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4 years ago

Match each expression written in standard form to the equivalent expression in factored form

Mathematics

1 answer:

den301095 [7]4 years ago

4 0

Answer:

1. 15x^7y^2 + 4x^3 => x^3(15x^4y^2 + 4)

2. 15x^7y^2 + 3x => 3x(5x^6y^2 + 1)

3. 15x^7y^2 + 6xy => 3xy(5x^6y + 2)

4. 15x^7 + 10y^2 => 5(3x^7 + 2y^2)

Step-by-step explanation:

To obtain the answer to the question, first let us factorise each expression. This is illustrated below:

1. 15x^7y^2 + 4x^3

Common factor is x^3, therefore the expression is written as:

x^3(15x^4y^2 + 4)

2. 15x^7y^2 + 3x

Common factor is 3x, therefore the expression is written as:

3x(5x^6y^2 + 1)

3. 15x^7y^2 + 6xy

Common factor is 3xy, therefore the expression is written as:

3xy(5x^6y + 2)

4. 15x^7 + 10y^2

Common factor is 5, therefore the expression can be written as:

5(3x^7 + 2y^2)

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Carlos and Ana were asked to find an explicit formula for the sequence -10,-4,2,8,...−10,−4,2,8,...Minus, 10, comma, minus, 4, c

mars1129 [50]

Answer:

Ana is correct

Step-by-step explanation:

Given

$Sequence:\ -10, -4, 2,8$

$Carlos; f(n) = -10 + 6n$

$Ana; f(n) = -10 + 6(n-1)$

Required

Determine who is right?

To do this, we simply test each sequence.

For Carlos:

When n = 1

$f(1) = -10 + 6 * 1 = -10 + 6 = -4$

When n = 2

$f(2) = -10 + 6 * 2 = -10 + 12 = 2$

This is incorrect because the first and second term of the sequence are -10 and -4 not -4 and 2

For Ana:

When n = 1

$f(1) = -10 + 6(1-1) = -10 + 6*0 = -10 + 0 = -10$

When n = 2

$f(2) = -10 + 6(2-1) = -10 + 6*1 = -10 + 6 = -4$

When n=3

$f(3) = -10 + 6(3-1) = -10 + 6*2 = -10 + 12 = 2$

When n = 4

$f(4) = -10 + 6(4-1) = -10 + 6*3 = -10 + 18 = 8$

This is correct.

Hence, Ana is correct

8 0

3 years ago

Read 2 more answers

A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are diff

kvasek [131]

Answer:

The proportion of young adults (18-25 years of age) in a certain city in the U.S. are not different from the proportion of the general population of young adults in the U.S.

Step-by-step explanation:

The hypothesis for the test can be defined as:

H₀: The proportion of young adults (18-25 years of age) in a certain city in the U.S. are not different from the actual proportion, i.e. P = p.

Hₐ: The proportion of young adults (18-25 years of age) in a certain city in the U.S. are different from the actual proportion, i.e. P ≠ p.

The test statistic is defined as:

$z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}$

Assume that the significance level of the test is, α = 0.05.

The decision rule is:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected. And vice-versa.

It is provided that the p-value of the test is, p-value = 0.076.

The p-value = 0.076 > α = 0.05.

Thus, the null hypothesis will not be rejected at 5% level of significance.

Conclusion:

The proportion of young adults (18-25 years of age) in a certain city in the U.S. are not different from the proportion of the general population of young adults in the U.S.

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4 years ago

Find the solution(s) to (x- 3) = 49. Check all that apply.

natima [27]

Answer:

B.x= -4 and E. x= 10 are the answers

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3 years ago

Perform the operation : Multiply 0.03(4 − x) by 100.

shutvik [7]

Answer:

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