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3 years ago

What are the x-intercepts of y=x^2+2x-15

Mathematics

1 answer:

Sedbober [7]3 years ago

8 0

Answer:

$(-5,0)$ and $(3,0)$

Step-by-step explanation:

Think about it.

What two numbers multiply to -15 and add up to 2?

The answers are 5 and -3.

So plug that into the factored form of a parabola.

$y=(x+5)(x-3)$

To find the x-intercepts, plug in 0 for $y$ .

$(x+5)(x-3)=0$

Since we are multiplying, at least one of the terms has to equal 0.

$x+5=0 \\ x-3=0 \\ \\ x=-5,3$

So the x-intercepts are $(-5,0)$ and $(3,0)$ .

You might be interested in

Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and th

Marizza181 [45]

Answer:

$\mu = 8.8\\\sigma = 1.9$

Now we are supposed to find probabilities that the response time is between 5 and 10 minutes i.e P(5<x<10)

Formula : $z= \frac{x-\mu}{\sigma}$

at x = 5

$z= \frac{5-8.8}{1.9}$

$z=-2$

at x = 10

$z= \frac{10-8.8}{1.9}$

$z=0.6315$

P(-2<z<0.6315)=P(z<0.6315)-P(z<-2)

Refer the z table

P(-2<z<10)=0.7357-0.0228=0.7129

So, the probability that response time is between 5 and 10 minutes is 0.7129

b)the response time is less than 5 minutes

at x = 5

$z= \frac{5-8.8}{1.9}$

$z=-2$

P(x<5)=P(z<-2)=0.0228

So, the probability that the response time is less than 5 minutes is 0.0228

c)the response time is more than 10 minutes

at x = 10

$z= \frac{10-8.8}{1.9}$

$z=0.6315$

P(x>10) = 1-P(x<10) = 1-P(z<0.63) = 1-0.7357 = 0.2643

So, The probability that the response time is more than 10 minutes is 0.2643

4 0

3 years ago

A student working on a summer internship in the economic research department of a large corporation studied the relation between

OverLord2011 [107]

Answer:

Step-by-step explanation:

Hello!

Y: sales of a product in a marketing district (million dollars)

X: population in a marketing district (million persons)

The objective is to test if there is a linear association between the sales of a product and the population of a marketing district.

Parameter; Estimated Value; 95 Percent Confidence limits

Intercept 7.43119 -1.18518 16.0476

Slope 0.755048 0.452886 1.05721

To test if there is or not an association between these two variables, you have to do a hypothesis test for the slope. If the slope is equal to zero, there is no linear association between the two variables, if the slope is different from zero, then there is a linear association between the variables.

So the student's hypotheses are:

H₀: β = 0

H₁: β ≠ 0

The data the student used to conclude is the 95%CI for the slope [0.452886;1.05721]

To be able to decide over an hypothesis test using a confidence interval there are several conditions to be met, one of them is that the confidence level and the significance level should be complementary, this means that if the interval was constructed using 1 - α= 0.95, then the hypothesis test should be conducted with a significance level of α= 0.05.

Considering that the value of the slope stated in the null hypothesis is not included in the given interval, i.e. zero is not included in the CI, then the decision is to reject the null hypothesis.

Then it can be concluded that there is a linear association between the sales of a product and the population in a marketing district.

Although in the context of the variables of study it makes no sense that the estimate of the intercept takes negative numbers, keep in mind that mathematically if possible and correct. This means that obtaining a negative estimate of the intercept does not represent a calculation error or problem for the regression model. In general, when this occurs, a footnote is made indicating has no biological meaning or sense in context.

After all, what you have done with the estimate is a mathematical assertion of the social variables.

I hope it helps!

3 0

3 years ago

8=16+8n (can you show rhe solving steps too please?)

irakobra [83]

Answer:

Step-by-step explanation:

8=16+8n

8-16=16-16+8n

-8=8n

-8/8=8n/8n