Hank's pickup can travel 42 miles on 3 gallons of gas. How many gallons will​ Hank's pickup need to travel 28 ​miles?

Using a system of equations, it is found that for the room's dimensions:

The perimeter of a rectangle of length l and width w is given by:

[tex]P = 2(l + w)[/tex]

The length of a rectangular room is 2 feet longer than twice the width, hence:

[tex]l = 2w + 2[/tex]

The room's perimeter is 196 feet, hence:

[tex]2l + 2w = 196[/tex]

From the second equation:

[tex]2(2w + 2) + 2w = 196[/tex]

[tex]6w = 194[/tex]

[tex]w = \frac{194}{6}[/tex]

[tex]w = 32.33[/tex]

Then:

[tex]l = 2w + 2 = 2(32.333) + 2 = 66.67[/tex]

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The dimensions of the room are 32 feet by 66 feet, with a total area of 2112 square feet, which can be calculated for carpet replacement based on the room's perimeter.

To find the dimensions of a rectangular room where the length is 2 feet longer than twice the width and the perimeter is 196 feet, we first need to establish equations based on the given information. Let the width of the room be represented by w and the length be represented by l. From the problem, we have that l = 2w + 2. The perimeter P of a rectangle is given by P = 2l + 2w. Plugging in what we know, we can set up the equation:

196 = 2(2w + 2) + 2w

Solving this, we get:

Now, we use the width to find the length:

So, the dimensions of the room are 32 feet by 66 feet. Since the student wants to determine the square footage for carpet replacement, we can calculate the area by multiplying the length and width:

Area = 32 feet × 66 feet = 2112 square feet

Answer:

As mention in the explanation steps.

Step-by-step explanation:

Te following steps may be helpful for using a compass and a straightedge to construct a line perpendicular to a given line through a point not lying on the given line (as shown in the figure).

Step - 1. Draw a line (line AB)

Step- 2. Take a point (point P), that do not lie on the line AB.

Step - 3. Assume point p as a center an draw as arc which intersect the line AB at two point (point C and point D).

Step - 4. Now draw a line XY that is  the perpendicular bisector of line segment CD. This recurred line XY is the  line perpendicular to a given line (line AB) through a point not lying on the given line.  

Answer:

square root of 40

Step-by-step explanation:

a^(2)+b^(2)=c^(2)

3^(2)+b^(2)=7^(2)

9+b^(2)=49

9-9+b^(2)=49-9

b^(2)=40

sqr b^(2)=sqr 40

b=6.32455532034

therefore,the square root of 40 is the answer

Answer:

7x - 2 = 2y

7x = 2y + 2

so

7x = 2y + 2

3x = 2y - 1  

----------------subtract

4x = 3

 x = 3/4

7x - 2 = 2y

7(3/4) - 2 = 2y

21/4 - 2 = 2y

21/4 - 8/4 = 2y

13/4 = 2y

so

y = 13/4 * 1/2

y = 13/8

answer

(3/4, 13/8)

Step-by-step explanation:

The two names for the​ segment are AC and CA that has endpoints A and C the answer would be AC and CA.

A segment bisector is a line, ray, line segment, or point that divides a line segment into two equal halves at its center.

It is given that:

A segment has endpoints A and C.

As we know, the line segment is the line that goes to the endpoints on both sides.

The line segment can be represented as AC and CA

Or

The bar(AC) and bar(CA)

Thus, the two names for the​ segment are AC and CA that has endpoints A and C the answer would be AC and CA.

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Plot the inequality on the number line. the graph is attached below.

Use the tool that has solid dots at both ends

Explanation :

Plot the inequality on the number line.

−7≤x≤−2

We start plotting the point at -7. we use closed circle at -7 because we have less than or equal to sign at -7

Now we plot another point at -2. here also we use closed circle that is solid circle .

Now shaded the region between -7 and -2 because x lies between -7 and -2

The graph of number line is attached below

The tool uses here is a line with solid dot at both ends

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a. We are given that the formula for Celsius (c) to Kelvin (k) is:

k = c + 273.15

Now to solve for the formula for c, simply subtract 273.15 from both sides, so that:

k – 273.15 = c + 273.15 – 273.15

k – 273.15 = c

Rearranging:

c = k – 273.15

b. We are given that k = 300 Kelvin, therefore find for c:

c = k – 273.15

c = 300 – 273.15

c = 26.85°C

The formula to convert temperature from Kelvin to Celsius is c = k - 273.15. When you use this formula to convert 300 Kelvin to Celsius, the answer is 26.85°C.

The formula k = c + 273.15 is used to convert temperatures from Celsius to Kelvin. To solve for 'c' (Celsius), you would subtract 273.15 from both sides of the equation which gives c = k - 273.15.

If you have a temperature of 300 Kelvin and you want to convert this to Celsius using the formula c = k - 273.15, you would substitute 300 in place of k. This gives: c = 300 - 273.15, which equals 26.85°C.

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A) Variable = x ( miles Tim walked )

B)  Tim walked X miles, Molly walked 4+x miles ( 4 more than Tim)

 Equation:  x + x+4 = 10

C) x +x+4 = 10

2x+4 = 10

2x =6

x = 3

D)

 Tim walked 3 miles, Molly walked 7 miles

Answer:

reflex

Step-by-step explanation:

Answer:

The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

Step-by-step explanation:

The rule we have is (x, y)→(2x, 2y).  This means that each x-coordinate and each y-coordinate are multiplied by 2.  This is a dilation by a factor of 2.

This will stretch the image by a factor of 2; this means the sides will be twice as long.  This means they will not be congruent.

Answer: The triangles are not congruent because △D′E′F′ is a dilation of △DEF .

Step-by-step explanation:

Rigid motions form congruent figures, the common rigid motions are:  

1) translation (moves figure about some distance)

2) reflection (creates mirror image)

3) rotation (rotate figure about some degrees)

Dilation : It does not create congruent images. It creates an image that is the exactly same shape as the original, but have a different size with the help of a scale factor k .

Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.

Here the coordinates of the image are increased by using a scale factor 2.

So △D′E′F′ must be an enlargement of △DEF.

⇒△D′E′F′ is a dilation of △DEF

It means : The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

The required inequality is -6<x<8

An inequality is an inequation separated by <,>≥,≤. In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

Given here: A number x is more than -6 and at most 8.

Clearly we can infer that the number lies between the interval (-6,8)

Thus we can construct the inequality for x as

-6<x<8 or x has 11 integral values

Hence, The required inequality is -6<x<8

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To graph the equation f(x) = -3/4x - 4, choose values for x, substitute them into the equation to find corresponding y values, and plot the points on a graph.

The given equation is f(x) = -3/4x - 4. To graph this equation, we can choose several values for x and substitute them into the equation to find the corresponding values for y. Then, we plot these points on a coordinate plane and connect them to form a line.

For example, let's choose x = 0. Substituting this value into the equation, we get f(0) = -3/4(0) - 4 = -4. This gives us the point (0, -4) on the graph. Similarly, we can choose other values for x and find their corresponding y values to plot more points and complete the graph of f(x).