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3 years ago

Factor Completely. 3x^2-30x+63

Mathematics

2 answers:

Paladinen [302]3 years ago

8 0

Answer:

The correct answer is,

3x² - 30 x + 63 = 3(x - 3)(x - 7)

Step-by-step explanation:

The given polynomial is 3x² - 30 x + 63

Factorization of 3x² - 30 x + 63

Splitting method

3x² - 30 x + 63 = 3(x² - 10 x + 21) (taking 3 as common)

= 3(x² - 3 x - 7x + 21) (middle term splitting)

= 3[x (x - 3) -7(x - 3)] (taking x and -7 as common)

= 3[(x - 3)(x - 7)]

Therefore 3x² - 30 x + 63 = 3(x - 3)(x - 7)

The correct answer is 3(x - 3)(x - 7)

N76 [4]3 years ago

3 0

Answer:

3(x-3)(x-7)

Step-by-step explanation:

We have given a expression.

3x²-30x+63

We have to calculate the factor of given expression.

taking 3 common from given expression, we have

3(x²-10x+21)

Splitting the middle term of given expression, we have

3(x²-3x-7x+21)

Making groups , we have

3(x(x-3)-7(x-3))

Taking (x-3) as common, we have

3(x-3)(x-7) which is the answer.

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What is the y-value in the solution to this system of linear equations?

Westkost [7]

Answer:

Step-by-step explanation:

Given the 2 equations

4x + 5y = - 12 → (1)

- 2x + 3y = - 16 → (2)

Eliminate the x- term by multiplying (2) by 2 and adding the result to (1)

- 4x + 6y = - 32 → (3)

Add (1) and (3) term by term

11y = - 44 ( divide both sides by 11 )

y = - 4

3 0

3 years ago

Read 2 more answers

According to the National Bridge Inspection Standard (NBIS), public bridges over 20 feet in length must be inspected and rated e

slamgirl [31]

Answer:

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Step-by-step explanation:

For each bridge, there are only two possible outcomes. Either it has rating of 4 or below, or it does not. The probability of a bridge being rated 4 or below is independent from other bridges. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

For the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.

This means that $p = 0.09$

Use the forecast to find the probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Either less than 4 have a rating of 4 or below, or at least 4 does. The sum of the probabilities of these events is 1.

$P(X < 4) + P(X \geq 4) = 1$

We want $P(X \geq 4)$

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{12,0}.(0.09)^{0}.(0.91)^{12} = 0.3225$

$P(X = 1) = C_{12,1}.(0.09)^{1}.(0.91)^{11} = 0.3827$

$P(X = 2) = C_{12,2}.(0.09)^{2}.(0.91)^{10} = 0.2082$

$P(X = 3) = C_{12,3}.(0.09)^{3}.(0.91)^{9} = 0.0686$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3225 + 0.3827 + 0.2082 + 0.0686 = 0.982$

Finally

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.982 = 0.0180$

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

6 0

3 years ago

I need help this is due tomorrow and I have to write an essay so please help!!!

HACTEHA [7]

2.) 6k - 9
*can't see #3*
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3 years ago

A line passes through the point (2,3) and has a slope of -2. Which is the equation of the line in point-slope form?

almond37 [142]

Answer:

7-2x=y

Step-by-step explanation:

When a point passes through a line it satisfies its equation

(X-x0 )m= y-y0

Slope = m = -2

(X-2 )(-2)=y-3

4-2x=y-3

7-2x=y

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3 years ago

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Ber [7]

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3 years ago