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3 years ago

What are the x and y intercepts of the graph y=x^2+7x+12

Mathematics

1 answer:

koban [17]3 years ago

5 0

Answer:

x-intercepts are (-3,0) and (-4,0).

y-intercept is (0,12).

Step-by-step explanation:

x-intercept is a point where the value of y is zero.

y-intercept is a point where the value of x is zero.

Given equation is :

y=x²+7x+12

put x=0 in given equation to find y-intercept.

y=(0)²+7(0)+12

y= 0+0+12

y= 12

hence, y-intercept is (0,12).

put y=0 in given equation to find x-intercept.

0=x²+7x+12

split the middle term of above equation to make the equation into two groups such that the sum of two numbers should be 7 and their product be 12.

x²+3x+4x+12=0

making two groups and taking common out:

x(x+3)+4(x+3)=0

take (x+3) common,

(x+3)(x+4)=0

x+3=0 or x+4=0

x=-3 or x=-4

hence, x-intercepts are (-3,0) and (-4,0).

You might be interested in

a set of average city temperatures in december are normally distributed with a mean of 16.3°C and a standard deviation of 2°C. w

koban [17]

Answer:

19.74% of temperatures are between 12.9°C and 14.9°C

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 16.3, \sigma = 2$

What proportion of temperatures are between 12.9°C and 14.9°C?

This is the pvalue of Z when X = 14.9 subtracted by the pvalue of Z when X = 12.9.

X = 14.9

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

$Z = \frac{14.9 - 16.3}{2}$

$Z = -0.7$

$Z = -0.7$ has a pvalue of 0.2420

X = 12.9

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

$Z = \frac{12.9 - 16.3}{2}$

$Z = -1.7$

$Z = -1.7$ has a pvalue of 0.0446

0.2420 - 0.0446 = 0.1974

19.74% of temperatures are between 12.9°C and 14.9°C

3 0

3 years ago

∠3 and ∠4 are supplementary angles. If ∠3 measures 50°, what is the measure of ∠4

Sidana [21]

Answer:

130

Step-by-step explanation:

Supplementary angles are angles that are equal to 180 degree so if one is 50 degrees then the other must be added to it and get 180

180= 50 + ∠4

-50 -50

130=∠4

6 0

3 years ago

PLEASE PLEASE HELP!!

Sloan [31]

Answer:

Step-by-step explanation:

11)

A= (B x H)/2

A= (2.9x3.2)/2= 4.64cm²

12)

A= (B+b)H /2

A= (12+10)5.6 /2 = 61.6in

3 0

3 years ago

Read 2 more answers

How do you factorize 8x-16y

IRINA_888 [86]

8x - 16y = a common factor would be 8...so factor out 8
8(x - 2y)

5 0

3 years ago

The U.S. Department of Agriculture claims that the mean consumption of coffee by a person in the United States is 24.2 gallons p

Dmitry_Shevchenko [17]

Answer:

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to reject the claim

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 24.2 \ gallons \ per \ year$

The sample size is n = 101

The sample mean is $\= x = 23.5 \ gallons\ per\ year$

The standard deviation is $\sigma = 3.2 \ gallons$

The null hypothesis is $H_o : \mu = 24.2$

The alternative hypothesis is $H_a : \mu \ne 24.2$

Generally the test statistics is mathematically represented as

$z = \frac{ \= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }$

=> $z = \frac{ 23.5 - 24.2 }{ \frac{ 3.2}{ \sqrt{ 101} } }$

=> $z = -2.198$

From the z table the area under the normal curve to the left corresponding to -2.198 is

$P(Z < -2.198 ) = 0.013975$

Gnerally the p-value is mathematically represented as

$p-value = 0.013975 * 2$

=> $p-value = 0.02795$

From the value obtained we have that $p-value \ < \ \alpha$ hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to reject the claim

Using the Rejection Regions for a z-test method

Generally from the z table the critical value of $\frac{\alpha }{2}$ is

$z_{critical} = \pm 1.96$

Not we are using $\frac{\alpha }{2}$ because it is a two - tailed test

Now comparing the critical value and the test statistics we see that the

region covered by the test statistics (i.e $2.198 < z < -2.198$ ) is greater than the region covered by the critical value (i.e $1.96 < z < -1.96$ )

Hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is sufficient evidence to reject the claim

4 0

3 years ago