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3 years ago

Factor by completing the square 5x^2-21=10x

1 answer:

4 0

Solve for x over the real numbers:
5 x^2 - 21 = 10 x

Subtract 10 x from both sides:
5 x^2 - 10 x - 21 = 0

Divide both sides by 5:
x^2 - 2 x - 21/5 = 0

Add 21/5 to both sides:
x^2 - 2 x = 21/5

Add 1 to both sides:
x^2 - 2 x + 1 = 26/5

Write the left hand side as a square:
(x - 1)^2 = 26/5

Take the square root of both sides:
x - 1 = sqrt(26/5) or x - 1 = -sqrt(26/5)

Add 1 to both sides:
x = 1 + sqrt(26/5) or x - 1 = -sqrt(26/5)

Add 1 to both sides:
Answer: x = 1 + sqrt(26/5) or x = 1 - sqrt(26/5)

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AfilCa [17]

Use the volume of a cylinder equation, V = pi*r^2*h to find the volume of the cylinder. To find the answer to the second one, find the volume of the square and subtract the volume of the cylinder from it.

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3 years ago

Mark invests $6,700 in an online savings account which gives 4.2% simple annual interest. He also invests $6,000 in a savings ac

dalvyx [7]

Answer:

$4,221.00 for online and 6,210.00 for the instore

Step-by-step explanation:

Calculation:

First, converting R percent to r a decimal

r = R/100 = 4.2%/100 = 0.042 per year.

Solving our equation:

A = 6700(1 + (0.042 × 15)) = 10921

A = $10,921.00

The total amount accrued, principal plus interest, from simple interest on a principal of $6,700.00 at a rate of 4.2% per year for 15 years is $10,921.00.

Calculation:

First, converting R percent to r a decimal

r = R/100 = 6.9%/100 = 0.069 per year.

Solving our equation:

A = 6000(1 + (0.069 × 15)) = 12210

A = $12,210.00

The total amount accrued, principal plus interest, from simple interest on a principal of $6,000.00 at a rate of 6.9% per year for 15 years is $12,210.00.

5 0

3 years ago

Tracy McKinney is a disc jockey at radio station WMMM. Her annual salary is $52,750. What is her monthly salary?

attashe74 [19]

Okay, so since her annual salary is <span>$52,750 (the amount she gets a year, all twelve months combined) you're trying to find how much she gets monthly. That would mean we would have to divide her annual salary by 12 to find her monthly salary.

</span>$52,750 ÷ 12 = 4,395.8333333333333
<span>
And since that's a (bothersome) repeating decimal, we're going to have to round it. Once rounded, you would get $</span>4,395.83. That is her monthly salary.

5 0

3 years ago

17x-3y=4 2x-4y=1 the solution to the system of equations is

Burka [1]

ANSWER

$x=\frac{13}{62}$

and

$y= \frac{-9}{62}$ e have

EXPLANATION

$17x-3y=4---(1)$

$2x-4y=1$

Let us make y the subject and call it equation (2)

$2x=1+4y$

$x=\frac{1}{2}+2y--(2)$

We put equation (2) in to equation (1)

$17(\frac{1}{2}+2y)-3y=4$

$\frac{17}{2}+34y-3y=4$

$34y-3y=4- \frac{17}{2}$

Simplify to get,

$31y= \frac{8-17}{2}$

$31y= \frac{-9}{2}$

Divide both sides by 31,

$y= \frac{-9}{2} \div 31$

$y= \frac{-9}{2} \times \frac{1}{31}$

$y= \frac{-9}{62}$

We put this value in to equation (2) to get,

$x=\frac{1}{2}+2\times -\frac{9}{62}$

$x=\frac{1}{2} -\frac{18}{62}$

We collect LCM to obtain,

$x=\frac{31-18}{62}$

$x=\frac{13}{62}$

7 0

3 years ago

Write word problems that represent each way you can use a remainder in a division problem. Include solutions. PLEASE COULD YOU H

babymother [125]

Division Problem: 90 people were invited to the party.

1. How many tables are needed, if each table can seat 8 people?

2. How many tables will be completely full?

3. How many people will be at an incomplete table?

Solution:

You have that 90=8·11+2 (8 - divisor, 11 - quotient, 2 - remainder).

Since the quotient is 11, 12 tables are needed, 11 tables will be completely full and the last 12th table will be incomplete, only 2 people will be at this table.

Answer: 1. 12 tables, 2. 11 tables, 3. 2 people

4 0

3 years ago

Read 2 more answers