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Elden [556K]
3 years ago
6

After breaking your penny bank, you notice that you have $4.87 in quarters ($0.25), dimes ($0.10), nickels ($0.05), and pennies

($0.01). If there are twice as many pennies as nickels and one and a half time the number of nickels as dimes and 34 more pennies than quarters, how many pennies do you have? A. 17 B. 34 C. 42 D. 44
Mathematics
1 answer:
ira [324]3 years ago
3 0

Answer: Option 'c' is correct.

Step-by-step explanation:

Let the number of dimes  be 'x'.

Let the number of nickels  be '\dfrac{3}{2}x'.

Let the number of pennies be \dfrac{3}{2}\times 2x=3x

Let the number of quarters be '3x-34'.

As we know that

1 quarter = $0.25

1 dime = $0.10

1 nickel = $0.05

1 penny = $0.01

According to question, we get that

0.10x+0.05\times \dfrac{3x}{2}+0.01\times 3x+0.25(3x-34)=4.87\\\\0.10x+0.075x+0.03x+0.75x-8.5=4.87\\\\\\0.955x=4.87+8.5\\\\0.955x=13.37\\\\x=\dfrac{13.37}{0.955}\\\\x=14

So, the number of pennies is given by

3x=3\times 14=42

Hence, Option 'c' is correct.

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Aaron is 5 years younger than
dusya [7]

Answer:

Roy is 6 years old and Aaron is 1 year old.

Step-by-step explanation:

A is Aaron's age,

R is roy's age,

A = R - 5

R + 4 = 2(A+4)

We can distribute first,

R + 4 = 2A + 8

Subtract 4 from each side,

R = 2A + 4

Since A = R - 5, you can substitute in R - 5 for A in the equation,

R = 2(R-5) + 4

Distribute,

R = 2R - 10 + 4

Since - 10 + 4 = -6, we can do this,

R = 2R - 6

Subtract R from both sides,

0 = R - 6

Add 6 to both sides and you have part of your answer;

R = 6

Since A = R - 5,

A = 6 - 5

A = 1, so Aaron's age is 1.

7 0
3 years ago
In 10 years, a child’s age will be 6 years less than triple her current age. Find the child’s current age.
Pavel [41]

Answer:

Her current age is 8 years old.

Step-by-step explanation:

Current age: x

"In 10 years, a child’s age will be 6 years less than triple her current age."

In 10 years: <u>x + 10</u>

6 years less than triple: <em>3x - 6</em>

<u>x + 10</u> = <em>3x - 6</em>

<em>solve.</em>

<em>16 = 2x</em>

<em>x = 8</em>

5 0
3 years ago
What are the vertical asymptotes of the function f(x) = 2x + 8 / x2 + 5x + 6?
Irina18 [472]
I'm assuming the function is f(x) = (2x+8)/(x^2+5x+6). If so, make sure to use parenthesis to indicate that you're dividing all of "2x+8" over all of "x^2+5x+6" as one big fraction. Otherwise, things are ambiguous and it leads to confusion.

Side Note: x^2 means "x squared"

Factor the numerator: 2x+8 = 2(x+4)
Factor the denominator: x^2+5x+6 = (x+2)(x+3)

There are no common factors between the numerator and denominator. So there is nothing to cancel out. 

Recall that you cannot divide by zero. Something like 1/0 is undefined. 
We need to find the x values that cause the denominator to be zero.
Set the denominator equal to zero and solve for x
x^2+5x+6 = 0
(x+2)(x+3) = 0
x+2 = 0 or x+3 = 0
x = -2 or x = -3

The x values x = -2 or x = -3 will lead to the denominator being zero. This means that the vertical asymptotes are x = -2 or x = -3 as shown by the blue dashed vertical lines in the attached image.

4 0
3 years ago
If two lines intersect, what angle measures will add to 180°?
Alinara [238K]
Answer= Supplementary Angles

Supplementary angles are two angels whose sum is 180°
8 0
3 years ago
Read 2 more answers
Due today pls helppppp
LiRa [457]
<h3>Answer:   19.1</h3>

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

Work Shown:

tan(angle) = opposite/adjacent

tan(C) = AB/BC

tan(theta) = x/BC

tan(23) = (8.1)/BC

BC*tan(23) = 8.1

BC = (8.1)/tan(23)

BC =  19.0824041631723

BC = 19.1

In this case, rounding to 3 sig figs means we round to the nearest tenth.

Make sure your calculator is in degree mode.

3 0
3 years ago
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