Ben deposited $500 into a savings account at a local bank that earned 5% interest per
year. How much interest does he earn per year?

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Problem 1

I'm assuming your teacher means "list all the possible rational roots".

If so, then we use the rational root theorem. This is the idea where we'll divide the factors of the last term over the factors of the first coefficient.

If we divide said factors in the order mentioned, then we get this list of possible positive rational roots:

1/1, 1/3, 5/1, 5/3

That list simplifies to

1, 1/3, 5, 5/3

That takes care of the positive possible rational roots. We double the list to incorporate the negative possible rational roots as well

-1, -1/3, -5, -5/3

Note: We can rewrite that list in bold into [tex]\pm 1, \pm\frac{1}{3}, \pm 5, \pm \frac{5}{3}[/tex] to shorten it.

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Problem 2

We'll follow the same idea as the previous problem

Factors of 36:  1, 2, 3, 4, 6, 9, 12, 18, 36

Factors of 4:  1, 2, 4

To keep track of everything, I made a spreadsheet table. Refer to the diagram below. The factors of 36 are laid across the top while the factors of 4 are along the left side. Each inner cell represents dividing the headers.

For example, 36/4 = 9 is in the bottom right corner. The first table is before the fractions are reduced, and the second table after the fractions are reduced.

As the second table shows, we have a few repeats. The unique items here are:

1,2,3,4,6,9,12,18,36,1/2,3/2,9/2,1/4,3/4,9/4

We'll then mirror this set to include negative values as well to write the full list of all possible rational roots.

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Problem 3

Divide the factors of 15 over the factors of 5 to get

1/1, 1/5, 3/1, 3/5, 5/1, 5/5, 15/1, 15/5

That list reduces to

1, 1/5, 3, 3/5, 5, 1, 15, 3

we can then toss out the duplicates to get

1, 3, 5, 15, 1/5, 3/5

Don't forget to include the negative values as well

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Problem 4

The steps will be effectively the same as before. You can write out the factors like done in problem 3, or make a table like done in problem 2. I'll skip the steps shown here unless you need me to go over them.

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Problem 5

There's not really much new here, except for the fact that the first term has coefficient of 1. This is a special case where all we have to do is list the factors of the last term -40 to generate all the roots we need. This is because each time we're dividing over +1 or -1 which doesn't really change the overall result (except for the sign part).

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

Don't forget the negative values as well

Answer:

you may

2x+15+4x+21=90 simplified is 6x+36=90

m<a=33º

m<b=90º

m<c=57º

Step-by-step explanation:

6x+36=90

6x=54

x=9

2(9)+15=33

4(9)+21=57

Step-by-step explanation:

You need to find the total number of students the pie chart will represent:

17 + 35 + 38 = 90

So you know, 360° represents 90 people

You can then find out the angle for each person: 360 ÷ 90 = 4

Each person is 4°

a)

1. 17 people took French so you would do 4° × 17 = 68°

2. 35 people took German so you would do 4° × 35 = 140°

3. 38 people took Italian so you would do 4° × 38 = 152°

b)

17 out of 90 people chose french so the probability would be 17/90

Answer:

Minor Gridlines will separate units that are traced or delineated by major gridlines. They will also only appear for value axes.

I hope this helps

Answer:

the number is -2/7

Step-by-step explanation:

let the number be x

2x ×4= 7x-2/7

8x = 7x-2/7

collect like terms

8x-7x = -2/7

X= -2/7

Similar triangles may or may not be congruent.

The congruent criterion to use in her proof is (b) SAS theorem

From the question, we understand that she draws an angle bisector from [tex]\mathbf{\angle Q}[/tex] to side PR

This means that, either sides of angle Q are congruent. (this is represented by A i.e. angle)

When [tex]\mathbf{\angle Q}[/tex] is bisected, sides PB and RB become congruent

i.e. [tex]\mathbf{PB \cong RB}[/tex] ... (this is represented by S i.e. side)

Lastly, both triangles share a common side at QB .. (this is also represented by S i.e. side)

So, we have: SAS

Hence, the congruent criterion to use in her proof is (b) SAS theorem

Read more about similar and congruent triangles at:

https://brainly.com/question/19589236

1. Given

2. Given

3. Alternate Interior Angles

4. Reflexive Property

5. SAS

Hope this helps!! :)

Answer:

2.32142857143

Step-by-step explanation:

to the tenth- 2.3

to the hundreth- 2.32

Answer:

2.321 or 65 / 28

Step-by-step explanation:

you can either get the answer in decimal or lowest fractional form you can't get a whole number

Answer:

x = 7

Step-by-step explanation:

Rearrange the equation to make x the subject.

Original:

7x + 3 = 52

subtract 3 from both sides

7x = 52 -3

7x = 49

Divide both sides by 7

x = 49/7

x = 7

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Value of m is equal to :

[tex] \large \boxed{ \mathfrak{Explanation}}[/tex]

➢ 15 = 2m - 9

➢ 15 + 9 = 2m

➢ 2m = 24

➢ m = 24 ÷ 2

➢ m = 12

[tex] \mathfrak{hope \: \: it \: \: helps\;\; Rainbow ~ \: \: }[/tex]

Answer: you didn’t fully put the question

Step-by-step explanation:

Step-by-step explanation:

according to your question if we take away five from twelve the answer is 7

Answer:

Linear pair

Step-by-step explanation:

∠6 and ∠7 are linear pair angles.

Answer:

x = 10        m∠3 = 74

Step-by-step explanation:

(10x + 6) + (7x + 4) = 180 degrees

17x + 10 = 180

17x = 170

x = 10

check answer

(10(10) + 6) + (7(10) + 4) = 180

106 + 74 = 180

180 = 180

true!

angle 5 is vertical angles with 3, so they are congruent

use same equation as 5

7(10) + 4

70 + 4

74 :)

Answer:a I think although I’m really tired

Step-by-step explanation:

Answer:

[tex] \frac{x}{3} = \frac{7x}{12x - 15} \\ 12 {x}^{2} - 15x = 21x \\ 12 {x}^{2} -36x = 0 \\ 12x(x - 3) = 0 \\ \boxed{x = 0} \: or \: \boxed{x = 3} \\ \\ \frac{25 - 3x}{x + 5} = 1 \\ 25 - 3x = x + 5 \\ 3x + x = 25 - 5 \\ 4x = 20 \\ \boxed{ x = 5} \\ \\ \frac{3x - 2}{x} = - \frac{8}{x} \\ 3 {x}^{2} - 2x = - 8x \\ 3 {x}^{2} -6x = 0 \\ 3x(x - 2) = 0 \\ \boxed{x = 0} \: or \: \boxed{x = 2} \\ \\ \frac{3 - x}{x} = \frac{x + 1}{2x} \\ 6x - 2 {x}^{2} = {x}^{2} + x \\ 3 {x}^{2} - 5x = 0 \\ x(3x - 5) = 0 \\ \boxed{x = 0} \: or \: \boxed{x = \frac{5}{3} }[/tex]

Answer:

n^2+2n+1

Step-by-step explanation:

-2-8-18-32-50

difference=-6-10-14-18

common differences=-4-4-4-4-4

 -2-8-18-32-50

n^2=1,4,9,16,25

minus it

=-1,-4,-9,-16,-25

differences 2,5,7,9

common differences=2

2,4,6,8

so 2n+1

so the answer is n^2+2n+1

Answer:

2.5 x [tex]10^{15}[/tex] miles

Answer:

265.2 and 5970.8

Step-by-step explanation:

Answer:

b = 12

Step-by-step explanation:

hi! so this looks like a right triangle because it has a right angle which is 90 degrees! that means we can use the Pythagorean theorem to solve for the missing leg.

The Pythagorean theorem: [tex]a^{2} + b^{2} = c^{2}[/tex]

Let's solve for the missing leg now!

1) first, we need to plug in the missing numbers into the equation

[tex]5^{2} + b^{2} = 13^{2}[/tex]

2) next, let's simplify the problem

[tex]25 + b^{2} = 169[/tex]

3) now, let's isolate the variable, b

[tex]b^{2} = 144[/tex]

4) finally, we have to take the square root of b so it will be b not [tex]b^{2}[/tex]

b = 12

Let's plug in our answer to the equation to check if it is correct!

[tex]5^{2} + 12^{2} = 13^{2}[/tex]

25 + 144 = 169

169 = 169 hooray!

you do not have to do all of this work if you memorize the Pythagorean triples!

comment or message if you have any questions :)

Answer:

15%

Step-by-step explanation:

4590 = 5400 - D% × 5400

4590 = 5400 - D/100 * 5400

4590 = 5400 - 54D

54D = 5400 - 4590

D = 810 / 54

D = 15%

Dont forget to give me the brainliest.

Answer:

x^2-10x+25

Step-by-step explanation:

(a+b)^2=a^2+2ab+b^2 so a=x and b=-5 so the expression is x^2-10x+25

Answer:

x^2-10x+25

Step-by-step explanation:

Distribute

(x-5)(x-5)

x(x-5)-5(x-5)

Distribute again

x(x-5)-5(x-5)

x^2-5x-5(x-5)

Distribute one last time

x^2-5x-5(x-5)

x^2-5x-5x+25

combine like terms

x^2-5x-5x+25

x^2-10x+25

Answer:

The answer is D) 12

There are two trips, but the distances are the same.

Trip #1: uphill, at 9 mph

Trip #2: downhill at 18 mph

Total round trip is 30 minutes.

Since he's going half the speed uphill, Trip #1 takes twice as long as Trip #2.

So if the time for Trip #2 is x, then the time for Trip #1 is 2x.

     x + 2x = 30, so x=10

Trip #2 takes 10 minutes.

Trip #1 takes 20 minutes.

Trip #1: 20 minutes at 9 mph = 3 miles

Trip #2: 10 minutes at 18 mph = 3 miles

This means his school is 3 miles away.

If you want an equation to solve,

Let d = distance to school.  We use d = r·t formula to set up that t = d/r

let t1 = time going to school and t2 = times going home

t1 + t2 = 30 and t1 = d/9 and t2 = d/18.

    d/9 + d/18 = 0.5    (it's 0.5, because we need the time in hours)

      mutiply both sides b 18

    2d + d = 9

     3d = 9

       d = 3

I believe the answer is B 3/4

THIS IS NOT A SCAM LINK ITS REAL

https://brainly.in/question/27761729

Answer:

a) Δt = vf - vi ÷ a

b) (a × Δt) + vi = vf

Answer:

0.8

Step-by-step explanation:

just use guess and check. Divide each of the constants by the width of one point. When you  find a constant that matches, try that out with all the other widths, if it works with the other widths, then you found the right constant!