Aaron's car used 2 gallons of gas to drive 32 miles. At what rate does his car use gas in miles per gallon?

Answer:

x=19/6, x=-9/13, x=33/4

Step-by-step explanation:

1) 2^(6x+10)=2^(12x-9), 6x+10=12x-9, x=19/6

2) 3^(4x+6)=3^(-9x-3), 4x+6=-9x-3, x=-9/13

3) 2^(x+6)*2^(3x-27)=2^(6), 4x-27=6, x=33/4

Answer:

(8, -7)

Step-by-step explanation:

Hi there!

We are given this system:

y=-3x+17

2x+3y=5

And we want to solve the system

Let's solve it by substitution.

In the first equation, we are given y=-3x+17, which we can substitute -3x+17 as y into the second equation

2x+3(-3x+17)=5

Now do the distributive property

2x+-9x+51=-5

Combine like terms

-7x+51=-5

Subtract 51 from both sides

-7x=-56

Divide both sides by -7

x=8

Now substitute 8 as the value of x in y=-3x+17 to find the value of y

y=-3(8)+17

y=-24+17

y=-7

The answer is x=8, y=-7. If you need it as a point, it's (8, -7)

Hope this helps!

Answer:0.60$

Step-by-step explanation:

15=9$

 1=0.60$

Answer:

60 cents

Step-by-step explanation:

Answer:

.............................

Answer:

5.5

Step-by-step explanation:

(segment piece) x (segment piece) = (segment piece) x (segment piece)

11*2 = x*4

22 = 4x

Divide each side by 4

22/4 = 4x/4

11/2 =x

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

Explanation:

We can immediately rule out choice C because we don't have info about all three pairs of sides. So that's why we can't use the SSS rule.

We may be able to use SAS however. This rule says that if we know a pair of sides are proportional, and if the angles between them are congruent, then we have similar triangles.

However, note the jump from XZ = 2 to XW = 8 is "times 4" while the jump from XY = 3 to XV = 9 is "times 3". The two multipliers don't match up. We would need them to be the same for the sides to be proportional.

Put another way, the equation

8/2 = 9/3

is a false equation

If we tried the equation

8/3 = 9/2

then that's also false. No matter what combos we try, the sides aren't proportional.

So ultimately, we can't use SAS either. This eliminates choice B.

Consequently, it means that we know the triangles aren't similar. If they were similar, then we'd be able to use SAS to prove them to be so.

Therefore, we do have enough information to conclude that the triangles are not similar.

This is why choice D is the final answer.

Answer:

y = -2x-8 ------> the equation of the line

Step-by-step explanation:

y = mx + b

8 = -2(-8)+b

  = 16 + b

-16      -16

-----------

-8 = b

y^2 - y^1 / x^2 - x^1

= 8-(-6) / -8-(-1)

= -14/7

= m = -2

Final answer: y = -2x-8

Answer: 2x - 7y - 40 = 0

Step by step explanation:

(-1,-6) (-8,-8)

Slope (m) = y-y/x-x

m = (-8- -6)/(-8 - -1)

m = 2/7

y-y=m(x-x). Use one of the points: (-1,-6)

y - - 6 = 2/7 (x - - 1)

y+6=2/7(x+1)

y+6=2/7x+2/7

Multiply both sides by 7

7y+42=2x+2

2x—7y-40=0

Standard form =

Answer:

Below

Step-by-step explanation:

Front = 3 x 4 = 12 cm^2

Back = 3 x 4 = 12 cm^2

Right = 3 x 4 = 12 cm^2

Left = 3 x 4 = 12 cm^2

top = 3 x 3 = 9 cm^2

Add em all up : 57 cm^2

Hope this helped!

Answer: 57 cm^2

Step-by-step explanation:

4(3)(4)+(3)(3) = 57

Answer:

1000cm²=0.1m²

so 7000cm²=0.7m²

Step-by-step explanation:

please mark me as brainliest

Answer:

0.7

Step-by-step explanation:

Make ratio:

1 square centimeter = 0.0001 square meter

x square meters = 7000 square centimeters

Multiply:

0.0001 × 7000 = 0.7

Hope this helped.

In geometry, several transformations (such as dilation, rotation, reflection, etc.) can be applied to move a parent function to a new function. The function that represents g(x) is [tex]g(x) = 3|x|[/tex]

Given that:

[tex]f(x) = |x|[/tex]

First, we reflect over the y-axis.

The rule of this transformation is: [tex](x,y) \to (-x,y)[/tex]

So, the function becomes

[tex]f'(x) = |-x|[/tex]

[tex]f'(x) = |x|[/tex]

Next, shrink horizontally by 1/3

The rule of this transformation is: [tex](x,y) \to (\frac{x}{a},y)[/tex]

Where:

[tex]a = \frac{1}{3}[/tex]

So, we have:

[tex]g(x) = |\frac{x}{1/3}|[/tex]

[tex]g(x) = |3x|[/tex]

[tex]g(x) = 3|x|[/tex]

Hence, the function that represents g(x) is [tex]g(x) = 3|x|[/tex]

Read more about function transformations at:

https://brainly.com/question/12865301

Triangle HIJ is similar to triangle MNO  by the angle-angle similarity theorem if ∠O ≅ ∠J.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two triangle are said to be similar if the ratio of their corresponding sides are in the same proportion and corresponding angles are congruent.

Triangle HIJ is similar to triangle MNO  by the angle-angle similarity theorem if ∠O ≅ ∠J.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

x=pi/8 and 7pi/8

Step-by-step explanation:

2cos(2x)=sqrt(2), cos(2x)=1/sqrt(2). 2x=pi/4 and 7pi/4, x=pi/8 and 7pi/8

Answer:

2 remaining slices

Step-by-step explanation:

It sounds complicated so firstly, let's break it down.

Ron and two of his friends

There are three people involved in this question.

ate one fourth each

These three people ate one fourth of the pizza each

of an eight slice pizza.

From a pizza with eight slices

Find remaining slice of the pizza ​

The main question : remaining slice of the pizza

So since there were three people and they ate one fourth of the pizza

( One fourth's [tex]\frac{1}{4}[/tex] by the way )

We need to find out how much have they ate.

Simply multiply 3 with [tex]\frac{1}{4}[/tex] .

3 × [tex]\frac{1}{4}[/tex] = [tex]\frac{12}{4}[/tex] × [tex]\frac{1}{4}[/tex]

= [tex]\frac{3}{4}[/tex]

And there you go! Ron and his friends ate [tex]\frac{3}{4}[/tex] of the pizza.

But that's not the end.

The main question : Remaining slice of the pizza

It's an eight slice pizza, so a slice would be : [tex]\frac{1}{8}[/tex]

A full eight slice pizza would be one.

So, to find the remaining slice of pizza, simply subtract [tex]\frac{3}{4}[/tex] from 1.

1 -  [tex]\frac{3}{4}[/tex] =  [tex]\frac{4}{4}[/tex] -  [tex]\frac{3}{4}[/tex]

= [tex]\frac{1}{4}[/tex]

Now there's a remainding of [tex]\frac{1}{4}[/tex] of the pizza.

But the question asked for remaining slices.

So, simply convert the denominator into 8!

( Just in case you don't know what's a denominator )

[tex]\frac{numerator}{denominator}[/tex]

So, simply multiply the denominator by 2 to turn 4 into 8!

And also, whenever the denominator is multiplied/ divided by any number, so do the numerator.

[tex]\frac{1 times 2}{4 times 2}[/tex] = [tex]\frac{2}{8}[/tex]

Your answer's the numerator, 2!

So your final answer should be 2 remaining slices out of the eight sliced pizza.

Answer:

y = 3

Step-by-step explanation:

Both y = 3 and y = 0 have zero slopes. Therefore, they are parallel.

30^∘ Another boy is standing on the roof of a 10 second string be x mIn Δ ABC sin 30^∘ = AC/AB 1/2 = AC/100 AC =

Answer: hope this helps ♡

The kite was 16.9 feet high.

Step-by-step explanation:

Pythagorean theorem

b = [tex]\sqrt{c^{2} - a^{2} }[/tex]

b = [tex]\sqrt{22^{2} - 14^{2} }[/tex]

b = [tex]\sqrt{484 - 196}[/tex]

b = [tex]\sqrt{288}[/tex]

b = 16.9

Answer:

Step-by-step explanation:

29/9 or 3 2/9

Answer:

1155

Step-by-step explanation:

Total number of cards is 2730+3570=6300

Since Kim now has 3 times the card of Julie so Julie must have 6300/4=1575.

So, Julie gave 2730-1575=1155

Answer:

1155 cards

Step-by-step explanation:

3(2730-x)=3570+x

8190 - 3x = 3570 + x

4620 - 3x = x

4620 = 4x

1155 = x

Answer:

33.14 ft^2

Step-by-step explanation:

First find the area of the circle

The diameter is 20 ft so the radius is 1/2 of the diameter of 20*1/2 = 10 ft

A = pi r^2 = pi ( 10)^2 = 100 pi

The central angle is 38

That is a fraction of the circle, which is 360 degrees

38/360 = 19/180

Multiply the fraction of the circle by the area

19/180 * 100 pi

19/9 * 5 pi

Using 3.14 for pi

33.144444

To the nearest hundredth

33.14 ft^2

The area of the slice of pie that was cut, rounded to the nearest hundredth   33.14 ft^2.

We have to first find the area of the circle.

The diameter is 20 ft so the radius is 1/2 of the diameter of

20*1/2 = 10 ft.

The area of a circle [tex]A = \pi r^2[/tex]

By using the formula we have,

A= pi ( 10)^2

A = 100 pi

The central angle is 38.

That is a fraction of the circle, which is 360 degrees

38/360 = 19/180

Multiply the fraction of the circle by the area

19/180 * 100 pi

19/9 * 5 pi

Using 3.14 for pi

33.144444

To the nearest hundredth, it is 33.14 ft^2.

To learn more about the circle visit:

https://brainly.com/question/24375372

Answer:

game1321.netlify.app

Step-by-step explanation:

This is a test sorry I'm trying to see if you can post links in comments

Answer:

No answer is possible

Step-by-step explanation:

First, we can identify what the parabola looks like.

A parabola of form ax²+bx+c opens upward if a > 0 and downward if a < 0. The a is what the x² is multiplied by, and in this case, it is positive 2. Therefore, this parabola opens upward.

Next, the vertex of a parabola is equal to -b/(2a). Here, b (what x is multiplied by) is 1 and a =2, so -b/(2a) = -1/4 = -0.25.

This means that the parabola opens upward, and is going down until it reaches the vertex of x=-0.25 and up after that point. Graphing the function confirms this.

Given these, we can then solve for when the endpoints of the interval are reached and go from there.

The first endpoint in -2 ≤ f(x) ≤ 16 is f(x) = 2. Therefore, we can solve for f(x)=-2 by saying

2x²+x-4 = -2

add 2 to both sides to put everything on one side into a quadratic formula

2x²+x-2 = 0

To factor this, we first can identify, in ax²+bx+c, that a=2, b=1, and c=-2. We must find two values that add up to b=1 and multiply to c*a = -2  * 2 = -4. As (2,-2), (4,-1), and (-1,4) are the only integer values that multiply to -4, this will not work. We must apply the quadratic formula, so

x= (-b ± √(b²-4ac))/(2a)

x = (-1 ± √(1-(-4*2*2)))/(2*2)

= (-1 ± √(1+16))/4

= (-1 ± √17) / 4

when f(x) = -2

Next, we can solve for when f(x) = 16

2x²+x-4 = 16

subtract 16 from both sides to make this a quadratic equation

2x²+x-20 = 0

To factor, we must find two values that multiply to -40 and add up to 1. Nothing seems to work here in terms of whole numbers, so we can apply the quadratic formula, so

x = (-1 ± √(1-(-20*2*4)))/(2*2)

= (-1 ± √(1+160))/4

= (-1 ± √161)/4

Our two values of f(x) = -2 are (-1 ± √17) / 4 and our two values of f(x) = 16 are (-1 ± √161)/4 . Our vertex is at x=-0.25, so all values less than that are going down and all values greater than that are going up. We can notice that

(-1 - √17)/4 ≈ -1.3 and (-1-√161)/4 ≈ -3.4 are less than that value, while (-1+√17)/4 ≈ 0.8 and (-1+√161)/4 ≈ 2.9 are greater than that value. This means that when −2 ≤ f(x) ≤ 16 , we have two ranges -- from -3.4 to -1.3 and from 0.8 to 2.9 . Between -1.3 and 0.8, the function goes down then up, with all values less than f(x)=-2. Below -3.4 and above 2.9, all values are greater than f(x) = 16. One thing we can notice is that both ranges have a difference of approximately 2.1 between its high and low x values. The question asks for a value of a where a ≤ x ≤ a+3. As the difference between the high and low values are only 2.1, it would be impossible to have a range of greater than that.

If x/y = 2/3, then all we have to do is multiply x/y by 6. Another way to look at this (the same thing) would be to see 6 as 6/1, so 6 is multiplied by x, and y is multiplied by 1.

But, all the same, you multiply 6 by x/y and you get (2·6)/3 = 12/3 = 4

Answer:

6 out of the 20 values are below 2.  6/20 = 30%.

Since 30% of the values are below 2, 2 is located at the 30th percentile.

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

6/100=3/y

Let y be the total number of items on the test

[cross multiply]

6×y =3×100

6y = 300

divide both sides by 6

y = 50

Step-by-step explanation:

think that the answer is 10° degrees

Answer:

11.31 units

Step-by-step explanation:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Step 1.

Plug in the points inside the formula where the first point = [tex](x_1,y_1)[/tex] and the second point = [tex](x_2-y_2)[/tex]

Let the first point be C and the second point be D

[tex](-4,-5)\\ (x_1,y_1)[/tex]  [tex](4,3)\\ (x_2,y_2)[/tex]

Answer: [tex]d=\sqrt{(4--4)^2+(3--5)^2}[/tex]

Step 2. Simplify the parentheses "( )"

Answer: [tex]d=\sqrt{(8^2)+(8^2)}[/tex]

Step 3. Simplify the exponents "[tex]?^2[/tex]"

Answer: [tex]d=\sqrt{64 +64}[/tex]

Step 4. Add 64 and 64

Answer: [tex]d=\sqrt{128}[/tex]

Step 5. Simplify the square root

Answer: [tex]d=11.31[/tex]

Therefore, the distance between points C and D is 11.31 units

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doomdabomb: all brainliest and thanks are appreciated and would mean a lot to me, thanks!

Answer:

B

Step-by-step explanation:

Values of y are decreasing where x is in the range (-4;02)

Answer: 5sqrt2, 10sqrt2/2

Step-by-step explanation:

The isosceles triangle, or 45-45-90 rule states that the hypotenuse is x × square root of 2.

Divide the hypotenuse, 10, by sqrt 2 to get 5sqrt2

However , if you're looking to keep it in fraction form, you will need to rationalize the denominator. Multiply the numerator and denominator to get the fraction, 10sqrt2/2

Answer:

1. 30:100 = 30/100=3/10

2. 2:8, 3:12

3. 60:12 = 5:1 or 5/1

Step-by-step explanation:

  B is correct

Step-by-step explanation:

Answer:

[tex](\frac{-3+\sqrt{15} }{4-\sqrt{15} })^{2} -4\\[/tex]

Step-by-step explanation:

[tex]a=4-\sqrt{15}[/tex]

[tex]a^{4} +\frac{1}{a^{4} }\\=a^{2^{2} } +\frac{1}{a^{2^{2} } }\\\\=(x^{2} +\frac{1}{a^{2} } )^{2} -2a^{2} \frac{1}{a^{2} } \\=(a +\frac{1}{a } )^{2} -2a \frac{1}{a}-2\\=(4-\sqrt{15} +\frac{1}{4-\sqrt{15} }) ^{2} -4\\\=(\frac{16-15-4+\sqrt{15} }{4-\sqrt{15} })^{2} -4\\=(\frac{-3+\sqrt{15} }{4-\sqrt{15} })^{2} -4\\[/tex]