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3 years ago

What is the solution set of the following equation?

Mathematics

1 answer:

Maslowich3 years ago

8 0

$-8x + x + 15 = -7x + 12\\\\-8x+x+7x=12-15\\\\0=-3\\\\x\in\emptyset$

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The roots of the function f(x) = x2 – 2x – 3 are shown. what is the missing number? x = –1 and x =

andrey2020 [161]

we have

$f(x)=x^{2}-2x-3$

Find the roots

Equate the function to zero

$x^{2}-2x-3=0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$x^{2}-2x=3$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$x^{2}-2x+1=3+1$

$x^{2}-2x+1=4$

Rewrite as perfect squares

$(x-1)^{2}=4$

Square root both sides

$(x-1)=(+/-)2$

$x=1(+/-)2$

$x=1+2=3$

$x=1-2=-1$

therefore

<u>the answer is</u>

$x=3$

5 0

3 years ago

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Anna has a 30-year, 5.75% mortgage on her $250,000 home. She has been

poizon [28]

Answer:

Her new monthly payment is now $1,378.91¢

Step-by-step explanation:

For us to calculate the new monthly mortgage payment that Anna will start paying from now on, we need to input the formula for calculating monthly mortgage payments.

The formula is:-

$M = P [\frac{r(1+r)^{n} }{(1+r)^{n}-1}]$

Where M is the monthly mortgage payment.

P is the principal

r is the monthly interest rate calculated by dividing your annual interest rate by 12

n is the number of payments(the number of months you will be paying the loan).

In this case, the new principal that Anna must pay back is $231,905.47¢. The annual interest rate has been reduced to 5.17% from 5.75% so the new monthly interest rate will be obtained by dividing the new annual interest rate by 12

= 5.17%/2

= 0.431%

This is the new monthly interest rate.

Since she has been paying her mortgage loan diligently for 5 complete years. It means she now has just 25 years to complete the payment. If 12 months make up one year, then there are - 12 × 25 = 300 more months to go.

300 is therefore "n" that is required for the calculation.

All the terms needed for the calculation of her new monthly mortgage is now complete.

P = $231,905.47¢

r = 0.431%

n = 300

$M = 231,905.47[\frac{0.00431(1+0.00431)^{300} }{(1+0.00431)^{300} -1}]$

$= 231,905.47[\frac{0.00431(3.634)}{2.634}]$

= 231,905.47 × 0.005946

M = $1,378.91¢

Therefore her new monthly mortgage payment will become $1,378.91¢

4 0

3 years ago

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6 out of 24 employees at the water slides are temporary employees what percentage of the employees at the water slide are tempor

kykrilka [37]

Answer:

25%

Step-by-step explanation:

The question is:

6 is what percent of 24?

Set up the problem:

6 x

---- = -----

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Check your answer:

25% + 25% + 25% + 25% = 100%

6 + 6 + 6 + 6 = 24

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156 revolutions in 180 seconds. how many revolutions in 2 minutes

Alona [7]

180 seconds is 3 minutes. If you divide 156 by 3, you will get 52. If you are looking for 2 minutes, you have to multiply 52 by 2. The answer is 104 revolutions in 2 minutes.

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3 years ago

What is the measure of C?

Rufina [12.5K]

Since the shape is a quadrilateral, the interior angles add to 360 degrees. Thus, angle C is 360 - 82 - 92 - 102 = 84 degrees.

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3 years ago

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