All categories

4 years ago

Factor 6x^3 + 33^2 - 63x

1 answer:

5 0

This factors out to $3x (x + 7) (2x - 3)=0$ .

First, notice that the greatest common factor of this set is $3x$ .

Once you factor that out, you have a quadratic $2x^2+11x-21=0$ .

You can solve this by factoring using the ac method, to find two factors whose product is -42 and whose sum is 11. These factors are 14 and -3.

You can split the middle term b to write $2x^2+14x-3x-21=0$ .

Then, you can factor to write $2x(x+7)-3(x+7)=0 \\ (2x-3)(x+7)=0$ . Finally, don't forget the 3x from earlier!

This factors out to $3x (x + 7) (2x - 3)=0$ .

You might be interested in

James takes off from Cooma and flies 452 km due south. He then turns and flies N37°E until he is due east of Cooma. How far is J

yuradex [85]

Answer: $\mathbf{341 km}$

Step-by-step explanation:

Given

James takes off from Cooma and flies 452 km to south

after that he travels $37^{\circ}$ East of North to reach east of Cooma

Suppose he is $\mathbf{x}\ km$ from Cooma

Form the figure, it can be written

$\Rightarrow \tan37^{\circ}= \dfrac{x}{452}\\\\\Rightarrow x=452\tan 37^{\circ}\\\Rightarrow x=340.6\ km\approx 341\ km$

Thus, James is $\mathbf{341 km}$ east to initial position.

3 0

3 years ago

Which one of the following is always true?a. The coefficient of variation measures variability in a positively skewed data set r

Tom [10]

Answer:

C. The coefficient of variation is a measure of relative dispersion that expresses the standard deviation as a percentage of the mean, for any data on a ratio scale and an interval scale

Step-by-step explanation:

Th Coefficient of Variance is a measure of dispersion that can be calculated using the formula:

$CV = \frac{\sigma_{x} }{\mu_{x} } * 100%$

Where $\sigma{x}$ is the Standard Deviation

and $\mu_{x}$ is the sample mean

From the formula written above, it is shown that the Coefficient of Variation expresses the Standard Deviation as a percentage of the mean.

Coefficient of variation can be used to compare positive as well as negative data on the ratio and interval scale, it is not only used for positive data.

The Interquartile Range is not a measure of central tendency, it is a measure of dispersion.

3 0

3 years ago

Solve for the equation for x 3x+y/=2

avanturin [10]

Answer: x= 2/3 - 1/3y

Explanation step by step:

Step 1: Move variable to the right hand side and change its sign.

3x = 2-y

Step 2: divide both sides of the equation by 3.

x= 2/3 - 1/3y

3 0

3 years ago

In the ΔABC, the altitude AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC.

bekas [8.4K]

AB = 30 in and BC = 50 in.

We use Pythagorean theorem to solve this. Since AN is an altitude, this means that it is perpendicular to BC. This means BN and AN are the legs of one right triangle, with AB being the hypotenuse:

18²+24² = AB²
324 + 576 = AB²
900 = AB²

Take the square root of both sides:
√900 = √AB²
30 = AB

NC and AN form the legs of the other right triangle, with AC being the hypotenuse:

24²+NC² = 40²
576 + NC² = 1600

Subtract 576 from both sides:
576 + NC² - 576 = 1600 - 576
NC² = 1024

Take the square root of both sides:
√NC² = √1024
NC = 32

BC = BN + NC = 18 + 32 = 50

4 0

3 years ago

In the app you are creating, a duck is going to fly from the coordinates (1, 3) then go 3 units right. And 6 units down. Write a

quester [9]

Answer:

y=-2x+5. (4,-3)

Step-by-step explanation:

1) What's being asked in other words is to write a function. So the initial point is (1,3). In x-axis, a translation movement can only be to the right or to the left. Similarly for y-axis the possible movements are shifting up or down. The question says, 3 units right for x-cordinate and 6 units down for y cordinate. So the final point of this translation would be (1+3,3-6) =(4,-3)

2) To write a linear function we need to find out the slope:

$m=\frac{-3-3}{4-1}=m=\frac{-6}{3} m=-2$

$3=1(-2)+b\\3+2=b\\ b=5\\ \\-3=4(-2)+b\\ b=8-3\\ b=5$

y=-2x+5

<u>Proof:</u>

x=1

y=-2(1)+5

y=3 Then (1,3)

x=4

y=-2(4)+5

y=-8+5

y=-3 Then (4,-3)

4 0

3 years ago