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3 years ago

Factor completely 3x2 + x + 7.

Mathematics

2 answers:

lianna [129]3 years ago

7 0

Answer:

Can not be factorized further

Step-by-step explanation:

Here we are asked to factorize the expression $3x^2+x+7$

In order to factorize a quadratic polynomial , we have to follow the following steps.

step 1. We have to find the product of coefficient of $x^2$ and the constant term. In this case the coefficient of $x^2$ is 3 and constant term is 7. Hence the product is 3*7=21

Step 2: Now we have to find all the possible factors of this product. In our case the factors will be

21=1*21

21=3*7

Step 3: We have to select one pair of those factors such that their sum or difference is equal to the coefficient of middle term that is $x$ . In this case it is 1. And we can see that in our polynomial , none of the pair gives you 1 either as sum or difference.

As there does not exist any such pair , it can not be further factorize.

Step2247 [10]3 years ago

4 0

Answer:

-1

Step-by-step explanation:

3 • 7 = 21

Find two factors of 21 whose sum equals the coefficient of the middle term, which is -1 .

-21 + -1 = -22

-1 + -21 = -22

1 + 21 = 22

21 + 1 = 22

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Solve for c: c=5 5/6 x 2

Marina86 [1]

Hi there!

c=11 2/3

1.Convert 5 5/6 into mixed number:

$5 \frac{5}{6}=\frac{35}{6}$

2.Convert 2 into fraction term:

$2=\frac{2}{1}$

3.Convert both fraction into same denominator:

$\frac{35}{6}=\frac{35}{6}$

$\frac{2}{1}=\frac{12}{6}$

4.Multiply the two terms:

$\frac{35}{6}$ · $\frac{12}{6}=\frac{70}{6}$

5.Simplfly the fraction term:

$\frac{70}{6}=\frac{35}{3}$

$\frac{35}{3}=11 \frac{2}{3}$

Therefore, c=11 2/3.

4 0

3 years ago

If a shirt costs 45 dollars, it's marked down to 30% off, what is the amount of the discount?

otez555 [7]

Answer:

$31.50

Step-by-step explanation:

30% of 45 is 13.5

45-13.5=31.5

4 0

3 years ago

Determine the equation of the line that passes through the points of intersection of the graphs of the quadratic functions f(x)

timofeeve [1]

Answer: $x-2y-2=0$

Step-by-step explanation:

Given :

$f(x) = x^2 - 4 \\ g(x) = - 3x^2 + 2x + 8$

Point of intersection :

$f(x)=g(x)\\x^2-4=-3x^2+2x+8\\4x^2-2x-12=0\\2x^2-x-6=0\\2x^2-4x+3x-6=0\\2x(x-2)+3(x-2)=0\\(x-2)(2x+3)=0\\x=2\,,\,\frac{-3}{2}$

$x=2\,;f(2)=2^2-4=0\\x=\frac{-3}{2}\,; f\left ( \frac{3}{2} \right )=\left ( \frac{3}{2} \right )^2-4=\frac{-7}{4}=-1.75$

So, we have points $\left ( 2,0 \right )\,,\,\left ( -1.5,-1.75\ \right )$

Equation of line passing through two points $\left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right )$ is given by $y-y_1=\frac{y_2-y_1}{x_2-x_1}\left ( x-x_1 \right )$

Let $\left ( x_1,y_1 \right )=\left ( 2,0 \right )\,,\,\left ( x_2,y_2 \right )=\left ( -1.5,-1.75\ \right )$

So, equation is as follows :

$y-0=\frac{-1.75-0}{-1.5-2}\left ( x-2 \right )\\y=\frac{-1.75}{-3.5}\left ( x-2 \right )\\y=\frac{1}{2}(x-2)\\2y=x-2\\x-2y-2=0$

4 0

4 years ago

Does the sample provide strong evidence that the mean weight of the bags is lower than the 35.6 grams listed on the package? Gro

kirill115 [55]

Answer:

As probability of that happening is very small; Yes, 33.6 is less than 35.6 grams because it provide strong evidence that the mean weight of the bags is lower than the 35.6 grams listed on the package.

Step-by-step explanation:

For a normal distribution Z-score

$Z = \frac{X-\mu}{\sigma}$

Given that :

the mean ( $\mu$ ) = 35.6

standard deviation ( $\sigma$ ) = 5.2

sample size (n) = 35

standard error: $\sigma_x = \frac{\sigma}{\sqrt{n}}$

$\sigma_x = \frac{5.2}{\sqrt{35}}$

$\sigma_x = 0.879$

The probability that a random sample of 35 bags has a mean weight of 33.6 grams or less is :

P(X<33.6) = P(Z < - 2.28)

= 0.0114

Conclusion:

As probability of the happening is very small; Yes, 33.6 is less than 35.6 grams because it provide strong evidence that the mean weight of the bags is lower than the 35.6 grams listed on the package.

7 0

4 years ago

What is the value of x? X° 65° 79° ОА. 36° ов. 14° Ос. 144° OD. 56°

vlada-n [284]

Answer:

A. 36

Step-by-step explanation:

65+79=144

180-144=36

3 0

3 years ago

Read 2 more answers