At the beginning of the year, the odometer on an SUV read 37,532 miles. At the end
of the year, it read 52,412 miles. If the car averaged 24 miles per gallon, how many
gallons of gasoline did it use during the year?

Answer:

6x +24

Step-by-step explanation:

you factor out the 6 so 6x and 6*4 is 24

Answer:

158 m^2

Step-by-step explanation:

l = 5 m, w = 3 m, h = 8 m

S.A. = [tex]2(lw+wh+lh)[/tex]

S.A. = 2{(5)(3) + (3)(8) + (5)(8)}

S.A. = 2(15 + 24 + 40)

S.A. = 2(79)

S.A. = 158 m^2

Hope this help!!!

Have a nice day!!!

Answer:

x => y

0 => 0

2 => 3

4 => 6

-2 => -3

Step-by-step explanation:

The equation of a proportional relationship is represented as y = kx,

where, k = y/x

We are given that k = ³/2

This means that, equation of the relationship therefore would be:

y = ³/2x

Use this equation to solve for each missing value on the table given:

✔️Where, y = 0, substitute y = 0 into y = ³/2x to find x:

0 = ³/2x

0 * 2 = 3x

0 = 3x

0/3 = x

x = 0

✔️Where, x = 2, substitute x = 2 into y = ³/2x to find y:

y = ³/2(2)

y = 3

✔️Where, y = 6, substitute y = 6 into y = ³/2x to find x:

6 = ³/2x

6 * 2 = 3x

12 = 3x

12/3 = x

x = 4

✔️Where, x = -2, substitute x = -2 into y = ³/2x to find y:

y = ³/2(-2)

y = -3

Answer:

8,-9,9

Step-by-step explanation:

The answer is 1/x^2y^2

The given expression is [tex] \frac{ {x}^{0} y { - }^{3} }{ {x}^{2}y { - }^{1} } [/tex]

We know that any number raised with zero power equals 1. Thus, [tex] {x}^{0} = 1[/tex]

Hence, the expression becomes

[tex] \frac{y { - }^{3} }{ {x}^{2} y { - }^{1} } [/tex]

Now, apply the quotient rule,[tex] \frac{ {x}^{ \alpha } }{ {x}^{b} } = {x}^{ \alpha - b} [/tex]

Using this rule, we have

[tex] \frac{1}{ {x}^{2} y { - }^{1 - ( - 3)} } [/tex]

[tex] = \frac{1}{ {x}^{2} y { - }^{1 + 3} } [/tex]

Hence, the simplified expression is [tex] \frac{1}{ {x}^{2} {y}^{2} } [/tex]

Answer:

The x-coordinates for which the gradient of the curve is 5 is at x = -1/2 and x = 1/2.

Step-by-step explanation:

We have the function:

[tex]\displaystyle y=\frac{x^2 -1}{x}[/tex]

And we want to find the x-coordinates for which the gradient (or slope) at the point is 5.

The gradients of a curve at a point is given by its derivative. Find the derivative:

[tex]\displaystyle \frac{dy}{dx}=\frac{d}{dx}\left[\frac{x^2-1}{x}\right][/tex]

Use the quotient rule:

[tex]\displaystyle \frac{dy}{dx}=\frac{(x^2-1)'(x)-(x^2-1)(x)'}{(x)^2}[/tex]

Simplify:

[tex]\displaystyle \frac{dy}{dx}=\frac{(2x)(x)-(x^2-1)(1)}{x^2}[/tex]

Simplify:

[tex]\displaystyle \frac{dy}{dx}=\frac{x^2+1}{x^2}[/tex]

Since the gradient is 5, substitute 5 for dy/dx and solve for x:

Multiply both sides by x² (x ≠ 0):

[tex]5x^2=x^2+1[/tex]

Subtract x² from boths sides:

[tex]4x^2=1[/tex]

Solve for x:

[tex]\displaystyle x=\pm\sqrt{\frac{1}{4}}=\frac{1}{2}\text{ or } -\frac{1}{2}[/tex]

So, the x-coordinates for which the gradient of the curve is 5 is at x = -1/2 and x = 1/2.

Answer:

x = 40

Step-by-step explanation:

Two triangles are similar so we can use similarity ratio to find x

x/16 = 35/14 cross multiply expressions

14x = 560 divide both sides by 14

x = 40

Answer:

below

Step-by-step explanation:

cost of the machinery = $14,400

he paid a deposit of $1400

then later paid $576.18 for two years

two years = 24 months

= $576.18 *24

=$13,828.32

total amount paid

= initial deposit + amount paid in two years

= $1,400 + $13,828.32

=$15,228.32

so he finally paid $15,228.32

interest = selling price - original cost

= $15,228.32 - $14,400

=$828.32

therefore interest = $828.32

Answer:

It's B (1÷13=3) for Part a

1 whole is equal to 3/3. One batch of brownies uses up to 1/3 of butter. So 1 ÷ 1/3 = 3.

Step-by-step explanation:

Answer:

m∠ACD = 130

Step-by-step explanation:

If ABC is an isosceles, AB = AC and m∠A = 80°, then m∠B and m∠C is equal to 50°.

This is because angles in a triangle adds up to 180°.

180° - 80° = 100°/2 = 50°

∴ m∠ACD = 130°, this is because the interior opposite angles in a triangle is supplementary to the opposite exterior angle:

50° + 80° = 130°

Or

Angles on a straight line adds up to 180°.

180° - 50° = 130°

Answer:

12

Step-by-step explanation:

Just substitute 3 for n and solve.

Solve the expression [tex]2+(3-1)5\\[/tex]

Use PEMDAS and solve.

(3-1) = 2 so it becomes 2 + (2)5

Then multiply 2 and 5 to get 10.

Then add 2 so you get 12.

[tex]a_{3}[/tex]=12

answer:

ABCD is not congruent to KLMN

ABCD cannot be mapped onto KLMN

Answer:

(-∞, - 2/3)

Step-by-step explanation:

Given the inequality :

6x-9≤3x-11

Collect like terms :

6x - 3x ≤ - 11 + 9

3x ≤ - 2

Divide both sides by 3

3x/3 ≤ - 2/3

x ≤ - 2/3

(-∞, - 2/3)

Answer:

21.2

Step-by-step explanation:

BODMAS : First bracket, then Division then multiplication.

[tex]53 \div (13-8) \times 2\\53 \div 5 \times 2\\10.6 \times 2\\21.2[/tex]

Step-by-step explanation:

pool = 1600 sq.cm

1600 sq.sm = 50cm × 32cm

AB = 50cm

the area of the park of A'B' :

50cm×4=200 sq.cm

Answer:

$3360

Step-by-step explanation:

4200(.80) = 3360

anything less than 1.00 will be a decreasing amount, so i just took the 80% and put it as a decimal and multiplied to find the current cost of the car

9514 1404 393

Answer:

  zero solutions

Step-by-step explanation:

The first inequality has a boundary line with a slope of 3 and a y-intercept of 9. Shading is above the boundary line.

The second inequality has a parallel boundary line with a slope of 3 and a y-intercept somewhat lower, at -1. Shading is below this boundary line.

There is a gap between the shaded areas, so no points will be solutions to both inequalities.

Answer:

a) 30.60

b) 1010/33 = 30.60

Step-by-step explanation:

9514 1404 393

Explanation:

Divide the figure into areas for which you have a surface area formula. Use the appropriate formula for each area, then add up the results.

Formulas are available for surface areas of a cone, cylinder, sphere, pyramid, rectangular prism, and for plane shapes that are circles, ellipses, triangles, rectangles, trapezoids, and regular polygons.

Most of the figures for which you are asked to find the area will decompose to some subset of these shapes. Take care to identify the relevant dimensions of each of the constituent parts of the area, and to make sure that all parts are accounted for. Do not allow your parts of the area to overlap, unless you intend to account for that overlap by subtracting the area that is counted more than once.

Also, use your common sense. A semicircle will have half the area of a circle, for example.

In some cases, it may be expedient to compute the area of a larger figure than the one you have, then subtract the part of that area that is missing from your figure.

Hi my name is Fabian and 69% because 69 is a man which is multi colour hair

Answer:

Both are correct

I'm only checking the first page

Step-by-step explanation:

Answer:

Step-by-step explanation:

The 3rd page both are wrong the correct answers are 6 degrees C and Ice would form on the top of the lake like it does now.

The 4th page the bottom one is wrong the correct answer is -22.

Answer:

45 is 54.9 percent of 82.

26 is 520% of 5.

Answer:

45 is 55% of 82 and 520% of 5 is 26.

Step-by-step explanation:

First you want to set up a proportion, using the is over of formula (Is/of= %/100). In the first problem, 45 will be the is, 82 will be the of, for % will be the x, and 100 will go on the bottom (it will look something like this: 45/82=x/100). When you solve it, you get around 55 (45x100/82.) Same thing for the next equation, use the same formula (is/of=%/100) which turns into: 5/26= x/100 and you get 520%.

An angle of depression is measured from the horizon downwards and an angle of elevation is measured from the horizon upwards.

When solving for the sides or angles of a right triangle you can use trigonometry. The sine of an angle is found by the ratio of the opposite side and the hypotenuse. The cosine of an angle is found by the ratio of the adjacent side and the hypotenuse. The tangent of an angle is found by the ratio of the opposite side and the adjacent side.

The opposite side is always the leg opposite the angle that you are using. The adjacent side is the leg that forms one of the sides of the angle you are talking about and the hypotenuse is always across from the right angle.

If you know two lengths you can find the third leg length by using the Pythagorean Theorem.

Answer:

Step-by-step explanation:

12. To find the carpet needed. Find the area :

   The figure is combination of semi circle and a rectangle.

   So Area = Area of semi circle + Area of rectangle

      [tex]Area \ of \ semi \ circle = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi \times 25 = 39.25 \ ft^2 \\\\Area \ of \ rectangle = Length \times Breadth = 15 \times 10 =150 \ ft^2[/tex]

     Area = 150 + 39.25 = 189.25 sq ft

13.   Cost per square feet = $$9.95

     Therefore cost for 189.25 square feet = 9.95 x 189.25 = $1883.04

Answer:

≈ 5.5 minutes.

Step-by-step explanation:

Let m = number of minutes on the trampoline.

[tex]1.45m+7.25=15.23\\1.45m=7.98\\m=5.5[/tex]

She was on the trampoline for approximately 5.5 minutes.

Answer:

= 5.5 minutes

Step-by-step explanation:

1.45  + 7.25  = 15. 23

1. 45 = 15. 23 - 7. 25

1. 45 = 7 . 98

m = 5.5

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

The dimensions are four by two by two meters.

Step-by-step explanation:

The volume for a rectangular prism is given by:

[tex]V=\ell wh[/tex]

Where l is the length (or depth), w is the width, and h is the height.

Since the height and width are both two meters less than the depth, we can write that:

[tex]h=\ell -2\text{ and } w = \ell -2[/tex]

We are also given that the total volume is 16 cubic meters. Substitute:

[tex]16=\ell(\ell -2)(\ell -2)[/tex]

Expand:

[tex]16=\ell(\ell^2 -4\ell +4)[/tex]

Distribute:

[tex]16=\ell ^3-4\ell ^2+4\ell[/tex]

Isolate the equation. So:

[tex]\ell ^3-4\ell ^2+4\ell -16=0[/tex]

We can factor by grouping. From the first two terms, factor out a l² and from the last two terms, factor out a 4:

[tex]\ell ^2(\ell -4)+4(\ell -4)=0[/tex]

Factor:

[tex](\ell ^2+4)(\ell -4)=0[/tex]

Zero Product Property:

[tex]\ell ^2+4=0\text{ or } \ell - 4=0[/tex]

Solve for each case:

[tex]\ell^2=-4\text{ or } \ell =4[/tex]

Since we cannot take the square root of a negative number, we can ignore the first case.

Therefore, the length (or depth) of the storage space is four meters.

Thus, the dimensions are four by two by two meters.

point D is the answer

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