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2 years ago

What is the following solution to |x+3|=12

2 answers:

vladimir1956 [14]2 years ago

5 0

$|x|=a\iff x=a\ or\ x=-a\\==============================\\|x+3|=12\iff x+3=12\ or\ x+3=-12\ \ \ \ |subtract\ 3\ from\ both\ sides\\\\\boxed{x=9\ or\ x=-15}$

deff fn [24]2 years ago

4 0

$|x+3|=12\\
x+3=12 \vee x+3=-12\\
x=9 \vee x=-15$

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Please help! <br> Simplify. Your answer should contain only positive exponents.

maxonik [38]

Answer:

$\frac{1}{4k^3}$

Step-by-step explanation:

It's already in a form that only ha positive exponents. Just to state it though you could rewrite it as $k*(4k^{4})^{-1}$ or $k*4^{-1}*k^{-4}$ The question asks for positive exponents though so yu don't need to do that.

You also need to know $\frac{x^a}{x^b}=x^{a-b}$ so in this case $\frac{k}{k^4}=\frac{k^1}{k^4} =k^{1-4}=k^{-3}=\frac{1}{k^3}$

so $\frac{k}{4k^4}=\frac{1}{4}*\frac{k}{k^4}=\frac{1}{4}*\frac{1}{k^3}=\frac{1}{4k^3}$

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2 years ago

Write an equation in slope-intercept<br> form through (-8,9) through (-6,-6).

fgiga [73]

Answer:

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly different from 0.36. With

Dafna11 [192]

Answer:

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.36 so then we need to conduct a two tailed test, the system of hypothesis are.:

Null hypothesis: $p=0.36$

Alternative hypothesis: $p \neq 0.36$

Since is a bilateral test the p value would be:

$p_v =2*P(z>2.074)=0.0381$

Step-by-step explanation:

Data given and notation n

n represent the random sample taken

$\hat p$ estimated proportion of interest

$p_o=0.36$ is the value that we want to test

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.36 so then we need to conduct a two tailed test, the system of hypothesis are.:

Null hypothesis: $p=0.36$

Alternative hypothesis: $p \neq 0.36$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

Calculate the statistic

For this case the statistic is given:

$z = 2.074$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z>2.074)=0.0381$

5 0

3 years ago

HELP ME DO THIS PLZZZZ

andrezito [222]

Answer:

Step-by-step explanation:

y = -x^2+4x-6x +24

y = -x^2 -2x + 24

Vertex (x) = 2/-2 = -1

Vertex (y) = -100/ -4 = 25

Vertex (-1, 25)

axis of symmetry: x= -1

-x^2 -2x + 24 = 0

Δ/4 = 1+24 = 25

x1 = (1 + 5)/-1 = -6

x2 = (1-5)/-1 = 4

left x intercept = (-6,0)

right x intercept = (4,0)

The DOMAIN is the set of all numbers

The range is y less than or equal to 25

4 0

2 years ago

Find the zeros, vertical asymptote, horizontal asymptote, slant asymptote, and graphing points.

kramer

Zeroes
set numerator to zero
x^2=0
x=0
zeroes are at (0,0)

for p(x)/q(x)

when degree of p(x)<q(x), HA=0

when degree of p(x)=q(x), HA= leading coef of p(x) divided by leading coef of q(x)

when degree of p(x)>q(x) you probably have a slant assymtote

degrees are same (no slant assymtote)

leading coefs

1/1=1

HA is y=1

does it cross?

1=(x^2)/(x^2-4)

x^2-4=x^2

minus x^2 both sides

-4=0

false, it does not cross the HA

simplify the fraction (it can't)

set the denomenator to zero

(x-2)(x+2)=0

VA's at x=2 and x=-2

so to graph

graph the point (0,0)

draw the lines

y=1

x=-2

x=2

reemmber, plus, minus, plus

so from left, it goes from above the HA right up to the VA of x=-2

then goes upside down U shape in between VA's going through (0,0)

then from top of VA x=2 down to y=1 then gets closer to y=1 but never touches

5 0

3 years ago