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Assoli18 [71]
3 years ago
7

[Quick Answer Needed] Which of the following shows the extraneous solution to the logarithmic equation?

Mathematics
1 answer:
Nitella [24]3 years ago
6 0

Answer:

C

Step-by-step explanation:

Given the logarithmic equation

\log_4x+\log_4(x-3)=\log_4(-7x+21)

First, notice that

x>0\\ \\x-3>0\Rightarrow x>3\\ \\-7x+21>0\Rightarrow 7x

So, there is no possible solutions, all possible solutions will be extraneous.

Solve the equation:

\log_4x+\log_4(x-3)=\log_4x(x-3),

then

\log_4x(x-3)=\log_4(-7x+21)\\ \\x(x-3)=-7x+21\\ \\x^2-3x+7x-21=0\\ \\x^2+4x-21=0\\ \\D=4^2-4\cdot 1\cdot (-21)=16+84=100\\ \\x_{1,2}=\dfrac{-4\pm 10}{2}=-7,\ 3

Hence, x=3 and x=-7 are extraneous solutions

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Find the prime factorizations foor the following numbers 36 and 84
Varvara68 [4.7K]
Answer:

36 = 2² * 3²
84 = 2² * 3 * 7


Explanation:

Pf of 36 = 2 * 2 * 3 * 3 which then becomes 2 (to the power of 2) times 3 (to the power of 2)

Pf of 84 = 2 * 2 * 3 * 7 which then becomes 2 (to the power of 2) * 3 * 7

If this helps it would be greatly appreciated if you thanked me.
6 0
3 years ago
CAN SOMEONE PLEASE HELP!!!!!!!
AveGali [126]

Answer:

-11

Step-by-step explanation:

Add all the negative numbers.

Hope this helps!

4 0
3 years ago
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What is the vertex of y=-3x^2+6x+15? Help is much appreciated.
DENIUS [597]

Answer:

<u>(1, 18)</u>

Step-by-step explanation:

Rewrite the equation in vertex form by completing the square for -3x^2 + 6x + 15. This = -3(x - 1)^2 + 18.

Set y equal to the new right side.

y = -3(x - 1)

Use the vertex form, y = a(x - h)^2 + k, to determine the values of a, h, and k.

a = -3

h = 1

k = 18

Vertex = (h, k) / (1, 18)

5 0
3 years ago
Gina is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 12 inches by 14 1/4 inc
Fittoniya [83]

Answer:

278.63 square inches

Step-by-step explanation:

Gina needs to cut two types of rectangles.

Dimensions of one rectangle is given as,

Width = 12 inches

Length = 14\frac{1}{4} = \frac{57}{4} inches

So, the area of this rectangular paper will be

Area = width × length = 12\times \frac{57}{4} = 171 inches²

Dimensions of the other rectangular paper has been given as

Width = 10\frac{1}{4} = \frac{41}{4} inches

Length = 10\frac{1}{2} = \frac{21}{2} inches

So, the area of this rectangle will be

Area = width × length = \frac{41}{4} \times \frac{21}{2} = 107.63 inches²

Thus the total area she need to cut = 171 + 107.63 = 278.63 square inches.

6 0
3 years ago
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Por favor alguien me puede ayudar con esto
Gnoma [55]
No entiendo....................
7 0
3 years ago
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