In order to answer this question, remember that gasoline costs $2.56/gallon and the tank takes 15 gallons.


You have another person who wants to carpool with you and your friend. The tank will be split evenly. How much do you and your friend each save by having a third person sharing the tank of gas?

Answer:

Our two numbers are:

[tex]2+4\sqrt{2} \text{ and } 4\sqrt{2}-2[/tex]

Or, approximately 7.66 and 3.66.

Step-by-step explanation:

Let the two numbers be a and b.

One positive real number is four less than another. So, we can write that:

[tex]b=a-4[/tex]

The sum of the squares of the two numbers is 72. Therefore:

[tex]a^2+b^2=72[/tex]

Substitute:

[tex]a^2+(a-4)^2=72[/tex]

Solve for a. Expand:

[tex]a^2+(a^2-8a+16)=72[/tex]

Simplify:

[tex]2a^2-8a+16=72[/tex]

Divide both sides by two:

[tex]a^2-4a+8=36[/tex]

Subtract 36 from both sides:

[tex]a^2-4a-28=0[/tex]

The equation isn't factorable. So, we can use the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 1, b = -4, and c = -28. Substitute:

[tex]\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-28)}}{2(1)}[/tex]

Evaluate:

[tex]\displaystyle x=\frac{4\pm\sqrt{128}}{2}=\frac{4\pm8\sqrt{2}}{2}=2\pm4\sqrt{2}[/tex]

So, our two solutions are:

[tex]\displaystyle x_1=2+4\sqrt{2}\approx 7.66\text{ or } x_2=2-4\sqrt{2}\approx-3.66[/tex]

Since the two numbers are positive, we can ignore the second solution.

So, our first number is:

[tex]a=2+4\sqrt{2}[/tex]

And since the second number is four less, our second number is:

[tex]b=(2+4\sqrt{2})-4=4\sqrt{2}-2\approx 3.66[/tex]

Answer:

[tex]2+4\sqrt{2}\text{ and }4\sqrt{2}-2[/tex]

Step-by-step explanation:

Let the large number be [tex]x[/tex]. We can represent the smaller number with [tex]x-4[/tex]. Since their squares add up to 72, we have the following equation:

[tex]x^2+(x-4)^2=72[/tex]

Expand [tex](x-4)^2[/tex] using the property [tex](a-b)^2=a^2-2ab+b^2[/tex]:

[tex]x^2+x^2-2(4)(x)+16=72[/tex]

Combine like terms:

[tex]2x^2-8x+16=72[/tex]

Subtract 72 from both sides:

[tex]2x^2-8x-56=0[/tex]

Use the quadratic formula to find solutions for [tex]x[/tex]:

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] for [tex]ax^2+bx+c[/tex]

In [tex]2x^2-8x-56[/tex], assign:

Solving, we get:

[tex]x=\frac{-(-8)\pm \sqrt{(-8)^2-4(2)(-56)}}{2(2)},\\x=\frac{8\pm 16\sqrt{2}}{4},\\\begin{cases}x=\frac{8+16\sqrt{2}}{4}, x=\boxed{2+4\sqrt{2}} \\x=\frac{8-16\sqrt{2}}{4}, x=\boxed{2-4\sqrt{2}}\end{cases}[/tex]

Since the question stipulates that [tex]x[/tex] is positive, we have [tex]x=\boxed{2+4\sqrt{2}}[/tex]. Therefore, the two numbers are [tex]2+4\sqrt{2}[/tex] and [tex]4\sqrt{2}-2[/tex].

Verify:

[tex](2+4\sqrt{2})^2+(4\sqrt{2}-2)^2=72\:\checkmark[/tex]

Answer:

No

Step-by-step explanation:

This relation is a function because the x values have a repeating number (15).

Answer:

t < -3

Step-by-step explanation:

-3t + 11 > 20

subtract 11 from both sides

-3t > 9

Divide both sides by -3

when multipying or dividing by a negative the inequality must be reversed

t < -3

Step-by-step explanation:

21/1

When a denominator is equal to 1, the fraction might be simplified, using this formula:

a/1=a

21/1=21

3/12

Reduce fraction

3/12=3÷3/12÷3

=1/4 or 0.25

Answer and Step-by-step explanation:

The answer is -7 (A.)

This is determined by looking at the graph. If you to to the x-point of -3 units, you will see there is a point at a y-value of -7 (units down).

#teamtrees #PAW (Plant And Water)

Answer:

1 square unit

Step-by-step explanation:

Area of the shaded region

= Area of the triangle with base 3 units and height 1 unit - Area of triangle with base 1 unit and height 1 unit.

= 1/2 *3*1 - 1/2 *1*1

= 1.5 - 0.5

= 1 square unit

Answer:

y = (x + 1)²

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (- 1, 0) , then

y = a(x + 1)² + 0

To find a substitute (0, 1), the y- intercept into the equation

1 = a(0 + 1)² = a

y = (x + 1)²

Answer:

what is it's perimeter?

Answer:

the answer is c you will thank us later

Answer:

EG = 26

Step-by-step explanation:

We use the angle-bisector theorem here

The theorem is that given an angle that is bisected in a triangle, it splits the opposite side into two parts, with the ratio of the sides facing the angle and the adjoining leg equal for the two bisections

So, we have this as;

EF/ED = GD/FG

x/24 = x+10/54

54(x) = 24)x + 10)

54x = 24x + 240

54x-24x = 240

30x = 240

x = 240/30

x = 8

But;

EG = EF + FG

EG = x + x + 10 = 2x + 10

EG = 2(8) + 10

EG = 16 + 10 = 26

Answer:

Dhhdhdhgdgdgd djjdhdhdhfh dbdjhdhfv djjdhfhhb is a hdhdh yhvggfff tghrh9

Answer:

45kg

Step-by-step explanation:

60.3/4=45

Answer:

56 months 12+12x2=56 hope this helps

Step-by-step explanation:

Answer:

5x=13.5

Step-by-step explanation:

Well, we know that 1x=2.7. So, if we want 5x we need to multiply 2.7*5 becuase 1x=2.7, so 5x=2.7*5.

Multiply. 2.7*5=13.5

So, 5x=13.5.

Hope this helps!

Answer:

13.5

Step-by-step explanation:

5x = ?

Replace 'x' with 2.7.

5(2.7) = ?

5(2.7) = 13.5

Hope this helps.

Answer:

The cost of tuition as a function of x, the number of years since 1990, is C(x)= 14*(x-1990) + 95

Step-by-step explanation:

A linear function is a polynomial function of the first degree that has the following form:

y= m*x + b

where

So, in this case: C(x)= m*( x-1990) + b where x is the number of years since 1990.

Given the coordinates of two points, it is possible to determine the slope m of the line from them using the following formula:

[tex]m=\frac{y2 - y1}{x2 - x1}[/tex]

In this case, you know that in 1990, the cost of tuition at a large Midwestern university was $95 per credit hour. And in 1999, tuition had risen to $221 per credit hour. So:

So the value of m is:

[tex]m=\frac{221 - 95}{1999 - 1990}[/tex]

[tex]m=\frac{126}{9}[/tex]

m= 14

So C(x)= 14*( x-1990) + b. In 1999, tuition had risen to $221 per credit hour. Replacing:

221= 14*(1999 - 1990) + b

221= 14*9 +b

221= 126 + b

221 - 126= b

95= b

Finally, the cost of tuition as a function of x, the number of years since 1990, is C(x)= 14*(x-1990) + 95

Answer:

44

Step-by-step explanation:

divide 24 by 6 then multiply it by all the number then add it all

please make me brainliest

Answer:  Choice C)  [tex]\frac{8+2\sqrt{6x}}{8-3x}[/tex]

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

Work Shown:

[tex]y = \frac{4}{4-\sqrt{6x}}\\\\y = \frac{4(4+\sqrt{6x})}{(4-\sqrt{6x})(4+\sqrt{6x})}\\\\y = \frac{4(4+\sqrt{6x})}{4^2 - (\sqrt{6x})^2}\\\\y = \frac{4(4+\sqrt{6x})}{16-6x}\\\\y = \frac{2*2(4+\sqrt{6x})}{2(8-3x)}\\\\y = \frac{2(4+\sqrt{6x})}{8-3x}\\\\y = \frac{8+2\sqrt{6x}}{8-3x}\\\\[/tex]

This shows why choice C is the answer.

----------------

Notes:

Answer:

Option (1)

Step-by-step explanation:

We have to graph the system of inequalities given.

y > 2x + 1 -----(1)

y > |x| --------(2)

For inequality (1),

Solution area will be the area above the dotted line y = 2x + 1

Similarly, solution area of the second inequality will be the area above the dotted lines of y = |x|

Solution area of the system of inequalities will be the common area of both the graphs of the given system.

That will lie in quadrants 1 and 2.

Option (1) will be the answer.

Answer:

Δy = 5  Δx = 1

slope = [tex]\frac{5}{1}[/tex] = 5

Step-by-step explanation:

Step-by-step explanation:

answer is in photo above

Answer:

62

Step-by-step explanation:

12+12+3+3+7+10+15

you just add all the sides

Answer:

[tex]-2 < 2x - 3 < 1 \ = \ \frac{1}{2} < x < 2[/tex]

Step-by-step explanation:

[tex]-2 < 2x - 3 < 1\\\\-2 + 3 < 2x - 3 + 3 < 1 + 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ adding \ by\ 3 \ ]\\\\1 < 2x + 0 < 4\\\\1 < 2x < 4\\\\\frac{1}{2} < \frac{2x}{2} < \frac{4}{2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ divide \ by \ 2 \ ]\\\\\frac{1}{2} < x < 2[/tex]

Answer:

1/2 < x < 2

Step-by-step explanation:

-2<2x-3<1​

Add 3 to all sides

-2+3<2x-3+3<1​+3

1<2x<4

Divide all sides by 2

1/2 < 2x/2 <4/2

1/2 < x < 2

Answer:

79

Step-by-step explanation:

78 +2 ÷ 2

PEMDAS says divide first

78 + (1)

Then add

79

Answer:

(x+y)+2

hope this helps

Answer:

see below

Step-by-step explanation:

Slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = x-7

m = 1

b = -7

y = 4

m=0

b = 4

y = -2x+3

m = -2

b = 3

Answer: 0.662201

Step-by-step explanation:

Number of five thousand dollar bills in circulation = 1,765,000

Number of ten thousand dollar bills in circulation = 3,460,000

Total bills in circulation = 1,765,000 + 3,460,000 = 5225000

If one one bill is chosen at random, the probability that it is a ten thousand dollar bill will be:

= Number of ten thousand dollar bills in circulation / Total bills in circulation

= 3,460,000 / 5225000

= 0.662201

The probability that it is a ten thousand dollar bill is 0.662201.

Answer:

y = 3x - 30

Step-by-step explanation:

First, put both equations into slope-intercept form.

x + 3y - 4 = 0

3y = -x + 4

y = (-1/3)x + (4/3)

2x + 5y - 20 = 0

5y = -2x + 20

y = (-2/5)x + 4

For a line to be perpendicular to y = (-1/3)x + (4/3), its slope should be the opposite and reciprocal of this line's slope.

The slope of y = (-1/3)x + (4/3) is (-1/3). The slope of a perpendicular line is 3.

To find the x-intercept of y = (-2/5)x + 4, plug in 0 for y and find x.

0 = (-2/5)x + 4

x = 10

The equation of the line right now is y = 3x + b

Plug in (10, 0) to find the y-intercept.

0 = 3(10) + b

b = -30

The equation of the line is y = 3x - 30