(3b-5)^2-c^2 how do I factor this using grouping?

Answers

Answer 1

Answer: so you see it is the difference of 2 perfect squares
a^2-b^2=(a+b)(a-b)
so
(3b-5)^2-c^2=(3b-5+c)(3b-5-c)

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How big is 2000 sq.ft in yards?

Answers

200 square feet = 222.2222 square yards.

There are three feet in a yard and nine square feet in a square yard. Divide 2000 by 3 and then divide by 3 again to get 222.222 square yards.

A student was asked to use the formula for the perimeter of a rectangle, p = 2l 2w, to solve for l. the student came up with an answer, p -2w=2l. what error did the student make? explain. then solve for l

Answers

A student was asked to use the formula for the perimeter of a rectangle, p = 2l 2w, to solve for l. the student came up with an answer, p -2w=2l. what

A rental car agency charges $240 per week plus $0.25 per mile to rent a car. The charge of a minivan is $180 per week plus $0.40 per mile .After how many miles is the total charge for each vehicle the same

Answers

Final answer:

To find out how many miles the total charge for each vehicle is the same, set up an equation and solve for x.

Explanation:

To find out how many miles the total charge for each vehicle is the same, we need to set up an equation.

Let's suppose the number of miles is x. For the first vehicle, the total charge can be represented as 240 + 0.25x, and for the minivan, it can be represented as 180 + 0.40x.

Setting up the equation, we have:

240 + 0.25x = 180 + 0.40x

Now, we can solve this equation to find the value of x.

Subtracting 0.25x from both sides, we have:

240 = 180 + 0.15x

Subtracting 180 from both sides, we have:

60 = 0.15x

Dividing both sides by 0.15, we get:

x = 400

Therefore, after 400 miles, the total charge for each vehicle is the same.

Learn more about the Total charge for rental cars here:

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The brain has 100 billion brain cells. If you counted each cell at 1 per second, how long would it take you to count all 100 billion cells?

Answers

100 billion seconds because you do 100 billion times 1 to get 100 billion/ second

Are all diagonals also lines of symmetry for any given polyhon

Answers

the diagonals arent a line of symmetry at all

Use the method of quadrature to estimate the area under the curve y=-x^2+5 and above the x-axis from x=0 to x=2.

Answers

Answer:

Area = $(22)/(3)$

Step-by-step explanation:

Given is a curve

$y=-x^2+5$

we have to find the area of this curve above x axis from 0 to 2

By method of quadrature we know that area of a curve above x axis is given by,

$\int\limits^a_bf( {x} )\, dx$

Here a= 0 and b =2

Substitute to get

Area = $\int\limits^0_2 {-x^2+5} \, dx \n=(-x^3)/(3) +5x$

Substituting limits

Area = $(-8)/(3) +10 =(22)/(3)$

I'm a calculus teacher at the high school level and I have never heard of quadrature. I teach from an AP approved college-level text so...I'll do it using the antiderivative! Setting that up to integrate we have $- \int\limits^2_0 { (x^2-5)} \, dx$ . If you notice, I pulled the negative out in front of the integral and changed the signs in the function. So it could really be rewritten as $-1 \int\limits^2_0 {(x^2-5)} \, dx$ . Integrating we have $-1[ (x^3)/(3) -5x]$ from 0 to 2. Subbing in those bounds, we have $-1[( (2^3)/(3)-5(2))-( (0^3)/(3)-5(0))]$ which simplifies to $-1( (8)/(3)-10)$ . Distributing the -1 in gives us $10- (8)/(3)= (22)/(3)$

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