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Marysya12 [62]
2 years ago
6

Factor the following expression. Simplify your answer. 5t( -2t + 3)^2/3 +2( -2t + 3)^5/3

Mathematics
1 answer:
4vir4ik [10]2 years ago
7 0

Answer:

(t+6)(-2t+3)^{\frac{2}{3}}

Step-by-step explanation:

\textsf{Given expression}:

5t(-2t+3)^{\frac{2}{3}}+2(-2t+3)^{\frac{5}{3}}

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

\implies 5t(-2t+3)^{\frac{2}{3}}+2(-2t+3)^{\frac{3+2}{3}}

\implies 5t(-2t+3)^{\frac{2}{3}}+2(-2t+3)^{\frac{3}{3}}(-2t+3)^{\frac{2}{3}}

\implies 5t(-2t+3)^{\frac{2}{3}}+2(-2t+3)(-2t+3)^{\frac{2}{3}}

\textsf{Factor out common term }(-2t+3)^{\frac{2}{3}}:

\implies (-2t+3)^{\frac{2}{3}}(5t+2(-2t+3))

\textsf{Simplify}:

\implies (-2t+3)^{\frac{2}{3}}(5t-4t+6)

\implies (-2t+3)^{\frac{2}{3}}(t+6)

\implies (t+6)(-2t+3)^{\frac{2}{3}}

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What properties can be used to solve 7y-15=-29. Identity property of multiplication,addition property of equality ,distributive
Sveta_85 [38]

Answer:

Addition Property of Equality.

Inverse property of multiplication.

Step-by-step explanation:

Given the equation:

7y-15=-29

First of all, let us use Addition Property of Equality.

According to the property, if we add a number on both sides of an equality, there is no change in the equality.

In other words, the equality will be same if we add the same number on Left Hand Side and Right Hand Side of the equality.

First of all, let us add 15 on both sides of the equality:

7y-15+15=-29+15\\\Rightarrow 7y=-14

Now, let us Inverse property of multiplication.

i.e. Multiplication of a number with its inverse is equal to 1.

a\times \frac{1}{a} = 1

So, let us multiply the given equation with \frac{1}7

7y \times \dfrac{1}{7}=-14 \times \dfrac{1}{7}\\\Rightarrow 1y =-2\\\Rightarrow y=-2

The properties used are:

Addition Property of Equality.

Inverse property of multiplication.

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Some students performed an experiment in which they dropped a rubber ball from a height of 920 centimeters. They noticed that af
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The equation models the height, H, for n bounces, will be H = 920 (0.56)ⁿ.

<h3>What is an exponent?</h3>

Consider the function:

y = a (1 ± r) ˣ

Where n is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, then there is exponential growth happening by r fraction or 100r %

If there is a minus sign, then there is exponential decay happening by r fraction or 100r %

Some students performed an experiment in which they dropped a rubber ball from a height of 920 centimeters.

They noticed that after each bounce, it reached 56% of its previous height.

Then the equation models the height, H, for n bounces will be

H = 920 (0.56)ⁿ

More about the exponent link is given below.

brainly.com/question/5497425

#SPJ1

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