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4 years ago

Select the correct answer from each drop-down menu. Factor the expression 8x3y − 8x2y − 30xy. 8x3y − 8x2y − 30xy = ( )( )

Mathematics

1 answer:

pychu [463]4 years ago

8 0

Answer:

$8x^3y-8x^2y-30xy=2xy(2x+3)(2x-5)$

Step-by-step explanation:

we are given an expression as

$8x^3y-8x^2y-30xy$

Firstly, we will find factors

$(2xy)\times 4x^2-(2xy)\times 4x-(2xy)\times 15$

We can see that 2xy is common in all terms

so, we can factor out 2xy from all terms

and we get

$8x^3y-8x^2y-30xy=2xy(4x^2-4x-15)$

now, we can factor again

$4x^2-4x-15=(2x+3)(2x-5)$

we get

$8x^3y-8x^2y-30xy=2xy(2x+3)(2x-5)$

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In a recent study, volunteers who had 8 hours of sleep were three times more likely to answer questions correctly on a math tes

Shalnov [3]

Answer:

Step-by-step explanation:

Sleep Deprivation

In a recent study, volunteers who had 8 hours of sleep were three times more likely to answer correctly on a math test than were sleep-deprived participants.

(a) Identify the sample used in the study.

(b) What is the sample's population?

(d) Make an inference based on the results of the study?

Solution

A. The samples used is the hours of sleep and math test scores of the volunteers

B. The samples population is hours of sleep and math test scores of people in general

C. The part of the study that represent the descriptive branch of statistics is "three times more likely"

D.Inference: To perform well in a math test, a person should get at least 8 hours of sleep the night before.

3 0

4 years ago

The number of members over time in an online music sharing club can be modeled by an exponential function. the club started with

Paraphin [41]

Answer:

a.) $N(x) = N_{0} e^{bx}$

b.) therefore b = $\ln \frac{2142}{2100} = \ln (1.02) = 0.0198$

b is the rate of increase of number of members

c.) The club will not be able to get more than 5000 members during its first year.

Step-by-step explanation:

i) the club started with 2100 members.

so we can write $N_{0}$ = 2100.

a.) so we can write the equation as an exponential function given by

$N(x) = N_{0} e^{bx}$ where x is in months and b is a constant and N(x) is the number of members in the online music sharing club .

therefore 2142 = 2100 $\times (e^{b\times 1})$ = 2100 $e^{b}$

b.) therefore b = $\ln \frac{2142}{2100} = \ln (1.02) = 0.0198$

b is the rate of increase of number of members

c.) Will the club have more than 5000 members during its first year? Justify your reasoning.

5000 = 2100 $e^{0.0198x}$

therefore x = $\frac{1}{0.0198} \ln{(\frac{5000}{2100} )} = 43.81 \hspace{0.1cm}months$

The club will not be able to get more than 5000 members during its first year.

7 0

3 years ago

Please help me <br> Show your work <br> 10 points

Svet_ta [14]

<h2>Answer</h2>

After the dilation $\frac{5}{3}$ around the center of dilation (2, -2), our triangle will have coordinates:

$R'=(2,3)$

$S'=(2,-2)$

$T'=(-3,-2)$

<h2>Explanation</h2>

First, we are going to translate the center of dilation to the origin. Since the center of dilation is (2, -2) we need to move two units to the left (-2) and two units up (2) to get to the origin. Therefore, our first partial rule will be:

$(x,y)$ → $(x-2, y+2)$

Next, we are going to perform our dilation, so we are going to multiply our resulting point by the dilation factor $\frac{5}{3}$ . Therefore our second partial rule will be:

$(x,y)$ → $\frac{5}{3} (x-2,y+2)$

$(x,y)$ → $(\frac{5}{3} x-\frac{10}{3} ,\frac{5}{3} y+\frac{10}{3} )$

Now, the only thing left to create our actual rule is going back from the origin to the original center of dilation, so we need to move two units to the right (2) and two units down (-2)

$(x,y)$ → $(\frac{5}{3} x-\frac{10}{3}+2,\frac{5}{3} y+\frac{10}{3}-2)$