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3 years ago

Factor completely. 81-100x^2

Mathematics

2 answers:

Mandarinka [93]3 years ago

5 0

Answer:

(9-10x)(9+10x) (I think this is the answer but I'm not one hundred percent sure)

Step-by-step explanation:

First, you can recognize that both numbers (-100x^2 and 81) are a difference of squares, in which means that they both can be square routed. Then, plug in the square routes of the numbers into (9-10x)(9+10x). 9 is the square route of 81 and 10 is the square route of 100. Make sure that when you put the numbers in the parenthesis that there is one negative and positive number since a negative multiplied by a positive makes a negative, hence making 100 negative. I hope that helped.

rusak2 [61]3 years ago

4 0

Answer:

(9 + 10x)(9 - 10x)

Step-by-step explanation:

81-100x²

recall that 81 = 9² and 100 = 10²

hence,

81 - 100x²

= 9² - 10²x²

= 9² - (10x)²

recall the algebraic property:

a² - b² = (a+b)(a-b)

applying this to our question,

9² - (10x)²

= (9 + 10x)(9 - 10x)

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State whether the given measurements determine zero, one, or two triangles.

german

Let's apply the law of sine to calculate angle C
sin(81)/26 = sin(C)/28
0.1646 = sin(C)/28 and sin(C) =1.063. Sine sin(α) cannot be > than 1, so this triangle is invalid

6 0

3 years ago

Read 2 more answers

Given QT = SR, QV = SU, and the diagram, prove that triangles QUT and SVR are congruent. Write a paragraph proof.

QveST [7]

Answer:

Triangles QUT and SVR are congruent because the defining two sides and an included angle of triangles QUT and SVR are equal

Step-by-step explanation:

Here we have QT = SR and

QV = SU

Therefore,

QT = √(UT² + QU²)........(1)

RS = √(VS² + RV²)..........(2)

Since QS = QU + SU = QV + VS ∴ QU = VS

Therefore, since SR = QT and QU = VS, then from (1) and (2), we have UT = RV

Hence since we know all sides of the triangles QUT and SVR are equal and we know that the angle in between two congruent sides of the the triangles QUT and SVR that is the angle in between sides QU and UT for triangle QUT and the angle in between the sides RV and VS in triangle SVR are both equal to 90°, therefore triangles QUT and SVR are congruent.

5 0

3 years ago

what is an equation of the line that is parallel to the line with y=-.60x+2 and passes through the point (10,-10)

sp2606 [1]

y = -0.60x - 4

because the slope stays the same because it is parallel and the y intercept for the new equation ends up being -4

4 0

3 years ago

In a binomial distribution, n = 8 and π=0.36. Find the probabilities of the following events. (Round your answers to 4 decimal p

skelet666 [1.2K]

Answer:

$\mathbf{P(X=5) =0.0888}$

P(x ≤ 5 ) = 0.9707

P ( x ≥ 6) = 0.0293

Step-by-step explanation:

The probability of a binomial mass distribution can be expressed with the formula:

$\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}$

$\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}$

where;

n = 8 and π = 0.36

For x = 5

The probability $\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}$

$\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}$

$\mathtt{P(X=5) =0.0887645}$

$\mathbf{P(X=5) =0.0888}$ to 4 decimal places

b. x ≤ 5

The probability of P ( x ≤ 5) $\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})$

${P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +$ $\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )$