What is the answer to this?

Answers

Answer 1

Answer: I got / 33/4. If I’m wrong sorry

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Write an equation in slope intercept form of a line that passes through the point (2,4) and is perpendicular to the graph of x-6y=2

Answers

-6y=2-x
y=x/6-1/3
so the slope for this line is 1/6,
therefore the slope for line perpendicular to this line is -6
y=mx+b
subsitute (2,4)in
4=-6*2+b
you get b=16
so the equation is y=-6x+16

Prove that: (a2 - b2)3 + (b2-c2)3+ (c2-a2)3 = 3 (a+b) (b+c) (c+a) (a-b) (b-c) (c-a).

Answers

$L=(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3=(*)\n\n(a^2-b^2)^3=a^6-3a^4b^2+3a^2b^4-b^6\n\n(b^2-c^2)^3=b^6-3b^4c^2+3b^3c^4-c^6\n\n(c^2-a^2)^3=c^6-3c^4a^2+3c^2a^4-a^6\n\n(*)=a^6-3a^4b^2+3a^2b^4-b^6+b^6-3b^4c^2+3b^2c^4-c^6+c^6-\dots\n\dots-3c^4a^2+3c^2a^4-a^6\n\n=-3a^4b^2+3a^2b^4-3b^4c^2+3b^2c^4-3c^4a^2+3c^2a^4\n\n=3(-a^4b^2+a^2b^4-b^4c^2+b^2c^4-a^2c^4+a^4c^2)$

$R=3(a+b)(a-b)(b+c)(b-c)(c+a)(c-a)\n\n=3(a^2-b^2)(b^2-c^2)(c^2-a^2)\n\n=3(a^2b^2-a^2c^2-b^4+b^2c^2)(c^2-a^2)\n\n=3(a^2b^2c^2-a^4b^2-a^2c^4+a^4c^2-b^4c^2+a^2b^4+b^2c^4-a^2b^2c^2)\n\n=3(-a^4b^2+a^2b^4-b^4c^2+b^2c^4-a^2c^4+a^4c^2)\n\nL=R$

$(a^2 - b^2)^3 + (b^2 - c^2)3 + (c^2 - a^2)^3 = 3(a + b)(b +c)(c + a)(a - b)(b - c)(c - a)$
$(a^2 - b^2)^3 + (b^2 - c^2)3 + (c^2 - a^2)^3 = 3(a + b)(a - b)(b + c)(b - c)(c + a)(c - a)$
$(a^2 - b^2)^3 + (b^2 - c^2)3 + (c^2 - a^2)^3 = 3(a^2 - b^2)(b^2 - c^2)(c^2 - a^2)$

$(a^2 - b^2)^3 = (a^2 - b2)(a^2 - b^2)(a^2-b^2) = a^6 - 3a^4b^2 + 3a^2b^4 - b^6$
$(b^2 - c^2)^3 = (b^2 - c^2)(b^2 - c^2)(b^2 - c^2) = b^6 - 3^4c^2 + 3b^2c^4 - c^6)$
$(c^2 - a^2)^3 = (c^2 - a^2)(c^2 - a^2)(c^2 - a^2) = c^6 - 3a^2c^4 + 3a^4c^2 - a^6$

$a^6 - 3a^4b^2 + 3a^2b^4 - b^6 + b^6 - 3b^4c^2 + 3b^2c^4 - c^6 + c^6 - 3a^2c^4 + 3a^4c^2 - a^6$
$-3a^4b^2 + 3a^2b^4 - 3b^4c^2 + 3b^2c^4 - 3a^2c^4 + 3a^4c^2$
$3(-a^4b^2 + a^2b^4 - b^4c^2 + b2^c^4 - a^2c^4 + a^4c^2)$

$3(a^2 - b^2)(b^2 - c^2)(c^2 - a^2) = 3(-a^4b^2 + a^2b^4 - b^4c^2 + b^2c^4 - a^2c^4 + a^4c^2)$

$3(-a^4b^2 + a^2b^4 - b^4c^2 + b^2c^4 - a^2c^4 + a^4c^2) = 3(-a^4b^2 + a^2b^4 - b^4c^2 + b^2c^4 - a^2c^4 + a^4c^2$

I need to simplify...help

Answers

Answer:

The answer to your question is $(3a^(5)b)/(4)$

Step-by-step explanation:

$(6a^(2)b^(-2))/(8a^(-3)b^(3))$

Process

To solve this problem, just remember the exponent's laws, in the division, exponents subtract and the coefficients just simplify.

1.- Simplify the coefficients

$(6)/(8) = (3)/(4)$

2.- Simplify "a's"

a² a⁺³ = a⁵

3.- Simplify "b's"

b⁻² b³ = b

4.- Write the expression

$(3a^(5)b)/(4)$

Plz help me I need so much help

Answers

Answer:

see below

Step-by-step explanation:

We have to assume that the question is referring to the doubly-shaded length, the one that is 10 bright blue units long.

You can read the overall length of the shaded area as 5/4, from the markings.

For the next part, you need to count the number of units that are shaded bright blue (10) and the number that are shaded blue overall (15). As a fraction of those shaded blue overall, the ones shaded bright blue are 10/15 = 2/3.

So, the length shaded bright blue is 2/3 of the overall length of 5/4. It is represented by the product ...

$\boxed{(2)/(3)*(5)/(4)}$

In a survey, 44% of the people said they voted for Mr. Johnson, while 2/5 of the people said they voted for Ms. Smith. Which group is larger? Explain.

Answers

Since 2/5 is equivalent to 4/10 = 40%, then the group which voted for Mr. Johnson is the larger group since they are 44%.

44% Is Bigger Because 2/5 is Only 40%

What is the volume and surface area of a sphere if the diameter is 7.5 feet?

Answers

The volume of a sphere is expressed as the four thirds of the product of pi and the cube of its radius. The surface area, on the other hand, is expressed as four times the product of pi and the square of its radius. Radius is half the diameter. Calculations are as follows:

V = 4/3 X (πr^3) = 4/3 X (π x 3.75^3) =220.89 ft^3
SA = 4πr^2 = 4 x π x 3.75^2 = 176.71 ft^2

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