Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 510 miles on 20 gallons of gas. How far could you drive on 65 gallons of gas?

The relationship between the areas of the floors is [tex]A_s = \frac{3\sqrt 3}{4} A_t[/tex]

Let the side length of the base of the square building be l, and the side length of the base of the equilateral triangle building be s

So, the perimeter of both buildings is

Both perimeters are equal.

So, we have:

4l = 3s

Divide both sides by 4

[tex]l = \frac 34s[/tex]

Square both sides

[tex]l^2 = \frac{9}{16}s\²[/tex]

The area of an equilateral triangle is:

[tex]A_t = \frac{\sqrt 3}{4}s^2[/tex]

And the area of a square is

[tex]A_s = l^2[/tex]

Make s^2 the subject in [tex]A_t = \frac{\sqrt 3}{4}s^2[/tex]

[tex]s^2 = \frac{4A_t}{\sqrt 3}[/tex]

Substitute [tex]s^2 = \frac{4A_t}{\sqrt 3}[/tex] and [tex]A_s = l^2[/tex] in [tex]l^2 = \frac{9}{16}s\²[/tex]

[tex]A_s = \frac{9}{16} * \frac{4A_t}{\sqrt 3}[/tex]

Evaluate

[tex]A_s = \frac{9}{4} * \frac{A_t}{\sqrt 3}[/tex]

Rationalize

[tex]A_s = \frac{3\sqrt 3}{4} A_t[/tex]

Hence, the relationship between the areas of the floors is [tex]A_s = \frac{3\sqrt 3}{4} A_t[/tex]

Read more about perimeter and area at:

https://brainly.com/question/24571594

Answer:  2.48

Step-by-step explanation:

We have the ad that shows:

6 lemons for .....................1.86 dollars

8 lemons..............................?

the cost for 8 lemons= (8*1.86)/6=2.48

of course we can use another method,

1.86/6=0.31 cents for 1 lemon

8*0.31=2.48 and we get the same answer

Answer:

$2.48

Step-by-step explanation:

1.86/6=0.31 which is the cost for 1 lemon. 0.31*8=2.48 which is for 8 lemons.

Answer:

that would be 26

Step-by-step explanation:

you got this!

Answer:

Principal = $9,152.93

Step-by-step explanation:

A = $9,152.93

A = P + I where

P (principal) = $7,500.00

I (interest) = $1,652.93

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 10/100

r = 0.1 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 7,500.00(1 + 0.1/12)(12)(2)

A = 7,500.00(1 + 0.008333333)(24)

A = $9,152.93

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $7,500.00 at a rate of 10% per year compounded 12 times per year over 2 years is $9,152.93.

Answer:

13020

Step-by-step explanation:

Answer:

first two are right because the scatterplots align well with both graphs in the direction described

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

a and B are the roots of

[tex] {x}^{2} - 2(p + 1)x + {p}^{2} + 8 = 0[/tex]

[tex] {x}^{2} - 2px - 2x + {p}^{2} + 8 = 0[/tex]

This look like a parabola since p will be a constant so let use a quadratic formula

[tex] {x}^{2} -(2p + 2)x + {p}^{2} + 8 = 0[/tex]

[tex]2p + 2± \frac{ \sqrt{4 {p}^{2} + 8p + 4 - (4 {p}^{2} + 32) } }{2} [/tex]

[tex]2p + 2± \frac{ \sqrt{8p - 28} }{2} [/tex]

[tex]2p + 2± \frac{2 \sqrt{2p - 7} }{2} [/tex]

[tex]2p + 2± \sqrt{2p - 7} [/tex]

So the roots are

[tex]2p + 2 + \sqrt{2p - 7} [/tex]

and

[tex]2p + 2 - \sqrt{2p - 7} [/tex]

We know the distance between these two points are

2 so

[tex] |(2p + 2) + \sqrt{2p - 7} - (2p + 2) - \sqrt{2p - 7} | = 2[/tex]

[tex] | \sqrt{2p - 7} + \sqrt{2p - 7} | = 2[/tex]

[tex] |2 \sqrt{2p - 7} | = 2[/tex]

[tex]2 \sqrt{2p - 7} = 2[/tex]

[tex]p = 4[/tex]

Let plug it in to see.

[tex] {x }^{2} - 2(4 + 1)x + {4}^{2} + 8 = 0[/tex]

[tex] {x}^{2} - 10x + 24 = 0[/tex]

[tex](x - 6)(x - 4) = 0[/tex]

[tex]x = 4[/tex]

[tex]x = 6[/tex]

So they have a distance of 2.

Answer:

This day is going to be perfect

The kind of day of which I dreamed since I was small

Everypony will gather round

Say I look lovely in my gown

What they don't know is that I have fooled them all

Step-by-step explanation:

Answer:

x=-4 and x=4

Step-by-step explanation:

solution to equation is 4

odd numbers are numbers which are divisible by 3,5,7 etc.....odd numbers between 60 and 70 are 63 65 67 and 69 the sum is 264

Answer:

she'd have 13 left hope this helps:)

Answer:

I don't know honestly sorry

Step-by-step explanation:

I tried

Answer:

see explanation

Step-by-step explanation:

5x + 3y = 6 → (1)

- 4x - 3y = - 3 → (2)

the most efficient method here would be elimination.

add (1) and (2) term by term to eliminate y

x + 0 = 3

x = 3

substitute x = 3 into either of the 2 equations and solve for y

substituting into (1)

5(3) + 3y = 6

15 + 3y = 6 ( subtract 15 from both sides )

3y = - 9 ( divide both sides by 3 )

y = - 3

solution is (3, - 3 )

Answer:

[tex](3,-3)[/tex]

Step-by-step explanation:

[tex]5x + 3y = 6[/tex]

The most efficient method for this equation is elimination.

[tex]x + 0 = 3[/tex]

[tex]5(3) + 3y = 6[/tex]

Substitute x = 3 into any of the equation and solve for y.

[tex]5(3) + 3y = 6[/tex]

[tex]15 + 3y = 6[/tex]

[tex]-15 -15[/tex]

[tex]3y = - 9[/tex]

[tex]\frac{3y}{3}=\frac{-9}{3}[/tex]

[tex]y=-3[/tex]

[tex](3,-3)[/tex]

Answer:

Sorry but I don't know the answer too this question

Answer:

Assuming you want to know what fraction of the original amount you have.

a = allowance

(1/2)a = what have left after Monday

(1/2(1/2)a = what you have after Tuesday

(1/2)(1/2)(1/2)a = what you have after Wednesday.

Doing the multiplication.

(1/8)a = what you have left.

You have 1/8 of what you had at the start.

Hope this help u

Answer:

1/8 i think

Step-by-step explanation:

Answer:The winner recieved 4,500 more votes than the loser

Step-by-step explanation:

Answer:

5,250

Step-by-step explanation:

The first step is to set up a porportion like this one

[tex]\frac{?}{15,000} \frac{65}{100}[/tex]

Next, you cross multiply and divide. 15,000 times 65 is 975,000

Then divide this by 100 which is 9750. This is the number of votes the winning candidate received. Subtract this number from 15,000 to get 5,250. Hope this helps!

When the change of base formula is applied to log subscript 4 baseline (x+2), the result is [tex]\dfrac{log(x+2)}{log4}[/tex].

There are four basic properties of logarithms:

[tex]\rm log_aU+ log_aV = log_a(UV)\\\\log_aU - log_aV = log_a(\dfrac{U}{V})\\\\log_aU^n = n\ log_aU\\\\\log_ab = \dfrac{log_xb}{log_xa}\\\\[/tex]

When the change of base formula is applied to log subscript 4 baseline (x 2), the result expression will be,

[tex]\rm log_4(x+2)=\dfrac{log_{10}(x+2)}{log_{10}4}=\dfrac{log(x+2)}{log4}[/tex]

Hence, when the change of base formula is applied to log subscript 4 baseline (x+2), the result is [tex]\dfrac{log(x+2)}{log4}[/tex].

Learn more about Logarithms:

https://brainly.com/question/7302008

Answer:

a - StartFraction log (x + 2) Over log 4 EndFraction

Step-by-step explanation:

edge 2022

In the given question, we have to factorise the equation:

Therefore, by using the middle term splitting method:

➙ 3c² + 2c -16

➙ 3c² - 6c + 8c - 16

➙ ( 3c² - 6c )+ (8c - 16 )

➙ 3c( c - 2 ) + 8 ( c - 2 )

➙ ( c - 2 ) ( 3c + 8 )

Factorisation of a quadratic polynomial of the type ax² + bx + c where (a ≠ 1) .

Consider the factorisation of 3c² + 2c – 16 .

We have to find two numbers whose sum is +2 and product (3 × 16) = 48 .

Obviously, the two numbers are 6 and 8 .

[tex]{ \qquad \sf { \dashrightarrow{ 3c {}^{2} + 2c - 16 }}}[/tex]

So, We can write it as,

[tex]{ \qquad \sf { \dashrightarrow{ 3c {}^{2} + 8c - 6c - 16 }}}[/tex]

[tex]{ \qquad \sf { \dashrightarrow{ c (3c + 8) -2 (3c + 8) }}}[/tex]

[tex]{ \qquad \sf { \dashrightarrow{ ( c -2 )(3c + 8) }}}[/tex]

Graph attached

Answer:

vertex = (-4, 7)

(-3, 3) and (-2, -9)

(-6, -9) and (-5, 3)

Step-by-step explanation:

Given function:  [tex]f(x) = -4(x + 4)^2 + 7[/tex]

Vertex form of a quadratic function:  [tex]f(x)=a(x-h)^2+k[/tex]
(where (h, k) is the vertex)

From inspection, we can see that the given function is in vertex form.

h = -4 and k = 7

Therefore, the vertex is at (-4, 7)

As [tex]a[/tex] is negative, the parabola will open downwards.

When graphing functions, it is useful to determine the axis intercepts.

The curve will intercept the y-axis when x = 0.

Substituting x = 0 into the function:

[tex]f(0) = -4(0 + 4)^2 + 7=-57[/tex]

Therefore, the y-intercept is at (0, -57)

**cannot plot this on the given graph area as it is out of range**

The curve will intercept the x-axis when y = 0.

Setting the function to 0 and solving for x:

[tex]-4(x + 4)^2 + 7=0[/tex]

[tex]\implies -4(x + 4)^2=-7[/tex]

[tex]\implies (x + 4)^2=\dfrac74[/tex]

[tex]\implies x+4=\pm\sqrt{\dfrac74}[/tex]

[tex]\implies x=-4\pm\dfrac{\sqrt{7}}{2}[/tex]

Therefore, the x-intercepts are at (-2.7, 0) and (-5.3, 0) to 1 dp.

Finally, input values of x either sides of the x-intercepts for further plot points:

(-3, 3) and (-2, -9)

(-6, -9) and (-5, 3)

Answer:

12

Step-by-step explanation:

61 62 64 16 12 14 26 21 24 46 41 and 42

Answer:

The last one.

Step-by-step explanation:

Answer:

y^5 cubed root x^2 y^2

Step-by-step explanation:

edge 2023

Answer:

So I think your answer is Zero

I think it will help you.

Answer:

Step-by-step explanation:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

(−∞,∞)

Set-Builder Notation:

{x|x∈R}

The range is the set of all valid y

values. Use the graph to find the range.

Interval Notation:

[0,∞)

Set-Builder Notation:

{y|y≥0}

Determine the domain and range.

Domain: (−∞,∞),{x|x∈R}

Range: [0,∞),{y|y≥0}

Explanation:

Refer to the diagram below. The point (-4,3) marked in red is outside the blue shaded region. So it doesn't make both inequalities true, and therefore not considered a solution.

In contrast, a point like (-5,1) is a solution as it is in the shaded region.

Put another way, the set of all solution points must be below both the solid line and the dashed line. Points can be on the solid line, but must be adjacent to the blue shaded region. The fact (-4,3) is on the solid line doesn't count because its not below the dashed line.

Answer:

Step-by-step explanation:

Answer:

4.99750499002

Step-by-step explanation:

Answer:

1984

Step-by-step explanation:

(2001 + 2002 + 2003 + 2004 + 2005) by 2004

10015/2004

4 remainder 1984

Hope this helps!