The rate traveled from Amarillo to Austin by a bus averages 65 miles per hour. The bus arrived in Austin after eight hours of travel. An automobile averages 80 miles per hour. Using the inverse variation relationship, show what the time would be for the automobile to complete the trip.

Answers

Answer 1

Answer: If it takes 8 hours for a bus with an average velocity of 65mph to travel from Amarillo to Austin then,
d = 65 (8) = 520 miles

The distance from Amarillo to Austin (or vice versa) is 520 miles.

If the function to get the distance traveled by the automobile is given by:
d(x) = 80 t
Then, the inverse variation relationship would be
d-1(x) = t = d / 80
Since d = 520
t = 520 / 80
t = 6.5 hours

It takes 6.5 hours for the automobile to complete the trip

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Since slope is calculated using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction, the slope of both lines is equivalent to ________. It is given that the lines are parallel, and we calculated that the slopes are the same. Therefore, parallel lines have the same slopes.
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the glee club has 120 cupcakes to sell. they have decided to arrange the cupcakes in the shape of a rectangle, such that the rows have an even number of cupcakes and the columns have an odd number of cupcakes. How many arrangements of cupcakes can they create? Explain.

Can someone help me out with this question ( giving brainliest)

Answers

Answer:

0.6

Step-by-step explanation:

the reason is because there are 5 different colors of marbles in the bag. it specifically says that each color has the same number of marbles for each color. so that would mean that there is 20% of each color of marble from the bag. its asking for three of the 5 colors. which means you would have a 60% chance of getting one of the colored marbles. which is were i got .6 from

Answer:

option d is a correct answer.....

A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?

Answers

Answer: The co-ordinates of the center are (-7, -1) and length of the radius is 6 units.

Step-by-step explanation: The given equation of a circle is as follows :

$x^2+y^2+14x+2y+14=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the co-ordinates of the center and the length of the radius of the circle.

We know that

the standard equation of a circle with center at the point (h, k) and radius r units is given by

$(x-h)^2+(y-k)^2=r^2.$

From equation (i), we have

$x^2+y^2+14x+2y+14=0\n\n\Rightarrow (x^2+14x+49)+(y^2+2y+1)+14-49-1=0\n\n\Rightarrow (x+7)^2+(y+1)^2-36=0\n\n\Rightarrow (x+7)^2+(y+1)^2=36\n\n\Rightarrow (x-(-7))^2+(y-(-1))^2=6^2.$

Comparing with the standard equation, we get

the co-ordinates of the center, (h, k) = (-7, -1)

and

length of the radius, r = 6 units.

Thus, the co-ordinates of the center are (-7, -1) and length of the radius is 6 units.

(-7, -1), 6 units Is The Answer

Factor completely 12x^5 6x^3 8x^2

Answers

the answer is: 2x^2(6x^3+3x+4)

Write these values in order, starting with the smallest.
0.2
1/2
2%

Answers

Step-by-step explanation:

In this case we need to arrange the given number in a order starting with the smallest.

First number is 0.2

Second number is 1/2

Third number is 2%

Firstly, we need to convert these number in same form i.e. decimal form.

1/2 can be written as 0.5

2% can be written as $(2)/(100)=0.02$

Now, it is required to arrange these number from smallest to largest. So,

0.02 is the smallest number and 0.5 is the largest number.

Order is : 0.02, 0.2, 0.5

Choose the number that is equal to: 2/3 divided by (-3) A.)-2 B.) -2/9 C.)2/9 D.) 2

Answers

Answer

B

Explanation
Dividing by -3 is same as multiplying by -1/3. Multiply those two fractions to get -2/9

The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form.The bigger square is x+3 on all 3 sides.
The smaller square is x on every side.

Answers

Given:
Big square: side length = x + 3
Small square: side length = x

Area of a square = a² where a represents the side length.

Area of big square = (x+3)²
A = (x+3)(x+3)
A = x(x+3) + 3(x+3)
A = x² + 3x + 3x + 9
A = x² + 6x + 9

Area of small square = x²

Total Area = Area of Big square + Area of Small square
Total Area = x² + 6x + 9 + x²
Total Area = 2x² + 6x + 9

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