You are traveling down the interstate averaging 50 mph. How much time has passed when you have traveled 120 miles

Ray Cupple bought a basic car costing $26,500.00, with options costing $725.00. There is a 6% sales tax in his state and a combi

Alenkinab [10]

Given:
cost: 26,500
option: 725
total 27,225
tax (27,225 * 6%) 1,633.50
total 28,858.50
license & reg. fee 50.00
total cost 28,908.50 Choice D.

5 0

3 years ago

Read 2 more answers

Taylor buys nail polish from a shop that cost $3.95 each. She has a maximum of $30 to spend on nail polish purchases. The total

kati45 [8]

Answer:

$C_t=3.95x,\ 0\leq x\leq 7$

Step-by-step explanation:

Modeling With Functions

It's a common practice to try to mathematically represent the relation between two or more variables. It allows us to better understand the behavior of the phenomena being observed and, more importantly, to be able to predict future values.

The specific situation stated in the question relates how Taylor buys nail polish for $3.95 each, with a maximum of $30 to spend. If x is the number of nail polish purchased, then the total cost will be

$C_t=3.95x$

But we know Taylor has a limited budget of $30, so the total cost cannot exceed that amount

$3.95x\leq 30$

Solving the inequality for x

$x\leq 30/3.95$

$x\leq 7.6$

We round down to

$x\leq 7$

Of course, the lower limit of x is 0, because Taylor cannot purchase negative quantities of nail polish

Our model is now complete if the state the limits of x, or its domain

$\boxed{C_t=3.95x,\ 0\leq x\leq 7}$

3 0

3 years ago

Given f(x)=3x^3+2x+k and x+1 is a factor of f(x) then what is the value of k

yaroslaw [1]

Answer:

k = 5

Step-by-step explanation:

Given that (x + 1) is a factor of f(x) then f(- 1) = 0

f(- 1) = 3(- 1)³ + 2(- 1) + k

= 3(- 1) - 2 + k

= - 3 - 2 + k

= - 5 + k

Then - 5 + k = 0 ( add 5 to both sides )

k = 5

3 0

3 years ago

Find the length of the segment AB if points A and B are the intersection points of the parabolas with equations y=−x^2+9 and y=2

11Alexandr11 [23.1K]

Answer:

The length of the segment AB is √48

Step-by-step explanation:

Given the two equations, the idea is to find the solution to the system

y = x² + 9

y = 2x² - 3

you can use the equality method to find the "x" and "y" of the solution.

x² + 9 = 2x² - 3 ⇒ x² - 2x² = -3 - 9 ⇒ -x² = -12 ⇒ x² = 12 ⇒ x = ±√12.

With this value we return to the original equations and replace it to find "y" values.

y = (±√12)² + 9 ⇒ y = 21

The solutions to the system are (-√12, 21) and (√12, 21). Now you need to find the distance between this points.

d= √[(x2-x1)² + (y2-y1)²] ⇒ d = √48.

The length of the segment AB is √48.

6 0

4 years ago

One 8.3 ounce can of Red Bull contains energy in two forms: 27 grams of sugar and 80 milligrams of caffeine. One 23.5 ounce can

bulgar [2K]

Answer:

41) 2 Red Bull and 1 Jolt Cola

42) 1 Red Bull and 3 Jolt Cola

43) 2 Red Bull and 2 Jolt Cola

44) 3 Red Bull and 4 Jolt Cola

Determine the number of cans of each drink that when combined will contain 403 grams sugar and 1200 milligrams caffeine: 1 Red Bull and 4 Jolt Cola

Step-by-step explanation:

Let X be the cans of Red Bull.

Let Y be the cans of Jolt Cola.

41)

One can of Red Bull has 27g of sugar. One can of Jolt cola has 94g of sugar. So we have the equation:

X(27)+Y(94)=148...(1)

One can of Red Bull has 80mg of caffeine. One can of Jolt cola has 280mg of caffeine. So we have the equation:

X(80)+Y(280)=440...(2)

We find the answear by solving the system of equations:

27X+94Y=148...(1)

80X+280Y=440...(2)

Solving the system:

27X+94Y=148...(1)

27X=148-94Y

X=148/27 -(94/27)Y

Substituting X in (2)

80X+280Y=440...(2)

80[148/27 -(94/27)Y]+280Y=440

(11840/27)-(7520/27)Y+280Y=440

(11840/27)+(40/27)Y=440

(40/27)Y=440-(11840/27)

(40/27)Y=40/27

Y=1

Substituting Y in (1)

27X+94Y=148...(1)

27X+94(1)=148

27X+94=148

27X=148-94

X=54/27

X=2

So we need 2 cans of Red Bull and 1 of Jolt Cola to get 148g of sugar and 440mg of caffeine.

42) Following the same steps we have:

27X+94Y=309...(1)

80X+280Y=920...(2)

Solving the system:

27X+94Y=309...(1)

27X=309-94Y

X=309/27 -(94/27)Y

Substituting X in (2)

80X+280Y=920...(2)

80[309/27 -(94/27)Y]+280Y=920

(24720/27)-(7520/27)Y+280Y=920

(24720/27)+(40/27)Y=920

(40/27)Y=920-(24720/27)

(40/27)Y=40/9

Y=3

Substituting Y in (1)

27X+94Y=309...(1)

27X+94(3)=309

27X+282=309

27X=27

X=1

So we need 1 can of Red Bull and 3 of Jolt Cola to get 309g of sugar and 920mg of caffeine.

43) Following the same steps we have:

27X+94Y=242...(1)

80X+280Y=720...(2)

Solving the system:

27X+94Y=242...(1)

27X=242-94Y

X=242/27 -(94/27)Y

Substituting X in (2)

80X+280Y=720...(2)

80[242/27 -(94/27)Y]+280Y=720

(19360/27)-(7520/27)Y+280Y=720

(19360/27)+(40/27)Y=720

(40/27)Y=720-(19360/27)

(40/27)Y=80/27

Y=2

Substituting Y in (1)

27X+94(2)=242...(1)

27X+188=242

27X=54

X=2

So we need 2 can of Red Bull and 2 of Jolt Cola to get 242g of sugar and 720mg of caffeine.

43) Following the same steps we have:

27X+94Y=457...(1)

80X+280Y=1360...(2)

Solving the system:

27X+94Y=457...(1)

27X=457-94Y

X=457/27 -(94/27)Y

Substituting X in (2)

80X+280Y=1360...(2)

80[457/27 -(94/27)Y]+280Y=1360

(36560/27)-(7520/27)Y+280Y=1360

(36560/27)+(40/27)Y=1360

(40/27)Y=1360-36560/27

(40/27)Y=160/27

Y=4

Substituting Y in (1)

27X+94Y=457...(1)

27X+94(4)=457

27X+376=457

X=3

So we need 3 cans of Red Bull and 4 of Jolt Cola to get 457g of sugar and 1360mg of caffeine.

Determine the number of cans of each drink that when combined will contain 403 grams sugar and 1200 milligrams caffeine

Following the same steps we have:

27X+94Y=403...(1)

80X+280Y=1200...(2)

Solving the system:

27X+94Y=403...(1)

27X=403-94Y

X=403/27 -(94/27)Y

Substituting X in (2)

80X+280Y=1200...(2)

80[403/27 -(94/27)Y]+280Y=1200

(32240/27)-(7520/27)Y+280Y=1200

(32240/27)+(40/27)Y=1200

(40/27)Y=1200-(32240/27)

(40/27)Y=160/27

Y=4

Substituting Y in (1)

27X+94Y=403...(1)

27X+94(4)=403

27X=-94(4)+403

X=1

So we need 1 can of Red Bull and 4 of Jolt Cola to get 403g of sugar and 1200mg of caffeine.

4 0

4 years ago