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3 years ago

Factoring Quadratic Trinomials 6n^2 - n - 40 =

Mathematics

1 answer:

Sophie [7]3 years ago

6 0

Answer:

(3n - 8)(2n + 5)

Step-by-step explanation:

6n² - n - 40

Consider the factors of the product of the coefficient of the n² term and the constant term which sum to give the coefficient of the n- term

product = 6 × - 40 = - 240 and sum = - 1

The factors are - 16 and + 15

Use these factors to split the n- term

6n² - 16n + 15n - 40 ( factor the first/second and third/fourth terms )

2n(3n - 8) + 5(3n - 8) ← factor out (3n - 8) from each term

(3n - 8)(2n + 5)

Then

6n² - n - 40 = (3n - 8)(2n + 5)

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Find the area. Simplify your answer. X+4 2x

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Answer:

x² +4x

Step-by-step explanation:

Area of triangle= ½ ×base ×height

Given: base= 2x, height= x +4

Area of triangle

= ½(2x)(x +4)

= x(x +4)

= x(x) +x(4) (expand)

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3 years ago

What equation in slope-intercept form represents the line that passes through the points

Mumz [18]

<h2>Answer: y = - x + 1 </h2>

<h3>Step-by-step explanation: </h3>

For us to write the equation for this line, we need to (1) find the slope of the line, and (2) use one of the points to write an equation:

The question gives us two points, (-3, 4) and (2, -1), from which we can find the slope and later the equation of the line.

Finding the Slope

The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)

= (4 - (- 1)) ÷ ((-3) - 2)

= - 1

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We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:

⇒ y - (-1) = - 1 (x - 2)

y + 1 = - (x - 2)

we could also transform this into the slope-intercept form ( y = mx + c) by making y the subject of the equation:

since y + 1 = - (x - 2)

∴ y = - x + 1

To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.

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3 years ago

Suppose that the distance, in miles, that people are willing to commute to work is an exponential random variable with a decay p

garik1379 [7]

Answer:

m = $\frac{1}{20}$
μ = 20
σ = 20

The probability that a person is willing to commute more than 25 miles is 0.2865.

Step-by-step explanation:

Exponential probability distribution is used to define the probability distribution of the amount of time until some specific event takes place.

A random variable X follows an exponential distribution with parameter m.

The decay parameter is, m.

The probability distribution function of an Exponential distribution is:

$f(x)=me^{-mx}\ ;\ m>0, x>0$

Given: The decay parameter is, $\frac{1}{20}$

X is defined as the distance people are willing to commute in miles.

The decay parameter is m = $\frac{1}{20}$ .
The mean of the distribution is: $\mu=\frac{1}{m}=\frac{1}{\frac{1}{20}}=20$ .
The standard deviation is: $\sigma=\sqrt{variance}= \sqrt{\frac{1}{(m)^{2}} } =\frac{1}{m} =\frac{1}{\frac{1}{20}} =20$

Compute the probability that a person is willing to commute more than 25 miles as follows:

$P(X>25)=\int\limits^{\infty}_{25} {\frac{1}{20} e^{-\frac{1}{20}x}} \, dx \\=\frac{1}{20}|20e^{-\frac{1}{20}x}|^{\infty}_{25}\\=|e^{-\frac{1}{20}x}|^{\infty}_{25}\\=e^{-\frac{1}{20}\times25}\\=0.2865$

Thus, the probability that a person is willing to commute more than 25 miles is 0.2865.

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3 years ago

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Paraphin [41]

Answer:

C. 10z(x - 2y)

Step-by-step explanation:

10xz − 20y

Factor the terms

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Factors of -20yz = (-1) × 2 × 2 × 5 × y × z

Identify their greatest common factor

The common factors are 2, 5, and z. The greatest common factor is 10z.

Rewrite them with the GCF as a factor

10xz = 10z × x

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Replace the terms in the original expression with the factored terms

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