Which expressions are equivalent to the given expression?

The volume of a pyramid is 47 3. The height of the pyramid is 6 meters. What is the area of

AlladinOne [14]

473x6= 2,838

the answer should be 2,838?

8 0

3 years ago

Read 2 more answers

A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre o

Bess [88]

Answer:

6

Step-by-step explanation:

So to find how much sheep there were on each acre, you divide.

250/40

You do this because you are splitting the 250 sheep into 40 acres.

250/40 = 6.25

There cannot be .25 of a sheep, and since it says on average the answer does not need to be exact. So you would round it off to 6 as your answer.

4 0

3 years ago

The equation a<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D" id="TexFormula1" title="x^{2}" alt="x^{2}" align="absmiddle" class=

andrezito [222]

Answer:

$\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)$

Step-by-step explanation:

We are given the equation:

$ax^2+bx+c=0$

Which has roots α and β.

And we want to express (α + 1)(β + 1) in terms of a, b, and c.

From the quadratic formula, we know that the two solutions to our equation are:

$\displaystyle x_1 = \frac{-b+\sqrt{b^2-4ac}}{2a}\text{ and } x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}$

Let x₁ = α and x₂ = β. Substitute:

$\displaystyle \left(\frac{-b+\sqrt{b^2-4ac}}{2a} + 1\right) \left(\frac{-b-\sqrt{b^2-4ac}}{2a}+1\right)$

Combine fractions:

$\displaystyle =\left(\frac{-b+2a+\sqrt{b^2-4ac}}{2a} \right) \left(\frac{-b+2a-\sqrt{b^2-4ac}}{2a}\right)$

Rewrite:

$\displaystyle = \frac{\left(-b+2a+\sqrt{b^2-4ac}\right)\left(-b+2a-\sqrt{b^2-4ac}\right)}{(2a)(2a)}$

Multiply and group:

$\displaystyle = \frac{((-b+2a)+\sqrt{b^2-4ac})((-b+2a)-\sqrt{b^2-4ac})}{4a^2}$

Difference of two squares:

$\displaystyle = \frac{\overbrace{(-b+2a)^2 - (\sqrt{b^2-4ac})^2}^{(x+y)(x-y)=x^2-y^2}}{4a^2}$

Expand and simplify:

$\displaystyle = \frac{(b^2-4ab+4a^2)-(b^2-4ac)}{4a^2}$

Distribute:

$\displaystyle = \frac{(b^2-4ab+4a^2)+(-b^2+4ac)}{4a^2}$

Cancel like terms:

$\displaystyle = \frac{4a^2+4ac-4ab}{4a^2}$

Factor:

$\displaystyle =\frac{4a(a+c-b)}{4a(a)}$

Cancel. Hence:

$\displaystyle = \frac{a+c-b}{a}\:\: \left(\text{ or } 1+\frac{c-b}{a}\right)$

Therefore:

$\displaystyle \left(\alpha+1\right)\left(\beta + 1\right) = \frac{a+c-b}{a}$

4 0

3 years ago

11,285 rounded to the nearest hundred

Volgvan

Answer:

11,300

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

A city lot measures 100 feet x 250 feet. The city zoning ordinance specifies that maximum lot coverage is 40% of the lot. What i

BaLLatris [955]

Answer:

10,000 square feet is the maximum size for a building on this slot.

Step-by-step explanation:

A city lot measures 100 feet x 250 feet. The city zoning ordinance specifies that maximum lot coverage is 40%of the lot.

First we find the total area of city = 100 x 250

Area = 25,000 square feet

Maximum coverage area is 40% of city area

Maximum size of for building on this lot = 40% of 25,000

Now we calculate 40% of 25,000

Maximum size for building = 0.40 x 25000 = 10,000 square feet

Thus, 10,000 square feet is the maximum size for a building on this slot.

7 0

3 years ago