MATHEMATICS
MIDDLE SCHOOL

5× =20

Answer:

Answer:

4

Step-by-step explanation:

5 times 4 = 20

20 divided by 5 = 4

Answer:

the answer is x=4 let me know if that helps

HIGH SCHOOL

Sondra wants to put a fence in a triangular area of her backyard as shown in the illustration. The fence will enclose a right triangle, with two of the sides measuring 8 yards and 15 yards long. How long will the third side of the triangle be? (the question did not contain an illustration)

17 yards. The fence that enclose Sondra's backyard is a right triangle whose sides measuring 8 yards, 15 yards and 17 yards respectively.

The key to solve this problem is using the Pythagorean Theorem that dictates; In every right triangle the square of the hypotenuse is equal to the sum of the squares of the legs and the equation hypotenuse²=leg1²+leg2².

For this problem we know the measuring of two side, which mean that we can apply Pythagorean Theorem equation as follow:

Let's say that one of the side is a = 8yards, and the other side is b = 15yards. So, we want to know how long the third side c long.

Applying the Pythagorean Theorem:

Substituting the values of the sides a and b:

Answer:

17 yds

Step-by-step explanation:

Lacking further info about this situation, I will assume that 8 yards and 15 yards represent the two legs of this right triangle, and not the hypotenuse. If that's the case, then the hypotenuse is found by applying the Pythagorean Theorem:

(8 yd)² + (15 yd)² = hyp², or

64 yd² + 225 yd² = 289 yd²

Taking the square root of this result yields 17 yds.

The third side will be 17 yds long.

MIDDLE SCHOOL

Seven increased by the product of two numbers

Seven increased by the product of two numbers

Whats the two numbers?

COLLEGE

An executive invests $27,000, some at 8% and the rest at 7% annual interest. If he receives an annual return of $2,050, how much is invested at each rate

8%X + 7%(27000-X) = 2050

.08X + 1890 + .07X = 2050

.15X = 160

X = $1067.67

.08X + 1890 + .07X = 2050

.15X = 160

X = $1067.67

Let x be the amount invested at 8%

the remaining amount (27,000 - x) was invested at 7%. After one year

$x yielded an interest A₁ OR A₁ = x(0.08)

The remained yielded an interest of A₂ = (27000 - x) (8%)

A₁ = x(0.08)

A₂ = (27000 - x) (8%)

---- ---------------------------------

A₁+A₂ = x(0.08) + (27000 - x) (8%)

2050 = x(0.08) + (27000 - x) (8%)

2050 = 0.08x - 0.07x +1890

2050 - 1890 = 0.01x

x = 160/0.01 = $16,000 @ 8% and $11,000 @ 7%

the remaining amount (27,000 - x) was invested at 7%. After one year

$x yielded an interest A₁ OR A₁ = x(0.08)

The remained yielded an interest of A₂ = (27000 - x) (8%)

A₁ = x(0.08)

A₂ = (27000 - x) (8%)

---- ---------------------------------

A₁+A₂ = x(0.08) + (27000 - x) (8%)

2050 = x(0.08) + (27000 - x) (8%)

2050 = 0.08x - 0.07x +1890

2050 - 1890 = 0.01x

x = 160/0.01 = $16,000 @ 8% and $11,000 @ 7%

HIGH SCHOOL

A bolt extends through 3/4” thick plywood, a washer that is 1/8” thick, and a nut that is 3/16” thick. The bolt should be 5/8” longer than the sum of the thickness of the plywood, washer and nut. What is the minimum length of the bolt?

Answer:

Minimum length of bolt

Step-by-step explanation:

The bolt should be longer than the sum of the thickness of the plywood, washer and nut.

Thickness of the plywood =

Thickness of the washer =

Thickness of the nut =

Length of bolt = Thickness of the plywood+Thickness of the washer+Thickness of the nut

Minimum length of bolt

(3/4" +1/8" +3/16" +5/8") = (12 +2 +3 +10)/16" = 1 11/16"

The bolt needs to be a minimum of 1 11/16 inches in length.

The bolt needs to be a minimum of 1 11/16 inches in length.