catmg

Hi Guest!

Background

If you need help with converting these to fractions, check out this video: 

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-repeating-decimals/v/coverting-repeating-decimals-to-fractions-1 

0.1(with line)

We start by simplifying this number, which is 1/9. 

.01(with line)

This number simplified is 1/99

Addition

1/9 + 1/99 

11/99 + 1/99

12/99

Answer

Our final answer is 12/99

I hope this helped. :))))

=^._.^=

Hi Guest!

Is there perhaps a bit more context to the question?

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Hi mzhu23!

Chart

Let's make a chart where r is the number Rob has, s is the number of glue sticks Sydney has, and k is the number of glue sticks Koreb has at the beginning. 

Rob    Sydney    Koreb

r         s               k                 # Sydney gives Rob and Koreb as many glue sticks as each of them then has

2r       s - r - k      2k               # Koreb gives Sydney and Rob as many glue sticks as each has

4r       2(r - s - k)  3k - s - 2r

What do we know?

So from the graph what do we know. 

We know that: 

r + s + k = 48

4r = 16

2(s - r - k) = 16

3k - s - 2r = 16

Solving r

4r = 16

r = 4

Plugging r in past equations

4 + s + k = 48

s + k = 44 # New equation

2(s - r - k) = 16

s - r - k = 8

s - 4 - k = 8

s - k = 12 # New equation

3k - s - 2(4) = 16

3k - s = 24

Finding s and k

Two important equations from above are... s + k = 44 and s - k = 12. 

So, if we add them together, 2s = 56. 

s = 27. 

That would make k 15 (27 - 15 = 12)

Answer

Rob had 4 gluesticks. 

Sydney had 27 gluesticks. 

Koreb had 15 gluesticks. 

I hope this helped. :))))

=^._.^=

Hi Guest!

Background

--x = + x

-+x = -x

+-x = -x

++x = x

Following these rules, let's simplify the answer options. 

Simplifying

A. 35 + 7 - 5

B. 35 - 7 + 5

C. 35 - 7 - 5

D. 35 + 7 + 5

What is the question asking for?

The question is asking for how much she has left. 

Spending means she's subtracting from the total. 

Thus, our equation should be 35 - 7 - 5. 

Answer

Looking at our answer choices, it's clear that C is the same as 35 - 7 - 5, meaning our final answer is C. 

I hope this helped. :)))))

=^._.^=

Hi Guest!

Formula

First, we need to know the formula. 

|found - exact| / exact * 100

Variables

Found = 495

Exact = 500

Solving

|495 - 500| / 500 * 100

5/500*100

1

Answer

So, ther percent error was 1%

I hope this helped. :))))))))

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You're welcome. :DDDDDD

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Hi Guest!

Background

To solve this question, we should use the quadartic equation. 

If you don't know what that is, here's a wiki page: https://en.wikipedia.org/wiki/Quadratic_equation

Whether or not a quadratic has a real answer is based on it's discriminant, b^2 - 4ac. 

If the discriminant is negative, then the solutions won't work since you can't square root a negative number. 

Equation

5x^2 - kx + 88 = 0

Discriminant

b^2 - 4ac

(-k)^2 - 4(5)(88)

Solving

So, we're looking for the greatest k value where (-k)^2 - 4(5)(88) is negative and an integer. 

(-k)^2 - 4(5)(88)

k^2 - 1760 < 0 

k^2 < 1760

k < sqrt(1760)

The largest integer that fufils this is 41. 

Answer

Thus, our answer is 41. 

I hope this helped. :))))

=^._.^=

Hi Guest!

Question 1 - Part A

First, let's start by expanding the (x + a)^2 part of the question. 

(x + a)^2 = x^2 + 2ax + a^2

We can then replace it. 

x^2 - 7x + c = x^2 + 2ax + a^2

We can quickly see that a = -3.5 since 2a = 7. 

Question 1 - Part B

We can also see that c = a^2. 

c = (-3.5)^2

c = 12.25

I hope this helped. :)))))

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Hi Guest!

1 hour and 25 minutes = 85 minutes. 

So if it takes 10 minutes putting everything away, then it means she spent 75 minutes washing cars (85 - 10).

75 minutes for 3 cars means that each car takes 25 minutes to wash (75/3).

I hope this helped. :))))

=^._.^=

Hi Guest!

The biggest square length is 3*brown - green. 

3*(2) - (1) = 5. 

The second biggest square length is 5-1 = 4. 

The first side of the large rectangle is the largest square length + brown = 7

The second side is  large rectangle is largest square + second biggest square = 9.

Thus, the area is 7*9 = 63

I hope this helped. :)))

=^._.^=