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4 years ago

Which expressions are solutions to the equation (3/4)x = 15? Select all that apply.

Mathematics

1 answer:

marshall27 [118]4 years ago

7 0

Answer:

Step-by-step explanation:

(3/4)x=15

x=15 ÷ 3/4

x=20

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If you spin an eight-part spinner numbered from 1 to 8, and flip a coin, what is the probability that you will get a number less

DaniilM [7]

May 1/8 idk if i'm right good luck

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4 years ago

What is the truth value for the following conditional statement? p: true q: false p → q T F → F T F → T F T → T F F → T

Daniel [21]

the answer would be true

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4 years ago

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(5/6)^4x=(36/25)^9-x, please help solve for x, and the 9-x is all superscript

stiks02 [169]

$\frac{36}{25}=\frac{6^2}{5^2}=\left(\frac{6}{5}\right)^2=\left(\frac{5}{6}\right)^{-2}\\\\therefore:\\\\\left(\frac{5}{6}\right)^{4x}=\left[\left(\frac{5}{6}\right)^{-2}\right]^{9-x}\\\\\left(\frac{5}{6}\right)^{4x}=\left(\frac{5}{6}\right)^{-2(9-x)}\iff4x=-2(9-x)\\\\4x=-2\cdot9-2\cdot(-x)\\\\4x=-18+2x\ \ \ \ \ |subtract\ 2x\ from\ both\ sides\\\\2x=-18\ \ \ \ \ \ |divide\ both\ sides\ by\ 2\\\\\boxed{x=-9}$

$Use:\\a^{-n}=\left(\frac{1}{a}\right)^n\\\\\left(a^n\right)^m=a^{n\cdot m}\\\\\left(\frac{a}{b} \right)^n=\frac{a^n}{b^n}$

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3 years ago

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The answer choices are 11 1 2.48 6

Fudgin [204]

Answer:

The ball reached its maximum height of ( $11\ yards$ ) in ( $1\ second$ ).

Step-by-step explanation:

This question is essentially asking one to find the vertex of the parabola formed by the given equation. One could plot the equation, but it would be far more efficient to complete the square. Completing the square of an equation is a process by which a person converts the equation of a parabola from standard form to vertex form.

The first step in completing the square is to group the quadratic and linear term:

$h(t)=-5t^2 + 10t + 6\\\\h(t) = (-5t^2 + 10t) + 6$

Now factor out the coefficient of the quadratic term:

$h(t)=-5(t^2 -2t) + 6$

After doing so, add a constant such that the terms inside the parenthesis form a perfect square, don't forget to balance the equation by adding the inverse of the added constant term:

$h(t) = -5(t^2 -2t) + 6\\\\h(t) = -5(t^2 -2t + 1 -1 ) + 6$

Now take the balancing term out of the parenthesis:

$\\\\h(t)=-5(t^2 -2t + 1) + 6 + ((-1)(-5))$

Simplify:

$h(t) = -5(t^2 -2t + 1) + 6 + 5\\\\h(t) = -5(t-1)^2 + 11$

The x-coordinate of the vertex of the parabola is equal to the additive inverse of the numerical part of the quadratic term. The y-coordinate of the vertex is the constant term outside of the parenthesis. Thus, the vertex of the parabola is:

$(1, 11)$

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3 years ago

There are 90 girls and 60 boys in the sixth grade at a middle school. Of these students, 7 girls and 2 boys write left-handed. W

Radda [10]

Answer:

Step-by-step explanation:

90 + 60 = 150
7 + 2 = 9
Set up a proportion: $\frac{9}{150} = \frac{x}{100}$
Cross multiply, then divide: 9 × 100 = 900, 900 ÷ 150 = 6
So, 6% of students in 6th grade were left-handed

I hope this helps!

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3 years ago

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