A customer purchases a pair of jeans and a few shirts. Each shirt costs the same amount. The expression 60 + 20x represents the cost before tax.

What do the different parts of the expression model?



Drag the parts of the expression into the boxes to match each description.

cost of jeans | Total cost of the shirts
60, 20x, 20, x

The equation of the line that has a slope of -4 and passes through the point (4, -1) is y = -4x + 15.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of a line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:
An equation,

y = x/4 - 2.

The slope of the line that is perpendicular to the line y = x/4 - 2 is,

= -(1/1/4)

= -4.

The equation of the line that has a slope of -4 and passes through the point (4, -1) is,

y + 1 = -4(x - 4)

y = -4x +16 -1

y = -4x + 15

Therefore, the equation is y = -4x + 15.

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The second and fourth graphs represent linear functions.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

To determine which of the given graphs represents a linear function, we need to check whether the graph is a straight line.

The first graph passes through the points (-3, 0), (-1, -4), and (1, 0). We can plot these points and see that they do not lie in a straight line. Therefore, the first graph does not represent a linear function.

The second graph passes through the points (-4, 0), (0, -4), (4, 0), and (0, 4). We can plot these points and see that they do lie on a straight line. Therefore, the second graph represents a linear function.

The third graph passes through the points (-4, -2), (-4, -1), and (-4, 0). We can plot these points and see that they lie on a vertical line. Therefore, the third graph does not represent a linear function.

The fourth graph passes through the points (-4, 0), (-2, -1), and (0, -2). We can plot these points and see that they do lie on a straight line. Therefore, the fourth graph represents a linear function.

Therefore, the second and fourth graphs represent linear functions.

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Answer: It is the second one

Step-by-step explanation:

Because It makes the most sense

Answer:

There is exactly one solution: (1, 2).

Step-by-step explanation:

For this, it's already in slope intercept form so all you have to do is graph the two and see at what point do these two lines cross, which is (1, 2).

Hope this helps!

Answer: Yes

Step-by-step explanation:

We don't know the value of n and you are subtracting it from both sides.

The image of (3, -3) is (1, -1).

The image of (-4, 7) is (-12, 21).

The image of (3, 3) after a dilation by a scale factor of 5 is (15, 15).

The image of (-8,-8) is (-2, -2).

The scale factor is the size by which the shape is enlarged or reduced. It is used to increase the size of shapes like circles, triangles, squares, rectangles, etc.

To find the image of (3, -3) after a dilation by a scale factor of 1/3 centered at the origin, multiply the coordinate by 1/3. That is:

image = (1, -1)

For image of (-4, 7) after a dilation by a scale factor of 3, multiply the coordinate by 3:

image = (-12, 21)

For the image of (3, 3) after a dilation by a scale factor of 5, multiply the coordinate by 5:

image = (15, 15)

For the image of (-8,-8) after a dilation by a scale factor of 1/4, multiply the coordinate by 1/4:

image = (-2, -2)

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Complete Question

What is the image of (3, -3) after a dilation by a scale factor of 1/3 centered at the origin?

What is the image of (-8,-8) after a dilation by a scale factor of 1/4 centered at the origin?

The equation of line is y= -1/4x+ 6.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

passes through the point (4, 5);

slope = -1/4

Using the slope intercept form

y = mx + b

y= -1/4x + b

As the point passes through (4, 5) then

5 = -1/4 (4) + b

5 + 1 = b

b= 6

So, the equation of line is y= -1/4x+ 6.

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The plan that costs less if Hans makes 300 minutes of long distance calls is Plan A by $ 4.

The number of long distance minutes till the plans cost the same is 350 minutes.

If the time spent on long distance calls is more than this amount, the plan that costs less is Plan B.

The cost per plan can be seen on the graph. At 300 minutes of long distance calls, Plan A costs $ 24 and plan B costs $ 28 so the cheaper plan is Plan A by :

= 28 - 24

= $ 4

The number of minutes till they cost the same is 350 minutes which is where they intercept and after this, Plan B will cost less.

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Two different values are possible for the length of Rectangle jklm.

When we say that two rectangles are congruent, we indicate that their sides are equal. The rectangles' lengths and widths have to be comparable. It's feasible that jm will be 4 or 7 inches long given that one rectangle has dimensions of 4 and 7. Two lengths are conceivable as the solution. The length and breadth make up the rectangle shape. A rectangle has four sides, and its opposing sides are all the same length. You are given the perimeter of a rectangle. The perimeter, as you know, is the total distance along the outside of the rectangle.

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Answer: Can't help I tried to figure it out, but it was wrong.

Step-by-step explanation: I'm sorry.

Answer:

Step-by-step explanation:i cant see words need closer view

The number of participants that shopped in:

- BJ's Wholesale Club only: 32
- Costco only: 22
- Sam's Club only: 27
- Exactly one of these warehouse stores: 81
- BJ's Wholesale Club and Costco: 11
- BJ's Wholesale Club and Sam's Club: 10
- Sam's Club and Costco: 7
- None of these warehouse stores: 17

To answer this question, we can use a Venn diagram to visualize the data and find the number of participants that shopped in each category.

First, we'll create a venn diagram with three circles, one for each store (BJ's Wholesale Club, Sam's Club, and Costco). Then, we'll fill in the data from the question.

1. Start with the center of the venn diagram, where all three circles overlap. This represents the 5 participants who shopped in all three stores.
2. Next, fill in the overlapping sections between two circles. These represent the participants who shopped in two of the stores, but not the third.
- BJ's Wholesale Club and Sam's Club: 15 - 5 = 10
- BJ's Wholesale Club and Costco: 16 - 5 = 11
- Sam's Club and Costco: 12 - 5 = 7
3. Finally, fill in the sections that do not overlap with any other circles. These represent the participants who shopped in only one of the stores.
- BJ's Wholesale Club only: 58 - 10 - 11 - 5 = 32
- Sam's Club only: 49 - 10 - 7 - 5 = 27
- Costco only: 45 - 11 - 7 - 5 = 22

Now, we can use the venn diagram to answer the questions:
- BJ's Wholesale Club only: 32
- Costco only: 22
- Sam's Club only: 27
- Exactly one of these warehouse stores: 32 + 22 + 27 = 81
- BJ's Wholesale Club and Costco: 11
- BJ's Wholesale Club and Sam's Club: 10
- Sam's Club and Costco: 7
- None of these warehouse stores: 17

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Answer:

approximate number

Step-by-step explanation:

Hi this a great question. A number close to an exact value is an approximate number. That is a number that is close but not exactly equal to another number. It is the counterpart to exact numbers. There is no uncertainty in an exact number, while the definition of an approximate number is one in which uncertainty exists.

Answer:

Step-by-step explanation:

the volume of top triangular prism :

(16x21)/2x15=2520 yd^3

the volume of bottom:

22x16x15=5280 yd^3

so the volume of the figure:

2520+5280=7800 yd^3

Using the conversion formula of converting inches to centimeters, we get 1.5 inch is 3.81 centimeters.

To convert 1.5 inches to centimeters, we can use the formula:

1 inch = 2.54 centimeters

So, 1.5 inches = 1.5 x 2.54 = 3.81 centimeters

Therefore, 1.5 inches is equal to 3.81 centimeters.

The conversion factor between inches and centimeters is based on the definition of the inch and centimeter units. The inch is a unit of length in the imperial system of measurement, while the centimeter is a unit of length in the metric system. The conversion factor between the two systems is based on the definition of the meter, which is the primary unit of length in the metric system. In summary, 1.5 inches is equal to 3.81 centimeters, and this conversion is based on the relationship between the inch and centimeter units, as well as the definition of the meter as the primary unit of length in the metric system.

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The exponential equation is N ( t ) = a ( b )^t , where a = 50 and b = 3

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the number of bacteria in the culture at a given time be N ( t )

The culture increases by a factor of 2

So , the value of r = 200 % , r = 2

Now , when t = 0 , the number of bacteria in the culture N ( 0 ) = 50

So , the exponential equation is

N ( t ) = N ( 0 ) ( 1 + r )^t

Substituting the values in the equation , we get

N ( t ) = 50 ( 1 + 2 )^t

N ( t ) = 50 ( 3 )^t

On simplifying the equation , we get

N ( t ) = a ( b )^t , where a = 50 and b = 3

Hence , the exponential equation is N ( t ) = 50 ( 3 )^t

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1 cm is defined as 1/100 of a meter. One foot is defined as 1/3 of a yard or 12 inches in length. We know that, 1 inch = 2.54 cm and therefore, 23.5 centimeter = 9.252 inches

Centimeters :

The centimeter (cm) is the fractional part of the meter, the international standard unit of length, and equals approximately 39.37 inches. It is defined as 1/100 of a meter.

The centimeter is based on the SI unit of measurement and is equal to one hundredth of a meter as indicated by the prefix "centi". The metric prefix ranges from 10-18 to 1018 in decimal, and the base (metric in this case) has no prefix and a modulus of 1. Exploring the most commonly used metric prefixes such as kilogram, mega, giga, tera, centi, milli, micro, and nano can be useful for quickly navigating metric units.

Inch:

Inches is a unit of length or distance in several systems of measurement, including traditional American units and British Imperial units. An inch is defined as 1/12 of a foot, so 1/36 of a yard. By modern definition, 1 inch equals 25 exactly 4 mm.

The term "inch" comes from the Latin unit "uncial", equivalent to "1/12" in Roman terms. There were several standards for inches in the past and the current definition is based on international yards. One of the earliest definitions of an inch was based on a barley grain, where an inch equals the length of three dry round grains of barley laid end to end. Another version of the inch is believed to be derived from the width of a person's thumb, where length was obtained by averaging the widths of three thumbs (small, medium, and thumb).

By multiplying  the value in centimeters by the conversion factor 0.3937007874021.

So, 23.5 centimeters = 23.5 × 0.39370078740213

                                   = 9.25196850395 inches.

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According to the information, the line plots of points 6 and 7 have several values that are repeated more than once as shown in the graphs.

To make a line plot we must identify the values that we must locate on the number line. Once we know the values we must place a point or symbol above the corresponding numerical value. For each number we must put a point, so we can count the frequency of different values.

Based on the above, we can infer that the line plots of points 6 and 7 would look like this:

attached images

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The bedroom has a surface space of 17.4225 m² and the closet has a surface area of 2.5875 m².

In mathematics, the area is a measure of the amount of two-dimensional space taken up by a shape. It is a scalar quantity, meaning it has only magnitude and no direction. The unit of measurement used for area depends on the units used for the length of the sides of the shape. Common units used to measure area include square centimeters, square meters, square inches, and square feet. The formula for finding the area of a shape depends on the specific type of shape. For example, the area of a rectangle is given by the formula A = lw, where l is the length and w is the width of the rectangle. The area of a triangle is given by the formula A = (1/2)*bh, where b is the base and h is the height of the triangle.

Here,

area of bedroom=l*w

l=5.05 m

w=3.45 m

area of bedroom=5.05*3.45

=17.4225 m²

area of closet=l*w

l=0.75 m

w=3.45 m

area=0.75*3.45

=2.5875 m²

The area of the bedroom is 17.4225 m² and that of closet is 2.5875 m².

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The model [tex]p = 200.3^d[/tex] satisfies the statement, A population of cells starts at 200 and triples every day.

The formula for exponential growth is [tex]y = y_0.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0.e^{(-kt)}.[/tex]

Given, A population of cells starts at 200 and triples every day.

Where 'p' is the number of cells and 'd' is the number of days.

The situation is represented by [tex]p = 200.3^d[/tex].

Now, Three times 200 is 600 and Nine times 200 is 1800.

At d = 1.

[tex]p = 200.3^1[/tex].

[tex]p = 600[/tex].

And,

At, d = 2.

[tex]p = 200.3^2[/tex].

[tex]p = 1800[/tex].

So, The model satisfies the statement and it is true.

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The total volume of all the tents is 1920 cubic feet

From the question, we have the following parameters that can be used in our computation:

Number of tents = 6

Base area of the tents = 96 square ft

Height of the tent = 10 ft

The total volume of all the tents is calculated as

Volume = Number of tents * Base area of the tents * Height of the tent/3

Substitute the known values in the above equation, so, we have the following representation

Volume = 6 * 96 * 10/3

Evaluate

Volume = 1920

Hence, the volume is 1920 cubic feet

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Answer:

Goku died you I just started watching

A linear function has a constant rate of change, which means that the change in the value of y is proportional to the change in the value of x. This means that if we plot the points (x,y) for a linear function, they will fall on a straight line.

To determine which of the tables represents a linear function, we can calculate the rate of change between the points. If the rate of change is the same for all pairs of points, then the table represents a linear function.

For the first table:

Rate of change between (−2,4) and (−1,1) = (1−4)/(−1−(−2)) = −3

Rate of change between (−1,1) and (0,−2) = (−2−1)/(0−(−1)) = −3

Rate of change between (0,−2) and (1,−5) = (−5−(−2))/(1−0) = −3

Rate of change between (1,−5) and (2,−8) = (−8−(−5))/(2−1) = −3

Since the rate of change is constant (equal to −3) for all pairs of points, the first table represents a linear function.

For the second table:

Rate of change between (−2,4) and (−1,1) = (1−4)/(−1−(−2)) = −3

Rate of change between (−1,1) and (0,0) = (0−1)/(0−(−1)) = 1

Rate of change between (0,0) and (1,1) = (1−0)/(1−0) = 1

Rate of change between (1,1) and (2,4) = (4−1)/(2−1) = 3

Since the rate of change is not constant (it changes from −3 to 1 to 3), the second table does not represent a linear function.

For the third table:

Rate of change between (2,−2) and (2,−1) is undefined since x does not change.

Rate of change between (2,−1) and (0,0) = (0−(−1))/(0−2) = 0.5

Rate of change between (0,0) and (2,2) = (2−0)/(2−0) = 1

Rate of change between (2,2) and (2,−2) is undefined since x does not change.

Since the rate of change is not constant (it changes from undefined to 0.5 to 1 to undefined), the third table does not represent a linear function.

For the fourth table:

Rate of change between (0,−2) and (1,1) = (1−(−2))/(1−0) = 3

Rate of change between (1,1) and (2,0) = (0−1)/(2−1) = −1

Rate of change between (2,0) and (3,1) = (1−0)/(3−2) = 1

Rate of change between (3,1) and (4,−2) = (−2−1)/(4−3) = −3

Since the rate of change is not constant (it changes from 3 to −1 to 1 to −3), the fourth table does not represent a linear function.

Therefore, the only table that represents a linear function is the first one.

The population of the bees when it was first measured was 500 bees

The bees are  growing by the same factor each week. The answer is yes

At the fist time the bees where measured, we have to measure from the origin of the graph.

The first point on the graph is at the population of 500

2. To get if the growth is by the same factor, we have to observe how the growth is taking place weekly

In the first week, it grew from 500 to 1000

1000 / 500 = 2

In the second week, the growth is from 2000 to 1000

2000 / 1000 = 2

In the third week. the growth is from 2000 to 4000

4000 / 2000 = 2

Hence there is a growth constant of 2 across the weeks

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~4 - 1~~)^2 + (~~2 - 5~~)^2} \implies \implies AB=\sqrt{( 3 )^2 + ( -3 )^2} \\\\\\ AB=\sqrt{ 9 + 9 } \implies AB=\sqrt{ 18 }\implies AB\approx 4.24[/tex]

now, we could do the same thing for CD,  however, notice, the y-coordinates are the same, meaning is just a horizontal line, we can just count the units off the grid, from 2 to 6, 4 units.

The measure of the major arc along the perimeter of the circle between Stanley and Frank is 264°.

A circle's arc, or circumference, is a section of the circle. The difference between an arc length and an arc measure is the angle the arc creates with the circle's center. It is possible to measure this arc in radians or degrees.

Given:

Fifteen friends are playing Duck, Duck, and Goose.

The friends sit equally spaced in a circle.

So, 360/15 = 24° is the angle measure of an arc.

There are three people between Stanley and Frank.

That means there are 11 people between Stanley and Frank.

So, 11 x 24 = 264° is the measure of the major arc.

And the perimeter of the major arc is 264°

Therefore, the perimeter of the major arc is 264°

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The measure of the angles given in the rhombus are given as follows:

A rhombus is a type of parallelogram with the following properties:

To obtain the following, therefore, here is the premise behind each assertion:

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The numerical values of x and y are 14 and 54 respectively.

The sum of angles on a straight line is equal to 180 degrees.

From the diagram, angle (9x + 2)° and angle (5x - 18)° are on a straight line,

Since the sum of angles on a straight line is equal to 180 degrees.

(9x + 2)° + (5x - 18)° = 180°

Solve for x

9x + 2 + 5x - 18 = 180

14x - 16 = 180

14x = 180 + 16

14x = 196

x = 196/14

x = 14

Now, angle (9x + 2)° and angle (2y + 20)° are corresponding angles.

Since corresponding angles are congruent.

(9x + 2)° = (2y + 20)°

Plug in x = 14 and solve for y

9( 14 ) + 2 = 2y + 20

126 + 2 = 2y + 20

128 = 2y + 20

128 - 20 = 2y

108 = 2y

2y = 108

y = 108/2

y = 54

Therefore, the value of x is 14 and y is 54.

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Answer:

Liberty Hill

Step-by-step explanation:

To determine which hill is the steepest, calculate the absolute value of m for each hill and compare them:

|m|= |Slope (or gradient)|

    = |[tex]\frac{VerticalDistance}{HotizontalDistance}[/tex]|

The hill with the greatest absolute value of m is the steepest:

|[tex]m_{Dixie} = |\frac{40}{80}|[/tex]

            = 0.5

[tex]|m_{Bell}| =|\frac{20}{80}|[/tex]

          = 0.25

[tex]|m_{Liberty}| = |\frac{60}{80}|[/tex]

               = 0.75

Liberty Hill has the greatest absolute value of m of 0.75, therefore it is the steepest