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faust18 [17]
3 years ago
5

Which statement about g(x) = x^2 - 576 is true?

Mathematics
1 answer:
Zina [86]3 years ago
7 0

Answer:

The second option.

Step-by-step explanation:

Let's see if this will work.

(x+24)(x-24)

Let's open the brackets

x^2 - 24x +24x - 576

= x^2 - 576

Please give brainliest

I hope you understand. If you don't. Please, leave a comment below.

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What is 4 1/3 × 2 3/5? express it in lowest terms​
soldier1979 [14.2K]

We have,

4\dfrac{1}{3}\cdot2\dfrac{3}{5}=\dfrac{13}{3}\cdot\dfrac{13}{5}=\dfrac{13\cdot13}{3\cdot5}=\dfrac{169}{15}=\boxed{11.2\bar{6}}

To express periodic number calculated we use:

x=11.2\bar{6}\\10x = 112.\bar{6}\\100x=1126.\bar{6}\\90x=100x-10x\Longrightarrow90x=1126.\bar6-112.\bar6\\90x=1014\\x=\dfrac{1014}{90}=\boxed{11\dfrac{24}{90}}

Hope this helps.

r3t40

3 0
3 years ago
Proving Pythagorean Theorem
MrRissso [65]

Answer:

45

Step-by-step explanation:

{a}^{2}  +  {b}^{2}  =  {c}^{2}

ssubstitute a and b for any of the numbers (3 or 6) and get 36+9 which is 45

45 =

{c}^{2}

so you would need to find the square root to get c

4 0
2 years ago
Calculus Problem
Roman55 [17]

The two parabolas intersect for

8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2

and so the base of each solid is the set

B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, |x^2-(8-x^2)| = 2|x^2-4|. But since -2 ≤ x ≤ 2, this reduces to 2(x^2-4).

a. Square cross sections will contribute a volume of

\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x

where ∆x is the thickness of the section. Then the volume would be

\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x

We end up with the same integral as before except for the leading constant:

\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx

Using the result of part (a), the volume is

\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x

and using the result of part (a) again, the volume is

\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}

7 0
2 years ago
I have two bags of counters.
STatiana [176]

Answer:

a. 4/21

b. 4/7

Step-by-step explanation:

Please kindly check the attached files for explanation.

8 0
3 years ago
Read 2 more answers
Find the midpoint of the segment with the following endpoints.<br> (2,9) and (8,1)
vazorg [7]

Answer:

\displaystyle (5,5)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right<u> </u>

<u>Algebra I</u>

  • Coordinates (x, y)
  • Midpoint Formula: \displaystyle (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Step-by-step explanation:

<u>Step 1: Define</u>

Point (2, 9)

Point (8, 1)

<u>Step 2: Identify</u>

(2, 9) → x₁ = 2, y₁ = 9

(8, 1) → x₂ = 8, y₂ = 1

<u>Step 3: Find Midpoint</u>

Simply plug in your coordinates into the midpoint formula to find midpoint

  1. Substitute in points [Midpoint Formula]:                                                         \displaystyle (\frac{2+8}{2},\frac{9+1}{2})
  2. [Fractions] Add:                                                                                                  \displaystyle (\frac{10}{2},\frac{10}{2})
  3. [Fractions] Divide:                                                                                              \displaystyle (5,5)
7 0
3 years ago
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