Write an equation to model each situation and solve. Be sure to label the solution.
7. A rectangle has a length of 2x - 12 units and a width of 3 units. The value of the
rectangle's area is equal to the value of its perimeter. Write an equation to represent this
situation. Then, solve the equation.
Need a equation and a solution.

The slope of the lined graph is 5 / 3

The formula for determining the slope of a line is expressed as;

Slope = y2 - y1/ x2 - x1

From the graph shown;

Now, let's substitute the values

Slope, m = 4 - (-1) / 3 - 0

Find the differences

Slope, m = 4 + 1/ 3

Slope, m = 5 / 3

Thus, the slope of the lined graph is 5 / 3

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Step-by-step explanation:

2 × 7 × 7.................

The point on the graph y = -f(x) is (-2 , -8)

According to the question the coordinates we have been given is (-2 , 8) and it is on the graph y = f(x)

That is we have been given that

                f(-2) = 8            (1)

Now we have to find the point on the graph y = -f(x)

So we will choose the value of x = -2 in f(x)

 Thus, putting the required value we get

                y = - f(-2)

As the value of f(-2) is 8 from equation (1). we will equate the value in the above equation we get

               y = -(8)

               y = -8

Hence the point on the graph is (-2 , -8)

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The length of the rectangle is 21 cm and the width is 16 cm.

A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

The perimeter of the rectangle is defined as the sum of all the sides of the rectangle.

The formula to calculate the perimeter is,

P = 2 ( L + W)

Here

P  = Perimeter

L  = length of the rectangle

W = Width of rectangle

Given that the length of a rectangle is 7 cm more than the width. The perimeter is 78 cm.

The equations can be formed as,

L = 7 + W

P = 2(L+W)

78 = 2 ( 7  + W + W )

39 = 7 + 2W

W = 32/2

W = 16 cm

L = 7 + W

L = 7 + 16 = 21 cm

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Answer: 1/9

Step-by-step explanation:

The area of the shaded region is [tex](4/2)^2 \pi =4\pi[/tex]

The area of the entire circle is [tex](6)^2 \pi=36\pi[/tex]

So, the probability is [tex]\frac{4\pi}{36\pi}=1/9[/tex]

Answer:

[tex]77, 385[/tex]

Step-by-step explanation:

Start by writing the equations in symbolic form. I will represent one number with an x and the other with a y.

One number is one-fifth of the other number:

[tex]x=\frac{1}{5}y[/tex]

The difference between the two numbers is 308:

[tex]y-x=308[/tex]

This difference is positive, therefore I am assuming that y is the larger number. In the first equation, I made x a part of y, so this should check out.

Now we have a system of equations:

[tex]\left \{ {{x=\frac{1}{5}y } \atop {y-x=308}} \right.[/tex]

I will rewrite the first equation for simplicity:

[tex]5x=y[/tex]

Now, I will substitute y from the first equation for y in the second equation:

[tex]5x-x=308[/tex]

Simplify:

[tex]4x=308\\x=77[/tex]

Now, use x to find y using the second equation:

[tex]y-77=308\\y=385[/tex]

Now, I can check the solutions by plugging them into the first equation!

[tex]x=\frac{1}{5}y\\ 77=\frac{1}{5}(385)\\77=77[/tex]

The solution is correct!

The residual plot represents a linear model because (a) there is no clear pattern

The given parameters are:

The graph

The table

For a residual plot to represent a linear model, the following must be true

The points on the residual plot must be randomly dispersed on the plot

This means that all residual plots that have random points are linear models

From the attached graph, we can see that the points on the graph are randomly dispersed

Hence, the residual plot represents a linear model because (a) there is no clear pattern

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The type of model that would be the most appropriate would be the exponential model: An exponential model is appropriate because the relationship between days and the natural log of views is linear, and the residual plot does not show a clear pattern.

This is the term that is used to refer to the process that is known to show a growth that is double its rate of growth. That is, it is used to show that there is the existence of a speed up in the rate at which the data is growing and it would follow a particular patter. This can be shown as:  y = ab^x.

This is the term that is used to show the graphical representation that is done by showing the existing relationship that exists between two variables in a graph. That would be the x variable and the y variable.

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The evaluation of function will give the result f(3) = 1

To find the value of function given in question, we will simply keep the desired value in place of variable x.

Rewriting the equation

f(3) = 2x - 5

Keep the value of x in equation, as given in question

f(3) = 2×3 - 5

Performing multiplication to find the value of x in equation given in question

f(3) = 6 - 5

Performing subtraction to find the value of x in equation given in question

f(3) = 1

Therefore, the result of evaluation of given function is f(3) = 1.

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Answer:

14x+14

Step-by-step explanation:

9x+5+5x+9

=9x+5+5x+9

=(9x+5x)+(5+9)

=14x+14

The slope of the line passing through the coordinates (0, 0) and (6, 3) is 1/2

The formula for calculating the slope of a line is expressed according to the equations:

Slope = y₂-y₁/x₂-x₁

Using the coordinate points (0, 0) and (6, 3) on the line. On substituting, we will have;

Slope = 3-0/6-0

Slope = 3/6

Simplify

Slope =1/2

Hence the slope of the line passing through the coordinates (0, 0) and (6, 3) is 1/2

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Answer:

In standars form it would look like so:

28,936

In expanded form it would look like so:

20,000 + 8,000 + 900 + 30 + 6

Step-by-step explanation:

Your welcome! Hope it helps! =D

We need to know about a composite bar chart to solve the question. The answer for (a) is Tim received 8 texts on Monday, (b) Tim received 4 emails on Thursday and (c) 0.52 of the messages were emails.

A composite bar chart is used when there are two sets of data that are connected and their frequencies are combined.In this question there are two sets of data emails and texts but both of them belong to the same category which is messages. For question (a) we can easily say from the diagram that the number of texts Tim received on Monday is 8.

For question (b) we need to find out the number of emails Tim received on Thursday, for this we have to look at the bar for Thursday and subtract the number of texts received from total number of messages to get the number of emails received that means, 15-11=4, so Tim received 4 emails on Thursday.

For question (c) we need to find the total number of messages received by Tim for five days, total number of emails received and then calculate the fraction of emails out of messages.

Total number of messages=14+16+14+15+14=73

Total number of emails=6+10+10+4+8=38

Fraction of emails over messages=[tex]\frac{38}{73}[/tex]=0.52

Thus 0.52 of the messages were emails.

We analysed the composite bar chart to find out the answers of the three questions, Tim received 8 texts on Monday,4 emails on Thursday and 0.52 of the messages were emails.

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Answer:

a= 5

b= 7

c=

Step-by-step explanation:

Answer:

[tex] \sf \large \: x≤6 \: or \: x≥10[/tex]

Step-by-step explanation:

Let's solve your inequality step-by-step.

x2−16x+60≥0

Let's find the critical points of the inequality.

x2−16x+60=0

(x−6)(x−10)=0(Factor left side of equation)

x−6=0 or x−10=0(Set factors equal to 0)

x=6 or x=10

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x≤6(Works in original inequality)

6≤x≤10(Doesn't work in original inequality)

x≥10(Works in original inequality)

Answer:

===============================

Use angle addition postulate:

Substitute the values and solve for x:

Find the angle measures:

Answer:

25 Hours

Step-by-step explanation:

It says it in the text

Because the height are in proportion, a possible value of the height of the tree is 70 m

The complete question is added as an attachment

The given parameters from the question are given as:

In the above expression, we have the following observations:

From the figure, we can see  that the height of the tree is about 5 times the height of the castle tower

This is represented as

Height of the tree = k * Height of the castle tower

Where

Scale factor, k = 5

Substitute the known values in the above equation

So, we have

Height of the tree = 5 * 14 m

Evaluate the products

So, we have

Height of the tree = 70 m

Hence, the possible height of the tree is 70 m

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Answer:

Step-by-step explanation:

Answer:

  9.2

Step-by-step explanation:

You want the distance between A(2, 0) and B(0, 9).

The distance formula is based on the Pythagorean theorem. It tells you the distance between (x1, y1) and (x2, y2) is ...

  d = √((x2 -x1)² +(y2 -y1)²)

For the given points, this becomes ...

  d = √((0 -2)² +(9 -0)²) = √(4+81) = √85

  d ≈ 9.2

The distance between A and B is about 9.2 units.

Answer:

0+15 =15

Step-by-step explanation:

it is said that the sum should have a 0

Answer:

Step-by-step explanation:

The number of monthly calls for which Plan 1 is more economical than Plan 2 is 200 calls

If more than 200 calls are made, the plan 1 charge will be more than plan 2.

Let the number of charges per month be x

If plan 2 charges ​$16 per month plus ​$0.04 per call, this is expressed as 0.04x + 16

Price that pan 1 charges = $24

If Plan 1 is more economical than Plan 2, this is expressed as:

0.04x + 16 > 24

Subtract 16 from both sides:

0.04x + 16 - 16 > 24 - 16

0.04x > 8

x = 6/0.04

x = 200

This shows that if more than 200 calls are made, the plan 1 charge will be more than plan 2.

Answer:

Yes si true

Step-by-step explanation:

If you analyze the figures you will realize that they are the same, the size differentiates it but they have the same angles.

Zendaya will travel $ 1 and 17/21  of a mile per hour on her roller skates.

Zendaya travels $5 and 3/7 of a mile in 3 hours on her roller skates. We can simply write this statement in mathematical form as,

Total distance covered by Zendaya in 3 hours on her roller skates = $( 5 + ( 3/7 )  of a mile

Total distance covered by Zendaya in 3 hours on her roller skates = $ ( ( 35 + 3)/7 ) of a mile

Total distance covered by Zendaya in 3 hours on her roller skates = $ ( 38/7 )

Total distance covered by Zendaya in 1 hours on her roller skates = $ (( 38/7 )/3 ) = $ (38/21) of a mile

or we can write also write  ( 38 /21 ) miles per hour as ( 1 and 17/21 ) miles per hour.

So, Zendaya will travel $ 1 and 17/21  of a mile per hour on her roller skates.

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &1 \end{cases} \\\\\\ I = (5000)(0.025)(1) \implies I = 125[/tex]

Answer:

D = 0.4(L)

Step-by-step explanation:

D = 0.4(L)

Answer: 0.4L=d  

Step-by-step explanation:

40%=0.4

0.4L=d    ==> 40% of L, the listed price, is d, the discount.

Solving a system of equations, we conclude that 35 tickets for movie a were sold

Let's define the variables:

Here we know that a total of 47 tickets were sold, then:

x + y = 47

And they sold for a total of $200, then:

x*$4 + y*$5 = $200

So we have a system of equations:

x + y = 47

x*$4 + y*$5 = $200

We want to solve this for x, then we need to isolate the variable y in one of the equations, doing that in the first one we get:

y = 47 - x

Now we can replace that in the other equation to get:

x*$4 + (47 - x)*$5 = $200

x*$4 + $235 - x*$5 = $200

$235 - x*$1 = $200

$235 - $200 = x*$1

$35 = x*$1

$35/$1 = x = 35

This means that 35 tickets for the movie a were sold.

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Answer:

3.57

Step-by-step explanation:

25/7 is the same as 25÷7 which is 3.57

The function that is positive for the entire interval [-3,-2] is given by:

On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).

We have to look at the graph of the function relative to the x-axis, as follows:

The graphs for this function are given at the end of the answer, and the only function for which it is positive, that is, above the x-axis, in the entire interval [-3,-2] is the second, hence the correct option is:

On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).

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