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3 years ago

4. Solve the following inequality for b, showing all of your work carefully and completely

Mathematics

1 answer:

spin [16.1K]3 years ago

3 0

Answer:

b > -15

Step-by-step explanation:

4b - 12 - 55 < 9b + 8

Combine terms.

4b - 67 < 9b + 8

Subtract 9b from both sides.

-5b - 67 < 8

Add 67 to both sides.

-5b < 75

Divide both sides by -5. When dividing by a negative, flip the sign.

b > -15.

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Answer:

Step-by-step explanation:

5=k× $\frac{1}{36}$

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3 years ago

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2. There were 35 children and 10 adults at a cookout.

qwelly [4]

Answer:

a.2:7

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c.4:5

hope it helps

Explanation -

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c. as original ratio is 40:50 , we reduce it to 4:5

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If the area of sector AOC is 12π cm² and the measure of the radius is 6 cm, what is the measure of the central angle in radians?

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Answer:

Step-by-step explanation:

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3 years ago

Please help solve for x..

aalyn [17]

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

$x^{100}-4^x \cdot x^{98}-x^2+4^x=0$

Factor out -1:

$\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0$

Divide both sides by -1:

$\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0$

Rearrange the terms:

$\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0$

$\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:$

$\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0$

Factor the first two terms and the last two terms separately:

$\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0$

Factor out the common term $(x^{98}-1)$ :

$\implies (4^x-x^2)(x^{98}-1)=0$

<u>Zero Product Property</u>: If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the <u>Zero Product Property</u>, set each factor equal to zero and solve for x (if possible):

$\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}$

Therefore, the solutions to the given equation are: x = 1 or x = -1

Learn more here:

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