Find the domain and range of the relation, and state ...



Find the domain and range of the relation, and state whether or not the relation is a function. {(1, 4), (1, 5), (1, 6), (1, 7)}

Solution:

Domain = {1}, Range = {4, 5, 6, 7}

The relation is not a function.

Find the slope of the line passing through the points (7, 0) and (0, 10).

Solution:

Slope = (10 -0)/(0-7) = -10/7

Find the coordinates of the x-intercept. -x - 2y = 6

Solution:

For finding x-intercept, put y = 0

-x = 6 => x = -6

x-intercept will be (-6, 0).

Answer: (-6, 0)

Find the y-intercept. -2x - y = -10

Solution:

For finding y-intercept, put x = 0

-y = -10 => y = 10

y-intercept is (0, 10).

Answer: (0, 10)

Janet invested $26,000, part at 6% and part at 3%. If the total interest at the end of the year is $1,080, how much did she invest at 6%?

Solution:

Let the amount invested at 6% be x then the amount invested at 3% will be 26,000 – x

Equation will be

0.06x + 0.03(26000 – x) = 1080

After solving, we will get x = 10,000

Answer: $10,000

Find the y-intercept. x + 4y = -4

Solution:

For finding y-intercept, put x = 0

4y = -4 => y = -1

y-intercept is (0, -1).

Answer: (0, -1)

Determine whether the system is consistent, inconsistent, or dependent. 3x + 2y = 15 6x + 4y = 30

Answer: Consistent and dependent

Find the slope of the line passing through the points (0, -4) and (-6, 7).

Slope = (7 –(-4))/(-6-0) = -11/6

A tent is shaped like a pyramid. It has a square base measuring 8 feet on a side and a height of 6 feet. What is the volume of the tent?

Solution:

Volume of tent = (1/3)b²h = (1/3)*8^2*6 = 128 ft3

Answer: 128 ft3

In triangle ABC, angle C is a right angle. Find the measure of angle B if side b = 105 m and side c = 139 m.

sinB = 105/139

B = arcsin(105/139)

B = 49.06 degrees

Answer: B = 49.06 degrees

Find the circumference and area of the circle if d yd = 30. Use ? = 3.14.

Solution:

Given d = 30 yd

Circumference = π d = 3.14*30 = 94.2 yd

Area = πr^2 = 3.14*15*15 = 706.5 square yards

Find the circumference of the circle (6cm). Use ? = 3.14.

I am assuming radius is 6cm.(please confirm)

Circumference = 2πr = 2*3.14*6 = 37.68 cm

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