Find the slope of the line that passes through points (2,8) and (1,3)

2/3 to the fourth power

Stella [2.4K]

The correct answer is 16/81. Hope this helps.

5 0

3 years ago

Read 2 more answers

Determine whether the lines are parallel, perpendicular, or neither. <br> x = 3<br> and y = 4

Katyanochek1 [597]

I think they’re perpendicular lines

5 0

3 years ago

Maria drove to a business appointment at 50mph in the morning. Her average speed on the return trip in the afternoon was 40 mph.

MakcuM [25]

Answer:

Distance to appointment point = 5 miles

Step-by-step explanation:

Let s be the distance to the appointment point,

We have Maria drove to a business appointment at 50mph in the morning.

Time taken in the morning

$t_m=\frac{s}{50}=0.02s$

Her average speed on the return trip in the afternoon was 40 mph.

Time taken in the afternoon

$t_a=\frac{s}{40}=0.025s$

Given that the return trip took 1/4hr longer because of traffic.

That is

$t_a-t_m=\frac{1}{4}hr=0.025hr$

Substituting

$t_a-t_m=0.025hr\\\\0.025s-0.02s=0.025\\\\s=5miles$

Distance to appointment point = 5 miles

7 0

3 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

3 years ago

After four years in college, Josie owes $21000 in student loans. The interest rate on the federal loans is 3% and the rate on th

klasskru [66]

Answer:

$104.27 is the amount at 3% and $20895.73 is the amount at 4.4%

Step-by-step explanation:

We are given that Josie owes $21000 in student loans.

Let x be principal at 3% rate of interest

Time = 1 year

Formula: $A=P(1+r)^t$

$A=x(1+0.03)^1$

A=1.03x

Interest = Amount - Principal

Interest = 1.03x-x=0.03x

So, (21000-x) is the principal at 4.4% rate of interest

Formula: $A=P(1+r)^t$

$A=(21000-x)(1+\frac{4.4}{100})^1$

A=21924-1.044x

Interest = 21924-1.044x-21000-x=924-2.044x

The total interest she owes for one year was $714.00

So, 0.03x+924-2.044x=714

x=104.27

So, $104.27 is the amount at 3%

The principal at 4.4% rate of interest =21000-x=21000-104.27=20895.73

Hence $104.27 is the amount at 3% and $20895.73 is the amount at 4.4%

7 0

2 years ago