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2 years ago

Show all work to factor x^4 − 17x^2 + 16 completely.

Mathematics

1 answer:

FrozenT [24]2 years ago

6 0

Answer:

it looks like it is completely factored out to me at least there is a high possibility I am wrong because that looks complicated I wish I could help

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Given the Standard Form equation y - 6x = 4

malfutka [58]

Answer: <u>6 is the slope and 4 is the y-intercept.</u>

Step-by-step explanation:

Based on the question, I feel this is the best way to answer your question. I'm assuming you are in a basic graphing class.

The best, most useful thing for you right now would be to learn slope-intercept form, y = mx + b, where m and b are constants.

Simply add 6x to both sides to get into this form

y = 6x + 4.

In slope-intercept form, m is the slope, and b is the y-intercept. Thus, 6 is the slope and 4 is the y-intercept.

Hope it helps and lmk if you need more <3 :)

7 0

2 years ago

Pens and Pencils

Lina20 [59]

Pen=x
Pencil=y
y+0.15=x
y+x=0.69
y+y+0.15=0.69
2y=0.69-0.15
2y=0.54
y=0.54/2
y=0.27 pencils
y+0.15=x
0.27+0.15=x
0x=0.42 pen
150 pencils x0.27=40.5$
225 pens x 0.42=94.5$
Total 40.5$ + 94.50$=135 $
Supplier is right about a priče.

6 0

2 years ago

Please I need help!

Monica [59]

Answer:

$\text{ Slope = -3}$

$y+4=-\frac{7}{8}(x-7)$

$y=-\frac{7}{8}x+\frac{17}{8}$

Step-by-step explanation:

We want to write the equation of the line that passes through the points (7, -4) and (-1, 3) first in point-slope form and then in slope-intercept form.

First and foremost, we will need to find the slope of the line. So, we can use the slope-formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let (7, -4) be (x₁, y₁) and let (-1, 3) be (x₂, y₂). Substitute them into our slope formula. This yields:

$m=\frac{3-(-4)}{-1-7}$

Subtract. So, our slope is:

$m=\frac{7}{-8}=-7/8$

Now, let's use the point-slope form:

$y-y_1=m(x-x_1)$

We will substitute -7/8 for our slope m. We will also use the point (7, -4) and this will be our (x₁, y₁). So, substituting these values yield:

$y-(-4)=-\frac{7}{8}(x-7)$

Simplify. So, our point-slope equation is:

$y+4=-\frac{7}{8}(x-7)$

Finally, we want to convert this into slope-intercept form. So, let's solve for our y.

On the right, distribute:

$y+4=-\frac{7}{8}x+\frac{49}{8}$

Subtract 4 from both sides. Note that we can write 4 using a common denominator of 8, so 4 is 32/8. This yields:

$y=-\frac{7}{8}x+\frac{49}{8}-\frac{32}{8}$

Subtract. So, our slope-intercept equation is:

$y=-\frac{7}{8}x+\frac{17}{8}$

And we're done!

7 0

3 years ago

Read 2 more answers

Max bicycled 6.25 mi in 30.5 on average how far did he bicycle each minute round to the nearest tenth

ollegr [7]

6.25/30.5= 0.2049180327868852 = 0.2 Miles per minute

6 0

3 years ago

Suppose the number of children in a household has a binomial distribution with parameters n=12n=12 and p=50p=50%. Find the proba

nadya68 [22]

Answer:

a) 20.95% probability of a household having 2 or 5 children.

b) 7.29% probability of a household having 3 or fewer children.

c) 19.37% probability of a household having 8 or more children.

d) 19.37% probability of a household having fewer than 5 children.

e) 92.71% probability of a household having more than 3 children.

Step-by-step explanation:

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.

In this problem, we have that:

$n = 12, p = 0.5$

(a) 2 or 5 children

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

$P(X = 2) = C_{12,2}.(0.5)^{2}.(0.5)^{10} = 0.0161$

$P(X = 5) = C_{12,5}.(0.5)^{5}.(0.5)^{7} = 0.1934$

$p = P(X = 2) + P(X = 5) = 0.0161 + 0.1934 = 0.2095$

20.95% probability of a household having 2 or 5 children.

(b) 3 or fewer children

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

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

$P(X = 0) = C_{12,0}.(0.5)^{0}.(0.5)^{12} = 0.0002$

$P(X = 1) = C_{12,1}.(0.5)^{1}.(0.5)^{11} = 0.0029$

$P(X = 2) = C_{12,2}.(0.5)^{2}.(0.5)^{10} = 0.0161$

$P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.0537$

$P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0002 + 0.0029 + 0.0161 + 0.0537 = 0.0729$

7.29% probability of a household having 3 or fewer children.

(c) 8 or more children

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)$

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

$P(X = 8) = C_{12,8}.(0.5)^{8}.(0.5)^{4} = 0.1208$

$P(X = 9) = C_{12,9}.(0.5)^{9}.(0.5)^{3} = 0.0537$

$P(X = 10) = C_{12,10}.(0.5)^{10}.(0.5)^{2} = 0.0161$

$P(X = 11) = C_{12,11}.(0.5)^{11}.(0.5)^{1} = 0.0029$

$P(X = 12) = C_{12,12}.(0.5)^{12}.(0.5)^{0} = 0.0002$

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.1208 + 0.0537 + 0.0161 + 0.0029 + 0.0002 = 0.1937$

19.37% probability of a household having 8 or more children.

(d) fewer than 5 children

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

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

$P(X = 0) = C_{12,0}.(0.5)^{0}.(0.5)^{12} = 0.0002$

$P(X = 1) = C_{12,1}.(0.5)^{1}.(0.5)^{11} = 0.0029$

$P(X = 2) = C_{12,2}.(0.5)^{2}.(0.5)^{10} = 0.0161$

$P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.0537$

$P(X = 4) = C_{12,4}.(0.5)^{4}.(0.5)^{8} = 0.1208$

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0002 + 0.0029 + 0.0161 + 0.0537 + 0.1208 = 0.1937$

19.37% probability of a household having fewer than 5 children.

(e) more than 3 children

Either a household has 3 or fewer children, or it has more than 3. The sum of these probabilities is 100%.

From b)

7.29% probability of a household having 3 or fewer children.

p + 7.29 = 100

p = 92.71

92.71% probability of a household having more than 3 children.

5 0

3 years ago