The product of 9 and Jose's savings is 108. Use the variable j to represent Jose's savings. How do I translate the sentence into an equation.

Answer:

common ratio is 2/5

First term is  125/2

The sum of the first n terms is: [tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]

The infinite sum is: [tex]S_\infty =\frac{625}{6}[/tex]

Step-by-step explanation:

The 4th term is 4, and the seventh term is 32/125 so we use the definition of nth term of a geometric sequence to create the following two equations:

[tex]a_4=a_1\,*\,r^{4-1} = a_1\,*\,r^3\\4=a_1\,*\,r^3\\and\\a_7=a_1\,*\,r^{7-1} = a_1\,*\,r^6\\\frac{32}{125} = a_1\,*\,r^6[/tex]

Now we divide a7 by a4 to get rid of a1 and work on determining the common ratio of the sequence:

[tex]\frac{a_7}{a_4} =\frac{8}{125} =\frac{a_1\,r^6}{a_1\,r^3} =r^3\\then\\r=\sqrt[3]{\frac{8}{125} } =\frac{2}{5}[/tex]

So, the common ratio is 2/5

we can now determine the first term:

[tex]a_4=4=a_1\,*\,(2/5)^3\\a_1=\frac{125*4}{8} =\frac{125}{2}[/tex]

The sum of the first n terms is given by the formula:

[tex]S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{1-(2/5)} \\S_n=\frac{125}{2} \, \frac{1-(2/5)^n}{3/5}[/tex]

and therefore, the infinite sum is:

[tex]S_\infty = a_1\,\frac{1}{1-r} = \frac{125}{2} \,\frac{5}{3} =\frac{625}{6}[/tex]

Answer:

Because the weather was generally better this year compared to last year, the attendance may have increased.

Step-by-step explanation:

took test

Answer:

C.) The explanatory variable is the type of coupon. The response variable is number of number of coupons redeemed.

Step-by-step explanation:

edge 2020

Answer:

7 (2x+7)

Step-by-step explanation:

︎ ︎ ︎ ︎ ︎ ︎ ︎

︎ ︎ ︎︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎

︎ ︎ ︎︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎ ︎

Answer:

The greatest common factor is 7.

Step-by-step explanation:

7 x 2 = 14

7 x 4 = 28

7 x 3 = 21

Answer:

Therefore we understand that exactly 71 people will have to attend breakfast in order to raise 2414 dollars.

Step-by-step explanation

We understand that we have to calculate the amount of people paying for breakfast so if 71 people each pay $34 we would get 2414

= 2414 ÷ 34 (This would give us 71 we get this straight away when we read the problem)

We can also fact check this by doing

= 34 x 71 (This gives us 2414)

Answer:

48

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

When dividing fractions flip and multiply.

So 12 would become 1/12

and 1/4 would become 4/1

Now multiply

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

So the answer is 1/3

When dividing fraction remember to flip then multiply much easier that way!

Hope this helps!!

Answer:

100/35 = 2

35 goes into 100 2 times

Step-by-step explanation:

Answer: f(x) = -3/2x -2

Step-by-step explanation:

Slope form of a line is y=mx+b, where b is the y-intercept and m is the slope. We find the y-intercept when we look at when x is 0 which would be -2. The slope is graphing to plots and determining if the slope is positive- going up- or negative- going down. The slope is going down and after using y2 - y1 / x2 - x1, I found the slope was -3/2.

Answer:

2(30-7x)

Step-by-step explanation:

=14+14x-65-9

=14+14x-79

=60+14x

=2(30-7x)

Answer:

im gonna go with yes

Step-by-step explanation:

Answer:

is what a perfect square?

Step-by-step explanation:

there is no pic attached

This should be what you're looking for.

Answer:

9/35

Step-by-step explanation:

Answer:

It"s the second answer, "An 8-foot ramp leans....".

Step-by-step explanation:

Answer:

Step-by-step explanation:

⊕ An 8-foot ramp leans against a building 5 feet away.  

cos x = [tex]\frac{5}{8}[/tex] ⇒ x ≈ 51.3178°

Answer:

Hence the width, length is 20 cm and height is 10 cm

Step-by-step explanation:

Since the box has a square base, let length = width = x. Also, let the height = y, therefore:

The volume of box = width * length * height

4000 = x * x * y

4000 = x²y

y=4000/x²

The surface area (SA) = area of the base + sum of the area of each side

SA = x² + xy + xy + xy + xy

SA = x² + 4xy

substitute y = 4000/x²

SA = x² + 4x(4000/x²)

SA = x² + 16000/x

Taking the derivative:

SA' = 2x - 16000/x²

making SA' = 0:

0 = 2x - 16000/x²

2x = 16000/x²

2x³ = 16000

x³ = 8000

x = 20 cm

y = 4000 / x² = 4000 / 20² = 10 cm

Hence the width, length is 20 cm and height is 10 cm

Answer:

A

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)\\=(x-2)-(x^2+3x-4)\\=x-2-x^2-3x+4\\=-x^2-4x+2\\[/tex]

Therefore, answer is A.

Answer:

Step-by-step explanation:

Algebra II: Part 2 James Madison

Your quiz has been submitted successfully. 100%

Question 1  5 / 5 points

Given that f(x) = x – 2 and g(x) = x2 + 3x – 4, find (f – g)(x).

A: (f – g)(x) = –x2 –2x + 2

Question 2  5 / 5 points

Given that f(x) = x + 4 and g(x) = x + 7, find (g – f)(x).

A: (g – f)(x) = 3

Question 3  5 / 5 points

Let f(x) = 4x – 1 and g(x) = 2x. Find (f ∘ g)(–5).

A:  (f ∘ g)( – 5) = –41

Question 4  5 / 5 points

Which of the following is the inverse relation of the set below?

A:  {(3,–2), (–4,7), (7,3), (4,8)}

Question 5  5 / 5 points

What is the inverse of f(x) = 2x2 –4?

A:  y = ±x+24−−−√

Question 6  5 / 5 points

Which of the following function pairs are inverses?

A: f(x) = 2x – 3 and g(x) =x+32

Question 7  5 / 5 points

Which of the following is true?

A:  The horizontal line test is used to determine if a function's inverse will be a function.

Question 8  5 / 5 points

Evaluate81−−√4

A: 3

Question 9  5 / 5 points

Evaluate 1251⁄3.

A: 5

Question 10  5 / 5 points

Use the properties of exponents to simplify the expression 2(x13)65⋅y23.

A: 2x25⋅y23

Question 11  5 / 5 points

A population culture begins with 15 strands of bacteria and then doubles every 4 hours. This can be modeled as 15(2)t4, where t is time in hours. How many strands of bacteria are present at 12 hours?

A: 120 strands of bacteria

Question 12  5 / 5 points

Simplify 36√3√.

A: 23–√

Question 13  5 / 5 points

Simplify 73–√+12−−√−75−−√.

A: 43–√

Question 14  5 / 5 points

Simplify 2–√×22–√.

A: 4

Question 15  5 / 5 points

Simplify 83−−√.

A: 26√3

Question 16  5 / 5 points

Select the equation of the function shown in the graph.

A: f(x)=2x−−√4−5

Question 17  5 / 5 points

Identify the graph of f(x)=x−2−−−−√3−3.

t would not allow me to add the graft. But it is the answer with the line that goes all the way across the graft starting at -10 thru -4.5 and up to 10. The line looks like an "S"

Question 18  5 / 5 points

Identify the graph of f(x)=6x−−√4−1.

It would not allow me to add the graft. But it is -1 up to the right to about 9.5. Document uploaded

Question 19  5 / 5 points

Select the equation of the function shown in the graph.

A: f(x)=x−1−−−−√5+5

Question 20  5 / 5 points

Solve the inequality x+2−−−−√4>2.

A: x>14

Question 21  5 / 5 points

Solve the inequality −2x−−−−√−1<3.

A: −8<x≤0

Question 22  5 / 5 points

Solve the equation 2x−1−−−−−√=5.

A: x = 13

Question 23  5 / 5 points

Solve the equation x+1−−−−√+5=3.

A: There is no solution.

Question 24  5 / 5 points

Given thatf(x)=4x3x+3−−−−−√ and g(x)=2x+1−−−−√, find (fg)(x).

A: 2x3–√

Answer:

Alex can buy "3" socks

Step-by-step explanation:

75- 25 =50

50- 29.99 = 20.01

20.01/ 6.26= 3.02

Since you can't get a portion of a sock you just take the first number (which is 3). Therefore, Alex can only buy three socks.  

Answer:

x=6.5

Step-by-step explanation:

Cross multiply

4x=26

Divide 26/4 ( 6.5 )

x=6.5

Answer:

Yes

Step-by-step explanation:

Using the triangle formula: a+b>c , b+c>a , and c+a>b, we can conclude that these values can form a triangle because 14+18>19 , 14+19>18 , and 18+19>14.

Answer:

To confirm if this can form it, we take the lower of the two numbers , square them, and equal it to the biggest number squared. (AKA The Pythagorean Theorem).

Step-by-step explanation:

[tex]14^{2} +18^{2} = 19^{2}[/tex]

Now solve to see if it equates to be true.

196 + 324 = 361

520 [tex]\neq[/tex] 361

That means 14, 18, and 19 can't form a triangle.

Answer:

1) dividend

2) divisor

3) quotient

Answer:

Since the slope of KM and ST are different, they are not parallel

Step-by-step explanation:

Slope of line KM = [tex]\frac{5}{8}[/tex]

 Slope of ST = [tex]-\frac{8}{5}[/tex]

Determine whether the lines are perpendicular;

Solution:

We can use the slope of a line to determine whether they are perpendicular or parallel to one another.

Parallel lines do not meet one another

Perpendicular lines cross one another at an angle of 90°

Two lines are parallel if their slopes are the same;

  Since the slope of KM and ST are different, they are not parallel

Answer:

I think its 15600..

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

it's CASSANDRA business so she solve it herself

im not sure this one is confusing

Answer:

Step-by-step explanation:

Step 1             f(x) = [tex]\frac{3x+4}{8}[/tex]                 Given

Step 2            y = [tex]\frac{3x+4}{8}[/tex]                    Change f(x) to y

Step 3            x = [tex]\frac{3y+4}{8}[/tex]                    Switch x and y

Step 4            8x = 3y + 4              multiply each side by 8

Step 5            8x - 4 = 3y               Subtract 4 from each side

Step 6            [tex]\frac{8x-4}{3}=y[/tex]                   Divide by 3 on each side

Step 7            [tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]           Replace y by [tex]f^{-1}(x)[/tex]

Therefore, inverse of the function will be,

[tex]\frac{8x-4}{3}=f^{-1}(x)[/tex]

Sofia made a mistake in step 6. She should have divided both the sides by 3 instead of multiplying each side by 3.

Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.

The given function is [tex]f(x)=\dfrac{3x+4}{8}[/tex].

It is required to calculate the inverse of the function.

So, the steps involved in finding the inverse of the function will be,

Step 1:

Write the given function as,

[tex]f(x)=\dfrac{3x+4}{8}[/tex]

Step 2:

Change the function f(x) to y as,

[tex]y=\dfrac{3x+4}{8}[/tex]

Step 3:

Switch x and y as,

[tex]x=\dfrac{3y+4}{8}[/tex]

Step 4:

Multiply each side of the equation by 8 as,

[tex]8x=8\dfrac{3y+4}{8}\\8x=3y+4[/tex]

Step 5:

Now, subtract 4 from each side of the equation as,

[tex]8x-4=3y+4-4\\8x-4=3y[/tex]

Step 6:

Now, it is required to divide each side by 3.

[tex]\dfrac{8x-4}{3}=\dfrac{3y}{3}\\\dfrac{8x-4}{3}=y[/tex]

Step 7:

Now, replace y with [tex]f^{-1}(x)[/tex] as,

[tex]\dfrac{8x-4}{3}=f^{-1}(x)[/tex]

So, the required inverse function should be [tex]f^{-1}(x)=\dfrac{8x-4}{3}[/tex].

Therefore, Sophia has made mistake in step 6. She should have divided each side by 3 instead of multiplying.

For more details, refer to the link:

https://brainly.com/question/19606498

Answer:

It is 4,288,000.

Step-by-step explanation:

To round to the nearest thousand, you need to find the thousands place. In the thousands place there is a "7". Okay, we've found it, so the next step is rounding.

To round, there is a handing phrase that we can use to know whether we should round the place up or down. It is "4 or less, let it rest. 5 or more, add 1 more." We need to apply this phrase to the number behind the place we need to round (so apply it to the place behind the thousands place).

When we look behind the thousands place, we see there is a 9. Apply the rule to that. Since 9 is above 5 and not less than 4, we need to add one more to the thousands place.

That means after we round, the 7 turns into a 8. That's how you get 4,288,000.

Hope this makes sense <3

Answer:

If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar. The corresponding sides of similar triangles are in proportion.

I hope this might help you

Mark it as brainliest answer and follow me

Answer:

The relationship between the base angles does not change. The measures of the base angles of the isosceles triangle remain equal even if the vertices of the isosceles triangle change.

Step-by-step explanation:

Here is the answer from Plato. Hope this helps :)

Answer:

The relationship between the base angles does not change. The measures of the base angles of the isosceles triangle remain equal even if the vertices of the isosceles triangle change.

Step-by-step explanation:

Exact Edmentum sample answer

Answer:

250 centimeters

Step-by-step explanation:

2 meters into centimeters is 200 so 200+50=250

Answer:

100cm

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

you have 12 of something and Are adding 12 to it.