MATHEMATICS HIGH SCHOOL

what is the side length of the largest square tile that can be used to tile a rectangular floor measuring 12 ft by 38 ft if the tiles cannot be cut?

Answers

Answer 1
Answer:

A square tile 2ft by 2 ft will be used to tile the rectangular floor.

What is a Rectangle ?

A rectangle is a polygon with four sides , The opposite sides of the polygon is equal and parallel.

A rectangular floor has measure of

Length = 12ft

Width = 38 ft

The side of the square tile that can be used to tile the floor is ?

The highest common factor of the rectangular sides 38 and 12 is 2

Therefore a square tile 2ft by 2 ft will be used to tile the rectangular floor.

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Answer 2
Answer: The greatest common facter of 12 and 38 is 2 so the answer is:
2 ft

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A beverage manufacturer performs a taste-test and discovers the people like their fizzy beverages best when the radius of the bubbles is about 0.5 mm. According to the formula below, what would be the volume of the one of these bubbles?

Answers

The volume of the sphere will be 0.52 cubic mm. Then the correct option is C.

What is the volume of the sphere?

Let r be the radius of the sphere.

Then the volume of the sphere will be

V = 4/3 πr³ cubic units

The expression is given below.

\rm r = \sqrt[3]{(3V)/(4\pi)}

Where r is the radius of the sphere and V is the volume of the sphere.

A beverage manufacturer performs a taste test and discovers that people like their fizzy beverages best when the radius of the bubbles is about 0.5 mm.

The expression is solved for V, then the equation will be

\rm r^3 = (3V)/(4\pi)\n\nV = (4)/(3)\pi r^3

Then the volume of the sphere will be

V = (4/3) × π × 0.5³

V = 0.52 cubic mm

Thus, the volume of the sphere will be 0.52 cubic mm.

Then the correct option is C.

More about the volume of the sphere link is given below.

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Answer with explanation:

Radius of the Bubble = 0.5 mm

Volume of the bubble is given by the formula

r=[(3V)/(4\pi)]^{(1)/(3)}

Taking cube on both sides

V=(4\pi* r^3 )/(3)\n\n V=(4*3.14*(0.5)^3)/(3)\n\nV=(12.56* 0.125)/(3)\n\n V=(1.57)/(3)\n\nv=0.52333....

Gives,→ V=0.52 mm³(approx)

Option C: about 0.52 mm³

What is the answer to 8x+2(y+13)=10

Answers

If you were trying to convert it to the standard form equation of a line

Ax + By - C = 0
Ax + By = C.

Simply distribute the 2 inside.

8x + 2(y+13) = 10
8x + 2y + 26 = 10
8x + 2y + 26 - 26 = 10 - 26

8x + 2y = -16 or
8x + 2y + 16 = 0.

Solve the triangle.B = 73°, b = 15, c = 8
Select one:
a. C = 35.9°, A = 71.3°, a ≈ 15.2
b. C = 30.7°, A = 76.3°, a ≈ 15.2
c. C = 30.7°, A = 76.3°, a ≈ 21.3
d. Cannot be solved

Answers

Using the sine law of triangles to solve for angle C:

b / sin B = c / sin C

C = arcsin (c * sin B / b)
C = 30.7°

Since interior angles of a triangle always add up to 180°, we can use this to solve for angle A:

angle A = 180° - 73° - 30.7°
angle A = 76.3°

Having solved for angle A, we can solve for side a using the sine law.

a / sin A = b / sin B

a = b * sin A / sin B
a = 15.2

Therefore, the correct answer is B.

The slope of a given line is 1/3 . What is the slope of a line that is perpendicular to the given line? Type a numerical answer in the space provided. Do not type spaces in your answer. If necessary, use the / key to represent a fraction bar.

Answers

If slope of the line is 1/3,  then slope of the perpendicular line should be negative reciprocal, and so it is equal -3.
Answer: -3.

-9(m + 2) + 4(6 – 7m)

Answers

I think it is -37m+17 but I am not sure

Simplify 5 + 2{x - 4[3x + 7(2 - x)]}.
-34x - 107
34x - 107
34x + 107

Answers

5 + 2(x - 4[3x + 7(2-x)]) \n \n 5 + 2(x - 4(3x + 14-7x)) \n \n 5 + 2(x - 4((3x - 7x) + 14)) \n \n 5 + 2(x - 4(-4x + 14)) \n \n 5 + 2(x + 16x - 56) \n \n 5 + 2(17x - 56) \n \n 5 + 34x = 112 \n \n 34x - 107 \n \n Answer: \fbox {34x - 107}

Answer:

b) 34x - 107

Step-by-step explanation:
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