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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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3 years ago
Allison and Megan were at track practice. The track is 3/8 kilometers around.
Ad libitum [116K]

Allison ran 3/8 km (0.375 km) in 3 minutes.

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\frac{0.375\textrm{km}}{3 \textrm{min}} = \frac{1\textrm{km}}{x \textrm{min}}

Cross multiply to get:

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2 years ago
Can someone please help me with my homework
enyata [817]
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4 0
3 years ago
12 is what percentage of 80
PIT_PIT [208]

Answer:  " 15 % " .

_______________________________

     →   " 12 is <u>  15% </u> of 80 " .

_______________________________

Step-by-step explanation:

_______________________________

12 = (n/100) * 80 ;

12 = (80n) /100 ;  Solve for "n:

Note:  80/100 = (80/10) / (100/10) = (8/10) = 0.8  ;

12 = (0.8)n  ;

↔ (0.8n) = 12

Multiply each side of the equation by "10" ; to get rid of the "decimal" ;

 10 * (0.8n) = 10 * 12 ;

to get:

_______________________________

8n = 120 ;

Divide each side of the equation by "8" ;

to isolate "n" on ONE SIDE of the equation; & to solve for "n" ;

8n/8 = 120/ 8 ;

_______________________________

to get:

_______________________________

n = 15 .

_______________________________

Answer:  " 15 % " .

_______________________________

     →   " 12 is <u>  15% </u> of 80 " .

_______________________________

Hope this helps!

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4 0
3 years ago
A local high school has both male and female students.
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Answer:

a. P(male) = 0.4

b. P(no sport and male) = 0.1

c. Unclear question (isn't it the same as b.?)

Step-by-step explanation:

The data below is what I've worked according to, which isn't very clear from the question so the answers are only correct if this is the correct table of data;

\left[\begin{array}{ccc}&No \ Sports&Sports\\Female&10&32\\Male&7&21\end {array}\right]

a.

P(male) = \frac{7 + 21}{70} \\\\ = \frac{28}{70} \\\\ = \frac{2}{5}

b.

Using the tree diagram in the picture;

P(no \ sport \ and \ male) = \frac{2}{5} * \frac{1}{4} \\\\ = \frac{1}{10}

8 0
2 years ago
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