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2 years ago

Determine the solution set of (x - 4)2 = 12.

1 answer:

3 0

(x-4)2=12
First, you want to divide both sides by 2 to eliminate the 2 outside of the parenthesis. That leaves you with:
(x-4)=6
Then add four to both sides to eliminate the four inside the parenthesis:
x=10

To check work, substitute ten in for x in the original equation:
(10-4)2=12
(6)2=12
12=12, so this is correct :)

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If the width of the rectangle is three times the length and the perimeter of the rectangle is 72 ft, what are the length and wid

goblinko [34]

W=3L
W+W+L+L=72
Replace W with 3L: 3L+3L+L+L=72
8L=72
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8 0

2 years ago

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 5 − x 2 . What are the dimensions

kherson [118]

Answer:

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola

y=5−x^2. What are the dimensions of such a rectangle with the greatest possible area?

Width =

Height =

Width =√10 and Height $= \frac{10}{4}$

Step-by-step explanation:

Let the coordinates of the vertices of the rectangle which lie on the given parabola y = 5 - x² ........ (1)

are (h,k) and (-h,k).

Hence, the area of the rectangle will be (h + h) × k

Therefore, A = h²k ..... (2).

Now, from equation (1) we can write k = 5 - h² ....... (3)

So, from equation (2), we can write

$A =h^{2} [5-h^{2} ]=5h^{2} -h^{4}$

For, A to be greatest ,

$\frac{dA}{dh} =0 = 10h-4h^{3}$

⇒ $h[10-4h^{2} ]=0$

⇒ $h^{2} =\frac{10}{4} {Since, h≠ 0}$

⇒ $h = ±\frac{\sqrt{10} }{2}$

Therefore, from equation (3), k = 5 - h²

⇒ $k=5-\frac{10}{4} =\frac{10}{4}$

Hence,

Width = 2h =√10 and

Height = $k =\frac{10}{4}.$

8 0

2 years ago

2PLSS NEED HELP.........

Nonamiya [84]

Answer:

right

Step-by-step explanation:

The side ratios are ...

24 : 45 : 51 = 8 : 15 : 17

These numbers are a Pythagorean triple. The triangle is a right triangle.

24² + 45² = 576 +2025 = 2601 = 51² . . . . the Pythagorean theorem is satisfied

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1 year ago

paula and ricardo are serving cupcakes at a school party. if they arrange the cupcakes in groups of 2,3,4,5 or 6, they always ha

slega [8]

Find the smallest number that is divisible by 2, 3, 4, 5, 6 and add 1.
We need the least common multiple of 2, 3, 4, 5, 6.

2 = 2
3 = 3
4 = 2^2
5 = 5
6 = 2 * 3

LCM = product of common and not common prime factors with larger exponent.

LCM = 2^2 * 3 * 5 = 4 * 3 * 5 = 60

To always have a remainder of 1, you need of add 1 to 60.

The number is 61.

Check:
61/2 = 30 remainder 1
61/3 = 20 remainder 1
61/4 = 15 remainder 1
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3 years ago

There are 3 red and 8 green balls in a bag. If you randomly choose balls one at a time, with replacement, what is the probabilit

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I dont think is right so dont use it so use 8

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2 years ago

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