MATHEMATICS HIGH SCHOOL

Solve the equation.
2(x + 4) = x + 13

A. −3
B. −1
C. 5
D. 7

Answers

Answer 1
Answer: 2x + 8 = x + 13
x = 5
Answer 2
Answer: The answer is C) x = 5

Here are the steps I did.

1. Expand ( 2x + 8 = x + 13)

2. Subtract 8 from both sides ( 2x = x + 13 - 8)

3. Simplify x + 13 - 8 to x + 5 ( 2x = x + 5)

4. Subtract x from both sides ( 2x - x = 5)

5. Simplify 2x - x to x ( x = 5)

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An airplane over the Pacific Ocean sights an atoll at an 7° angle of depression. If the plane is 663 m above the water, how many kilometers is it from a point 663 m directly above the atoll?(Hint: Make sure your calculator is in degrees!)A. 5399.7 km
B. 5.4 km
C. 81.41 km
D. 760.8 km

Answers

You need to draw the diagram to understand the problem easily. Teh diagram will show the right triangle, acute angle with the base  7º, height is 663 m, and "x" is the base of the triangle. 

using the tangent ratio: 

tanΘ = opposite / adjacent

tan7º = 663 m / x 

x = 663 m / tan7º
x = 5,399.7 m 

change m to km. 1,000 m = 1km

5,399.7m * 1km/1,000 m = 5,399.7 km/1000 = 5.3997 km or 5.4 km

B. 5.4 km 

Harriet wants to buy items worth $248.50. She is using a store coupon for 25 percent off her purchases. She has to pay 5 percent sales tax. Calculate the total cost of the items.

Answers

Starting price is : $248.50
Price with 25% off :
$248.50 x ( 1 - 0.25 ) = $248.50 x 0.75 = $186.375
After that she has to pay 5 % sales tax:
$186.375  x 1.05 = $195.70
Answer:
The total cost of the items is $195.70.

Answer:   $195.70

Step-by-step explanation:

How do I do a question containing powers that are improper fractions?say for example 81 to the power of 3/2. thx

Answers

( 81 )^ ( 3 / 2 ) = ( 3 ^ 4 )^ ( 3 / 2 ) = 3 ^( 4 * 3 / 2 ) = 3 ^ 6 = 729.
81^{\tfrac{3}{2}}=\n(3^4)^{\tfrac{3}{2}}=\n3^{4\cdot\tfrac{3}{2}}=\n3^(2\cdot3)=\n3^6=\n729

What is the monthly payment of a financed amount of $14,452 with an APR of 8.9 percent? The term is for 5 years and the monthly payment per $100 is $2.41. $332.80 $348.29 $100.00 $241.00

Answers

Answer:

$348.29

Step-by-step explanation:

The payment is calculated by multiplying the rate per hundred times the number of hundreds. The latter is found by dividing the loan amount by $100.

$2.41 × $14,452/$100 ≈ $348.29

Answer:$299.16

 

Step-by-step explanation:

Financed amount = $14452

APR  = 8.9%

Period / time = 5 years

monthly payment = $100 for every $2.07

To calculate the monthly payment of a financed amount we multiply the financed amount by the ratio of the given amount paid per $100

The monthly payment would be =  14452 * 2.07/100 = 14452 * 0.0207

= $299.16 approximately

therefore the monthly payment of a financed amount of $14452 is equal to $299.16

A certain aquarium holds 20 gallons of water. How many quarts of water does the aquarium hold?

Answers

The aquarium holds 80 quarts of water.

We have,

In the United States customary system, there are 4 quarts in 1 gallon.

This conversion factor is a constant ratio that allows us to convert between gallons and quarts.

So, when we have 20 gallons of water, we can multiply it by the conversion factor of 4 quarts/gallon to find out how many quarts it is equivalent to:

20 gallons x 4 quarts/gallon = 80 quarts

Therefore,

The aquarium holds 80 quarts of water.

The conversion factor helps us determine the equivalent amount of one unit to another.

Learn more about unitconversion here:

brainly.com/question/13899873

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Let's find out what 1 gallon of water is first.1 gallon is equivalent to 4 quarts.20 gallon is equivalent to 80 quarts.What we do here is to multiply: 20 gallons • 4 quarts = 80 quartsThe answer is 80 quarts.

A man walks along a straight path at a speed of 4ft/s. A searchlight is located on the ground 20ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight.

Answers

Now note that tan(y) = x=20,
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At the instant describedin the problem,
x = 15 and the hypotenuse of the above triangle
thus has length25,
so we compute:(25/20)^2 dy/dt=1/20*4 ==>dy/dt=1/2*400/625

=16/125 rad/sec
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