MATHEMATICS
MIDDLE SCHOOL

Answer: About 37.7

square root of 12 = 3.5

132 divided by 3.5 = 37.7

square root of 12 = 3.5

132 divided by 3.5 = 37.7

HIGH SCHOOL

A blue spruce grows an average of 6 inches per year. A hemlock grows an average of 4 inches per year. If a blue spruce is 4 feet tall and a hemlock is 6 feet tall, when would you expect the trees to be the same height?

Answer: it will take 12 years for both trees to be of the same height.

Step-by-step explanation:

Let x represent the number of years that it will take for the blue spruce and the hemlock to be the same height.

A blue spruce grows an average of 6 inches per year. If a blue spruce is 4 feet tall,

1 inch = 0.0833 feet

6 inches = 6 × 0.0833 = 0.4998 feet

it means that its height in x years would be

0.4998x + 4

A hemlock grows an average of 4 inches per year. If a hemlock is 6 feet tall.

4 inches = 4 × 0.0833 = 0.3332 feet

it means that its height in x years would be

0.3332x + 6

The number of years that it will take both trees to be of same height is

0.4998x + 4 = 0.3332x + 6

0.4998x - 0.3332x = 6 - 4

0.1666x = 2

x = 2/0.1666

x = 12

COLLEGE

Sketch the following to help answer the question. Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P. Side QR = 10m and diagonal QS = 12m. Find the length of segment RP.

Short Answer RP = 8 meters.

Remark

A kite's diagonals bisect each other. (1/2) QS = QP.

Another fact about a kite is that the diagonals meet at right angles.

ΔQPR is a right triangle.

Step One

Find QP

QP = 1/2 QS

QS = 12 Given

QP = 1/2 12

QP = 6

Step Two

Find RP

Use the Pythagorean Theorem To solve for RP

Givens

QP = 6 From Step 1

QR = 10 Given

QP = ??

We are dealing with a right angle triangle.

RP^2 + QP^2 = QR^2

RP^2 + 6^2 = 10^2

RP^2 + 36 = 100 Subtract 36 from both sides.

RP^2 = 100 - 36

RP^2 = 64 Take the square root of both sides.

sqrt(RP^2) =sqrt(64)

RP = 8

Remark

A kite's diagonals bisect each other. (1/2) QS = QP.

Another fact about a kite is that the diagonals meet at right angles.

ΔQPR is a right triangle.

Step One

Find QP

QP = 1/2 QS

QS = 12 Given

QP = 1/2 12

QP = 6

Step Two

Find RP

Use the Pythagorean Theorem To solve for RP

Givens

QP = 6 From Step 1

QR = 10 Given

QP = ??

We are dealing with a right angle triangle.

RP^2 + QP^2 = QR^2

RP^2 + 6^2 = 10^2

RP^2 + 36 = 100 Subtract 36 from both sides.

RP^2 = 100 - 36

RP^2 = 64 Take the square root of both sides.

sqrt(RP^2) =sqrt(64)

RP = 8

Answer:

8m

Step-by-step explanation:

Sketch the following to help answer the question. Kite QRST has a short diagonal of QS and a long diagonal of RT. The diagonals intersect at point P. Side QR = 10m and diagonal QS = 12m. Find the length of segment RP.

6m

8m

10m

12m

Odyssey

HIGH SCHOOL

The square of a number is equal to 10 less than 7 times that number. What are the two possible solutions? Which of the following equations is used in the process of solving this problem?

x^2 - 7x + 70 = 0

x^2 - 7x + 10 = 0

The second equation, its setup is correct

HIGH SCHOOL

How do u right this Seven less than the quotient of x and 9

(x/9)-7 is the same as "Seven less than the quotient of x and 9"

Answer:

(x÷9)−7 is your answer.