Question 1

Solve the problem.
-The area of a circle of radius r is given by the polynomialal $$\pi r ^ { 2 },$$ , where π is an irrational number. Use 3.14 as an approximation of $\pi ,$ and find the area of a circle with radius 7 cm.

Accepted Answer

The area of a circle is calculated using the formula $A = \pi r^2$. Substituting $\pi = 3.14$ and $r = 7$ cm, we get $A = 3.14 \times 7^2 = 3.14 \times 49 = 153.86 \mathrm{cm}^2$.

Question 2

Give the degree of the polynomial and identify its leading coefficient.
-$21 x y z + 18 x ^ { 2 } z - 10 y ^ { 2 } z ^ { 3 } + 2 x y - x ^ { 2 } y ^ { 2 } z ^ { 2 }$

Accepted Answer

The degree of a polynomial is the highest sum of the exponents of the variables in any term of the polynomial. For the given polynomial, the term with the highest degree is $-x^2y^2z^2$, which has a degree of 6 (since $2+2+2=6$). The leading coefficient of this term, and thus of the polynomial, is -1.

Question 3

Solve the problem.
-The number of different committees of 2 students where the 2 students are selected from a group of n students is given by $c ( n ) = \frac { 1 } { 2 } \left( n ^ { 2 } - n \right)$ n). How many different committees of 2 students can be selected from a group of 10
Students?

Accepted Answer

The formula for the number of different committees of 2 students from a group of n students is $c(n) = \frac{1}{2}(n^2 - n)$. Substituting $n = 10$, we get $c(10) = \frac{1}{2}(10^2 - 10) = \frac{1}{2}(100 - 10) = \frac{1}{2}(90) = 45$.

Question 4

Solve the problem.
-The distance in feet it takes a car traveling at x mph to come to a full stop after hitting the brakes is given by $1.28 \mathrm { x } ^ { 2 } + 0.056 \mathrm { x }$ Find the stopping distance for a speed of 40 mph. Round to the nearest foot.

Accepted Answer

Substitute x = 40 into the formula: $1.28(40)^2 + 0.056(40)$. This equals 2048 + 2.24 = 2050.24, which rounds to 2050 ft.

Question 5

Evaluate the polynomial function at the given value.
-Find P(0.2)if P(x)= $0.2 x ^ { 2 }$ - 4.2x + 2.7

Accepted Answer

To find P(0.2), substitute x = 0.2 into the polynomial: P(0.2) = $0.2(0.2)^2 - 4.2(0.2) + 2.7 = 0.2(0.04) - 0.84 + 2.7 = 0.008 - 0.84 + 2.7 = 1.868$.

Question 6

Solve the problem.
-When a coin is dropped from a cliff of height 1800 feet, the height h of the coin from the ground (in feet)t seconds after being dropped is given by h = $- 16 t ^ { 2 }$ + 1800. How high is the coin above the ground 9 seconds
After being dropped?

Accepted Answer

To find the height of the coin above the ground 9 seconds after being dropped, substitute $t = 9$ into the equation $h = -16t^2 + 1800$. This gives $h = -16(9)^2 + 1800 = -16(81) + 1800 = -1296 + 1800 = 504$ feet.

Question 7

Evaluate the polynomial function at the given value.
-Find P(4)if P(x)= $x ^ { 2 } + 2 x + 4$

Accepted Answer

The answer of Evaluate the polynomial function at the given...

Question 8

Evaluate the polynomial function at the given value.
-Findd P( $P ( - 5 ) \text { if } P ( x ) = 2 x ^ { 2 } - 9 x - 6$

Accepted Answer

The answer of Evaluate the polynomial function at the given...

Question 9

Evaluate the polynomial function at the given value.
-$\text { Find } \mathrm { P } \left( \frac { 1 } { 2 } \right) \text { if } \mathrm { P } ( \mathrm { x } ) = - 2 \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 7$

Accepted Answer

The answer of Evaluate the polynomial function at the given...

Question 10

Give the degree of the polynomial and identify its leading coefficient.
-$$\frac { 8 } { 15 } m ^ { 3 } n ^ { 2 } p ^ { 4 } - m ^ { 6 } p ^ { 2 } - \frac { 5 } { 13 } m n ^ { 3 } p ^ { 6 }$$

Accepted Answer

The answer of Give the degree of the polynomial and...

Question 11

Solve the problem.
-The position of an object moving in a straight line is given by $\mathrm { s } = 11 \mathrm { t } ^ { 2 } - 7 \mathrm { t },$ where s is in where s is in meters and t is the time in seconds the object has been in motion. How far will an object move in 15 seconds?

Accepted Answer

To find the distance the object moves in 15 seconds, substitute $ t = 15 $ into the equation $ s = 11t^2 - 7t $. This gives $ s = 11(15)^2 - 7(15) = 11(225) - 105 = 2475 - 105 = 2370 $ meters.

Question 12

Solve the problem.
-The volume of a sphere is a function of its radius, r, where $\mathrm { V } ( \mathrm { r } ) = \frac { 4 } { 3 } \pi \mathrm { r } ^ { 3 }$ . Find the volume of a sphere if its radius is 7 inches. Use 3.14 as an approximation to the value of π. Round to the nearest tenth if necessary.

Accepted Answer

The answer of Solve the problem.
-The volume of a sphere...

Question 13

Evaluate the polynomial function at the given value.
-Find P(-2)if P(x)= -9x - 8.

Accepted Answer

The answer of Evaluate the polynomial function at the given...

Question 14

Solve the problem.
-The number of ways that the first-, second-, and third-place winners in a singing competition can be selected from n finalists is given by $P ( n ) = n ^ { 3 } - 3 n ^ { 2 } + 2 n$ . If there are6 finalists, how many ways can the first-, second-,
And third-place winners be selected?

Accepted Answer

The formula for the number of ways to select the first, second, and third-place winners is $P(n) = n^3 - 3n^2 + 2n$. Substituting $n = 6$, we get $P(6) = 6^3 - 3(6)^2 + 2(6) = 216 - 108 + 12 = 120$.

Question 15

Evaluate the polynomial function at the given value.
-Find P(-1)if P(x)= $x ^ { 2 } + 8$

Accepted Answer

To find P(-1), substitute x = -1 into the polynomial: P(-1) = (-1)^2 + 8 = 1 + 8 = 9.

Question 16

Evaluate the polynomial function at the given value.
-Find P(-2)if P(x)= $8 x ^ { 2 } - 2 x$

Accepted Answer

The answer of Evaluate the polynomial function at the given...

Question 17

Give the degree of the polynomial and identify its leading coefficient.
-$- 9 x ^ { 4 } - 7 w ^ { 3 } + 2 w - 4 y ^ { 5 } + 4$

Accepted Answer

The degree of a polynomial is the highest power of the variable in the polynomial, which in this case is 5 (from the term $-4y^5$). The leading coefficient is the coefficient of the term with the highest degree, which is -4.

Question 18

Give the degree of the polynomial and identify its leading coefficient.
-$3 q ^ { 2 } r ^ { 2 } + r s ^ { 3 } + 15 q r ^ { 3 } s$

Accepted Answer

The answer of Give the degree of the polynomial and...

Question 19

Solve the problem.
-The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is given by the polynomial equation C(x)= 0.6x + 27,000. Find the cost of producing 90,000 jars.

Accepted Answer

To find the cost of producing 90,000 jars, we need to substitute x = 90,000 into the equation C(x) = 0.6x + 27,000:
C(90,000) = 0.6(90,000) + 27,000
C(90,000) = 54,000 + 27,000
C(90,000) = 81,000
Therefore, the cost of producing 90,000 jars is $81,000, which corresponds to choice C. To find the cost of producing 90,000 jars, we need to substitute x=90,000 in the given equation:
C(90,000) = 0.6(90,000) + 27,000
C(90,000) = 54,000 + 27,000
C(90,000) = 81,000
Therefore, the cost of producing 90,000 jars is $81,000. The correct choice is (C).

Question 20

Solve the problem.
-The volume of a cube is a function of its side, s, where $$V ( s ) = s ^ { 3 }$$ . Find the volume of a cube if its side is 9 centimeters.

Accepted Answer

The volume of a cube is found by cubing the length of one side, so $V(s) = s^3 = 9^3 = 729 \, \text{cm}^3$.

Quiz 5: Polynomials and Polynomial Functions

Solve the problem. -The area of a circle of radius r is given by the polynomialal $\pi r ^ { 2 },$ , where π is an irrational number. Use 3.14 as an approximation of $\pi ,$ and find the area of a circle with radius 7 cm.

Give the degree of the polynomial and identify its leading coefficient. - $21 x y z + 18 x ^ { 2 } z - 10 y ^ { 2 } z ^ { 3 } + 2 x y - x ^ { 2 } y ^ { 2 } z ^ { 2 }$

Solve the problem. -The number of different committees of 2 students where the 2 students are selected from a group of n students is given by $c ( n ) = \frac { 1 } { 2 } \left( n ^ { 2 } - n \right)$ n) . How many different committees of 2 students can be selected from a group of 10 Students?

Solve the problem. -The distance in feet it takes a car traveling at x mph to come to a full stop after hitting the brakes is given by $1.28 \mathrm { x } ^ { 2 } + 0.056 \mathrm { x }$ Find the stopping distance for a speed of 40 mph. Round to the nearest foot.

Evaluate the polynomial function at the given value. -Find P(0.2) if P(x) = $0.2 x ^ { 2 }$ - 4.2x + 2.7

Solve the problem. -When a coin is dropped from a cliff of height 1800 feet, the height h of the coin from the ground (in feet) t seconds after being dropped is given by h = $- 16 t ^ { 2 }$ + 1800. How high is the coin above the ground 9 seconds After being dropped?

Evaluate the polynomial function at the given value. -Find P(4) if P(x) = $x ^ { 2 } + 2 x + 4$

Evaluate the polynomial function at the given value. -Findd P( $P ( - 5 ) \text { if } P ( x ) = 2 x ^ { 2 } - 9 x - 6$

Evaluate the polynomial function at the given value. - $\text { Find } \mathrm { P } \left( \frac { 1 } { 2 } \right) \text { if } \mathrm { P } ( \mathrm { x } ) = - 2 \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 7$

Give the degree of the polynomial and identify its leading coefficient. - $\frac { 8 } { 15 } m ^ { 3 } n ^ { 2 } p ^ { 4 } - m ^ { 6 } p ^ { 2 } - \frac { 5 } { 13 } m n ^ { 3 } p ^ { 6 }$

Solve the problem. -The position of an object moving in a straight line is given by $\mathrm { s } = 11 \mathrm { t } ^ { 2 } - 7 \mathrm { t },$ where s is in where s is in meters and t is the time in seconds the object has been in motion. How far will an object move in 15 seconds?

Evaluate the polynomial function at the given value. -Find P(-2) if P(x) = -9x - 8.

Evaluate the polynomial function at the given value. -Find P(-1) if P(x) = $x ^ { 2 } + 8$

Evaluate the polynomial function at the given value. -Find P(-2) if P(x) = $8 x ^ { 2 } - 2 x$

Give the degree of the polynomial and identify its leading coefficient. - $- 9 x ^ { 4 } - 7 w ^ { 3 } + 2 w - 4 y ^ { 5 } + 4$

Give the degree of the polynomial and identify its leading coefficient. - $3 q ^ { 2 } r ^ { 2 } + r s ^ { 3 } + 15 q r ^ { 3 } s$

Solve the problem. -The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is given by the polynomial equation C(x) = 0.6x + 27,000. Find the cost of producing 90,000 jars.

Solve the problem. -The volume of a cube is a function of its side, s, where $V ( s ) = s ^ { 3 }$ . Find the volume of a cube if its side is 9 centimeters.

Quiz 5: Polynomials and Polynomial Functions

Solve the problem. -The area of a circle of radius r is given by the polynomialal πr2,\pi r ^ { 2 },πr2, , where π is an irrational number. Use 3.14 as an approximation of π,\pi ,π, and find the area of a circle with radius 7 cm.

Give the degree of the polynomial and identify its leading coefficient. - 21xyz+18x2z−10y2z3+2xy−x2y2z221 x y z + 18 x ^ { 2 } z - 10 y ^ { 2 } z ^ { 3 } + 2 x y - x ^ { 2 } y ^ { 2 } z ^ { 2 }21xyz+18x2z−10y2z3+2xy−x2y2z2

Solve the problem. -The distance in feet it takes a car traveling at x mph to come to a full stop after hitting the brakes is given by 1.28x2+0.056x1.28 \mathrm { x } ^ { 2 } + 0.056 \mathrm { x }1.28x2+0.056x Find the stopping distance for a speed of 40 mph. Round to the nearest foot.

Evaluate the polynomial function at the given value. -Find P(0.2) if P(x) = 0.2x20.2 x ^ { 2 }0.2x2 - 4.2x + 2.7

Solve the problem. -When a coin is dropped from a cliff of height 1800 feet, the height h of the coin from the ground (in feet) t seconds after being dropped is given by h = −16t2- 16 t ^ { 2 }−16t2 + 1800. How high is the coin above the ground 9 seconds After being dropped?

Evaluate the polynomial function at the given value. -Find P(4) if P(x) = x2+2x+4x ^ { 2 } + 2 x + 4x2+2x+4

Evaluate the polynomial function at the given value. -Findd P( P(−5) if P(x) =2x2−9x−6P ( - 5 ) \text { if } P ( x ) = 2 x ^ { 2 } - 9 x - 6P(−5) if P(x) =2x2−9x−6

Evaluate the polynomial function at the given value. - Find P(12) if P(x) =−2x2+5x+7\text { Find } \mathrm { P } \left( \frac { 1 } { 2 } \right) \text { if } \mathrm { P } ( \mathrm { x } ) = - 2 \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 7 Find P(21​) if P(x) =−2x2+5x+7

Give the degree of the polynomial and identify its leading coefficient. - 815m3n2p4−m6p2−513mn3p6\frac { 8 } { 15 } m ^ { 3 } n ^ { 2 } p ^ { 4 } - m ^ { 6 } p ^ { 2 } - \frac { 5 } { 13 } m n ^ { 3 } p ^ { 6 }158​m3n2p4−m6p2−135​mn3p6

Evaluate the polynomial function at the given value. -Find P(-2) if P(x) = -9x - 8.

Evaluate the polynomial function at the given value. -Find P(-1) if P(x) = x2+8x ^ { 2 } + 8x2+8

Evaluate the polynomial function at the given value. -Find P(-2) if P(x) = 8x2−2x8 x ^ { 2 } - 2 x8x2−2x

Give the degree of the polynomial and identify its leading coefficient. - −9x4−7w3+2w−4y5+4- 9 x ^ { 4 } - 7 w ^ { 3 } + 2 w - 4 y ^ { 5 } + 4−9x4−7w3+2w−4y5+4

Give the degree of the polynomial and identify its leading coefficient. - 3q2r2+rs3+15qr3s3 q ^ { 2 } r ^ { 2 } + r s ^ { 3 } + 15 q r ^ { 3 } s3q2r2+rs3+15qr3s

Solve the problem. -The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is given by the polynomial equation C(x) = 0.6x + 27,000. Find the cost of producing 90,000 jars.

Solve the problem. -The volume of a cube is a function of its side, s, where V(s) =s3V ( s ) = s ^ { 3 }V(s) =s3 . Find the volume of a cube if its side is 9 centimeters.

Solve the problem. -The area of a circle of radius r is given by the polynomialal $\pi r ^ { 2 },$ , where π is an irrational number. Use 3.14 as an approximation of $\pi ,$ and find the area of a circle with radius 7 cm.

Give the degree of the polynomial and identify its leading coefficient. - $21 x y z + 18 x ^ { 2 } z - 10 y ^ { 2 } z ^ { 3 } + 2 x y - x ^ { 2 } y ^ { 2 } z ^ { 2 }$

Solve the problem. -The distance in feet it takes a car traveling at x mph to come to a full stop after hitting the brakes is given by $1.28 \mathrm { x } ^ { 2 } + 0.056 \mathrm { x }$ Find the stopping distance for a speed of 40 mph. Round to the nearest foot.

Evaluate the polynomial function at the given value. -Find P(0.2) if P(x) = $0.2 x ^ { 2 }$ - 4.2x + 2.7

Solve the problem. -When a coin is dropped from a cliff of height 1800 feet, the height h of the coin from the ground (in feet) t seconds after being dropped is given by h = $- 16 t ^ { 2 }$ + 1800. How high is the coin above the ground 9 seconds After being dropped?

Evaluate the polynomial function at the given value. -Find P(4) if P(x) = $x ^ { 2 } + 2 x + 4$

Evaluate the polynomial function at the given value. -Findd P( $P ( - 5 ) \text { if } P ( x ) = 2 x ^ { 2 } - 9 x - 6$

Evaluate the polynomial function at the given value. - $\text { Find } \mathrm { P } \left( \frac { 1 } { 2 } \right) \text { if } \mathrm { P } ( \mathrm { x } ) = - 2 \mathrm { x } ^ { 2 } + 5 \mathrm { x } + 7$

Give the degree of the polynomial and identify its leading coefficient. - $\frac { 8 } { 15 } m ^ { 3 } n ^ { 2 } p ^ { 4 } - m ^ { 6 } p ^ { 2 } - \frac { 5 } { 13 } m n ^ { 3 } p ^ { 6 }$

Evaluate the polynomial function at the given value. -Find P(-1) if P(x) = $x ^ { 2 } + 8$

Evaluate the polynomial function at the given value. -Find P(-2) if P(x) = $8 x ^ { 2 } - 2 x$

Give the degree of the polynomial and identify its leading coefficient. - $- 9 x ^ { 4 } - 7 w ^ { 3 } + 2 w - 4 y ^ { 5 } + 4$

Give the degree of the polynomial and identify its leading coefficient. - $3 q ^ { 2 } r ^ { 2 } + r s ^ { 3 } + 15 q r ^ { 3 } s$

Solve the problem. -The volume of a cube is a function of its side, s, where $V ( s ) = s ^ { 3 }$ . Find the volume of a cube if its side is 9 centimeters.