MATHEMATICS HIGH SCHOOL

Y = –2r +4 complete the missing value in the solution to the equation
(_,-2)

Answers

Answer 1

Answer:

Answer:

(3, -2)

Step-by-step explanation:

Answer 2

Answer:

Answer:

Step-by-step explanation:

(x, y) (__,-2)

-2 = -2r + 4

-2-4 = -2r

-6 = -2r

divide -2r on both sides

r=3 ---> x=3

(3,-2)

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A round barbecue pit is 2 meters in diameter. What is the distance around the barbecue pit? A. 3.14 meters
B. 12. 56 meters
C. 6.28 meters
D. 18.84 meters

Answers

The length of a circle is equal to 2π * diameter/2, where π = ~3.14. In our case we have 2*(~3.14) = 6.28 meters. So the correct answer is C.

Is the line description for x+3y=1 slanted downwards?

Answers

Yes it is (and instead of saying downwards, it's clearer to say that as the x value increases, y decrease).
If you chance the formula into y = mx +b form, you get y = -1/3 + 1/3, and since m, or the slope, is negative, the line will decrease from right to left across the graph

Answer: yes, it is

Step-by-step explanation:

8 4/9 + 5 3/8 = Please explain.

Answers

Ok, so first of all... You've got to get the same numerator. What's a number that 9 and 8 both share? Hmm... How about 72? So then, 9 would be multiplied by 8 and 8 by 9. And so do the denominators. So, your new fraction would be : 8 32/72 + 5 27/72 which equals 13 59/72 The addition part is actually pretty easy. Just add the whole numbers like a normal addition problem and add the denominators to the denominators and the numerator stays the same. Your final answer should be 13 59/72. Hope this helped!

Find the common denominators within the fractions. So take 4/9 and times the top and bottom by 8 to get 32/72 and 5/8 and times top and bottom by 9 so 45/72. So you will then have 8 32/72 + 5 45/72. Then plus them together. 13 77/72 which equals 14 5/72.

Tina Cole is a certified financial adviser. She purchased equipment for her office for $8,843. The trade-in value of the equipment is estimated to be $450 after 7 years of use. Using the straight-line method, what is the annual depreciation to the nearest cent?

Answers

Straight - line method allows the determination of the annual depreciation by dividing the total reduction in property value by the number of years. In the given above, The total depreciation of the value is $8,393. Dividing this value by 7 years gives $1,199/year.

Therefore, the annual depreciation is $1,199.0

Answer:

$1,199 per year.

Step-by-step explanation:

Tina Cole is a certified financial adviser.

She purchased equipment for her office costs = $8,843

After 7 years of use the trade-in value of the equipment is estimated = $450

Total depreciation in 7 years = 8,843 - 450 = $8,393

We have to calculate the annual depreciation using the straight-line method.

So we divide $8,393 by 7

$8,393 ÷ 7 = $1,199

The annual depreciation of the equipment is $1,199 per year.

A ball is dropped form a height of 100 inches. The ball bounces, each time reaching a lower and lower height. The height of each bounce is 75% of the previous bounce. What height will the ball reach after bouncing four times? How many bounces does it take for the ball to reach a height of less than one inch?

Answers

After the 'n'th bounce, the ball returns to a maximum height of

   (100) times (0.75)^n .

-- After 4 bounces, the maximum height is (100) (0.75)^4 = 31.64 inches.

-- To look for the maximum height of 1 inch,    (100) (0.75)^x = 1

Let's take the log of each side: log(100) + x log(0.75) = 0

Subtract log(100) from each side: x log(0.75) = -log(100)

Divide each side by log(0.75) :     x = -log(100) / log(0.75).

log(100) = 2 . So ... x = -2 / log(0.75) = -2 / -0.124939 = 16.00785

So the ball returns to a slim hair more than 1 inch high on the 16th bounce,
and returns to definitely less than 1 inch high on the 17th bounce.

75% of a number is as much as 3/4 of the same number, so:

1st bounce: 3/4 * 100 = 75
2nd bounce: 3/4 * 75 = 56,25
3rd bounce: 3/4 * 56,25 = 42,1875
4th bounce: 3/4 * 42,1875 = 31,640625
5th bounce: 3/4 * 31,640625 = 23,73046875
6th bounce: 3/4 * 23,73046875 = 17,7978515625
7th bounce: 3/4 * 17,7978515625 = 13,348388671875
8th bounce: 3/4 * 13,348388671875 = 10,01129150390625
9th bounce: 3/4 * 10,01129150390625 = 7,508468627929688
10th bounce: 3/4 * 7,508468627929688 = 5,631351470947266
11th bounce: 3/4 * 5,631351470947266 = 4,223513603210449
12th bounce: 3/4 * 4,223513603210449 = 3,167635202407837
13th bounce: 3/4 * 3,167635202407837 = 2,375726401805878
14th bounce: 3/4 * 2,375726401805878 = 1,781794801354408
15th bounce: 3/4 * 1,781794801354408 = 1,336346101015806
16th bounce: 3/4 * 1,336346101015806 = 1,002259575761855
17th bounce: 3/4 * 1,002259575761855 = 0,7516946818213909

Answers:

After bouncing four times, the ball will reach a height of 31,640625 inches.
The ball will reach a height of less than one inch after 17 bounces.

PS: I know it's kind of a walk-around, by it still gives us the answer :)

if you are asked to solve a system of equations in which there is no linear equation to start with, you can sometimes begin by isolating and substituting a variable that is squared in both equations.