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kondaur [170]
3 years ago
5

Factor: 3x4y3 – 48y3

Mathematics
1 answer:
kati45 [8]3 years ago
3 0

Answer:

3y3(x2 + 4)(x + 2)(x -2)

Step-by-step explanation:

3x4y3– 48y3.

= 3y3(x4 – 16).

= 3y3[(x2)2 - 42].

= 3y3(x2 + 4)(x2 - 4).

= 3y3(x2 + 4)(x2 - 22).

= 3y3(x2 + 4)(x + 2)(x -2).

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What is the length of ? A. 13 B. 9 C. 81 D. 11
andrew-mc [135]

Answer:

C. 81

Step-by-step explanation:

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3 years ago
2^x+5 = 3^1-x use logarithms to solve the exponential equation. round answer to 3 decimal places.
marysya [2.9K]
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x=\frac{log_23-5}{1+log_23}\\-------------\\log_23\approx1.5849625\\----------------\\x\approx\frac{1.5849625-5}{1+1.5849625}\approx-1.321
8 0
3 years ago
Read 2 more answers
For the parallelogram ABCD the extensions of the angle bisectors AG and BH intersect at point P. Find the area of the parallelog
natita [175]

Answer:

The area of a parallelogram is 360 in.²

Step-by-step explanation:

Where DG = GH

GP = 12 in.

AB = 39 in.

∠DAB + ∠ABC = 180° (Adjacent angles of a parallelogram)

Whereby ∠DAB is bisected by AG and ∠ABC is bisected by BH

Therefore, ∠GAB + ∠HBA = 90°

Hence, ∠BPA = 90° (Sum of interior angles of a triangle)

cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{AP}{39} = \dfrac{GP}{GH} =\dfrac{12}{GH}

We note that ∠AGD = ∠GAB (Alternate angles of parallel lines)

∴ ∠AGD = ∠AGD since ∠AGD = ∠GAB (Bisected angle)

Hence AD = DG (Side length of isosceles triangle)

The bisector of ∠ADG is parallel to BH and will bisect AG at point Q

Hence ΔDAQ  ≅ ΔDGQ ≅ ΔGPH and AQ = QG = GP

Hence, AP = 3 × GP = 3 × 12 = 36

cos(\angle GAB) = \dfrac{AP}{AB} = \dfrac{36}{39}

\angle GAB = cos^{-1} \left (\dfrac{36}{39}  \right )

∠GAB = 22.62°

cos(\angle GAB) =  \dfrac{36}{39} = \dfrac{12}{GH}

GH =  \dfrac{39}{36} \times {12}

GH = 13 in.

∴ AD 13 in.

BP = 39 × sin(22.62°) = 15 in.

GH = √(GP² + HP²)

∠DAB = 2 × 22.62° = 45.24°

The height of the parallelogram = AD × sin(∠DAB) =  13 × sin(45.24°)

The height of the parallelogram = 120/13 =  9.23 in.

The area of a parallelogram = Base × Height = (120/13) × 39 = 360 in.²

7 0
3 years ago
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The reading of a scale at one end is 3.5 cm and at the other end is 18.5 cm. Calculate the lengths of the needle
Bumek [7]

Answer:

15 cm

Step-by-step explanation:

Given that :

Reading at one end, initial reading = 3.5 cm

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6 0
3 years ago
In the system of equations below, which variable would it be easiest to solve for? x + 4 y = 14. 3 x + 2 y = 12 The easiest to s
Murljashka [212]

Answer:

<h2>The easiest to solve for is x in the first equation</h2>

Step-by-step explanation:

Given the system of equation, x + 4 y = 14. and 3 x + 2 y = 12, to solve for x, we can use the elimination method of solving simultaneous equation. We need to get y first.

x + 4 y = 14............ 1 * 3

3 x + 2 y = 12 ............ 2  * 1

Lets eliminate x first. Multiply equation 1 by 3 and subtract from equation 2.

3x + 12 y = 42.

3 x + 2 y = 12

Taking the diffrence;

12-2y =42 - 12

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From equation 1, x = 14-4y

x = 14-4(3)

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x = 2

It can be seen that the easiest way to get the value of x is by using the first equation and we are able to do the substitute easily <u>because the variable x has no coefficient in equation 1 compare to equation 2 </u>as such it will be easier to make the substitute for x in the first equation.

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