculated using the formula:
| (measured value - actual value) / actual value | * 100%
In this case, the measured value is 2.7 grams and the actual value is 2.58 grams. Substituting these values into the formula, we get:
| (2.7 - 2.58) / 2.58 | * 100% = 4.65%
Rounding this to the nearest hundredth of a percent, we get a percent error of 4.65%.
Therefore, the percent error in the student's measurement is 4.65%.
Given the system of linear equations:
{
y=−5 y=3x−2
Part A: Graph the system of linear equations.
Part B: Use the graph created in Part A to determine the solution to the system.
Part C: Algebraically verify the solution from Part B.
The equations y=−5 and y=3x−2 make up the system of linear equations
The solution to the system is (-1,-5)
The graph of the systemThe system of equation
y=−5
y=3x−2
See attachment for the graph of the system
The solution to the systemThis is the point where the lines of the equation intersect.
From the graph in (a), the lines intersect at point (-1,-5)
Hence, the solution to the system is (-1,-5)
How to verify the solutionIn (b), we have:
(x,y) = (-1,-5)
Substitute (x,y) = (-1,-5) in the system of equations.
So, we have:
-5 =−5
-5=3(-1)−2 -> -5 = -5
The above shows that the system of equations is true, for the solution
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32 is 32% of what?????
Answer:
32 is 32% of 100
Step-by-step explanation:
Answer: 100
Step-by-step explanation: 32 is 32% of 100
Which correctly shows the substitution step for the system?
y = x - 4
-4x - 6y = -16
O x-4 = -4x-6y
-4(x-4) - 6y = -16
O-4x-6(x-4) = -16
6y = x - 4
The solution to the system of equations is x = 4 and y = 0. In summary, the correct substitution step for the system is: -4x - 6(x - 4) = -16 .C answer is correct
To solve the given system of equations:
1) y = x - 4
2) -4x - 6y = -16
We can use the substitution method to eliminate one variable and solve for the other.
Step 1: Solve the first equation (1) for y in terms of x.
y = x - 4
Step 2: Substitute the expression for y from equation (1) into equation (2).
-4x - 6(x - 4) = -16
Step 3: Simplify and solve for x.
-4x - 6x + 24 = -16
-10x + 24 = -16
-10x = -16 - 24
-10x = -40
x = -40 / -10
x = 4
Step 4: Substitute the value of x back into equation (1) to solve for y.
y = 4 - 4
y = 0
Therefore, the solution to the system of equations is x = 4 and y = 0.
In summary, the correct substitution step for the system is:
-4x - 6(x - 4) = -16
By substituting the expression for y from equation (1) into equation (2) and simplifying, we obtain the equation -4x - 6y = -16, which can be further solved to find the values of x and y. C answer is correct
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Choose the expression that is equivalent to the expression n − n + n − n.
In a data distribution that is skewed left.
The median will be greater than the mean in a left-skewed distribution
We have,
In statistics, skewness is a measure of the asymmetry of a probability distribution around its mean.
A distribution is said to be skewed left if it has a long tail on the left side and the bulk of the data is on the right side.
When the data is skewed left, it means that the distribution is being pulled towards the left side.
This is because there are a few extreme values on the left side that are pulling the mean in that direction.
In contrast, the median is the middle value of the dataset, and it is not influenced by outliers.
For a left-skewed distribution,
The median will be greater than the mean because the mean is being pulled towards the left by the few extreme values.
In a data distribution that is skewed left, the mean will be less than the median.
This is because the mean is sensitive to outliers and is pulled towards the direction of the skewness, while the median is not affected by extreme values and is a more robust measure of central tendency.
Therefore,
The median will be greater than the mean in a left-skewed distribution
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If x = 2 and y = 6 , evaluate the following expression: 100 − 3 ( 3 y − 4 x )
Answer:
70
Step-by-step explanation:
100 - 3 ( 3(6) - 4(2) )
100 - 3 (18-8)
100 - 3 (10)
100 - 30= 70
In LMN if the hypotenuse MN=37 and LN=LM what is the measure of leg LN
Answer:
Step-by-step explanation:
If it has a hyptoenuse it is a right triangle.
The sides an be found by using:
a ² + b² = c²
since LN = LM the two legs are equal to each other - let's substitute a² for b² since a and be will be equal to each other.
a² + a² = 37²
2a² = 37²
√2a² = √37²
a√2 = 37
a\(\sqrt{2}\) /\(\sqrt{2}\) = 37 / \(\sqrt{2}\) (Divide each side by \(\sqrt{2}\) )
a = 26.16295
So LN = 26.16295 as well as LM
find the square root of 7
The value of the square root of 7 is,
⇒ √7 = 2.645
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
WE have to given that;
To find the value of the square root of 7 .
Since, the square root of 7 is,
⇒ √ 7
⇒ 2.645
Thus, The value of the square root of 7 is,
⇒ √7 = 2.645
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A cone-shaped paperweight is 5 inches tall, and the base has a circumference of about 12.56 inches. What is the area of a vertical cross section through the center of the base of the paperweight? Use 3.14 for π .
The area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.
To find the area of a vertical cross section through the center of the base of the cone-shaped paperweight, we need to determine the radius of the base first.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we know the circumference is about 12.56 inches, so we can set up the equation:
12.56 = 2πr
To solve for r, we divide both sides of the equation by 2π:
r = 12.56 / (2π)
Now we can calculate the radius:
r ≈ 12.56 / (2 × 3.14)
r ≈ 12.56 / 6.28
r ≈ 2 inches
The radius of the base is approximately 2 inches.
Since the vertical cross section passes through the center of the base, the shape of the cross section is a circle. The formula for the area of a circle is A = \(πr^2\), where A is the area and r is the radius.
Now we can calculate the area of the cross section:
A = \(πr^2\)
A ≈ 3.14 × \((2^2)\)
A ≈ 3.14 × 4
A ≈ 12.56 square inches
Therefore, the area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.
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Question 2/2
Question 1 Part B (01.02, 01.03 MC): A boutique owner needs to sell $1,200 in clothing each week. This week, she is within $125 of
her goal.
What does the variable in the equation represent? (2 points)
4 of 19
Back
A. Amount the owner needs to sell
B. Price per item
C. Number of items sold
D. Total sales for the month
1 answer(s) selected
Open notes navigator A
A boutique owner needs to sell $1,200 in clothing each week. This week, she is within $125 of her goal. The variable in the equation is
C. Number of items soldWhat is variable in math?A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem.
Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.
In the context of the problem, the boutique owner wants to make $1,200 in clothing each week. This amount in made by the number of items sold as this is added to get to the amount the boutique owner is targeting
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Complete the following indirect proof (proof by contradiction).
Given: Adjacent angles LA and ZB, formed by the intersection of two lines
Prove: At least one of the angles LA and B has measure 90° or greater
First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure \(90^{\circ}\) or greater" is true.
The assumption is equivalent to the following two statements:
(1) \(m\angle A\text{ } \boxed{ < 90^{\circ}}\)
(2) \(m\angle B\text{ } \boxed{ < 90^{\circ}}\)
Using (1) and (2) and the addition properties of inequalities, we conclude that \(m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}\).
On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles \(\angle A\) and \(\angle B\), \(m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}\).
Therefore, the assumption made is false, and the statement "at least one of the angles \(\angle A\) and \(\angle B\) has measure \(90^{\circ}\) or greater" is true.
The sum of a number and 16 is equal to 45. Find the number.
Answer:
The number is 29.
Explanation:
Let the number be x.
The sum of the number and 16 = n+16
Thus, the equation representing this situation is:
\(n+16=45\)Solve for n.
\(\begin{gathered} n=45-16 \\ n=29 \end{gathered}\)The number is 29.
original price is 45 and the new price is 56 what is the percent change
Answer:
podés hacerlo de varias formas cra
Cora hits the bullseye (the 75 point circle) 19 times during the archery season she hits the 33 point circle 238 times
What is the total number of points for those hits
The value of the given equation is 19 x 75 + 238 x 33 = 9279.
fundamental arithmetic operations:Addition, subtraction, multiplication, as well as division, are the four fundamental arithmetic operations. The division represents one of the most fundamental procedures in our daily work. A large group is divided into equal smaller groups. For instance, divide 25 by 5. The division fact, in this case, in this case, will be 25/5 = 5.
According to the given data:She hits the bullseye = 19 times.
she hits the 33 point circle 238 times.
Total number of points:
19 x 75 + 238 x 33 = 9279
19 x 75 = 1425
238 x 33 = 7854
So,
The value of the given equation is 19 x 75 + 238 x 33 = 9279.
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I understand that the question you are looking for is:
Cora hits the bullseye (the 75 point circle) 19 times during the archery season she hits the 33 point circle 238 times. What is the total number of points for those hits Complete the equation to model the situation_. Enter the correct numbers in the boxes. _ x 75 + _ x 33 =
In an arithmetic sequence, the seventh term is −9 and the nineteenth term is 39.
Find the common difference. Give only the exact value as your answer.
Answer:
37.5% that is the answer
Step-by-step explanation:
The required common difference is 4.
What is an arithmatic progression?An arithmetic progression or arithmetic sequence ( AP ) is a sequence of numbers such that the difference between the consecutive terms is constant.
Now it is given that,
the seventh term, T₇ = −9 and
the nineteenth term, T₉ = 39.
Let a be the first term, d is the common difference and n is the number of term.
Since Tn of the series is given as,
Tn = a + (n-1)d
Therefore,
T₇ = a + (7-1)d
⇒ -9 = a + 6d ...(i)
and,
T₉ = a + (19-1)d
⇒ 39 = a + 18d ...(ii)
Subtracting equation (ii) by (i) we get,
48 = 12d
or, d = 48/12
⇒ d = 4
Thus, the required common difference is 4.
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Convert 48 2/5 into a decimal
Answer:
48 and 2/5 converted into decimal form is 48.4
Answer:
\(48.4\)
Step-by-step explanation:
\(48 \frac{2}{5} \\ \frac{242}{5} \frac{ \times 20}{ \times 20} = \frac{4840}{100} \\ = 48.4\)
solve for y :
\(\longrightarrow \: \bold{3 + y = 18}\)
ty! ~
Answer:
y = 15
Step-by-step explanation:
Given :
3 + y = 18
This a simple algebraic equation.
Subtract 3 from both sides :
⇒ 3 + y - 3 = 18 - 3
⇒ y = 15
Answer:
y = 15
Step-by-step explanation:
Given equation:
3+y=18To Find:
Value of ySolution:
We can rewrite this equation as:
y+3 = 8[This'll ain't change the answer]
Now we could solve on a easy way.
STEPS:
Transpose +3 to the RHS, make sure to change it's sign from “+” to “-”.
=> y = 18-3
Subtract the integers which's on the RHS:
=> y = 15
Hence,the value of y will be 15.
\( \rule{225pt}{2pt}\)
A container with an open top is to have 10 m3 capacity and be
made of thin sheet metal. Calculate the dimensions of the box if it
is to use the minimum possible amount of metal.
The dimensions of the box if it is to use the minimum possible amount of metal are,
⇒ 2.714 m, 2.714 m, 1.358 m
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A container with an open top is to have 10 m³ capacity.
Now,
Let the dimensions are x, y and z.
Since, Volume of box = 10 m³
Hence, We get;
⇒ xyz = 10
⇒ z = 10/xy
Since, A container is open in top.
Hence, The surface area = 2xz + 2yz + xy
Substitute z = 10/xy;
⇒ S.A = 2x (10/xy) + 2y (10/xy) + xy
= 20/y + 20/x + xy
For minimum metal;
⇒ d (S.A)/ dx = 0
⇒ - 20/x² + y = 0
⇒ y = 20/x² ..(i)
And, d (S.A) / dy = 0
⇒ - 20/y² + x = 0
⇒ x = 20/y² ..(ii)
Divide equation (i) and ((ii);
⇒ x = y
Hence, We get;
⇒ xyz = 10
⇒ x³ = 10
⇒ x = 2.714
And, y = 2.714
So, The value of z is,
⇒ z = 10/xy
⇒ z = 10 / 2.714×2.714
⇒ z = 1.358 m
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what number times 1.1 equals 4.95
Answer:
4.5
Step-by-step explanation:
Let's set up an equation:
1.1n=4.95
n is the number
We can use a calculator to figure this out:
n=4.5
4. For each babysitting job, Adam charges a fee for his bus fare plus an hourly rate. The graph shows how he calculates the cost of a babysitting job. Write a linear function in the form
y = mx + b to represent the situation.
Ay = 3x+2
B. y = 3x+1
C. y = 6x+2
D. y = -6× + 2
y = 6x + 2 is the function which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.
The linear function in the form y = mx + b represents the situation where y represents the cost of the babysitting job
x represents the number of hours, "m" represents the hourly rate, and "b" represents the additional fee (bus fare).
y = 3x + 2 represents an hourly rate of 3 and an additional fee of 2.
y = 3x + 1 represents an hourly rate of 3 and an additional fee of 1.
y = 6x + 2 represents an hourly rate of 6 and an additional fee of 2.
y = -6x + 2 represents a negative hourly rate of -6 and an additional fee of 2.
Hence, y = 6x + 2 is the which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.
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find the measure of the indicated angle that makes lines u and v parallel
To make lines u and v parallel, the indicated angle must be 108°.
What are angles?An angle is a figure in Plane Geometry formed by two rays or lines that share a common endpoint. "Angle" comes from the Latin word "angulus," which means "corner." The two rays are referred to as the sides of an angle, and the common endpoint is referred to as the vertex.So, if two parallel lines n and m intersect, then all the angles generated in line m must be exactly the same as the angles generated in line n.
At the intersection of two lines, two adjacent angles must add up to 180°.According to the first criterion, the missing angle denoted by a "?" must have the same measure as the angle just below the 72° angle.According to the second (and previously used) criterion, we must have:
? + 72° = 180°When we solve that, we get:
? = 180° - 72° = 108°Therefore, to make lines u and v parallel, the indicated angle must be 108°.
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The National Park Service writes materials for students to use while in the parks. In a study of the effectiveness of some of these materials, a random sample of students was selected to take a short quiz about oak trees after using these materials. A random sample of park professionals also took the quiz. Investigators compared classifications (low, medium, and high) of the crown shapes—the general shapes of the leafy parts of the trees—made by students in s 6 through 12 with classifications made by professionals. Data from the study are shown in the table.
ProfessionalsStudentsTotalLow544397Medium483987High7916Total10991200
If the professionals and the students do not differ in the distributions of their responses, which of the following is equal to the expected number of students who classify the crown shapes as medium?
The expected number of students who classify the crown shapes as medium is approximately 38.3.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
To find the expected number of students who classify the crown shapes as medium, we need to use the assumption that the distributions of responses from the professionals and the students are the same. We can use the row and column totals to calculate the expected counts.
First, let's calculate the marginal totals for the students:
The total number of students is 91.
The total number of students who classified the crown shapes as low is 43.
The total number of students who classified the crown shapes as medium is 39.
The total number of students who classified the crown shapes as high is 9.
Now let's calculate the expected counts for the students who classified the crown shapes as medium:
The total number of classifications for the medium category is 87 (from the table).
The proportion of classifications in the medium category made by the professionals is 48/109.
The expected number of classifications in the medium category made by the students can be calculated as (proportion from professionals) x (total number of student classifications) = (48/109) x 87 = 38.3 (rounded to one decimal place).
Therefore, the expected number of students who classify the crown shapes as medium is approximately 38.3.
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Find the surface area of this cube 7m 7m 7m. Be sure to include the correct unit in your answer.
Answer:
294\(m^2\)
Step-by-step explanation:
The area of one face of the cube would be 7 x 7 = 49 \(m^2\)
Since there are 6 faces on a cube, the total surface area would therefore be 49 x 6 = \(294m^2\)
Which number is rational?
Answer:
D. Square root of 16
Step-by-step explanation:
Rational numbers are numbers that have simple answers. It is also considered as fractions, Integers, and possible square roots.
- If you chose the square root of 2 = 1.41
- Pi has a value of 3.14, It's not a fraction nor an integer so it's an Irrational number
- Square root of 10 is 3.16
- So Square root of 16 is 4 which is a regular number and a possible square root.
Thank you!
Answer:
last option- square root of 16 is a rational number
Can you help me find the area?
Answer:
52.72m
Step-by-step explanation:
half-circles)
\(c = \pi {r}^{2} \\ c = 3.14 \times 16 = 50.24 \div 2 = 25.12\)
rectangle)
\(4 \times 6 = 24\)
triangle)
\( {3}^{2} + {2}^{2} = {c}^{2} \\ 9 + 4 = 13 \\ \sqrt{13} = 3.6\)
Add everything-
\(3.6 + 25.12 + 24 = 52.72\)
What is 402,067 divided by 67 equal
Answer:
6001
Step-by-step explanation:
Answer:
6001
Step-by-step explanation:
Please someone help me ixl is hard for me
Answer:
1/6
Step-by-step explanation:
out of the 6 sides of the die, you can roll a 6 1 time. The formula = favorable/possible.
Hope this helps!