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2 years ago

WILL GIVE BRAINLIESTAND 5 STARS

Mathematics

2 answers:

Gnesinka [82]2 years ago

4 0

Steps to solve:

$6x^1^0 - 96x^2$

~Apply exponent rule

$6x^8x^2 - 96x^2$

~Rewrite the second half of the expression

$6x^8x^2 - 6 * 16x^2$

~Factor out common term

$6x^2(x^8 - 16)$ (Answer for Part A)

~Factor out whats in parenthesis

$6x^2(x^4)^2 - 4^2$

~Apply the difference of the two squares

$6x^2(x^4 + 4)(x^4 - 4)$

~Factor x^4 + 4

$6x^2(x^2 + 2)(x^2 - 2)(x^4 - 4)$

~Factor x^4 - 4

$6x^2(x^2 + 2x + 2)(x^2 - 2x + 2)(x^2 + 2)(x^2 - 2)$ (Answer for Part B)

Part A: $6x^2(x^8 - 16)$

Part B: $6x^2(x^2 + 2x + 2)(x^2 - 2x + 2)(x^2 + 2)(x^2 - 2)$

Best of Luck!

creativ13 [48]2 years ago

3 0

Answer:

A) 6x²(x⁸ - 16)

B) 6x²(x⁴ + 4)(x² - 2)(x² + 2)

Step-by-step explanation:

6x¹⁰ - 96x²

6x²(x⁸ - 16)

B) 6x²(x⁸ - 16)

6x²[(x⁴)² - 4²]

6x²[(x⁴ - 4)(x⁴ + 4)]

6x²(x⁴ + 4)[(x²)² - 2²]

6x²(x⁴ + 4)(x² - 2)(x² + 2)

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A rectangular swimming pool is to be built with an area of 1800 square feet. The owner wants 5-foot wide decks along either side

FrozenT [24]

The solution would be like this for this specific problem:

A = (l + 20) · (w + 10)

The area of the pool is 1800 square feet and can be computed also like l · w. Then l · w = 1800, and therefore l = 1800 w.

We plug in the values:

A = (1800 / w + 20) · (w + 10) = 1800 + 18000 / w + 20w + 200 = 18000 / w + 20w + 2000

dA /dw = − 18000 / w2 + 20

w = 30

l = 60

Since A = (l + 20) · (w + 10):

A = (60 + 20) · (30+ 10)

A = 3,200

A(x) = 1800 + 2*10(x+10)+ 2*5(1800/x) 
= 1800 + 20x + 200 + 18000/x 
= 2000 + 20 x + 18000/x

20 - 18000/x^2 = 0 
x = sqrt (900) = 30 
Pool length dimension = 1800/x = 60 
Lot dimensions: 80 x 40

I am hoping that these answers have satisfied your queries and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.

8 0

2 years ago

A garden supply store sells two types of lawn mowers. Total ales of mowers for the year were $8379.70. The total number of mower

Anestetic [448]

Answer:

The number of small mowers are 19 and the large mowers are 11.

Step-by-step explanation:

Given:

A garden supply store sells two types of lawn mowers. Total sales of mowers for the year were $8379.70. The total number of mowers sold the 30. The small mower cost $249.99 and the large mower costs $329.99.

Now, to find the number of each type of mower sold.

Let the number of small mower be $x.$

And the number of large mower be $y.$

So, total number of mowers are:

$x+y=30$

$x=30-y\ \ \ ....(1)$

Now, the total sales of mowers are:

$249.99(x)+329.99(y)=8379.70$

Substituting the value of $x$ from equation (1) we get:

$249.99(30-y)+329.99y=8379.70$

$7499.7-249.99y+329.99y=8379.70$

$7499.7+80y=8379.70$

Subtracting both sides by 7499.7 we get:

$80y=880$

Dividing both sides by 80 we get:

$y=11.$

The number of large mower = 11.

Now, to get the number of small mowers we substitute the value of $y$ in equation ( 1 ):

$x=30-y\\x=30-11\\x=19.$

The number of small mower = 19.

Therefore, the number of small mowers are 19 and the large mowers are 11.

6 0

2 years ago

Tickets to a school dance are sold for $10 each. The student council spent a total of $400 on set-up costs for the dance. The sc

svlad2 [7]

Answer:

P(t) = 10t - 400

Step-by-step explanation:

Selling price of each ticket = $10

Cost of setting up the dance= $400

Profit = Revenue - cost

Revenue = price × quantity

Revenue that will maximize profit = 10t

where t= quantity of tickets that maximises profits

Cost = $400

Profit(t) = Revenue - cost

P(t)= 10t - 400

8 0

2 years ago

In triangle FGH, FG = 12.3 cm, GH = 10.6 cm, Measure of angle G = 80 degrees, and Measure of angle H = 55 degrees. If Triangle A

aalyn [17]

Question:

In triangle FGH, FG = 12.3 cm, GH = 10.6 cm, m angle G=80 degrees, and m angle H=55 degrees. If triangle ABC GHF, which statement is true?

(A) AB = 12.3 cm

(B) AB = 10.6 cm

(D) m∠C = 80°

Answer:

Option B:

AB = 10.6 cm

Solution:

The image of the triangle is attached below.

In ΔFGH,

FG = 12.3 cm, GH = 10.6 cm, m∠G = 80° and m∠H = 55°

Option A: AB = 12.3 cm

Given ΔGHF $\sim$ ΔABC.

Corresponding parts of congruence triangles are congruent.

GH = AB = 10.6 cm

So, option A is not true.

Option B: AB = 10.6 cm

Already proved in option A that AB = 10.6 cm

So, option B is true.

Option C: m∠C = 55°

ΔGHF $\sim$ ΔABC

Corresponding parts of congruence triangles are congruent.

m∠G = m∠A = 80°

m∠H = m∠B = 55°

Sum of the angles of a triangle = 180°

⇒ m∠A + m∠B + m∠C = 180°

⇒ 80° + 55° + m∠C = 180°

⇒ m∠C = 180° – 80° – 55°

⇒ m∠C = 45°

So, option C is not true.

Option D: m∠C = 80°

Already proved in option C that m∠C = 45°.

So, option D is not true.

Hence option B is the true statement that AB = 10.6 cm.

7 0

2 years ago

Read 2 more answers

Help pls help plz help plz

ratelena [41]

Answer:

Step-by-step explanation:

(4+8)+6 = (6+4)+n

18 = 10+n

18-10 = n

n = 8

7 0

2 years ago

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