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andrew11 [14]
3 years ago
14

Find the vertex of y = x^2 – 2x – 15

Mathematics
2 answers:
svet-max [94.6K]3 years ago
7 0
The vertex is ( 1, -16 ).
solong [7]3 years ago
7 0

Answer:

The vertex is at (h, k), which here is (1, -16).

Step-by-step explanation:

One of the quicker ways to approach this proplem is to "complete the square," which puts the equation into "vertex form."

Starting with y = x^2 – 2x – 15, add 1 to, and then subtract 1 from,  x^2 – 2x :

y = x^2 – 2x + 1 - 1– 15

Now re-write   x^2 – 2x   as (x - 1)^2 - 1:

y = (x - 1)^2 - 1 – 15. or  y = (x - 1)^2 - 16, which has the form y = (x - h)^2 + k.  Comparing these two equations, we see that h = 1 and k = -16.

The vertex is at (h, k), which here is (1, -16).

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Blair is ordering 150 t-shirt to sell at the school carnival
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Then he should sell all of them for 3 dollars and he'll get $450 dollars from all 150 t-shirts
6 0
3 years ago
Which of the following represents the zeros of f(x) = 2x3 − 5x2 − 28x + 15?
likoan [24]

\mathrm{Use\:the\:rational\:root\:theorem}

a_0=15,\:\quad a_n=2

\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:3,\:5,\:15,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\:2

\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:3,\:5,\:15}{1,\:2}

-\frac{3}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+3

-\frac{3}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+3

\mathrm{Compute\:}\frac{2x^3-5x^2-28x+15}{x+3}\mathrm{\:to\:get\:the\:rest\:of\:the\:eqution:\quad }2x^2-11x+5

=\left(x+3\right)\left(2x^2-11x+5\right)

Factor: 2x^2-11x+5

2x^2-11x+5=\left(2x^2-x\right)+\left(-10x+5\right)

=x\left(2x-1\right)-5\left(2x-1\right)

2x^3-5x^2-28x+15=\left(x+3\right)\left(x-5\right)\left(2x-1\right)

\left(x+3\right)\left(x-5\right)\left(2x-1\right)=0

\mathrm{Using\:the\:Zero\:Factor\:Principle:}

thus zeros of f(x) is

x=-3,\:x=5,\:x=\frac{1}{2}

5 0
3 years ago
Read 2 more answers
HELP
mr Goodwill [35]

Answer:

b should be the answer i think

3 0
3 years ago
Read 2 more answers
A local police chief claims that 31% of all drug-related arrests are never prosecuted. A sample of 500 arrests shows that 27% of
Elis [28]

Answer:

z=\frac{0.27 -0.31}{\sqrt{\frac{0.31(1-0.31)}{500}}}=-1.933  

p_v =P(Z  

If we compare the p value obtained and the significance level given \alpha=0.02 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 2% of significance the proportion of arrests that were not prosecuted is not significanlty less than 0.31.  

Step-by-step explanation:

1) Data given and notation

n=500 represent the random sample taken

X represent the number of arrests that were not prosecuted.

\hat p=0.27 estimated proportion of arrests that were not prosecuted

p_o=0.31 is the value that we want to test

\alpha=0.02 represent the significance level

Confidence=98% or 0.98

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.31.:  

Null hypothesis:p\geq 0.31  

Alternative hypothesis:p < 0.31  

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 \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.27 -0.31}{\sqrt{\frac{0.31(1-0.31)}{500}}}=-1.933  

4) 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 significance level provided \alpha=0.02. The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

p_v =P(Z  

If we compare the p value obtained and the significance level given \alpha=0.02 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 2% of significance the proportion of arrests that were not prosecuted is not significanlty less than 0.31.  

3 0
3 years ago
ANswer today plz other wise its to late if you answer after 11:59 your to late plz answer before 11:59
Rom4ik [11]

Answer:

210 yd³

Step-by-step explanation:

V=LWH

V=(8 1/3)(4 1/5)(6)

V=(25/3)(21/5)(6)

V=(525/15)(6)

V=3150/15

V=210

Therefore, the volume of the prism is 210 yd³

5 0
3 years ago
Read 2 more answers
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