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2 years ago

Nalani says the expression 9+7r cannot be factored using the GCF. Is she correct? Explain why or why not

Mathematics

1 answer:

miv72 [106K]2 years ago

3 0

Answer:

Nalani is correct.

Step-by-step explanation:

Given - Nalani says the expression 9+7r cannot be factored using the GCF.

To find - Is she correct? Explain why or why not.

Proof -

GCF - Greater Common factor

Given that, the expression is - 9 + 7r

HCF(9, 7) = 1

So , we can not factor the expression.

i.e. there does not exist any number who is a multiple of 9 and 7 both.

So,

Nalani is correct.

Example -

Let the expression be 24 + 18x

HCF(24, 18) = 6

So,

24 + 18x = 6(4 + 3x)

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√(2x+1)<br> Evaluate the integral<br> 2<br> (2x + 1) In (2x + 1)<br> dx.

Crank

Substitute $y=\ln(2x+1)$ and $dy=\frac2{2x+1}\,dx$ , so that

$\displaystyle \int \frac2{(2x+1) \ln(2x+1)} \, dx = \int \frac{dy}y = \ln|y| + C = \boxed{\ln|\ln(2x+1)| + C}$

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1 year ago

Which is the graph of F(x)= (x+3)(x-2)

KonstantinChe [14]

Answer:

Vertex: (-1/2, -25/4)

Focus: (-1/2, -6)

Axis of Symmetry: x=-1/2

Directrix: y=-13/2

Step-by-step explanation:

x = -2, -1, -1/2, 1, 2

y = -4, -6, -25/4, -4, 0

4 0

2 years ago

Read 2 more answers

Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f

GalinKa [24]

Answer:

$\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }$

Step-by-step explanation:

Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).

$\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}$

The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.

$f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240$

We identify the coefficients for the like terms, it comes

a = -2 and 16a = -32 (which is equivalent). So, we can write in $\mathbb{R}$ .

$\\f(x)=(x^2+16)(x^2-2x-15)$

The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.

$f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}$

And we can write in $\mathbb{C}$

$f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

7 0

3 years ago

Please please find the area for this polygon!

zzz [600]

Answer:

508

Step-by-step explanation:

28*16= 448

6*6= 36

4*6= 24

448+36+24= 508

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3 years ago

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PLEASEE HELP I NEED THIS ASAP!!!!

Nadusha1986 [10]

Answer:

The second chart has a greater rate of change compared to the equation presented.

Step-by-step explanation:

The first equation has a rate of change of 6. While the chart has a rate of change of 7.

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3 years ago

Nalani says the expression 9+7r cannot be factored using the GCF. Is she ​correct? Explain why or why not

Nalani says the expression 9+7r cannot be factored using the GCF. Is she correct? Explain why or why not