If the function G(x) = (x - 8)2 + 6 has the same shape as F(x) = x2 + 6, how far to the right of F(x) is G(x) shifted?

Answers

Answer 1

Answer: $G(x) = (x - 8)^2 + 6\ \ \ and\ \ \ F(x) = x^2 + 6\n\nAns.\ G(x)\ is\ shifted\ 8\ units\ right\ to\ the\ F(x)$

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Solve 2(x + 1) = 2x + 2.

Answers

2(x+1)=2x+2
^^^^^^2 gets distributed to both sides in the brackets.
the answer comes out to 2x+2.
therefore, 2x+2=2x+2.

PLEASE HELP!!! WILL GIVE BRAINLIEST!!!

Answers

Angle 1 is 112

Angle 2 is 68

Angle 3 is 90

Angle 4 is 90

Angle 5 is 22

Angle 6 is 158

Factor this radical expression. 50a^2-10ab/20a^3b^3

Answers

remembe
(ax)/(bx)=(a/b)(x/x)=(a/b)1
find ones aka common factors and use distributive

top
50a^2-10ab
common facotrs is 10a
undistribute (ab+ac=a(b+c))
10a(5a-b)

bottom
20a^3b^3
see if 10a is also a common factor and undistribute that to cancel and make ones
10a(2a^2b^2)

now we have
$(10a(5a-b))/(10a(2a^(2)b^(3))$ = $(10a)/(10a)$ $(5a-b)/(2a^(2)b^(3))$

1)split into two fractions
$(50a^(2) )/(20a ^(3) b ^(3) )$ - $(10ab )/(20a ^(3) b ^(3) )$

2) cancel what you can on both sides
$(5)/(2ab ^(3) )$ - $(1)/(2a ^(2)b ^(2) )$

3) Make the denominators the same by cross multiplying and then put together as 1 fraction again
$(5a-b)/(2a ^(2)b ^(2) )$

Which expression is a difference of cubes? 9w^33-y^12 18p^15-q^21 36a^22-b^16 64c^15- a^26

Answers

we know that

A polynomial in the form $a^(3)-b^(3)$ is called adifference of cubes. Both terms must be a perfect cubes

Let's verify each case to determine the solution to the problem

case A) $9w^(33) -y^(12)$

we know that

$9=3^(2)$ ------> the term is not a perfect cube

$w^(33)=(w^(11))^(3)$ ------> the term is a perfect cube

$y^(12)=(y^(4))^(3)$ ------> the term is a perfect cube

therefore

The expression $9w^(33) -y^(12)$ is not a difference of cubes because the term $9$ is not a perfect cube

case B) $18p^(15) -q^(21)$

we know that

$18=2*3^(2)$ ------> the term is not a perfect cube

$p^(15)=(p^(5))^(3)$ ------> the term is a perfect cube

$q^(21)=(q^(7))^(3)$ ------> the term is a perfect cube

therefore

The expression $18p^(15) -q^(21)$ is not a difference of cubes because the term $18$ is not a perfect cube

case C) $36a^(22) -b^(16)$

we know that

$36=2^(2)*3^(2)$ ------> the term is not a perfect cube

$a^(22)$ ------> the term is not a perfect cube

$b^(16)$ ------> the term is not a perfect cube

therefore

The expression $36a^(22) -b^(16)$ is not a difference of cubes because all terms are not perfect cubes

case D) $64c^(15) -a^(26)$

we know that

$64=2^(6)=(2^(2))^(3)$ ------> the term is a perfect cube

$c^(15)=(c^(5))^(3)$ ------> the term is a perfect cube

$a^(26)$ ------> the term is not a perfect cube

therefore

The expression $64c^(15) -a^(26)$ is not a difference of cubes because the term $a^(26)$ is not a perfect cube

I'm adding a new case so I can better explain the problem

case E) $64c^(15) -d^(27)$

we know that

$64=2^(6)=(2^(2))^(3)$ ------> the term is a perfect cube

$c^(15)=(c^(5))^(3)$ ------> the term is a perfect cube

$d^(27)=(d^(9))^(3)$ ------> the term is a perfect cube

Substitute

$64c^(15) -d^(27)=((2^(2))(c^(5)))^(3)-(d^(9))^(3)$

therefore

The expression $64c^(15) -d^(27)$ is a difference of cubes because all terms are perfect cubes

The expression $\boxed{64{c^(15)} - {d^(27)}}$ is a difference of cubes.

Further Explanation:

Given:

The options are as follows,

(a). $9{w^(33)} - {y^(12)}$

(b). $18{p^(15)} - {q^(21)}$

(c). $36{a^(22)} - {b^(16)}$

(d). $64{c^(15)} - {a^(26)}$

(e). $64{c^(15)} - {d^(27)}$

Calculation:

The cubic formula can be expressed as follows,

$\boxed{{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}$

The expression is $9{w^(33)} - {y^(12)}.$

9 is not a perfect cube of any number, ${w^(33)}$ can be written as ${\left( {{w^(11)}} \right)^3}$ and ${y^(12)}$ can be represents as ${\left( {{y^4}} \right)^3}.$

$9{w^(33)} - {y^(12)}$ cannot be written as the difference of cube. Option (a) is not correct.

The expression is $18{p^(15)} - {q^(21)}.$

18 is not a perfect cube of any number, ${p^(15)}$ can be written as ${\left( {{p^5}} \right)^3}$ and ${q^(21)}$ can be written as ${\left( {{q^7}} \right)^3}.$

$18{p^(15)} - {q^(21)}$ cannot be written as the difference of cube. Option (b) is not correct.

The expression is $36{a^(22)} - {b^(16)}.$

36 is not a perfect cube of any number, ${a^(22)}$ is not perfect cube and ${b^(16)}$ is not a perfect cube.

$36{a^(22)} - {b^(16)}$ cannot be written as the difference of cube. Option (c) is not correct.

The expression is $64{c^(15)} - {a^(26)}.$

64 can be written as ${\left( {{2^2}} \right)^3}, {a^(26)}$ is not perfect cube and ${c^(15)}$ can be written as ${\left( {{c^5}} \right)^3}.$

$64{c^(15)} - {a^(26)}$ cannot be written as the difference of cube. Option (d) is not correct.

The expression is $64{c^(15)} - {d^(27)}.$

64 can be written as ${\left( {{2^2}} \right)^3}, {d^(27)}$ can be written as ${\left( {{d^9}} \right)^3}$ and ${c^(15)}$ can be written as ${\left( {{c^5}} \right)^3}.$

$\boxed{64{c^(15)} - {d^(27)} = {{\left( {{2^2}{c^5}} \right)}^3} - {{\left( {{d^9}} \right)}^3}}$

$64{c^(15)} - {d^(27)}$ can be written as the difference of cube. Option (e) is correct.

The expression $\boxed{64{c^(15)} - {d^(27)}}$ is a difference of cubes.

Learn more:

1. Learn more about unit conversion brainly.com/question/4837736

2. Learn more about non-collinear brainly.com/question/4165000

3. Learn more aboutbinomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponents and Powers

Keywords: Solution, factorized form, expression, difference of cubes, exponents, power, equation, power rule, exponent rule.

What are the real imaginary solutions of the polynomial equation?
x^3=216

Answers

When you look at it, you would wonder why this equation is considered to be a polynomial where in fact there is only one factor. The only reason to explain this is that the other factors have zero as the coefficient. On another note, to answer this problem, we need to get the cube root of 216 which is 6, which is also the answer to this problem.

If 125% of a number is 425, what is 65% of the number?
Can anyone explain this one?

Answers

$125\%\ \ \rightarrow\ \ 425\n\n65\%\ \ \rightarrow\ \ x\n \n125\cdot x=65\cdot425\ /:125\n\nx= (65\cdot425)/(125) \n\nx=(5\cdot13\cdot25\cdot17)/(5\cdot25)\n\nx=13\cdot17\n\nx=221$

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The means and mean absolute deviations of the individual times of members on two 4 times 400 meter relay track teams are shown in the table below. Means and Mean Absolute Deviations of Individual Times of Members of 4 times 400 meter Relay Track Teams Team A Team B Mean 59.32 s 59.1 s Mean Absolute Deviation 1.5 s 2.4 s What percent of Team B’s mean absolute deviation is the difference in the means? 9% 15% 25% 65%

What is the result of isolating x^2 in the equation below?10x^2-36y^2=100A. x^2=100+36/10 y^2B. x^2=10+36/10 y^2C. x^2=100+36 y^2D. x^2=10+6/10 y^2

Which of the following statements is false?

A surveyor find that the cross section of the bottom of a circular pound has the shape of a parabola. The pond is 24 feet in diameter. The middle of the pond is the deepest part at 8 feet deep. At a point 2 feet from shore the water is 3 feet deep. How deep is the pond at a point 6 feet from shore?