A driver stopped to purchase 27 gallons of gas and paid $62.10. What is the unit rate for gas?

$_______per gallon

Answer:

Answer

Given equation is:

x

2

−9x+20=0

⇒x

2

−5x−4x+20=0

⇒(x−4)(x−5)=0

⇒x=4andx=5

Given:

[tex]\dfrac{1}{4}\text{ to }\dfrac{1}{2}[/tex]

To find:

The percent of change, round to the nearest 10th of a percent.

Solution:

We have,

Initial value = [tex]\dfrac{1}{4}[/tex]

New value = [tex]\dfrac{1}{2}[/tex]

We know that, the percentage change is

[tex]\%\text{ change}=\dfrac{\text{New value - Initial value}}{\text{Initial value}}\times 100[/tex]

Putting the given values, we get

[tex]\%\text{ change}=\dfrac{\dfrac{1}{2}-\dfrac{1}{4}}{\dfrac{1}{4}}\times 100[/tex]

[tex]\%\text{ change}=\dfrac{\dfrac{2-1}{4}}{\dfrac{1}{4}}\times 100[/tex]

[tex]\%\text{ change}=\dfrac{\dfrac{1}{4}}{\dfrac{1}{4}}\times 100[/tex]

[tex]\%\text{ change}=1\times 100[/tex]

[tex]\%\text{ change}=100\%[/tex]

Here, the % change is positive, it represents the percent increase.

Therefore, the percent of change is 100% of increase.

Given:

A polynomial equation with rational coefficients has the roots   [tex]5, \sqrt{6}, 3, -\sqrt{7}[/tex].

To find:

The two additional roots.

Solution:

According to the irrational root theorem, if [tex]a+\sqrt{b}[/tex] is a root of a polynomial, then [tex]a-\sqrt{b}[/tex] is also the root of that polynomial.

It is given that, [tex]\sqrt{6}\text{ and }-\sqrt{7}[/tex] are roots of a polynomial.

By using irrational root theorem, [tex]-\sqrt{6}\text{ and }\sqrt{7}[/tex] are also the roots of that polynomial.

Therefore, the two additional roots are [tex]-\sqrt{6}\text{ and }\sqrt{7}[/tex].

k(×)×95=-0.75 sume k+95=***

g(x) is the function from the table which gives values that could come from the exponential function.

A relation is a function if it has only One y-value for each x-value.

We have to find the function from the table which gives values that could come from the exponential function.

The exponential function is a mathematical function denoted by .

As we observe the g(x) function.

When x =1, g(x)=2

x=2, g(x)=4

x=3, g(x)=8

g(x)=2ˣ is the required function which is in exponential form

Hence, g(x) is the function from the table which gives values that could come from the exponential function.

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9514 1404 393

Answer:

  47.71

Step-by-step explanation:

Two "special" triangles are involved.

ΔSWR is a 30°-60°-90° right triangle, so will have sides in the ratio 1 : √3 : 2.

ΔUVW is a 45°-45°-90° right triangle so will have sides in the ratio 1 : 1 : √2.

For ΔSWR, the side SW is given as 6, so the other sides are ...

  WR = 6√3

  RS = 2(6) = 12

For ΔUVW, the side WU is given as 8, so the other sides are ...

  UV = VW = 8/√2 = 4√2

Then the perimeter of the figure is ...

  P = RS +ST +TU +UV +VW +WR

  P = 12 +8 +6 +4√2 +4√2 +6√3 ≈ 47.71

Answer:

x=11

Step-by-step explanation:

15x+15=180      they are supplementary angles to each other so their sum is

                        equal to 180 degrees.

subtract 15 from both sides

15x=165

divide each side by 15

x=11

Answer: I use clickcaculators.com ;)

Step-by-step explanation:

Answer:

185

Step-by-step explanation:

Hope this helps

The solution to the given linear function at f(1) when calculated gives an output value of; 8

We are given the linear function represented by the equation;

f(x) = 7(x - 1) + 8

Now, to find f(1) simply means we substitute 1 for x in the given expression to obtain;

f(1) = 7(1 - 1) + 8

f(1) = 8

Thus, the solution is; f(1) = 8

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Answer: 10 years

Step-by-step explanation:

1720=960(1+0.061/12)

Answer:Triangle Inequality Theorem

The Triangle Inequality theorem states that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

The Converse of the Triangle Inequality theorem states that

It is not possible to construct a triangle from three line segments if any of them is longer than the sum of the other two.

The length of s is greater than 3 and less than 11

Step-by-step explanation:

Answer:

$24,800

Step-by-step explanation:

that's how much the car costs at year 0

Answer:

Step-by-step explanation:

The starting value, y intercept, is just the initial value as it has not depreciated when time or x is zero.

The equation described is y=24800(0.88)^x

Answer:

4 and then 15

Step-by-step explanation:

second one: 6:4

last one: 15:10

Answer:

3

Step-by-step explanation:

on a number line, we use the absolute values to find the difference.

the absolute value of -2 is 2

the absolute value of -5 is 5

5-2=3

so, the distance between -2 and -5 on a number line is 3

Answer:

Step-by-step explanation:

Because both points have -1 as X they are both located on the same line

This gives them no slope

Answer:

0.48

Step-by-step explanation:

Given the data:

X:

10,17,20,23,24,28,32,39,42,25,26,52,55,58,61,65,66,72,75,78,79,85,94,97,98

Sum of each of the numbers :

1, 8, 2, 5, 6, 10, 6, 12, 6, 7, 8, 7, 20, 13, 7, 11, 12, 9, 12, 15, 16, 13, 13, 16, 17

Probability that sum of the number's digit is odd:

Number of odd sum / total numbers

Number of odd sum = 12

Total numbers = 25

12 / 25

= 0.48

Answer:

2.82842712475

Step-by-step explanation:

when you square 2.82842712475 your answer is 8 so the number above Is answer

Answer:

8 = 64 √8 = 2.828

Step-by-step explanation:

√8 = √(4 * 2) = √4 * √2 = 2√2 ≈ 2.828427.

Hope this helps you!

Pythagorean theorem:  [tex]a^{2} +b^{2} =c^{2}[/tex]

When rewritten for coordinates plane:

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

where d is distance and (x,y) are the points.

Write down the coordinates of Emma's house and The Pool.

It is (-5,-3) and (2,2).

Substitute the numbers.

[tex]d=\sqrt{(2-(-3))^{2}+(2-(-5))^{2}}[/tex]

Calculate.

[tex]d=\sqrt{(5)^{2}+(7)^{2}}[/tex]

You should get [tex]\sqrt{74}[/tex] as your answer.

Answer:

Step-by-step explanation:

c=180-123=57

b=180-123=57

d=180-57-55=68

a=180-68-57=55

a,b,c,d=55, 57, 57, 68 degrees

Answer:

88

Step-by-step explanation:

[tex]a = lw[/tex]

[tex]a = (9)(4)[/tex]

[tex]a = 36 \: {yds}^{2} [/tex]

Answer:

Here we can understand that the shape is a rectangle as length is not equal to width.

Area of the rectangle in square yards when length is 9 yds and width is 4 yds will be,

Area of Rectangle = LENGTH × WIDTH

⇒ 9*4

⇒ 36 sd yds

Thus the are will be  36 sd yds

1017.88in^2

You need to use pi

Answer:

1017.88inches^2

Step-by-step explanation:

Area of a circle=pi * radius^2

324*pi=1017.88

Answer:

$3.996

Step-by-step explanation:

8%=0.08

49.95*0.08=3.996

Answer:

86×4 = 344

4×4= 16

3×3= 9

Step-by-step explanation:

I hope it help

Answer: 344, 16, 9

Step-by-step explanation:

Answer:

[tex]Monday = -2.5F[/tex]

[tex]Tuesday = -1.9F[/tex]

Step-by-step explanation:

Given

See attachment

Required

Days colder than -1.75°F

From the attachment, we have:

[tex]Monday = -2.5F[/tex]

[tex]Tuesday = -1.9F[/tex]

[tex]Wednesday = 0F[/tex]

[tex]Thursday = -1.5F[/tex]

[tex]Friday = 0.5F[/tex]

Days with temperature less than -1.75°F are colder.

-2.5 and -1.9 are less than -1.75

So, we have:

[tex]Monday = -2.5F[/tex]

[tex]Tuesday = -1.9F[/tex]

Answer:

:)

Step-by-step explanation:

Answer:

16 percent is left

Step-by-step explanation:

20/100×80

Hope it helps!!

The rate in miles per minute is 320

Step-by-step explanation:

2/20, 2/10 , 2/5

set them all to the same denominator of 20:

2/20, ,4/20, 8/20