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3 years ago

8

Paul has $75 in his wallet. He worked 8 hours at the theater and earned $8.50 per hour. He spent $72.50 in a pair of soccer Clai

ts. How much money does Paul has now?

1 answer:

Rudiy273 years ago

3 0

Answer:

$70.50

Step-by-step explanation:

8.50 x 8 = 68

68 + 75 = 143

143 - 72.50 = 70.50

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Match each series with the equivalent series written in sigma notation

PIT_PIT [208]

Answer:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

Step-by-step explanation:

Given

See attachment for complete question

Required

Match equivalent expressions

Solving (a):

$3 + 12 + 48 + 192 + 768$

The expression can be written as:

$3 \to 3*4^{0$ --- 0

$12 \to 3 * 4^{1$ ---- 1

$48 \to 3 * 4^{2$ --- 2

$192 \to 3 * 4^{3$ ---- 3

$768 \to 3 * 4^{4$ ---- 4

For the nth term, the expression is:

$Term = 3 * 4^{n$ ---- n

So, the summation is:

$3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n$

Solving (b):

$4 + 32 + 256 + 2048 + 16384$

The expression can be written as:

$4 \to 4 * 8^0$ --- 0

$32 \to 4 * 8^1$ ---- 1

$256 \to 4 * 8^2$ --- 2

$2048 \to 4 * 8^3$ ---- 3

$16384 \to 4 * 8^4$ ---- 4

For the nth term, the expression is:

$Term \to 4 * 8^n$ ---- n

So, the summation is:

$4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n$

Solving (c):

$2 + 6 + 18 + 54 + 162$

The expression can be written as:

$2 \to 2 * 3^0$ --- 0

$6 \to 2 * 3^1$ ---- 1

$18 \to 2 * 3^2$ --- 2

$54 \to 2 * 3^3$ ---- 3

$162 \to 2 * 3^4$ ---- 4

For the nth term, the expression is:

$Term \to 2 * 3^n$ ---- n

So, the summation is:

$2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n$

Solving (d):

$3 + 15 + 75 + 375 + 1875$

The expression can be written as:

$3 \to 3 * 5^0$ --- 0

$15 \to 3 * 5^1$ ---- 1

$75 \to 3 * 5^2$ --- 2

$375 \to 3 * 5^3$ ---- 3

$1875 \to 3 * 5^4$ ---- 4

For the nth term, the expression is:

$Term \to 3 * 5^n$ ---- n

So, the summation is:

$3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n$

5 0

3 years ago

Two angles are complementary angles if the sum of their measure is 90 degrees. Angle A and angle B are complementary angles, and

Marta_Voda [28]

Let's solve this problem step-by-step.

STEP-BY-STEP SOLUTION:

We will be using simultaneous equations to solve this problem.

First we will establish the equations which we will be using as displayed below:

Equation No. 1 -

A + B = 90°

Equation No. 1 -

A = 2B + 12

To begin with, let's make ( A ) the subject in the first equation as displayed below:

Equation No. 1 -

A + B = 90

A = 90 - B

Next we will substitute the value of ( A ) from the first equation into the second equation and solve for ( B ) as displayed below:

Equation No. 2 -

A = 2B + 12

( 90 - B ) = 2B + 12

- B - 2B = 12 - 90

- 3B = - 78

B = - 78 / - 3

B = 26°

Then we will substitute the value of ( B ) from the second equation into the first equation to solve for ( A ) as displayed below:

A = 90 - B

A = 90 - ( 26 )

A = 64°

ANSWER:

Therefore, the answer is:

A = 64°

B = 26°

Please mark as brainliest if you found this helpful! :)
Thank you <3

4 0

3 years ago

3x – y = 4 2x + y = 6 (2, 2) (3, 0) (–1, –7) (0, –4)

Vitek1552 [10]

The answer is 2,2

as 3*2 - 2 = 4
ans 2*2 +2 = 4

So it satisfies both eqautions

3 0

3 years ago

Read 2 more answers

sasho [114]

Answer:

$y = \frac{3}{4} x - \frac{3}{2}$

Step-by-step explanation:

$y = \frac{3}{4} x - 1→y - y1 = m( x - x1)$

$y - 6 = \frac{3}{4} (x - 6)→y - 6 = \frac{3}{4} x - 6$

$2(y - 6) = 2( \frac{3}{4} )(x - 6)$

$2y - 6= \frac{3}{2}( x - 6)$

$2y - 6 = \frac{3}{2} x - 9$

$- 6 \: from \: both \: sides$

$2y = \frac{3}{2} x - 3$

$divede \: by \: 2 \: on \: both \: sides$

$y = \frac{3}{4} x - \frac{3}{2}$

Hope this helps!

7 0

3 years ago

H(x)=2x^2+3x-7 <br> find h(-1)

nata0808 [166]

Answer:

que

Step-by-step explanation:

4 0

3 years ago