MATHEMATICS HIGH SCHOOL

I need help with number 19 please!

Answers

Answer 1

Answer:

Answer:

center: (4, 3)
radius: 5

Step-by-step explanation:

A graphing calculator can help you see the center is (4, 3) and the diameter is 10, so the radius is 5.

_____

Or, you can rearrange the equation to standard form by completing the squares.

x² -8x + y² -6y = 0 . . . . . subtract 6y, group terms

(x² -8x +16) +(y² -6y +9) = 16 +9 . . . . . complete the squares by adding the squares of half the coefficient of the linear term: (-8/2)²=16, (-6/2)²=9.

(x -4)² + (y -3)² = 25 . . . . . rewrite in standard form

Compare this to ...

(x -h)² + (y -k)² = r²

and recognize the center (h, k) is (4, 3), and the radius is √25 = 5.

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If a man can run p miles in x minutes, how long will it take him to run q miles at the samerate?

Answers

d = p*x = q*t => t = (p*x)/q;

Answer: it wouk take him x minutes because it said at the SAME rate.

Step-by-step explanation:

Solve h = −16t2 + 36t + 4.

Answers

I can do each of the things I asked above.
So, let's change this into vertex form:
$h=-16t^2+36t+4$
$h=(-16t^2+36t)+4$
$h=-16(t^2-2.25t)+4$
$h=-16(t^2-2.25t+1.27-1.27)+4$
$h=-16(t^2-2.25t+1.27)+20.32+4$
$h=-16(t-1.125)^2+24.32$
The vertex is at (1.125,24.32)
Answers may vary due to rounding

Factored Form:
$h = -16t^2 + 36t + 4$
$h = -4\left(4t^2-9t-1\right)$

Quadratic Formula:
$x = (-b +/- √(b^2-4(a)(c)))/(2a)$
h = -16t^2 + 36t + 4
a = -16 b = 36 c = 4
$h = (-(36) +/- √((36)^2-4(-16)(4)))/(2(-16))$
$h = (-36 +/- √(1552))/(-32)$
$h = ≈-0.11$
$h = ≈2.36$

Find the product.

(7q - 5)(7q + 5)

Answers

(7q−5)(7q+5) =(7q+−5)(7q+5) =(7q)(7q)+(7q)(5)+(−5)(7q)+(−5)(5) =49q2+35q−35q−25 =49q2−25

At what times of the day between 10:00 A.M. and 5:00 P.M. do the chemistry presentation and the recycling presentation start at the same time? SCIENCE MUSEUM
-Show Schedule-
Chemistry-Every 10 minutes
Electricity-Every 20 minutes
Recycling-Every 6 minutes
Fossils-Every 45 minutes

The first showing for all shows is at 10:00 A.M.

Answers

Okay, Chemistry runs every 10 minutes and the Recycling runs every 6 minutes. In order to find what time they both start at the same time you must find the lowest common multiple (if you are using mathematical terminology). To do this the long but visual way you can write out each of the times and find the first ones that are the same.
Chemistry: 10:00 10:10 10:20 10:30
Recycling: 10:00 10:06 10:12 10:18 10:24 10:30
As you can see both Chemistry and Recycling both have a LCM of 10:30 which tells us that the time for which both Chemistry and Recycling start at the same time during the show is 10:30AM.

Final answer:

The chemistry and recycling presentations coincide every 30 minutes starting from 10:00 A.M. They will occur at the same time at 10:30 A.M., 11:00 A.M., 11:30 A.M., etc., until 5:00 P.M.

Explanation:

To solve this problem, we need to find the common multiple of 10 and 6, which is the frequency in minutes of the chemistry and recycling presentations respectively. The least common multiple (LCM) of 10 and 6 is 30. So, the chemistry and recycling presentations will coincide every 30 minutes.

Starting at 10:00 A.M., they would coincide at 10:30 A.M., 11:00 A.M., 11:30 A.M., and continue in this pattern until 5:00 P.M.

Learn more about least common multiple here:

brainly.com/question/34291727

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David's car could cover one lap of the Indy 500 in about 90 seconds. Chris' car could cover one lap in about 54 seconds. If both cars left the same starting point at the same time, after how many seconds would they meet again at the starting point?

Answers

After 270 seconds, both cars will meet again at the startingpoint.

To find the time at which both cars meet again at the starting point, we need to find the least common multiple (LCM) of their lap times. The LCM is the smallest positive integer that is divisible by both lap times.

David's car lap time = 90 seconds

Chris' car lap time = 54 seconds

Now, let's calculate the LCM:

Find the prime factors of each lap time:

90 = 2 × 3² × 5

54 = 2 × 3³

Take the highest power of each prime factor:

LCM = 2 × 3³ × 5

= 2 × 27 × 5

= 270 seconds

So, after 270 seconds, both cars will meet again at the startingpoint.

To learn more on Number system click: