math final

Solve the following using proportions: If 4 cans of cat food sell for $1.92, how much will 12 cans sell for?

$5.76

Solve 1/3= 1/x + 5/6

-2

Solve the equation: 6 - x = 9

-3

Solve for the variable: 2.5x + 2.4 = -6.7

-3.64

Perform the division -14a^6/2a^6

-7

Raise the term to the indicated power: (-2/7)^3

-8/343

Identify the degree of the term: 6

0

An 18 oz box of cereal costs $3.51. Find the unit price.

0.195$

Change 12' 8" to decimal degree equivalent. Express the decimal to the nearest ten-thousandth.

0.2022

A berry picker can pick at the rate of one crate every 6 minutes. How many helpers, working at the same rate would the berry picker need to get a crate every 3 minutes?

1

Write the product: x^-3(x)(x^2)

1

A printing press can produce 1 day's newspaper in 4 hours. A higher-speed machine can do 1 day's newspaper in 2 hours. How much time would it take both presses to do the one job?

1 1/3 hours

A machine can pack a day's crab catch in 5 hours. A second machine can pack 1 day's catch in only 3 hours. How much time would it require for 1 day's catch to be packed if both machines were used together?

1 7/8 hours

Solve the inequality: x - 4 < 5 < 2x + 3

1 < x < 9

Solve for the variable: 8/y = 96

1/12

Write 7^-2 as an ordinary number.

1/49

Write the quotient using positive exponents: x^-2/x^6

1/x^8

An architect's drawing is scaled at 0.5 in = 4 ft. Find the actual measurement for a wall that is 1.25 in. on the drawing.

10 ft

Solve the given problem: It takes 60 oz. of grass seed to seed 3,000 ft2 of lawn. At this rate, how much would be needed for 5,000 ft2 of lawn?

100oz

Which of the following angle pairs is not supplementary?

105°, 85°

Simplify the expression: 8x^4 + 2x^4

10x^4

Solve the proportion: 3x+2/6 = 5/4

11/6

Write the statement as an equation and solve:Tracy Edwards' back yard is a rectangle whose length is two times the width. If the perimeter of the yard is 120 feet, what is the width of the yard?

120 = 2(2x + x); width is 20 feet

Use the FOIL method to find the product: (4x - 2y)(3x + y)

12x^2-2xy-2y^2

If distance = rate × time, how long did a trucker drive if she traveled 785.3 miles at 60 miles per hour?

13.1 hours

Solve for the variable: 4/7h + 1/2h = 1

14/15

The area of a rectangle where length = 37 and width = 39 m is:

1443m^2

Solve for the variable: 12/x = 4/5

15

Solve the proportion: x/6 = 5/2

15

Solve for the variable: 3.57 = R + 0.7R

2.1

Solve the following using a constant of variation:How much fertilizer does 3,246 square feet of lawn need if the fertilizer treats 1,500 square feet per gallon? Express to nearest tenth.

2.2 gal

Perform the multiplication: 3x^3(7x^2 + x - 3)

21x^5 + 3x^4 - 9x^3

Find the length of a rectangular work area if the perimeter is 64 in. and the width is 9 inches. Use the formula P = 2(l + w).

23 in

Which angle pair is complementary?

23°, 67°

A 10 lb bag of dog food costs $3.98 and a 25 lb bag of the same dog food costs $6.95. Which is the better buy?

25 lb bag

The swimming pool measures 60 ft by 28 ft. How much fencing is needed, including material for a gate, if the fence is to be built 10 ft from each side of the pool?

256ft

Find the special product: (5x - 2y)^2

25x^2 - 20xy + 4y^2

Change 0.45° to equivalent minutes and seconds. Round to the nearest second if necessary.

27'

Perform the multiplication: 4x3(7x)

28x^4

Perform the division 6x^3 +12x^2-3x / 3x

2x^2+4x-1

Arrange the polynomial in descending order: 5x^2 + 2x^4 + 3x^3

2x^4 + 3x^3 + 5x^2

A nurse can prepare dosages for the patients in 24 minutes. If she gets help from assistants who work at her rate, the preparation can be done in 6 minutes. How many helpers did she get to work with her?

3 helpers

Steve Lancaster wants to apply lime to a field with dimensions of 3/4 mi ×1/2 mi. Find the area in square miles.

3/8 mi^2

Perform the multiplications and simplify the expression: 5x(7x2 - 3x) - 2x2(x + 4)

33x^3-23x^2

A garden plot turned out to be a trapezoid whose parallel sides measured 18 feet and 42 feet respectively. The garden is 12 feet wide. What is the area of the garden plot?

360ft^2

Solve the given problem: The coffee beans from 16 trees are required to produce the 19 lb of coffee that each person in the United States drinks, on the average, each year. How many trees are required to produce 450 lb of coffee? (Hint: Any decimal part of a tree becomes a whole tree.)

379 trees

Solve the equation: 36 + x = 75

39

Rewrite as an exponential equation: log3 9 = 2

3^2=9

Simplify 5x - 2(x - 3) by applying the distributive principle and combining like terms.

3x+6

Perform the division -6x^5/-8x^2

3x^3/4

Identify the degree of the polynomial: 3x^2 + x^4 - 5x^3

4

What is the area of a triangular cast if the sides measure 33 mm, 44 mm, and 26 mm?

426.9mm^2

To make a mixture of nuts (3 lbs), 1 lb. of cashews is mixed with every 2 lb. of peanuts. In order to make 63 pounds of this mixture, how many pounds of peanuts are needed?

42lbs

Perform the division 15y^8 / 3y^4

5y^4

Solve the fractional equation, identifying excluded values: 2/5x + 6 = 1/2x

60

Rewrite as an exponential equation: log6 1/36 = -2

6^-2= 1/36

Simplify by applying the distributive principle: 3(2x - 5)

6x-15

Simplify by combining like terms: 5x + 2y - 8y + x

6x-6y

Solve the following using proportions: If 2 cans of beans cost $1.52, how many cans do you buy for $5.32?

7 cans

solve 7/12x - 3/4 = 2/9 - 2/3x

7/9

divide 14x^2+ 39xy+27y^2 / 2x+3y

7x+9y

If you drove 487 miles at 60 miles per hour, how long did your trip take?

8.12 hours

Solve for the variable: 0.34x + 0.52x = 7.482

8.7

Simplify the expression: (5x - 2y) + (3x + 8y)

8x + 6y

Solve the following problem: Five less than three times a number is the same as twice the sum of a number and two. Find the number.

9

A coffee company mixes 1.6 lb of French Roast beans with every 3.3 lb of Kona beans. How many pounds of French Roast are needed to make 3,000 lb. of the coffee blend?

979.6

Raise the term to the indicated power: (a^3 / b^7)^4

NOT - (a^12 / b^7) or (a^7/b^11) A?????

Use the FOIL method to find the product: (a + 5)(a - 3)

a^2+2a-15

write the product

a^6(a^-8)(a^4)

Which term is associated with an angle which measures 42°?

acute

A rectangle measures 12 m by 14 m. If the width is decreased by 3 m and the length is increased by 4 m, how much would the area change?

decrease by 6 m^2

10^-2 = 0.01 written in logarithmic form is:

log 0.01 = -2

2^-2 = 0.25 written in logarithmic form is:

log2 0.25 = -2

Rewrite as a logarithmic equation: 5^-2 = 1/25

log5(1/25) = -2

Solve the inequality: 3(x + 5) ≤ 3x + 7

no solution

Which of the following is associated with a 180° angle?

one-half of a rotation of a circle

Classify by name the angle that is one-fourth of a rotation.

right

If the sides of a triangle measure 15 m, 18 m, and 22 m, what kind of triangle is it?

scalene triangle

What is the name of a triangle with no equal sides?

scalene triangle

Determine the type of polynomial, according to the number of terms: a^2 + 5a - 2

trinomial

Solve the inequality: 5 + 2(x + 2) ≤ 7

x ≤ -1

Solve the inequality: 3x + 2x ≤ 20

x ≤ 4

Solve the inequality: 3/4 x + 1/2 ≤ 5/6x

x ≥ 6

Solve for x: log5 x = -2

x= 1/25

Solve the equation: 8x = 6

x= 3/4

Solve the equation: 5(x - 3) = 2(3x + 1)

x=-17

Solve the equation: 5 + x + 1 + x = 1 + 3x + 4x - 2

x=1 2/5

Solve the equation: -8x = -16

x=2

Solve the equation: 6x - 5 = x + 10

x=3

Solve the equation: 5x - (x - 3) = 9

x=3/2

Solve for x: log3 81 = x

x=4

Solve the equation: 0.2(3.6x + 2) = 4

x=5

Solve the equation: 5x - 2x = 21

x=7

Solve the equation: 7x + 2x = 75 - 3

x=8

Use the FOIL method to find the product: (x + 6)(x + 5)

x^2+11x+30

Simplify the expression: (4x^2 - 3x + 1) - (3x^2 - 5x + 4)

x^2+2x-3

Write the quotient using positive exponents: x^5 / x^2

x^3

Find the product: (x + 2)(x^2 -- 2x + 4)

x^3+8

Write the quotient, using positive exponents: x^8/x^2

x^6

Write the product: x^3(x^5)

x^8