The time required for a trip of a certain distance in a car varies indirectly as the rate the car travels. A trip took 18 hours traveling at 50 miles per hour. How long would this trip take if the car was traveling at 75 miles per hour?

Answer:

We are given

We are also given  and , which allows us to rewrite the equation as

(I substituted every "b" with "a" and every "c" with "9").

The solutions to this quadratic equation are -25 and 7. We discard -25 because a side with negative length would make no sense.

The required measure of side a of the rectangular prism is a = 9.3 meters.

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

Here,
SA = 2ab + 2bc + 2ac
434 = 2a² + 14a + 14a
434 = 2a² + 28a
2a² + 28a - 434 = 0
a² + 14a - 217 = 0
a² + 14a + 49 - 49 - 217 = 0
(a + 7)² = 266
a = 9.3 or a = -23.3

Since the negative measure of length can be neglected.
a = 9.3 = b

Thus, the required measure of side a of the rectangular prism is a = 9.3 meters.

Learn more about the surface area here: https://brainly.com/question/2835293

#SPJ5

Step-by-step explanation:

y - 3 = 16y original problem

y - 3 - y = 16y - y grouping variables

-3 = 15y Simplification

-3÷15 = 15y÷15 Isolating the variable

-1/5 = y the answer

I hope this helps!!!!!!

Answer:

£36

Step-by-step explanation:

3kg = 54

÷ 3

1kg = 18

18 × 2 = 36

hope this helps...

9514 1404 393

Answer:

  Paul is using 1 grid = 100%; Rebecca is using 2 grids = 100%

Step-by-step explanation:

We assume that a full grid and half of another are shaded.

If 1 grid is taken to be 100%, then the total amount shaded is 100% +50% = 150%, as Paul says.

__

If the two full grids are taken to be 100%, then the full shaded grid is 50% of the total, and the additional half-shaded grid is 25% of the total. That makes a total of 50% +25% = 75% of the total being shaded, as Rebecca says.

Answer:

D

Step-by-step explanation:

Answer: 20.77%

Step-by-step explanation:

There are 52 cards in a standard deck. Out of these cards, there are 12 face cards. Thus, the probability of drawing a face is 12/52.

On a 20-sided dice, there are 20 options of numbers to roll. Out of these 20 numbers, 18 of the numbers are greater than or equal to 3, making the probability 18/20, or 9/10.

To find the probability of two events, you need to multiply the probabilities together. Thus, you need to multiply 12/52 by 9/10.

(12/52) * (9/10) = 27/130

27/130 is about equal to 0.2077, or a 20.77% probability.

Answer:

The answer for the dropdown section in x section is 5 and the answer for the dropdown section in the y section is 75

Step-by-step explanation:

Answer:

2 Pumpkins / 15 Dollars

5 Pumpkins / 37.5 Dollars

10 Pumpkins / 75 Dollars

Step-by-step explanation:

2 pumpkins for 15 dollars

that is what we have to work with here

the first step would probably be to figure out how much one pumpkin is, so we should divide the amount that we spent by the amount of pumkins that we got, which would look like

15 / 2 = 7.5

so 1 pumpkin = 7.5 dollars

now, to figure out how many pumpkins you can buy with 37.5 dollars, you would divide the amount of money spent by the amount that each pumpkin costs, which turns out to be

37.5 / 7.5 = 5

Now, to figure out how much money you would need for 10 pumpkins, you would multiply the number of pumpkins by the cost of a single pumpkin, which ends up being

10 x 7.5 = 75

Answer:

7pie

Step-by-step explanation:

Answer:

Exact Form:

17/30

Decimal Form:

0.56

Step-by-step explanation:

Answer:

0.56 i think

Step-by-step explanation:

Answer:

C. and D.

Step-by-step explanation:

C.) Angle sum property, as XY = ZY

Answer:

136 ounces

Step-by-step explanation:

8.5*16=136

So 136 ounces

Answer:

Data collected shows that the more you water, the larger your plant will grow. If you use the following Equation, y = 1/2x + 2 How tall will a plant be at 25 weeks if x is the number of weeks watered and y represents the height of the plant? Show your work.

Step-by-step explanation:

Answer:

8x6= (4x6) + (4x6)

= 24+24

= 48

Step-by-step explanation:

Hope this helps :)

Answer:

8×6=48

4×6=24 and 24×2=48

So I'm guessing 4,24,48

Answer:

4 dollars a pound

Step-by-step explanation:

4x 10 = 40

Answer:

17 units

Step-by-step explanation:

just took the quiz

Answer:

17 units.

Step-by-step explanation:

Hope it helps!!!

Answer: The answer is 500 hope this helps!

Step-by-step explanation:

Answer:

A general line is written as:

y = a*x + b

where:

a is the slope

b is the y-intercept.

a) y-intercept = 2 and slope = 7.

This line is:

y = 7*x + 2

b) y-intercept =  -1 and is parallel to y= 5x - 7.

Now, if two linear equations are parallel if they have the same slope and different y-intercept. Then if we want a line parallel to  y= 5x - 7, this means that the slope of this line must also be equal to 5.

y = 5*x + (-1)

c) y-intercept 2 and is inclined at 45° to the x- axis. ​

When we have an inclination of A degrees from the x-axis, the slope of the equation is given by: a = Tan(A)

In this case, we have A = 45°

Then the slope is a = Tan(45°) =  1

Then the equation of this line is:

y = 1*x + 2

Answer:

m = 1

Step-by-step explanation:

We can use the x & y intercepts.

Rise = 2

Run = 2

m = Rise/Run = 2/2 = 1

Answer:

x=5

Step-by-step explanation:

substitute y to the first expression

4x-5(x-6)=25

4x-5x+30=25

-x=25-30

-x=-5

times left and right hand side with minus youll get

x=5

Step-by-step explanation:

Use the compound interest formula:

A = P( 1 + r/n)^nt

A is the amount at the end

P is the principal or original amount.

R is annual rate as a decimal (you have to convert)

N is the # of compounding periods in a year (quarterly means 4)

T is time in years

A = 500( 1 + 0.0475/4)^(4×20)

This would be $1285.64 when fully computed.

Answer:

a) SPAZ is equilateral.

b) Diagonals SA and PZ are perpendicular to each other.

c) Diagonals SA and PZ bisect each other.

Step-by-step explanation:

At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.

a) If figure is equilateral, then SP = PA = AZ = ZS:

[tex]SP = \sqrt{[4-(-4)]^{2}+[(-2)-(-4)]^{2}}[/tex]

[tex]SP \approx 8.246[/tex]

[tex]PA = \sqrt{(6-4)^{2}+[6-(-2)]^{2}}[/tex]

[tex]PA \approx 8.246[/tex]

[tex]AZ =\sqrt{(-2-6)^{2}+(4-6)^{2}}[/tex]

[tex]AZ \approx 8.246[/tex]

[tex]ZS = \sqrt{[-4-(-2)]^{2}+(-4-4)^{2}}[/tex]

[tex]ZS \approx 8.246[/tex]

Therefore, SPAZ is equilateral.

b) We use the slope formula to determine the inclination of diagonals SA and PZ:

[tex]m_{SA} = \frac{6-(-4)}{6-(-4)}[/tex]

[tex]m_{SA} = 1[/tex]

[tex]m_{PZ} = \frac{4-(-2)}{-2-4}[/tex]

[tex]m_{PZ} = -1[/tex]

Since [tex]m_{SA}\cdot m_{PZ} = -1[/tex], diagonals SA and PZ are perpendicular to each other.

c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:

[tex]M_{SA} = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot A(x,y)[/tex]

[tex]M_{SA} = \frac{1}{2}\cdot (-4,-4)+\frac{1}{2}\cdot (6,6)[/tex]

[tex]M_{SA} = (-2,-2)+(3,3)[/tex]

[tex]M_{SA} = (1,1)[/tex]

[tex]M_{PZ} = \frac{1}{2}\cdot P(x,y) + \frac{1}{2}\cdot Z(x,y)[/tex]

[tex]M_{PZ} = \frac{1}{2}\cdot (4,-2)+\frac{1}{2}\cdot (-2,4)[/tex]

[tex]M_{PZ} = (2,-1)+(-1,2)[/tex]

[tex]M_{PZ} = (1,1)[/tex]

Then, the diagonals SA and PZ bisect each other.

Step-by-step explanation:

1.8

8 is 1 decimal place

1./8

8 > 5

1 change to 2

2.0

Answer:

12% increase

Step-by-step explanation:

Divide the difference between the two prices by the original price:

1.05/8.95

= 0.12

So, the percent change is 12%

9514 1404 393

Answer:

  ∠16 = 47°

Step-by-step explanation:

Vertical and corresponding angles are congruent. The remainder are supplementary to those.

∠1≅∠4≅∠5≅∠7≅∠10≅∠12≅∠13≅∠15 = 133°

∠2≅∠3≅∠6≅∠8≅∠9≅∠11≅∠14≅∠16 = 47°

Answer:

its the second one

Step-by-step explanation:

it's the only one where the x number dosent repeat