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3 years ago

The expression: Can you explain how to factor out the 1/3 from 2 in detail I am having trouble.

SAT

1 answer:

slava [35]3 years ago

6 0

Answer:

Explanation:

If you multiply (x - k)(x + k), you get $x^{2} + k*x - k*x - k^{2}$ which is equal to $x^{2} -k^{2}$ . Now you can see that $\frac{1}{3} *x^{2} - 2$ must be equal to $\frac{1}{3}*(x^{2} - k^{2})$ which is equal to $\frac{1}{3}*x^{2} - \frac{1}{3}*k^{2}$ . Now we just need to solve $2 = \frac{1}{3}*k^{2}$ . The final answer is $k = +- \sqrt{6}$ .

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Based on Section 3, covered means:

Contact [7]

I think it’s c if not a

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3 years ago

Complete the following steps to calculate the altitude of the parallelogram using area methods. The area of the sheet of paper i

stiks02 [169]

Based on the calculations, we have the following:

The area of the sheet of paper is 96 square inches.
The combined area of the triangle cutouts is equal to 36 square inches.
The area of the parallelogram is equal to 60 square inches.
The altitude of the parallelogram is equal to 6.51 square inches.

<u>Given the following data:</u>

Dimension of paper = 12-inch by 8-inch.

<h3>How to calculate the paper's area.</h3>

Mathematically, the area of the paper is given by this formula:

$Area = length \times breadth\\\\Area = 12 \times 8$

Area = 96 square inches.

<u>For the four (4) right triangles:</u>

Dimension 1 = 2 inches by 9 inches.

Dimension 2 = 3 inches by 6 inches.

Therefore, the combined area of the triangle cutouts is given by:

$A_2= (2 \times \frac{1}{2} \times 2 \times 9) + 2 \times \frac{1}{2} \times 3 \times 6\\\\A_2=18+18\\\\A_2=36\;in^2$

<h3>The area of the parallelogram.</h3>

This would be determined by subtracting the area of the four (4) right triangles from the areas of the paper as follows:

$P = A_p -A_2\\\\P=96-36$

P = 60 square inches.

<h3>The altitude of the parallelogram.</h3>

$P = base \times altitude\\\\Altitude =\frac{P}{base} \\\\Altitude =\frac{60}{9.22}$

Altitude = 6.51 square inches.

Read more on parallelogram here: brainly.com/question/4459854

<u>Complete Question:</u>

A parallelogram is cut out of a 12-inch by 8-inch sheet of paper. There are four right triangle remnants. Two have the dimensions 2 inches by 9 inches, and the other two have the dimensions 3 inches by 6 inches. The resulting parallelogram has a base of approximately 9.22 inches.

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2 years ago

Read 2 more answers

Which notes do we say "ta, ti-ti" for?

vovangra [49]

Answer:

In the general rhythm counting system, you say “ta” for quarter notes and “ti ti” for eighth notes.

Explanation:

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4 years ago

Which function will have the steepest graph? y = –2x y = x y = x y = x.

pychu [463]

Answer:

y = 5/2x

Explanation:

I took the test

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3 years ago

Read 2 more answers

In casting experiments performed using a certain alloy.

jeyben [28]

Answer:
A) Cm = 2.232 s/mm²
B) Time taken to solidify = 74.3 seconds
Explanation:
(A) Since a side is 50mm and all sides of a cube are equal, thus, Volume of the cube is;V = 50 x 50 x 50 = 125,000 mm³
There are 6 faces of the cube, thus Surface Area A = 6 x (50 x 50) = 15,000 mm²
So, Volume/Area = (V/A) = 125,000/15,000 = 8.333 mm
Cm is given by the formula; Cm =[Tts] /(V/A)² where Tts is time taken to solidify and it's 155 seconds in the question. Thus;
Cm = 155/(8.333)²= 2.232 s/mm²
(B) For;Cylindrical casting with D = 30 mm and L = 50 mm.;
Volume of cylinder is;
V = (πD²L) /4
So,V = (π x 30² x 50)/4 = 35,343mm³
Surface area of cylinder is;
A = (2πD²)/4 + (πDL)
Thus, A = ((π x 30²)/2) + (π x 30 x 50) = 6126 mm²
Volume/Area is;
V/A = 35,343/6126 = 5.77 mm
Same alloy and mold type was hsed as in a above, thus, Cm is still 2.232 s/mm²
Since Cm =[Tts] /(V/A)²
Making Tts the subject, we have;
Tts =Cm x (V/A)²
Tts = 2.232 x (5.77)² = 74.3 seconds

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2 years ago