Shira's math test included a survey question asking how many hours students spent studying for the test. The scatter plot below shows the relationship between how many hours students spent studying and their score on the test. A line was fit to the data to model the relationship.

Which of these linear equations best describes the given model?

The value of x in the equation –x (–1) = 3x (–5) is x = 1

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the equation is given as

–x (–1) = 3x (–5)

Remove the bracket in the above equation

-x - 1 = 3x - 5

Collect the like terms in the above equation

3x + x = 5 - 1

Evaluate the like terms in the above equation

4x = 4

Divide both sides by 4 in the above equation

x = 1

Hence, the value of x in the equation –x (–1) = 3x (–5) is x = 1

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Answer:

-3, or D

Step-by-step explanation:

The equation which represents the explicit formula for a constant velocity arithmetic sequence is; Choice A; xₙ = x₁+(n-1)(v•△t).

It follows from convention that an arithmetic sequence is usually defined by an expression of the form;

T(n) = T(1) + (n-1)×d in which case, d = common difference.

Consequently, in the event that the velocity in discuss is constant, it follows that the required expression is; Choice A; xₙ = x₁+(n-1)(v•△t).

Therefore, xₙ = x₁+(n-1)(v•△t) represent the equation for explicit formula for a constant velocity arithmetic sequence.

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The pairs of angles that fit the description are

1. alternate exterior angles            S and Z; T and Y

2. alternate interior angles            U and X; V and W

3. consecutive interior angles       U and W; V and X

4. corresponding angles               S and W; T and X; U and Y; V and Z

5. vertical angles                           S and V; U and T; W and Z; Y and X

6. adjacent angles                         S and T; Y and Z

From the question, we are to list the angles that fit the given descriptions

1. alternate exterior angles            S and Z; T and Y

2. alternate interior angles            U and X; V and W;

3. consecutive interior angles       U and W; V and X

4. corresponding angles               S and W; T and X; U and Y; V and Z

5. vertical angles                           S and V; U and T; W and Z; Y and X

6. adjacent angles                         S and T; Y and Z

Hence, the pairs of angles that fit the description are

1. alternate exterior angles            S and Z; T and Y

2. alternate interior angles            U and X; V and W

3. consecutive interior angles       U and W; V and X

4. corresponding angles               S and W; T and X; U and Y; V and Z

5. vertical angles                           S and V; U and T; W and Z; Y and X

6. adjacent angles                         S and T; Y and Z

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The approximate area of the park on the grid is: E. about 40 km² to 50 km².

The number of square on a coordinate grid that is covered determines the area covered. We can make an estimate by counting how many of this square on the coordinate grid that is covered, then find out the area depending on how much square area each grid represents.

In the coordinate plane given, which shows a park, we are told that each of the square on the grid equals 1 k = square kilometer.

The number of each of these squares we can find that is covered by the park on the grid is: 48 squares.

Therefore, the area of 48 squares on the grid = 48 × 1 = 48 km². Since not all squares are fully covered by the park, we can state that the approximate area of the park on the grid is: E. about 40 km² to 50 km².

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Answer: B, C, E

Step-by-step explanation: a is wrong 32 tens is 320.  B is right. 321 tenths is 32.1 and 48 thousandths is 0.048 so C is correct. 32,148 hundredths is too much but 32,148 thousandths is 32.148

The percentage profit is 140%

What is percentage?

Percentage can be described as the expression of a number in hundredth.

The formula for calculating percentage profit is

profit/cost price × 100

cost price=  $50
selling price= $15
number of mats produced= 8

selling price of the mat= 15 × 8
= 120

Profit= selling price-cost price

= 120-50
$70

Therefore the percentage profit can be calculated as follows

= 70/50 × 100
= 1.4 ×100
= 140

Thus, the percentage profit is 140%


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The possible value of y are 16, 32 and 64

The table above is an exponential table.

Therefore, let's confirm the ratio of the y axis.

8 / 4 = 2

4 / 2 = 2

Therefore, the other y axis can be gotten as follows:

y = 8 × 2 =  16

y = 16 × 2 = 32

y = 32 × 2 = 64

y = 64 × 2 = 128

Therefore, the possible value of y are 16, 32 and 64

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Answer:$96.98

Step-by-step explanation: all you just do is to add it all up to the total amount.

Answer: $105.47

I hope you get the job!!!!!

Answer:

1/2.x+3(x-1)-5=30

1/2.x+3x-3-5=30

(1/2+3)x-8=30

7/2.x-8=30

7/2.x=38

7x=76

x=76/7

CMIIW

The height of the ground from the base of the window is 144 inches.

One angle of a right angle triangle is equals to 90 degrees.

Therefore, the sides and angles of the right triangle can be found using trigonometric ratios.

tan x = WY / XY

tan x  = opposite / adjacent

tan x = 24 / 8

x = tan⁻¹ 3

x = tan⁻¹ 3

x = 71.5650511771

x = 71.60°

tan 71.60 = h / 48

cross multiply

h = 48 tan 71.60

h = 48 × 3

h = 144 inches

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La ecuación estándar de la circunferencia es (x - 0.5)² + y² = 2.5².

En este problema debemos derivar la ecuación estándar de la circunferencia, cuyo diámetro está comprendido por el segmento de recta entre los puntos A(x, y) = (3, - 4) y B(x, y) = (- 2, - 4). La ecuación estándar de la circunferencia se presenta a continuación:

(x - h)² + (y - k)² = r²     (1)

Donde:

El centro de la circunferencia es el punto medio del segmento de recta AB:

(h, k) = 0.5 · (3, - 4) + 0.5 · (- 2, 4)

(h, k) = (1.5, - 2) + (- 1, 2)

(h, k) = (0.5, 0)

Y el radio de la circunferencia es la mitad de la longitud del segmento de recta AB:

[tex]r = \frac{1}{2}\cdot \sqrt{(-2 - 3)^{2}+[-4 - (-4)]^{2}}[/tex]

r = 2.5

Por tanto, la ecuación estándar de la circunferencia es (x - 0.5)² + y² = 2.5².

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Answer:  All-day ride passes cost $15 each

Step-by-step explanation:

It was $20 in total for everyone to get in, so subtract that from $65 to just focus on the all day passes

65-20=45

So the all day passes all together cost $45

Since your uncle bought it for you and 2 friends that's 3 people in total so divide 45 by 3

45 divided by 3 = 15

So each of the all day passes cost $15

Hope this helped  :)

Based on the fact that the number of points scored are consecutive numbers, the number of points scored by Lewis is D. 18 points.

Lewis is the player who scored the least amount of points as they are first in the order.

To find the total number of points scored in the game therefore, you need to assume Lewis's points based on the options, and then sum up the three numbers above it to see if they add up to 78 points.

If Lewis scored 19 points as the lowest then the total points would be:

= 19 + 20 + 21 + 22

= 82 points

If Lewis scored 20 points, the total points would be:

= 20 + 21 + 22 + 23

= 86 points

Lewis therefore scored less than 19 points.

If Lewis scored 18 points, the total is:

= 18 + 19 + 20 + 21

= 78 points

Lewis therefore scored 18 points.

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Answer:

  (b)  f(x) = 12.5(1.6^x)

Step-by-step explanation:

An exponential model is generally of the form ...

  f(x) = a·b^x

where 'a' is the initial value (for x=0), and 'b' is the growth factor, the multiplier when x increases by 1.

The ratio of the f(x) values for x=0 and x=1 is 20/12 ≈ 1.67. A number close to this will be the growth factor in the exponential function. There is only one answer choice showing a growth factor near 1.6. (Eliminates choices A, C, D.)

An exponential regression model can be produced by many graphing calculators and spreadsheets. The attachment shows a model that has the values matching choice B.

Answer:

100

Step-by-step explanation:

to turn whole numbers to a fraction it is whatever numbers out of 100

Answer:

99

Step-by-step explanation:

Rounding to the closest tenth of a cubic unit, the shaded solid's volume is 45.4 cubic units.

The 3D shape of a rectangular prism has six rectangular faces. Multiply a rectangular prism's three dimensions—length, width, and height—to determine its volume. Cubic units are used to measure volume.

The following formula can be used to determine a rectangular prism's volume:

Vr = Height * Width * Length

Triangular prism volume Vt is determined by its base area and height.

concerning the rectangular prism;

Vr = 1.7 × 1.7 × 4

Vr = 11.56 units in 3

Regarding the triangular prism

Vt = 0.5 × 5.7 × 5 × 4

Vt = 57 unit3

Volume of the solid shaded by Vt - Vr

The solid's shaded volume is equal to 57 - 11.56.

The colored solid's volume is 45.44 cubic units.

Due to this, the shaded solid's volume, when rounded to the nearest tenth of a cubic unit, is 45.4 cubic units.

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Answer:

[tex]y=x-1[/tex]

Step-by-step explanation:

The line of symmetry of an isosceles triangle is perpendicular to its base.

Given vertices of the isosceles triangle:

By sketching the triangle with the given points, we can see that AB is its base.  (See attached graph).

To find the equation for the line of symmetry, first find the slope of the line AB.  To do this, use the coordinates of points A and B and the slope formula.

Define the points:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{6-2}{3-7}=-1[/tex]

As the line of symmetry is perpendicular to line AB, its slope is the negative reciprocal of the slope of line AB.

Therefore, the slope of the line of symmetry = 1.

The line of symmetry will pass through point C (4, 3).

Therefore, substitute the found slope and the coordinates of point C into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-3=1(x-4)[/tex]

[tex]\implies y-3=x-4[/tex]

[tex]\implies y=x-1[/tex]

Therefore, the equation of the given isosceles triangle's axis of symmetry is:

[tex]y = x - 1[/tex]

If we graph the points

then we will get AC=CB

That means C is the point from where the axis of symmetry passes

Foot of perpendicular is midpoint of AB

Midpoint of AB

Find equation of C and foot of perpendicular

Slope

Equation

Answer:

In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer.

The answer is x = 4, y = -1 or (4, -1).

We are given :

Multiply the 1st equation with 3 and 2nd equation with 2.

3. 3(2x + 7y) = 3(1) ⇒ 6x + 21y = 3

4. 2(3x + 4y) = 2(8) ⇒ 6x + 8y = 16

Now, subtract : Equation 3 - Equation 4.

Substitute in the 1st equation.

Answer:

(4, - 1 )

Step-by-step explanation:

2x + 7y = 1 → (1)

3x + 4y = 8 → (2)

multiplying (1) by 3 and (2) by - 2 and adding will eliminate x

6x + 21y = 3 → (3)

- 6x - 8y = - 16 → (4)

add (3) and (4) term by term to eliminate x

0 + 13y = - 13

13y = - 13 ( divide both sides by 13 )

y = - 1

substitute y = - 1 into either of the 2 equations and solve for x

substituting into (1)

2x + 7(- 1) = 1

2x - 7 = 1 ( add 7 to both sides )

2x = 8 ( divide both sides by 2 )

x = 4

solution is (4, - 1 )

Answer:

-4

Step-by-step explanation:

Wehn dealing with order of operations, we can remember the expression PEMDAS, which stands for parentheses, exponents, multiplication, division, addition, and subtraction.

So, our first step in the above problem is the parentheses:

[tex]2(3-5)^3+4(-4+7)\\2(-2)^3+4(3)[/tex]

The second step is exponents:

[tex]2(-2)^3+4(3)\\2(-8)+4(3)[/tex]

The third step is multiplication:

[tex]2(-8)+4(3)\\-16+12[/tex]

The fourth and final step is addition:

[tex]-16+12\\-4[/tex]

The statements that are true regarding the angles formed by the transversal and parallel lines are:

A. m∠1 = 70°.

B. m∠2 = 110°

C. m∠6 = 70°.

E. m∠9 = 50°

H. m∠16 = 130°

Given the following angle measures formed when two parallel lines ( being cut by two transversals:

Using relevant theorems, let's determine which of the statements are true:

Angles 4 and 1 are vertical angles, therefore they are congruent based on the vertical angles theorem.

m∠4 = m∠1

m∠1 = 70°.

m∠2 = 180 - m∠4 [linear angles theorem]

m∠2 = 180 - 70

m∠2 = 110°

m∠6 = m∠4 [base on the alternate interior angles theorem]

m∠6 = 70°.

m∠9 = 180 - m∠12 [based on the linear angles theorem]

m∠9 = 180 - 130

m∠9 = 50°

m∠16 = m∠12 [based on the corresponding angles theorem]

m∠16 = 130°

The statements that are true are:

A. m∠1 = 70°.

B. m∠2 = 110°

C. m∠6 = 70°.

E. m∠9 = 50°

H. m∠16 = 130°

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the height of the endpoint of the kth rectangle equals the heights of the first and kth preceding rectangles.

= -2 +k*(5/n)

The study of geometry utilizing coordinate points is referred to as coordinate geometry (or analytic geometry). Finding the distance between two points, dividing lines in the m:n ratio, locating a line's midpoint, and computing the area of a triangle in the Cartesian plane can all be done using coordinate geometry.

The range for the definition of the function f(x) = x^2 + 4 is (-2, 2).

Between this interval, there are a total of 5 equal pieces.

Height of each rectangle's right endpoint equals if the interval is divided into n equal pieces. k=(5/n)

Therefore, the height of the endpoint of the kth rectangle equals the heights of the first and kth preceding rectangles.

= -2 + k*(5/n)

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The measure of centre includes mean median and mode and the measure of variability includes range, interquartile range and mean absolute deviation.

A measure of central tendency (measure of centre) is a value that attempts to describe a set of data by identifying the central position of the data set.

The measure of central tendency includes the mean, median and mode.

The measure of variation describes the amount of variability or spread in a set of data.

The common  measures of variability are the range, the interquartile range (IQR), variance, and standard deviation.

Therefore, the measure of centre includes mean median and mode and the measure of variability includes range, interquartile range and mean absolute deviation.

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Answer:

pi or 1 pi

Step-by-step explanation:

Area = 1/4 * pi * r^2 (because it is 1/4 of a full circle)

1/4 * pi * 2^2 (the radius is 2 because it is given in the picture)

1/4 * pi * 4 = 1 pi

area = pi

hope this helps! <3

Considering the given box-and-whisker plot, it is found that the bookstore sold between 2 to 12 books in 20 days.

A box and whisker plot shows three things:

From the plot given in this problem, the have that:

This means that the percentage of days in which between 2 to 12 books were sold is:

P = 75 - 25 = 50%.

Hence, out of 40 days, the amount of days is:

0.5 x 40 = 20 days.

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Answer:

2 7/12

Step-by-step explanation:

Simple fraction problem

Answer: it’s 128 (also what you did on my question was not cool, do better)

Step-by-step explanation:

We know the height is 6 and the length is 2 more than the height then the length is 8 (6+2=8) and then you solve for volume and get 128

The correct answer for the volume of the pyramid is [tex]128[/tex] cm³.

Given:

Square base edge  lenght 2 cm than the height of the pyramid.

Height of the pyramid is 6 cm.

Square base edge length = Height of pyramid + 2cm

= 8 cm.

Base area:

Area of the square is calculated as side².

Area of square = 8*8

= 64 cm²

Volume of pyramid is calculated as [tex]\dfrac{1}{3} *basearea*height[/tex]

[tex]\dfrac{1}{3}*64*6\\\\ =128[/tex]

The volume of the pyramid is [tex]128[/tex] cm³.

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The solution of the equation is (2, 1).

x=2 and y=1

A mathematical assertion that two expressions are equal is known as equating. It can be expressed as either an identity, in which case the variables can take on any value, or a conditional equation, in which case the variables can only have specific values (roots).

We have two options for finding the answer. The first is to solve the equations via term elimination:

x + 3y = 5  ..............1

x - 3y = -1  ...............2

2x = 4 ..............3

With the equation, we can determine x. (3)

x = 4/2

x = 2

To determine y, we may now swap out x=2 in equation (1).

x + 3y = 5

2 + 3y = 5

3y = 3

y = 1

We've discovered x and y now.

x=2

y=1

The second method involves removing x from equation 1.

x + 3y = 5

x = 5 - 3y

In the equation right now, we may substitute x = 5 - 3y.........  (2)

x - 3y = -1

(5 - 3y) - 3y = -1

5 - 6y = -1

6y = -6

y = 1

Currently, we can change y=1 in equations (1), (2), or (4) to find x.

We'll apply the equation (1)

x + 3y = 5

x + 3(1) = 5

x + 3 = 5

x = 2

The two variants x = 2 and y = 1 have allowed us to confirm this.

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The qualities of the set {(x,y): x>0,y>0} is as under:

Given a set {(x,y),x>0,y>0}.

We are required to determine the qualities of the set.

We know that a set is a collection of things,numbers, fractions, etc.

In any set the values of x represents the domain of the function and the values of y represents the value of codomain of the function with which the set belongs to.

Set={(x,y): x>0,y>0}

From the above set we can find the qualities stated below:

Hence the qualities of the set {(x,y): x>0,y>0} are that all values should be in first quadrant and all the values are positive.

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