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3 years ago

Consider the function f(x) = x2 + 12x + 11. x-intercepts?

Mathematics

2 answers:

IrinaK [193]3 years ago

8 0

The x-intercepts of this function are -11 and -1.

The easiest way to find the intercepts of this graph is by factoring. To factor a quadratic, we look for factors of the last number, that add up to the middle number. Below are the factors of the last number.

1 and 11

-1 and -11

Now we look for one that adds up to positive 12.

1 and 11

-1 and -11

Since these two add up to the middle number, we can use them in parenthesis with x + and factor. If there was not a pair, we would then have to use the quadratic equation.

f(x) = (x + 1)(x + 11)

Now to solve for the x-intercepts, we set each parenthesis equal to 0 and solve for x.

x + 1 = 0

x = -1

x + 11 = 0

x = -11

Nitella [24]3 years ago

6 0

Answer:

x intercept: (-1,0) & (-11,0)

y intercept: (0,11)

Step-by-step explanation:

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2 years ago

Given cscx =-5/2 between 270 and 360 find sin2x

ICE Princess25 [194]

Hello :
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3 years ago

Solve 8 = 22x − 1. 2 3 4 8

svetlana [45]

None of those answers work. The correct answer should be (9/22).

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3 years ago

Read 2 more answers

A random sample of 100 people from City A has an average IQ of 120 with a SD of 18. Independently of this, a random sample of 15

Sloan [31]

Answer:

$z=\frac{(120-116)-0}{\sqrt{\frac{18^2}{100}+\frac{15^2}{150}}}}=1.837$

$p_v =P(z>1.837)=1-P(Z$

Comparing the p value with a significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the average IQ on city A is signficantly higher than city B at 5% of singificance.

Step-by-step explanation:

$\bar X_{A}=120$ represent the mean for sample 1

$\bar X_{B}=116$ represent the mean for sample 2

$s_{A}=18$ represent the sample standard deviation for 1

$s_{B}=15$ represent the sample standard deviation for 2

$n_{A}=100$ sample size for the group 2

$n_{B}=150$ sample size for the group 2

$\alpha$ Significance level provided

z would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if residents of City A smarter on average, the system of hypothesis would be:

Null hypothesis: $\mu_{A}-\mu_{B}\leq 0$

Alternative hypothesis: $\mu_{A} - \mu_{B}> 0$

We don't have the population standard deviation's, but the sample sizes are large enough we can apply a z test to compare means, and the statistic is given by:

$z=\frac{(\bar X_{A}-\bar X_{B})-\Delta}{\sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

With the info given we can replace in formula (1) like this:

$z=\frac{(120-116)-0}{\sqrt{\frac{18^2}{100}+\frac{15^2}{150}}}}=1.837$

P value

Since is a one right tailed test the p value would be:

$p_v =P(z>1.837)=1-P(Z$

5 0

3 years ago

Match this median concurrent proof

Lapatulllka [165]

Answer:

E. (You always start with the given statement)

Step-by-step explanation:

The first line is given and therefore goes with E. Given.

The second line comes from the definition of median.

It bisects the opposite side from the vertex is being drawn from: So we have FA=FB, BE=EC, and CG=GA.

Second box goes with C.

Third line says FA/FB=1, BE/EC=1, and CG/GA=1.

How did they get this. It looks like they divided previous equation on both sides by right hand side's expression.

For example:

FA=FB

Divide both sides by FB you get:

FA/FB=FB/FB

FA/FB=1

So third line goes with A.

The fourth line is substitution property. 1=1(1)(1)=1(FA/FB)(BE/EC)(CG/GA). They replaced the 1's with what we had in the previous line.

Fifth line is Ceva's Theorem since it states that the FA:FB=BE:EC=CG:GA=1 implies the medians are concurrent.

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4 years ago