Bill’s car gets 30 miles to the gallon. For every gallon of gas it consumes, his car runs 30 miles. Use this information to determine whether this relation is a function
write a equation for the number of miles Bill travels, y, in terms how much gas it uses, x.

Hello! :)

Answer:

[tex]\huge\boxed{BC = 6.4 }[/tex]

Given ΔABC ~ ΔDEF, we can set up a proportion to solve for BC, where:

[tex]\frac{AC}{DF} = \frac{BC}{EF}[/tex]

Let BC = x:

[tex]\frac{8}{15} = \frac{x}{12}[/tex]

Cross multiply:

[tex]8 * 12 = 15 * x[/tex]

[tex]96 = 15x[/tex]

[tex]x = 6.4[/tex]

Therefore, BC = 6.4 units.

Hope this helped you!

Answer:

150 front tickets and 250 back tickets

Step-by-step explanation:

make 2 equations 25x + 15y = 7500 and x + y = 400 and do substitution on a graphing calculator or by your self.

let me know if this helps

Answer:

-1/20

Step-by-step explanation:

For a graph like this you should make the gallons of gas on y-axis and the miles driven on the x-axis.

To find slope the formula is (y2-y1)/(x2-x1)

So in this case it is 2-4/40-0

-2/40

This reduces to -1/20

Answer:

Identity Property of Multiplication

Step-by-step explanation:

The Identity Property of Multiplication states that any number multiplied by 1 will equal the same number.

Since we have one item that costs $14.50, we know that the total cost will be $14.50 since we are multiplying $14.50 by 1.

Hope this helped!

Answer:

Identity property of multiplication.

Step-by-step explanation:

When we multiply any number by 1, we will get the same number.

5 *1 = 5

-8 * 1 = -8

Step-by-step explanation:

For example:

Ex: 2:3 :: 6:9

In this question, the means are 3 and 6.

The extremes are 2 and 9.

We use this method to find whether the two ratios are equal or not.

We multiply the means and the extremes, and if there products are same, then these two ratios are proportional.

If these two ratios are proportional, their "means" = "extremes"

=> Means = Extremes

=> 3 x 6 = 2 x 9

=> 18 = 18

So, these two ratios are proportional.

Hope this helps you.

Answer:

120

Step-by-step explanation:

Answer:

(D) 6

Step-by-step explanation:

We can substitute the values of a (7) and b (-4) into the equation to find it's result.

[tex]\frac{|2a| -b}{3} \\\\\\\frac{|2\cdot7|-(-4)}{3}\\\\\frac{|14|+4}{3}\\\\\frac{14+4}{3}\\\\\frac{18}{3}\\\\ 6[/tex]

So 6 is the value of this expression when a is 7 and b is -4.

Hope this helped!

Answer:

x = s/2

Step-by-step explanation:

● s states have joined the union in 1788

● half of s have joined in 1889

Let x be the number of states that have joined in 1889

● x = (1/2)× s

● x = s/2

Answer:

About 706.5 square inches.

Step-by-step explanation:

Surface area of a sphere is: [tex]SA=4\pi r^2[/tex]

The radius is half the diameter. So, the radius of the given sphere is 7.5 in.

15/2 = 7.5

Find the surface area:

I use 3.14 for pi.

[tex]SA=4*3.14*7.5^2\\\\SA=4*3.14*56.25\\\\SA=12.56*56.25\\\\\boxed{SA=706.5}[/tex]

The surface area is about 706.5 square inches.

Hope this helps.

Answer:

SA=706.86 in²

Step-by-step explanation:

surface area of a sphere = 4πr²

radius r=d/2=15/2=7.5

SA=4(π)(7.5)²

SA=706.86 in²

Answer:

Step-by-step explanation:

A) 280 Km

B)  When D = 0:  speed, S = 280/59 = 4,9 Km/hour

C) 280 Km

D)  59 hours

Answer:

7 : 18

Step-by-step explanation:

1. Convert to the same units (cents)

70 cents = 70 cents

$1.80 = 180 cents

2. Simplify

70 : 180 (divide both by ten)

7 : 18

7 and 18 cannot be simplified any further.

Answer:

True

Step-by-step explanation:

Microsoft Excel is a great tool and has saved me on countless occasions in graphs and tables. I agree with the earlier answer by Hedland.

Answer:

(D) [tex]\begin{array}{*{20}c} {x=\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}[/tex]

Step-by-step explanation:

The quadratic formula is:

[tex]\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}[/tex]

Assuming that a is our x² term, b is our x term, and c is the constant, we can substitute inside the equation.

[tex]\begin{array}{*{20}c} {\frac{{ - (-5) \pm \sqrt {5^2 - 4\cdot1\cdot3} }}{{2\cdot1}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {25 - 12} }}{{2}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}[/tex]

So the answer is D, [tex]\begin{array}{*{20}c} {x=\frac{{ 5 \pm \sqrt {13} }}{{2}}} \end{array}[/tex].

Hope this helped!

Answer:

99

Step-by-step explanation:

x = 90 x 10/100 + 90

=> x = 900/100 + 90

=> x = 9 + 90

=> x = 99

Answer:

u^18

Step-by-step explanation:

(u^3)^6

=

u^(3*6)

=

u^18

Hope this helps!

Answer:

572 7s are needed to be added together

Step-by-step explanation:

Basically, what we are asked here is the multiple of 7 which is closest to but above 4,000

Then, from this multiple , the number of 7s which are added together to give it is our answer.

By multiplication; 7 * 572 = 4,004

This is the closest multiple of 7 to 4000 which is also above it.

So the fewest number of 7s which we can add together is 572

Answer:

$307.20

Step-by-step explanation:

8×24=192

Convert 192 square feet to square yards, which is 21.3333

Then multiple: 21.333×14.40=307.1999

Then round to the nearest hundredths

The final answer is $307.20

Answer:

d) More than 3.

Step-by-step explanation:

The polynomial (x - 5)(x + 2)  ( = x^2  - 3x + 10) has zeros of -2 and 5 but so have the polynomials formed by multiplying this by any integer:

- for example 2(x - 5)(x + 2) , 4(x - 5)(x + 2) and so on.

Answer:

A. No real solution

B. 5 and -1.5

C. 5.5

Step-by-step explanation:

The quadratic formula is:

[tex]\begin{array}{*{20}c} {\frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \end{array}[/tex], with a being the x² term, b being the x term, and c being the constant.

Let's solve for a.

[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {5^2 - 4\cdot1\cdot11} }}{{2\cdot1}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {25 - 44} }}{{2}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 5 \pm \sqrt {-19} }}{{2}}} \end{array}[/tex]

We can't take the square root of a negative number, so A has no real solution.

Let's do B now.

[tex]\begin{array}{*{20}c} {\frac{{ 7 \pm \sqrt {7^2 - 4\cdot-2\cdot15} }}{{2\cdot-2}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 7 \pm \sqrt {49 + 120} }}{{-4}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 7 \pm \sqrt {169} }}{{-4}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 7 \pm 13 }}{{-4}}} \end{array}[/tex]

[tex]\frac{7+13}{4} = 5\\\frac{7-13}{4}=-1.5[/tex]

So B has two solutions of 5 and -1.5.

Now to C!

[tex]\begin{array}{*{20}c} {\frac{{ -(-44) \pm \sqrt {-44^2 - 4\cdot4\cdot121} }}{{2\cdot4}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 44 \pm \sqrt {1936 - 1936} }}{{8}}} \end{array}[/tex]

[tex]\begin{array}{*{20}c} {\frac{{ 44 \pm 0}}{{8}}} \end{array}[/tex]

[tex]\frac{44}{8} = 5.5[/tex]

So c has one solution: 5.5

Hope this helped (and I'm sorry I'm late!)

Answer:

x = [tex]\frac{12-4y}{3}[/tex]

Step-by-step explanation:

Given

[tex]\frac{x}{4}[/tex] + [tex]\frac{y}{3}[/tex] = 1

Multiply through by 12 to clear the fractions

3x + 4y = 12 ( subtract 4y from both sides )

3x = 12 - 4y ( divide both sides by 3 )

x = [tex]\frac{12-4y}{3}[/tex]

Answer:

the perimeter of ΔABC is 32in

Step-by-step explanation:

We know that intersection point of the angle bisectors refers to the incenter of the triangle,.

Given tmthe radius of 4inch for the centre of the incircle.

One of the properties of the incircle is that the distances (d) from vertex C to the nearest touchpoints are equal and have the value

In an incircle , the distances (d) along vertex C and touchpoints have equal value and can be expressed as

d = 1/2(a +b -c)

And a, b, c represent lengths of the sides

We were given the hypotenuse (c) as 12 in, with the radius of 4inch for the

distance from the right-angle vertex C to the incircle touchpoints .

We can determine the sum a+b as

4 = (1/2)(a+b -12) .

4/(1/2)= (a+b -12)

8= (a+b -12)

20=a+b

Which is the addition of length of the two legs of the triangle.

We can determine the perimeter which is the addition of the leg lengths as well as the hypotenuse length.

perimeter = 20 in + 12 in = 32 in

Therefore, the perimeter of ΔABC is 32in

Answer:

center=0,0 vertices=(0,5)(0,-5) foci=(0,4)(0,-4)  

Step-by-step explanation:

used calculator

Answer:

A pear is 3.4

Step-by-step explanation:

Answer: A pear cost $4.

Step-by-step explanation:

If the total price of four oranges and five pears is $32 then we could represent it by the equation  4x + 5y = 32   where x is cost of one orange and y is the cost of one pear.

The same way we could represent the second statement by the equation

3x + 2y = 17      

We know have the two systems of equations:

4x + 5y = 32

3x + 2y = 17         Solve using the elimination method

  Multiply the top equation by -3 and the down equation by 4 to eliminate x.

-3(4x + 5y) = -3(32) =  -12x - 15y = -96

 4(3x +2y) = 4(17)  =   12x + 8y = 68    

We now have the two new equations:

-12x -15y = -96      Add both equations

12x + 8y = 68            

      - 7y = -28

     y= 4    

Which means the cost of one pear is $4.

Answer:

Answer choices A, B and C identifies the relevant information in the problem

Step-by-step explanation:

Sarah left the house at 12:15 pm

She spent $42.20 on two books for her children

She spent $5.67 on a toy for her dog

Sarah arrived home at 1:00 pm

How much did Sarah spent on each book?

If she spent $42.20 on two books for her children,

Then, it means she has two children and the book cost $21.10 each

Answer choices A, B and C identifies the relevant information in the problem

Answer:

its A all the other one dont make sence sorry if im wrong but i got it right on my test

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Given the following :

Number of boxes = 2

First box :

White balls = 3

Blue balls = 2

Second box:

White balls = 4

Blue balls = 1

What is the probability that Frida picked a ball from the first box if she has selected a blue ball?

Probability (P) = (required outcome / Total possible outcomes)

Probability of picking first box : P(F) = 1/2

Probability of not picking second box :P(S) 1/2

Probability of picking blue from first box : P(B | F) = 3/5

Probability of picking blue, but not from first box : P(Blue not from second box) P(B|S) = 1/5

probability that Frida picked a ball from the first box if she has selected a blue ball?

P(F) * P(B|F) ÷ (P(F) * P(B|F)) + (P(S) * P(B|S))

(1/2 * 3/5) ÷ ((1/2 *3/5) + (1/2 * 1/5)

3/10 ÷ (3/10 + 1/10)

3/10 ÷ 4/10

3/10 * 10/4

= 3/4

Answer:

Step-by-step explanation:

The variation p varies directly with T is written as

p = kT

where k is the constant of proportionality

To find p when T =500 we must first find the formula for the variation

That's

when p = 105 and T = 400

105 = 400k

Divide both sides by 400

So the formula for the variation is

when

T = 500

Substitute it into the above formula

That's

[tex]p = \frac{21}{80} \times 500[/tex]

Simplify

The final answer is

Hope this helps you

Answer:

  x = 1/2 or 2

Step-by-step explanation:

You can factor this as ...

  2x^2 -4x -x +2 = 0 . . . rewrite the middle term to enable factoring

  2x(x -2) -1(x -2) = 0 . . . . factor by grouping

  (2x -1)(x -2) = 0 . . . . factor out (x -2)

  x = 1/2, 2 . . . . . . values of x that make the factors zero

Answer:

A. 10

Step-by-step explanation:

As we know that

The length of the major axis of the ellipse is 10

i.e

2 a = 10

Also, the ellipse is the curve that consists of 2 focal points  in order that the total of the distance to the 2 focal points would remain constant for each and every point displayed in the curve

Now we assume that P is the curve point

So,

PF1 + PF2

i.e

2 a (blue line) + (red line)

2 a = 10

Therefore the sum of the length is 10

Answer:

10

Step-by-step explanation:

we can subtract the trapezium (white part) formed after from the trapezium (including white and grey) to get area of striped part

area of trapezium is [tex]\frac H2(a+b)[/tex] where $a$ and $b$ are parallel sides.

for bigger trapezium, $h=4$ parallel sides are $5$ and $5$

hence area is $\frac{4(5+5)}{2}=20$

similarily area of white trapezium, $\frac{4(3+3)}{2}=12$

and area of striped part is $20-12=8$