Math Module 8

A company distributes its product by train and by truck. The cost of distributing by train can be modeled as −0.06x^2 + 32x − 100, and the cost of distributing by truck can be modeled as −0.04x^2 + 26x − 170, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck.

-0.02x^2+6x+70

A company distributes its product by train and by truck. The cost of distributing by train can be modeled as −0.07x2 + 34x − 140, and the cost of distributing by truck can be modeled as −0.03x2 + 29x − 150, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck.

-0.04x^2+5x+10

Simplify (-5)^-3

-1/125

subtract (z^4+5z^2-2z)-(z^2+3z^4-z-6)

-2z^4+4z^2-z+6

simplify 5h^5*(-6h^2)

-30h^7

simplify (-2)^6*(-2)^3

-512

Simplify 9y^4*(-7y^7)

-63y^11

Write the expression using only positive exponent. Assume no denominator equals zero. -8z^-2

-8/z^2

Express in decimal notation 7.64*10^-4

0.000764

Express in decimal notation 1.31*10^-3

0.00131

A moving-van rental company uses the polynomial 84 + 0.45(m - 240) to calculate the rental charges if a customer drives a van more than 240 miles in one day. In the polynomial, m is the total number of miles that the customer drove the van during the day. Use the Distributive Property to write an equivalent expression for the total cost of renting the van and driving it more than 240 miles in one day.

0.45-24

Simplify 8^0

1

Write the product in scientific notation. (2.94×10^4)(3.5×10^5)

1.029*10^10

Order the list of numbers from least to greatest 3.6 × 10^19 , 1.3 × 10^8 , 6.2 × 10^8 ,5.1 × 10^10 , 7.7 × 10^19

1.3 × 10^8, 6.2 × 10^8, 5.1 × 10^10,3.6 × 10^19, 7.7 × 10^19

Order the list of numbers from least to greatest. 8.8 × 1021 , 6.2 × 102 , 2.8 × 1021 ,1.5 × 102 , 5.1 × 1012

1.5 × 10^2, 6.2 × 10^2, 5.1 × 10^12, 2.8 × 10^21, 8.8 × 10^21

The length of a piece of microfilm is 5^-3 inches. Evaluate this expression.

1/125

Simplify 4^-1

1/4

Write the expression using only positive exponents. Assume no denominator equals zero.(−2x ^3y^4 )^−2

1/4x^6*y^8

Simplify (-5)^-4

1/625

Simplify 4^-3

1/64

Evaluate the expression 3c −2 d −4 for c = 3 and d = 4.

1/768

simplify 3^-2

1/9

Write the expression using only positive exponents. Assume no denominator equals zero. (a^4b)^-2

1/a^8b^2

Write the expression using only positive exponents. Assume no denominator equals zero. m^-6

1/m^6

Simplify m^-6/n^7*c^0

1/m^6n^7

Write the expression as a single power using only positive exponents, if possible. Assume no denominator equals zero. x^-6/x^4

1/x^10

Simplify. Write the expression using only positive exponents. x^2(x^4)^-5 Assume no denominator equals zero.

1/x^18

Simplify. Write the expression using only positive exponents. (x^5)^-6*x^4 Assume no denominator equals zero.

1/x^26

Find the volume of a pyramid. length: 18 width: 13 height: 15

1170

Simplify (5x^2*y^4*z)^3

125x^6*y^12*z^3

Simplify 6^5/6

1296

Find the surface area of the cylinder formed by the net. radius: 4 height: 1.5

138.16

Simplify (4/p)^4(4q^4/3p)^-2 Assume no denominator equals zero.

144/p^2q^8

Simplify (4x^3*y^5)(-6xy^5)^2

144x^5*y^15

Find the surface area of the sphere. radius: 3.5

153.86

Simplify 6u^2 v + 17uv + 9u^2 v − 5uv + 5

15u^2v+12uv+5

Find the surface area of the right cone. radius: 13 height: 28

1673.62

Add (9j^3−j^2+9)+(7j^3−4j−7)

16j^3−j^2−4j+2

Divide. Write the quotient as a power. 17^10/17^8

17^2

19^6*19

19^7

Formula for the volume of a pyramid

1wh/3

Formula for surface area of a cylinder

2*3.14*r^2+2*3.14*rh

Simplify (1.05 × 10^14 ) ÷ (5 × 10^4 ) and write the answer in scientific notation.

2.1*10^9

There are 3.76 × 10^22 atoms in 1 gram of oxygen. How many atoms are there in 700 grams of oxygen? Write your answer in scientific notation. If necessary, round your answer to two decimal places.

2.63*10^25

Find the volume of the sphere. radius: 17

20,569.1

Find the surface area of the sphere. Use 3.14 for π. Round your answer to the nearest tenth. radius: 8

201

Simplify 16^7*17^2

216

Find the surface area of the square pyramid. base: 7 height: 12

217

Find the surface area of the prism. length: 6 width: 3 height: 12

252

Simplify (−4) ∙ (−4)^3

256

Find the volume of a sphere with a radius of 8.6 cm. Use 3.14 for π. Round your answer to the nearest tenth.

2663

SImplify (2/3)^-3

27/8

Add (20mn + 5n) + (7mn − 2n + 3n).

27mn+6n

Simplify (3x^7/x^3*y^3)^3

27x^12/y^9

formula for surface area of a rectangular prism

2lw+2lh+2wh

Express in decimal notation 3.69*10^6

3,690,000

formula for the volume of a cone

3.14*r^2*h/3

formula for surface area of a cone

3.14*r^2+3.14*rl

The planet Mercury has an average distance from the sun of about 36,000,000 miles. Write this number in scientific notation.

3.6*10^7

Find the surface area of the right cone. radius: 6 height: 10

301.4

Simplify 6(5p^3 − 6p)

30p^3-36p

Find the volume of the sphere. Use 3.14 for π. Round your answer to the nearest tenth. radius: 5

314

Add (28a^2 − 10) + (5a^2 − 2b + 6)

33a^2-2b-4

Find the surface area of the prism formed by the net. length: 15 width: 7 height: 3

342

Write the expression as a single power, if possible. 3^2*3*3^4

3^7

Evaluate (−2)^2

4

formula for surface area of a sphere

4*3.14*r^2

Evaluate the following and express the result in scientific notation 0.025*16,000

4.0*10^2

There are 6.02 × 1023 atoms in 1 gram of hydrogen. How many atoms are there in 800 grams of hydrogen? Write your answer in scientific notation. If necessary, round your answer to the nearest hundredth.

4.82*10^26

Evaluate the following and express the result in scientific notation. 0.005*0.99

4.95*10^-3

Write the expression using only positive exponents. Assume no denominator equals zero. 4y^-2

4/y^2

Find the surface area of the right cone. radius: 6 height: 16

414.48

Find the surface area of the prism formed by the net. length: 8 width: 5 hight: 13

418

Find the surface area of a square pyramid where the length of a side of the base is 10 cm and the slant height of the pyramid is 16 cm.

420

Find the surface area of the cylinder. radius: 3 height: 20

433.32

Find the surface area of the prism. length: 8 width: 4 height: 16

448

Find the volume of the cone. radius: 5 height: 18

471

Write the expression as a single power, if possible 4^2 · 4^5 · 4

4^8

Subtract (5.9xy − 3y) − (1.9xy − y)

4xy-2y

Add. (3y^6-y+4)+(y^6-5)

4y^6-y-1

Simplify −z^2 − 3 + 6z^4 + 8z^2 − 2z^4

4z^4 + 7z^2 − 3

Which of the following represents 0.0000054 in scientific notation?

5.4*10^-6

Find the surface area of the cylinder.term-25 radius: 5 height: 11

502.4

Identify the like terms. 4x^5+5x^2+4+4y^4+4x^2

5x^2, 4x^2

Find the degree of the polynomial −7b^4 + 4b − 5b^6

6

Simplify (4/5)^-4

625/256

Simplify. Write the expression using only positive exponents. (-5b^-2)^4 Assume no denominator equals zero.

625/b^8

Simplify (x^4*y^3)(-5xy^3)^4

625x^8*y^15

Write the expression using only positive exponents. Assume no denominator equals zero. (8a^7/7b^4)^2

64a^14/49b^8

Write the expression using only positive exponents. Assume no denominator equals zero. (v^2/4w)^-3

64w^3/v^6

Simplify (4x^9/x^5*y^5)^3

64x^12/y^15

Write the number 6.54 × 107 in standard notation.

65,400,000

Add. (2t^3−7t^2+8)+(4t^3−2t−1)

6t^3-7t^2-2t+7

find the degree of the polynomial -2y^7+3-7y^3

7

Find the surface area of the cylinder formed by the net. radius: 7 height: 11

791.28

Simplify (2/4)^-3

8

Simplify (8.1 × 10^15 ) ÷ (1 × 10^8 ) and write the answer in scientific notation.

8.1*10^7

Write in scientific notation 0.00084

8.4*10^-4

Find the volume of a sphere with a diameter of 11.6 m. Use 3.14 for π. Round your answer to the nearest tenth.

816.9

Subtract. (9c^5 − c^4 ) − (c^5 + 3c^4 − 1)

8c^5-4c^4+1

Subtract (10a^4 − a) − (a^4 + 2a − 2)

9a^4 − 3a + 2

8.30.3

Adding and Subtracting Polynomials

8.29.4

An Application of Exponents: Scientific Notation, Part 2

8.29.3

An Application of exponents: Scientific Notation Part 1

8.28.3

Integer Exponents Part 1

8.28.4

Integer Exponents Part 2

8.30.1

Introduction to Polynomials

8.28.1

Product and Power Properties of Exponents Part 1

8.28.2

Product and Power Properties of Exponents Part 2

8.28.5

Properties of Exponents Quiz

8.27.5

Quiz Volume and Surface area

8.29.5

Quiz: Exponents & Scientific Notation

8.30.4

Quiz: Introduction to Polynomials

8.29.1

Quotient Properties of Exponents Part 1

8.29.2

Quotient Properties of Exponents Part 2

8.30.2

Simplifying Polynomials

8.27.2

Surface Area of Prisms and Cylinders

8.27.3

Surface Area of Pyramids and Cones

Compare the volume and surface area of a sphere with a radius of 2 cm with that of a cube that has sides measuring 3.22 cm.

The volume of the sphere is approximately equal to the volume of the cube, but the cube has a greater surface area.

Compare the volume and surface area of a sphere with a radius of 4 m with that of a cube that has sides measuring 6.45 m.

The volume of the sphere is approximately equal to the volume of the cube, but the cube has a greater surface area.

8.27.4

Volume and surface area of spheres

8.27.1

Volume of Pyramids and Cones

formula for surface area of a pyramid

b+1/2*3.14

Classify the expression as a monomial, a binomial, a trinomial, or not a polynomial. 8g^5 − 9s^2

binomial

Classify the expression by the number of terms. 5x^6-x^4

binomial

Divide. Write the quotient as a power. 5^10/6^8

can not combine because the two powers are not the same

True or false? The expression is a monomial. 8x^2*y^-1

false One of the exponents in the expression is a negative integer; therefore, the expression is not a monomial.

Write the expression as a single power if possible. (f^2)^4(f^3)^6

m^18

simplify (m^6)^3term-70

m^18

Determine whether the expression is a monomial 3 1/3*x^3*y^6

monomial

Determine whether the expression is a monomial. 1 2/3*c^4*d^x

not a monomial

Simplify. Assume no denominator equals zero. 8^0*t^6*wu^6/t^2*w^4*u^6

t^4/w^3

Classify the expression as a monomial, a binomial, a trinomial, or not a polynomial 2b^3 − 8s^4 + 6z

trinomial

find the volume of the pyramid length: 19 width: 11 hight: 28

volume: 1950.7

find the volume of the pyramid length: 8 width: 7 hight: 21

volume: 196

find the volume of the pyramid length: 3.5 width: 5 hight: 10

volume: 58.3

find the volume of the cone radius: 18 hight: 10

volume: 847.8

find the volume of the cone radius: 3 hight: 10

volume: 94.2

Write the expression using only positive exponents. Assume no denominator equals zero. (x^5*y^2)^2

x^13/y^3

Subtract (b^4−8b^2+6b)−(9b^4−4b^3+4b^2+8b)

−8b^4+4b^3−12b^2−2b