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2 years ago

pls help Using the pattern learned for the square of a binomial, square (3x-5y^2) Explain the pattern.

Mathematics

1 answer:

Bess [88]2 years ago

6 0

Step-by-step explanation:

The binomial square product states that

$(x - y) {}^{2} = x {}^{2} - 2xy + {y}^{2}$

So this means

If there a coefficient in front of x are y, we multiple them as well.

In terms, this means that a binomial squared is equal to

The first term squared + the two terms multiplied together and by 2 + the last term squared.

$(3x - 5y {}^{2} ) {}^{2} = 9 {x}^{2} - 30xy {}^{2} + 25 {y}^{4}$

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2 years ago

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Find the vertex of f(x) = -x² + 2x + 7

baherus [9]

Answer: There are no like terms.

Answer:=−x^2+2x+7

Step-by-step explanation: Hope this help :D

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2 years ago

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Prove by mathematical induction that 1+2+3+...+n= n(n+1)/2 please can someone help me with this ASAP. Thanks

Iteru [2.4K]

Let

$P(n):\ 1+2+\ldots+n = \dfrac{n(n+1)}{2}$

In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:

$P(1):\ 1 = \dfrac{1\cdot 2}{2}=1$

So, the base case is ok. Now, we need to assume $P(n)$ and prove $P(n+1)$ .

$P(n+1)$ states that

$P(n+1):\ 1+2+\ldots+n+(n+1) = \dfrac{(n+1)(n+2)}{2}=\dfrac{n^2+3n+2}{2}$

Since we're assuming $P(n)$ , we can substitute the sum of the first n terms with their expression:

$\underbrace{1+2+\ldots+n}_{P(n)}+n+1 = \dfrac{n(n+1)}{2}+n+1=\dfrac{n(n+1)+2n+2}{2}=\dfrac{n^2+3n+2}{2}$

Which terminates the proof, since we showed that

$P(n+1):\ 1+2+\ldots+n+(n+1) =\dfrac{n^2+3n+2}{2}$

as required

4 0

2 years ago

If a polygon is rotated, which of the following characteristics of the polygon will always be the same? Select ALL that apply.

ASHA 777 [7]

Answer:

When we have a rotation about a given point, the distance between the rotated point and the axis of rotation will remain constant, the only thing that changes is the coordinates of the point.

This tell us that the main measures of any rotated shape will not change.

Then the side lengths will remain constant, this implies that the area also remains constant, and this also means that the angle measures should remain the same.

And because the perimeter is equal to the sum of all the side lengths, the perimeter also remains the same.

The only thing that changes will be the coordinates of our polygon.

4 0

2 years ago

A group of 6p people are renting a vacation house together the price of the rental is 3p to the 2nd power if they split the cost

Tanya [424]

So we just do
cost/number of people=cost per 1 person
so
(6p)/(3p^2)
remember that you can split it up and make ones
$\frac{6p}{3p^{2}}$ = $\frac{6}{3p}$ times $\frac{p}{p}$ = $\frac{2}{1p}$ times $\frac{p}{p}$ times $\frac{3}{3}$ = $\frac{2}{1p}$ times 1 times 1=2/p

easy way is
remember that
(x^m)/(x^n)=x^(m-n)
so
(6p)(3p^2)=6/(3p=2/p=2p^-1

each member pays 2/p

4 0

3 years ago