Factor the expression given below. Write each factor as a polynomial indescending order. Enter exponents using the caret (^).
125x^3+343y^3

Answers

Answer 1

Answer:

Final answer:

The expression 125x^3+343y^3 can be factored using the sum of cubes formula to obtain (5x+7y)(25x^2 -35xy + 49y^2).

Explanation:

The expression 125x^3+343y^3 is a sum of two cubes. The formula to factor a sum of cubes, a^3 + b^3, is (a+b)(a^2-ab+b^2). In this case, a is 5x and b is 7y, as (5x)^3 = 125x^3 and (7y)^3 = 343y^3. So, we apply the formula to obtain: (5x+7y)((5x)^2 - (5x)(7y) + (7y)^2), which simplifies to (5x+7y)(25x^2 -35xy + 49y^2).

Therefore, the factored form of the expression 125x^3+343y^3 is

= (5x+7y)(25x^2 -35xy + 49y^2).

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Answer 2

Answer:

Answer:

(5x + 7y)(25x² - 35xy + 49y²)

Step-by-step explanation:

125x³ + 343y³ ← is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b³) , thus

125x³ + 243y³

= (5x)³ + (7y)³

= (5x + 7y)((5x)² - 5x(7y) + (7y)² )

= (5x + 7y)(25x² - 35xy + 49y²)

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What is 8/32 is simplest form

Answers

$(8)/(32)=(8:2)/(32:2)=(4)/(16)=(4:2)/(16:2)=(2)/(8)=(2:2)/(8:2)=\boxed{(1)/(4)}$

8/32 is 1/4 in its simplists form as 8 is the highest number that divdes the top and bottom

Let R be the region in the first quadrant bounded by the graph of y=sqrt{x-2} and the line y=2.(a). Find the volume of the solid generated when R is revolved about the x-axis.
(b). Find the volume of the solid generated when R is revolved about the line y=-2.

Answers

Volume of the solid generated when R is revolved about the x-axis is 10π and the volume of the solid generated when R is revolved about the line y = -2 is 40π/3.

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The volume of the solid generated when R is revolved about the x-axis,

$V=\int\limits^a_b\pi {y^(2) } \, dx$

where a and b are the x-coordinates of the points of intersection of the curve y = √(x-2) and the line y = 2.

Solving y = √(x-2) and y = 2 for x, we get:

x = 6 and x = 2

Limits of integration are a = 2 and b = 6. Substituting y = √(x-2) into the formula for the volume, we get:

V = $\int\limits^6_2\pi\sqrt{(x-2)^(2) } \, dx$

V= π [(6²/2 - 2(6)) - (2²/2 - 2(2))]

=10π

Volume of the solid generated when R is revolved about the x-axis is 10π.

b. The volume of the solid generated when R is revolved about the line y = -2

$V=\int\limits^a_b\pi {(y+2)^(2) } \, dx$

Substituting y = √(x-2) into the formula for the volume, we get:

$V=\int\limits^2_6\pi (√(x-2)+2)^(2) \, dx$

We can simplify this by using the identity:

V =40π/3

Therefore, the volume of the solid generated when R is revolved about the line y = -2 is 40π/3.

Hence, Volume of the solid generated when R is revolved about the x-axis is 10π and the volume of the solid generated when R is revolved about the line y = -2 is 40π/3.

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A.) Find the volume of the solid generated when R is revolved about the x-axis.

Tia is planning a sailing party for her friends. The boat rental is $150 plus an additional $15 per person. Tia has saved up $400 dollars. What is the maximum number of people that can go sailing?

Answers

16 people is the answer :) Hope this helps, and a rate and thanks would be nice ;D

I took 400 - 150 divided by 15 and got 16. So believe that should could afford to bring 16 people.

What formula tells the cost, in dollars, if chocolate chip cookies are $2.50/ dozen and lemon frosteds are $1.50/dozen? let c=number of dozens of chocolate chip cookies;L=number of dozens of lemon frosted; T= total charge

Answers

c= # of dozens chocolate chip cookies= $2.50/dozen

L= # of dozens of lemon frosted= $1.50/dozen

T= total charge

Multiply the number of dozens of chocolate chip cookies by the cost per dozen. Multiply the number of lemon frosted by the cost per dozen. Add those two together to equal the total cost.

T= ($2.50 * c) + ($1.50 * L)
T= $2.50c + $1.50L

ANSWER: T= $2.50c + $1.50L

Hope this helps! :)

I am confused my old teacher got fired so we are learning stuff completely different and I am rlly confused in this assignment please help me.

Answers

Hello!

First, let's analyze these two quadrilaterals:

• Notice that the quadrilateral AB'C'D is ,smaller ,than the quadrilateral ABCD.

Let's try to solve it using the lines AB and AB':

• The measurement of the ,line AB is 14 units,.

• The measurement of the ,line AB' is 7 units,.

Knowing it, let's write the scale factor as:

$\text{ScaleFactor}=(AB^(\prime))/(AB)=(7)/(14)=(1)/(2)$

Answer: alternative D.

The cost to rent a moving truck is a flat fee of $25 plus $0.60 per mile. The equation c = 25 + 0.6m models the cost, c, in dollars for the number of miles, m, traveled in the truck.Identify the independent and dependent variables.

Answers

So you should know that an independent variable is a variable that is not changed by other variables but a dependent variable does change by other variables.
So in this question, c is a dependent variable and m is an independent variable :))))
I hope this is helpful
have a nice day

Answer:

Miles Traveled is independent.

Cost is the dependent.

Step-by-step explanation:

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