ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Lerok [7]

Answer:

Step-by-step explanation:

I understand it! (But I'm a high school math teacher so it might be unfair!) ; )

Anyway you have 2 numbers. You don't know what they are so we will call them x and y. Our first statement says that these numbers multiply to equal 120. So that first equation is

xy = 120

Our second statement says that they add to -22. So that second equation is

x + y = -22

Now we need to find the 2 numbers. We have 2 unknowns, x and y. That means that we have to have 2 equations. No more than 2 no less than 2. Solve the first equation for y. It doesn't matter which equation you pick and which variable you choose to solve for. If you do the work correctly, you will get the correct answers either way. Solving the first equation for y gives you:

$y=\frac{120}{x}$

Now tht we have a value for y, we can use the substitution property of equality to sub that value into the second equation for y:

$x+\frac{120}{x}=-22$

Instead of finding a common denominator, we are going to eliminate x in the denominator altogether. Do this by multiplying everything by x to get

$x^2+120=-22x$

Get everything on one side of the equals sign and factor:

$x^2+22x+120=0$

Because 12 * 10 = 120 and 12 + 10 = 22, our factors are 12 and 10:

$x^2+12x+10x+120=0$

Use factoring by grouping now.

$(x^2+12x)+(10x+120)=0$

From the first set of parenthesis you can factor out an x, and from the second set you can factor out a 10:

x(x + 12) + 10(x + 12) = 0

Now factor out the common x + 12 to get a factored quadratic:

(x + 12)(x + 10) = 0

By the Zero Product Property, either x + 12 = 0 or x + 10 = 0. Solving both for x gives you x = -12 or x = -10.

If x = -12, then

-12 + y = -22 so

y = -10

If x = -10, then

-10 + y = -22 so

y = -12.

The combinations of x and y are:

If x = -12, y = 10

If x = -10, y = -12

It doesn't matter which one is which. They are not asking you to specifically define x and y. They are asking you to find the numbers, and you did!

6 0

3 years ago

Principal is __________.

bearhunter [10]

Answer:

B. the initial amount of money invested

Step-by-step explanation:

Principal is the money invested or the money that a lender lend the borrower. Such money is the basis on which the interest payable will be calculated after considering the numbers of years and installments.

4 0

3 years ago

Which expression correctly displays the calculations to find the a^5b^4 term of (a+b)^8

LUCKY_DIMON [66]

Answer:

Step-by-step explanation:

THE BINOMIAL THEOREM shows how to calculate a power of a binomial -- (a + b)n -- without actually multiplying.

For example, if we actually multiplied out the 4th power of (a + b) --

(a + b)4 = (a + b)(a + b)(a + b)(a + b)

-- then on collecting like terms we would find:

(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 . . . . (1)

Note: The literal factors are all possible terms in a and b where the sum of the exponents is 4: a4, a3b, a2b2, ab3, b4.

The degree of each term is 4.

The first term is actually a4b0, which is a4 · 1.

Thus to "expand" (a + b)5, we would anticipate the following terms, in which the sum of all the exponents is 5:

(a + b)5 = ? a5 + ? a4b + ? a3b2 + ? a2b3 + ? ab4 + ? b5

The question is, What are the coefficients?

They are called the binomial coefficients. In the expansion of

(a + b)4, the binomial coefficients are

1 4 6 4 1

line (1) above.

Note the symmetry: The coefficients from left to right are the same right to left.

The answer to the question, "What are the binomial coefficients?" is called the binomial theorem. It shows how to calculate the coefficients in the expansion of (a + b)n.

The symbol for a binomial coefficient is The binomial theorem. The upper index n is the exponent of the expansion; the lower index k indicates which term, starting with k = 0.

For example, when n = 5, each term in the expansion of (a + b)5 will look like this:

The binomial theorema5 − kbk

k will successively take on the values 0 through 5.

(a + b)5 = The binomial theorema5 + The binomial theorema4b + The binomial theorema3b2 + The binomial theorema2b3 + The binomial theorem ab4 + The binomial theoremb5

Note: Each lower index is the exponent of b. The first term has k = 0 because in the first term, b appears as b0, which is 1.

Now, what are these binomial coefficients, The binomial theorem ?

The theorem states that the binomial coefficients are none other than the combinatorial numbers, nCk .

The binomial theorem = nCk

(a + b)5 = 5C0a5 + 5C1a4b + 5C2a3b2 + 5C3a2b3 + 5C4ab4 + 5C5b5

= 1a5 + The binomial theorema4b + The binomial theorema3b2 + The binomial theorema2b3 + The binomial theoremab4 + The binomial theoremb5

= a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5

The binomial coefficients here are

1 5 10 10 5 1.

8 0

3 years ago

The volume of which shapes can be found using the formula V = Bh?

Crazy boy [7]

Answer:

Triangular pyramid and Rectangular prism

Step-by-step explanation:

There are several different uses of the formula V = BH. For example, we used the formula V = BH for a cylinder, a rectangular prism, and a triangular pyramid. But be careful! All of the elements in the formulas don't mean the same! I really hope this helps you a bit!

5 0

3 years ago

Answer the following questions: 2/3 is what percent of 1/6 ?

Mrac [35]

Answer:

2/3=4/6 and that's 4 times 1/6. So the answer is 100% times 4 which is 400%

7 0

3 years ago

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