If you are given the graph of h(x)=log(6)x, how could you graph m(x)=log(6)(x+3)? Translate each point of the graph of h(x) 3 units up. Translate each point of the graph of h(x) 3 units down. Translate each point of the graph of h(x) 3 units right. Translate each point of the graph of h(x) 3 units left.

Answers

Answer 1

Answer:

Last option: Translate each point of the graph of h(x) 3 units left.

Step-by-step explanation:

There are some transformations for a function f(x). The following is one of these transformations:

If [tex]f(x+k)[/tex], then the function is shifted "k" units to the left.

Given the function  [tex]h(x)=log_6(x)[/tex] and the function  [tex]m(x)=log_6(x+3)[/tex], you can notice that the function m(x) is the function h(x) but shifted left 3 units.

Therefore, you could graph the function m(x) by translating each point of the graph of the function h(x) 3 units left.

This matches with the last option.

Answer 2

Answer:

Last option (D) Translate each point of the graph of h(x) 3 units left.


Related Questions

The lines shown below are perpendicular.if the green line has a slope of 3/4 what is the slope of the red line?

Answers

Answer:

-4/3

Step-by-step explanation:

because the line are perpendicular, so the slope of re line is -1/(3/4)=-4/3

Match each variable with what it represents in a sequence formula. 1. r the value of the first term 2. d the value of the nth term 3. n common ratio 4. an common difference 5. a1 term number

Answers

Answer:

r is the common ratio (in geometric sequence)

d is the common difference (in arithmetic sequence)

n is the term number

a1 is the value of the first term

an is the value of the nth term

Step-by-step explanation:

For the sequence formula, each term represent as follows,

[tex]r[/tex]: common ratio

[tex]d[/tex]: common difference

[tex]n[/tex]: term number

[tex]a_{n}[/tex]: the value of the [tex]nth[/tex] term

[tex]a_{1}[/tex]: the value of the first term

What is the sequence?

"Sequence is defined representation of a number in a particular order using some formula."

According to the question,

For the sequence formula,

Each variable is matched with the following term,

[tex]r[/tex]: common ratio

[tex]d[/tex]: common difference

[tex]n[/tex]: term number

[tex]a_{n}[/tex]: the value of the [tex]nth[/tex] term

[tex]a_{1}[/tex]: the value of the first term

Hence, for the sequence formula, each term represent as follows,

[tex]r[/tex]: common ratio

[tex]d[/tex]: common difference

[tex]n[/tex]: term number

[tex]a_{n}[/tex]: the value of the [tex]nth[/tex] term

[tex]a_{1}[/tex]: the value of the first term

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If f(x)=4x-12 what is f(2)

Answers

Answer:

-4

Step-by-step explanation:

plug 2 into the equation.

f(2)=4(2)-12

    = 8-12

    = -4

I hope this helped!

Answer:

f(2) =-4

Step-by-step explanation:

f(x)=4x-12

Let x=2

f(2) = 4(2) -12

      =8-12

       =-4

What should be added to the difference of 1 and 1/2 and 2/6 to get 1 and 2/3?​

Answers

Rewrite 1/2 to have a common denominator with 2/6

1/2 x 3 = 3/6

Now you have 1 and 3/6 - 2/6  = 1 and 1/6

Now rewrite 2/3 to have a common denominator with 1/6: 2/3 x 2 = 4/6

Subtract 1/6 from 4/6:

4/6 - 1/6 = 3/6 = 1/2

You will need to add 1/2

To get from the difference between 1 and 1/2 and 2/6 to 1 and 2/3, one must add 1/2 after ensuring both differences have a common denominator.

To find out what should be added to the difference between 1 and 1/2 and 2/6 to get 1 and 2/3, we need to perform a few steps involving fractions. First, let's convert 1 and 1/2 into an improper fraction by multiplying 1 (the whole number) by 2 (the denominator of the fractional part) and adding 1 (the numerator of the fractional part), which gives us 3/2. Now, to find the difference between 3/2 and 2/6, we must have a common denominator, which is 6 in this case. Multiplying the numerator and denominator of 3/2 by 3 gives us 9/6.

Now we subtract 2/6 from 9/6 to get the difference, which is 7/6 or 1 and 1/6. To find what needs to be added to this difference to get 1 and 2/3, we must also express 1 and 2/3 as an improper fraction. Multiplying 1 (the whole number) by 3 (the denominator) and adding 2 (the numerator) gives us 5/3.

To compare 7/6 with 5/3, we need the same denominator, which is 6. So we multiply the numerator and denominator of 5/3 by 2 to get 10/6. Subtracting 7/6 from 10/6, we find the missing number to be 3/6, which simplifies to 1/2.

Ben and Arnoldo are sharing snacks. They have peanut treats and coconut treats. Ben ate 2 of the peanut treats and 4 of the coconut treats for a total of 160 calories. Arnoldo ate 3 of the peanut treats and 2 of the coconut treats for a total of 140 calories. They wrote the system below to represent the number of calories there are in the two types of treats.

Answers

Answer:

The number of calories in a peanut treat is 30.

The number of calories in a coconut treat is 25.

Step-by-step explanation:

So we have Ben ate 2 peanut treats (let p represent the calories in each peanut treat) and 4 coconut treats (let c represent the calories in each coconut treat).  The sum of those calories is 160.

This is the equation for Ben:

2p+4c=160

I'm going to use the same representation here.  p for the number of calories in each peanut treat and c for the number of calories in each coconut treat.

Arnold ate 3 p's and 2 c's for a sum of 140 calories:

Alrnoldo's equation is:

3p+2c=140

So we have the system:

2p+4c=160

3p+2c=140

I'm going to divide the first equation by 2 because each term is divisible by 2:

p+2c=80

3p+2c=140

This system is setup for elimination because the equations are in the same form and the second column have the same variable expression, 2c.  So we are going to subtract to eliminate the variable c, that is 2c-2c=0.

p+2c=80

3p+2c=140

---------------------Subtract!

-2p+0=-60

-2p    =-60

Divide both sides by -2:

  p      =30

So if p=30 and p+2c=80 , then 30+2c=80.

So let's solve:

30+2c=80 for c

Subtract 30 on both sides:

     2c=50

Divide both sides by 2:

     c=25

The number of calories in a peanut treat is 30.

The number of calories in a coconut treat is 25.

Find X. Round to the nearest tenth if necessary.

Answers

Answer:

x = 9

Step-by-step explanation:

When 2 chords intersect inside a circle then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord, that is

2 × x = 3 × 6, that is

2x = 18 ( divide both sides by 2 )

x = 9

If rs 500 amounts to Rs 725 at 9% simple interest in sometime ,what will Rs 600amount to at 11% in same time?

Answers

Final answer:

To solve the student's question, we calculated the time period from the initial amount and interest rate, then used that to determine the amount that Rs 600 would become at an 11% interest rate over the same period, which is Rs 930.

Explanation:

The essence of the question revolves around the concept of calculating the future amount of money based on the principal, the rate of interest, and the time for which the money is lent or invested. In the given scenario, we have a principal of Rs 500 which, at a 9% simple interest rate, amounts to Rs 725 over a certain period.

To find the equivalent amount for Rs 600 at an 11% interest rate over the same period, we need to first understand the amount of interest accrued in the first situation and use its proportion to calculate the second.

The formula for simple interest is Interest = Principal × rate × time.

First, let's calculate the interest earned on the initial Rs 500:

Amount = Principal + InterestRs 725 = Rs 500 + InterestInterest = Rs 725 - Rs 500Interest = Rs 225

Now, we can calculate the time period using the simple interest formula:

Interest = Principal × rate × timeRs 225 = Rs 500 × 0.09 × timeTime = Rs 225 / (Rs 500 × 0.09)Time = 5 years

Knowing the time period, we can find the amount that Rs 600 would amount to at an 11% interest rate over the same period:

Interest = Rs 600 × 0.11 × 5 yearsInterest = Rs 330Amount = Principal + InterestAmount = Rs 600 + Rs 330Amount = Rs 930

So, Rs 600 will amount to Rs 930 at an 11% simple interest rate over the same time period of 5 years.

NEED HELP PLEASE ASAP Given: AEDFG AABF
Name the postulate or theorem you can use to prove AADE & AEBA
е СРСтс
AAS Theorem
HL Theorem
ASA Postulate

Answers

Answer:

H-L Theorem

Step-by-step explanation:

They tell you that they are right triangles, and you have your congruency marks. If they never had right angle indicators, this theorem would never work.

I hope this helps you out, and as always, I am joyous to assist anyone at any time.

Which of the following is the radical expression of a to the four ninths power?

4a9
9a4
fourth root of a to the ninth power
ninth root of a to the fourth power

Answers

Step-by-step explanation:

[tex]\sqrt[n]{a^m}=a^\frac{m}{n}\\\\\large\huge\boxed{a^\frac{4}{9}=\sqrt[9]{a^4}}[/tex]

Answer:

The radical expression which represents a to the four ninths power is:

         Ninth root of a to the fourth power.

Step-by-step explanation:

We are asked to find the radical expression for the word phrase:

             a to the four ninths power.

i.e. mathematically it could be written as:

[tex]a^{\dfrac{4}{9}}[/tex]

Now, we know that:

[tex]a^{\dfrac{m}{n}}=(a^m)^{\dfrac{1}{n}}=\sqrt[n]{a^m}[/tex]

Here we have:

[tex]m=4\ \text{and}\ n=9[/tex]

Hence, the expression cold be written as:

[tex]a^{\dfrac{4}{9}}=\sqrt[9]{a^4}[/tex]

Find the first three terms of the arithmetic series described.

a_1=1,a_n=19,S_n=100

Answers

Answer:

1, 3, 5

Step-by-step explanation:

The sum of an arithmetic series is:

S_n = n (a_1 + a_n) / 2

100 = n (1 + 19) / 2

n = 10

The nth term of an arithmetic sequence is:

a_n = a_1 + d (n − 1)

19 = 1 + d (10 − 1)

d = 2

The common difference is 2.  So the first three terms are 1, 3, and 5.

What is the volume of the prism below 4 height length 18 9width

Answers

The volume of the prism is [tex]\(V = 648 \, \text{cubic units}\).[/tex]

The formula for the volume (V) of a rectangular prism is given by [tex]\(V = lwh\),[/tex] where (l) is the length, (w) is the width, and (h) is the height. In this case, the provided dimensions are length (l = 18), width (w = 9), and height (h = 4). Substituting these values into the formula: [tex]\[ V = 18 \times 9 \times 4 = 648 \, \text{cubic units}. \][/tex] Therefore, the volume of the prism is [tex]\(648 \, \text{cubic units}\).[/tex]

Understanding the concept of volume in three-dimensional geometry is vital. The formula [tex]\(V = lwh\)[/tex] reflects the relationship between the length, width, and height of a rectangular prism. Multiplying these dimensions provides the total space enclosed by the prism in cubic units. In this instance, with a length of 18 units, a width of 9 units, and a height of 4 units, the volume calculation yields [tex]\(648 \, \text{cubic units}\),[/tex] representing the spatial capacity of the given prism.

Calculating the volume of prisms is a fundamental skill in geometry and has practical applications in various fields, including architecture and engineering. This calculation allows us to quantify the amount of space a three-dimensional object occupies, providing essential information for design and analysis. In this case, the resulting volume, [tex]\(648 \, \text{cubic units}\),[/tex] represents the capacity of the rectangular prism specified by the given dimensions.

How do you Divide 7÷135

Answers

By doing long division. Answer is 7/135

emily bought a new car for $22000. She paid 93% of the list price. What was the list price?​

Answers

To answer your question the list price for Emily's vehicle would have a $23,655.91 list price

Hope this helped

Aaron

Answer:  The list price of the car was $ 23655.91.

Step-by-step explanation:  Given that Emily bought a new car for $22000 and she paid 93% of the list price.

We are to find the list price of the car.

Let $ x denote the list price of the car.

Then, according to the given information, we have

[tex]93\%\times x=22000\\\\\\\Rightarrow \dfrac{93}{100}\times x=22000\\\\\Rightarrow 93x=22000\times100\\\\\Rightarrow 93x=2200000\\\\\Rightarrow x=\dfrac{2200000}{93}\\\\\Rightarrow x=23655.91.[/tex]

Thus, the list price of the car was $ 23655.91.

How would you get the answer of how much change he received

Answers

35 x $1.75= $61.25
$100- $61.25= $38.75

He would receive $38.75 in change.

Answer:

Step-by-step explanation:

Givens

I foot of sill = 1.75

35 feet of sill = x

Paid with 100 dollars.

Solution

First part

Solve the proportion

1/35 = 1.75/ x                 Cross multiply

1*x = 35 * 1.75

x = 61.25

=========

Second part

Get the change.

Change = 100 - 61.25

Change  = 38.75

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

The change =

3 tens                30.00

1 five                   5.00

3 ones                3.00

3 quarters           .75

Total                 38.75

A circle has a radius of 25 centimeters and a central angle EOG that measures 100°. What is the area of sector EOG?

Answers

Answer:

≈ 545.42 cm²

Step-by-step explanation:

The area (A) of sector EOG is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{100}{360}[/tex]

   = π × 25² × [tex]\frac{10}{36}[/tex]

   = 625π × [tex]\frac{10}{36}[/tex]

   = [tex]\frac{625(10)\pi }{36}[/tex] ≈ 545.42 ( to 2 dec. places )

Is the following relation a function? {(3, 2), (3, −2), (1, −4), (−1, 2)}

Answers

Step-by-step explanation:

no it is not because if 3 maps on 2, then it cannot map on -2 at the same time

Final answer:

A relation is considered a function if each input has only one output. The given set contains the input '3' with two different outputs '2' and '-2', therefore, it is not a function.

Explanation:

In mathematics, a relationship is considered a function if for every input there is only one output. In other words, no two pairs should have the same first element yet different second elements.

If we look at the set of ordered pairs provided, we have {(3, 2), (3, -2), (1, -4), (-1, 2)}. We can see that the input '3' corresponds to both '2' and '-2'. Since there are two outputs for the same input, we can determine that this relation is not a function.

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What is the slope-intercept form of the equation of the line graphed in the figure?

A. y = 5⁄3x + 1
B. y = –5⁄3x – 1
C. y = –3⁄5x + 1
D. y = 3⁄5x + 1

Answers

Answer:

D

Step-by-step explanation:

It crosses the y-axis at y=1 so the y-intercept is b=1.

The slope is count straight up from (-5,-2) to you are on the same horizontal level as (5,4).  The rise is 6

Once you get the same horizontal level as (5,4), you will count straight over to you get to (5,4). The run is 10.

Slope=rise/run=6/10=3/5.

Or you could find slope by using the slope formula.  I like to line up two pairs of points and subtract then put 2nd difference over first difference. Like so,

  (5,4)

-(-5,-2)

----------

 10   6

So the slope is 6/10 or 3/5 after reducing.

Slope-intercept form of a line is y=mx+b

Plug in m=3/5 and b=1

y=3/5 x +1

So the answer is D.

(3k/k-2)+(6/2-k)
3
-3
3k+6/k-2
3k+6/k+2

Answers

Answer:

Therefore, the answer is 3

Step-by-step explanation:

The given expression is:

[tex]\frac{3k}{k-2} + \frac{6}{2-k} \\\\Taking\ LCM\\= \frac{3k(2-k)+6(k-2)}{(k-2)(2-k)} \\=\frac{6k-3k^2+6k-12}{(k-2)(2-k)}\\= \frac{-3k^2+12k-12}{(k-2)(2-k)}\\\\Applying\ formula\\=\frac{-3(k^2-4k+4)}{(k-2)(2-k)}\\=\frac{-3((k)^2-2*2*k+(2)^2)}{(k-2)(2-k)}\\=\frac{-3(k-2)^2}{(k-2)(2-k)}\\=\frac{-3(k-2)}{(2-k)}\\=\frac{3(2-k)}{2-k}\\=3[/tex]

Answer: 2k

Step-by-step explanation:

-k + 3k = (-1 + 3)k = 2k

Find the surface area of the triangular prism

Answers

The answer is c 5112
The formula for the area of a triangle is 1/2bh. So you multiply 36 by 38 and 1/2 to get 684
You then have to fine the area of the rectangles and since they’re three of them you multiply 3 by 36 and 41 to her 4428.
When you add 4428 and 684 you get 5112 square inches

How do you find the focus and directrix of y=-2x^2 +8x-15?​

Answers

Answer: [tex]\bold{focus: \bigg(2, -7 \dfrac{1}{8}\bigg), \quad directrix: y = -6 \dfrac{7}{8}}[/tex]

Step-by-step explanation:

First, rearrange the equation into vertex form: y = a(x - h)² + k   where

(h, k) is the vertex[tex]a = \dfrac{1}{4p}[/tex]

NOTE: p is the distance from the vertex to the focus

      y = -2x² + 8x - 15

y + 15 = -2x² + 8x            → added 15 to both sides

y + 15 = -2(x² - 4x)           → factored out -2 from the right side

y + 15 + (-2)(4) = -2(x² - 4x + 4)    → completed the square

y + 7 = -2(x - 2)²                → simplified

     y = -2(x - 2)² - 7           → subtracted 7 from both sides

Now it is in vertex form where:

(h, k) = (2, -7)a = -2              ⇒    [tex]-2=\dfrac{1}{4p}[/tex]     ⇒    [tex]p=-\dfrac{1}{8}[/tex]

Focus = (2, -7 + p)  →  Focus = (2, -7 + (-1/8))   →  [tex]Focus = \bigg(2, -7 \dfrac{1}{8}\bigg)[/tex]

Directrix: y = -7 - p   →  Directrix: y = -7 - (-1/8)   →  [tex]Directrix: y = -6 \dfrac{7}{8}[/tex]

Find the range of the function f(x) = 4x - 1 for the domain (-1,0, 1, 2, 3}.

Answers

For this case we have a fucnion of the form [tex]y = f (x)[/tex]

Where:

[tex]f (x) = 4x-1[/tex]

By definition, the rank of a function is given by:

The set of the real values that the variable y or f (x) takes.

So:

[tex]f (-1) = 4 (-1) -1 = -4-1 = -5\\f (0) = 4 (0) -1 = 0-1 = -1\\f (1) = 4 (1) -1 = 4-1 = 3\\f (2) = 4 (2) -1 = 8-1 = 7\\f (3) = 4 (3) -1 = 12-1 = 11[/tex]

ANswer:

The range is: -5, -1,3,7,11

Answer:

{-5,-1,3,7,11}

Step-by-step explanation:

The range is the output of the function

We have the inputs

f(x) = 4x - 1

f(-1) = 4(-1)-1 = -4-1 = -5

f(0) = 4(0)-1 = 0-1 = -1

f(1) = 4(1)-1 = 4-1 = 3

f(2) = 4(2)-1 = 8-1 = 7

f(3) = 4(3)-1 = 12-1 = 11

The outputs for the given inputs are

{-5,-1,3,7,11}

What is the answer? Please help

Answers

Answer:

A

Step-by-step explanation:

One and three hundred and four thousand

1+                             3/100+          4/1000

The answer to this question is A!

Which equations and/or functions represent the graphed line? Select three options.

f(x)=1/5x-4
f(x)=1/2x+2
f(x)=1/2x+1
y-3=1/2(x-2)
y-1=1/2(x+2)

Answers

Answer:

f(x) = 1/2x + 2

y - 3 = 1/2(x - 2)

y - 1 = 0.5(x + 2)

Step-by-step explanation:

Final answer:

The equations that represent the graphed line are f(x) = 1/2x + 2, f(x) = 1/2x + 1, and y - 1 = 1/2(x + 2).

Explanation:

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept. In the given options, the equations that represent the graphed line are:

f(x) = 1/2x + 2f(x) = 1/2x + 1y - 1 = 1/2(x + 2)

These equations have the same slope and y-intercept as the graphed line.

derivative of f(x)=5.2x+2.3​

Answers

Answer:

5.2

Step-by-step explanation:

Since you have a linear function, asking for derivative is equivalent to asking for the slope.

The slope of y=5.2x+2.3 is 5.2 so the derivative is 5.2 .

However, if you really want to use the definition of derivative, you may.

That is, [tex]\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}[/tex].

We know [tex]f(x)=5.2x+2.3[/tex] so [tex]f(x+h)=5.2(x+h)+2.3[/tex].  All I did was replace any x in the 5.2x+2.3 with (x+h) to obtain f(x+h).

Let's plug it into our definition:

[tex]\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}[/tex]

[tex]\lim_{h \rightarrow 0} \frac{[5.2(x+h)+2.3]-[5.2x+2.3]}{h}[/tex]

Now we need to do some distributing.  I see I need this distributive property both for the 5.2(x+h) and the -[5.2x+2.3].

[tex]\lim_{h \rightarrow 0} \frac{5.2x+5.2h+2.3-5.2x-2.3}{h}[/tex]

There are some like terms to combine in the numerator.  The cool thing is they are opposites and when you add opposites you get 0.

[tex]\lim_{h \rightarrow 0} \frac{5.2h}{h}[/tex]

There is a common factor in the numerator and denominator. h/h=1.

[tex]\lim_{h \rightarrow 0}5.2[/tex]

5.2

[tex]f(x)=5.2x+2.3\\f'(x)=5.2[/tex]

u want to leave a 15% tip on a $33 meal. What is the total cost for the night?

Answers

Answer: The total cost would be 37.95

Step-by-step explanation:

Final answer:

The total cost for the night, including a 15% tip on a $33 meal, is $37.95.

Explanation:

To calculate the total cost for the night, we need to add the meal cost and the tip. For a $33 meal, a 15% tip would be calculated using the formula tip = meal cost x tip percentage/ 100. In this case, tip = $33 x 15/100= $4.95. Therefore, the total cost for the night (meal cost + tip) would be $33 + $4.95 = $37.95.

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What is the quotient ?

Answers

Answer

The answer after you divide one number by another

dividend ÷ divisor = quotient

Example: in 12 ÷ 3 = 4, 4 is the quotient

Write an equation for a circle with a diameter that has endpoints at (-10, 1) and (-8, 5). Round to the nearest tenth if necessary.

Answers

Answer:

The equation is (x+9)^2 + (y-3)^2 = 5

Step-by-step explanation:

The standard form for the equation of a circle is:

(x−h)^2+(y−k)^2=r2

The center of the circle is the midpoint of the diameter.

So the midpoint of the diameter at  (-10, 1) and (-8, 5) can be determined as:

(-10 +(-8))/2 , (1+5)/2

= -10-8/2, 1+5/2

= -18/2 , 6/2

= -9 , 3

Thus(-9,3) is the center of the circle.

Now we will use the distance formula to find the radius of the circle.

r^2=(-10-(-9))^2 + (1-3)^2

r^2=(-10+9)^2 +(-2)^2

r^2=(-1)^2 + (-2)^2

r^2=1 + 4

r^2= 5

Take square root at both sides.

√r^2= √5

r=√5

Now put the values in the 1st equation.

(x−h)^2+(y−k)^2=r2

where h = -9, k =3 and r = √5

(x-(-9))^2 + (y-3)^2= (√5)^2

(x+9)^2 + (y-3)^2 = 5

Thus the equation is (x+9)^2 + (y-3)^2 = 5 ....

The area of the trapezoid is 40 square units.


What is the height of the trapezoid?

3 units

5 units

10 units

12 units

Answers

Hey there!

The area of a trapezoid is h(a+b/2), where h is the height and a and b are the two bases. We already have our area, so let's solve for our height in the equation.

40= x(16/2)

40=8x

x=5

Therefore, the height is B) five units.

I hope this helps!

Answer:

answer is 5

Step-by-step explanation:

What's the answer of..
[tex] \frac{4a {}^{2} }{16a {}^{5} \: b {}^{2} } b {}^{5} [/tex]

Answers

Answer:

[tex]\large\boxed{\dfrac{1}{4}a^{-3}b^3=\dfrac{b^3}{4a^3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{4a^2b^5}{16a^5b^2}\qquad\text{use}\ \dfrac{x^n}{x^m}=x^{n-m}\\\\=\dfrac{4}{16}a^{2-5}b^{5-2}=\dfrac{1}{4}a^{-3}b^3\qquad\text{use}\ x^{-n}=\dfrac{1}{x^n}\\\\=\dfrac{b^3}{4a^3}[/tex]

A brand new motorcycle gets 70 miles per gallon of gas. If the motorcycle drives 520 miles before running out of gas, how much gas started in the tank? Write you answer as a mixed number.

Answers

Answer:

[tex]x=7 \frac{3}{7}[/tex] gallons

Step-by-step explanation:

So we are given:

70 miles   ->  1 gallon is used.

520 miles ->  x gallons is used.

Set up a proportional to solve.

I lined up everything already above:

[tex]\frac{70}{520}=\frac{1}{x}[/tex]

Cross multiply:

[tex]70(x)=520(1)[/tex]

[tex]70x=520[/tex]

Divide both sides by 70:

[tex]x=\frac{520}{70}[/tex]

Reduce the fraction (divide top and bottom by 10):

[tex]x=\frac{52}{7}[/tex]

How many 7's are in 52?  7 because 7(7)=49

How much is left over after seven 7's go into 52? 52-49=3

So the answer as a mixed fraction is:

[tex]x=7 \frac{3}{7}[/tex]

To find out how much gas was in the motorcycle's tank, divide the total distance driven by the fuel efficiency. In this case, 520 miles / 70 miles per gallon equals 7 2/5 gallons of gas.

To determine how much gas started in the tank of the motorcycle that gets 70 miles per gallon and drove 520 miles before running out of gas, we use the formula:

Calculate the number of gallons used by dividing the total distance driven by the mileage per gallon. This gives us the formula: Gallons Used = Total Miles Driven / Mileage (Miles per Gallon).Divide the total miles driven, which is 520 miles, by the mileage per gallon, which is 70 miles per gallon.The result is 520 miles / 70 miles per gallon = 7.4285714286 gallons.To express this as a mixed number, we take the integer part, which is 7 gallons, and then write the decimal part as a fraction. The decimal part is approximately 0.4286, which can be rounded to 4\/10 or simplified to 2/5. So the mixed number is 7 2/5 gallons.

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