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faust18 [17]
3 years ago
7

Find the x-intercepts of the parabola with vertex (5,-4) and y-intercept (0,96). Write your answer in this form: (x1,y1),(x2,y2)

. If necessary, round to the nearest hundredth. ​

Mathematics
1 answer:
lesya692 [45]3 years ago
4 0

Answer:

The x-intercepts are

(x1,y1)=(4,0)

(x2,y2)=(6,0)

Step-by-step explanation:

we know that

The equation of the given parabola is

(y-k)=a(x-h)^{2}

we have

the vertex is the point (5,-4)

substitute

(y+4)=a(x-5)^{2}

The y-intercept is the point (0,96)

substitute and solve for a

(96+4)=a(0-5)^{2}

100=a(25)

a=100/25=4

The equation of the vertical parabola is equal to

(y+4)=4(x-5)^{2}

Find the x-intercepts

Remember that

The x-intercepts are the values of x when the value of y is equal to zero

For y=0

4=4(x-5)^{2}

Simplify

1=(x-5)^{2}

Rewrite

(x-5)^{2}=1

square root both sides

(x-5)=(+/-)1

x=(+/-)1+5

x=(+)1+5=6

x=(-)1+5=4

therefore

The x-intercepts are

(x1,y1)=(4,0)

(x2,y2)=(6,0)

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Answer:

See answer below

Step-by-step explanation:

1), Probably, your implication is ∀x∃yP(x,y)⇒∃x∀yP(x,y).

This implication is false. Consider the predicate P(x,y):="x<y" for real numbers x,y. Then, ∀x∃yP(x,y) is true: for all real x, there exists some y greater than x (take y=x+1 for example). However, ∃x∀yP(x,y) is false, as it would imply that there exists some real number x such that x is smaller than all real numbers, which is not true (real numbers do not have a minimum or a lower bound).

A short explanation would be, even if for all elements you can find one that makes a predicate true, you can not find one element that makes the predicate true for all elements.

2) Again, I assume that the predicate is ∃x∀yP(x,y)⇒∀x∃yP(x,y)

This implication is false. Consider the predicate P(x,y):="x is integer and xy=0 " for real numbers x,y. Then ∃x∀yP(x,y) is true, we need to take x=0. However, ∀x∃yP(x,y) is false, if you take x=1/2, 1/2 will never be an integer, no matter the value of y.

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The conclusion is that there is sufficient evidence to support the claim that the percentage of vacant housing units in their district differs from the percentage of vacant housing units in the country.

Given that the total number of a housing units in her country is 550 and the number of vacant housing units in her country is 130.

The Null hypothesis is p₀=13%=0.13, n=550 and x=130

Significance level α=0.05

Claims given: percentage other than 13%

The claim is anyone of the null hypothesis or the alternative hypothesis. The null hypothesis shows that the proportion of the population is equal to the value stated in the claim. If the null hypothesis is a claim, then the alternative hypothesis states the opposite of the null hypothesis.

H₀:p=13%=0.13

Hₐ:p/0.13

I'm interested in testing population proportion claims, so I'll use z-text with proportions.

Conditions: Random sample, 10% condition, pass / fail condition

Sample: I'm happy because the housing units were randomly selected.  10% Condition: We are happy because the sample of 550 homes in your county is less than 10% of the population.

Pass/ fail condition: Satisfied because both np₀ and n(1-p₀) are both at least 10.

np₀=550(0.13)=71.5≥10

n(1-p₀)=550(1-0.13)=478.5≥10

Therefore, we conclude that all the conditions are met.

The sample percentage is the number of successes divided by the sample size.

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Determines the value of the test statistic:

\begin{aligned}z&=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \\ &=\frac{0.2364-0.13}{\sqrt{\frac{0.13(1-0.13)}{550}}}\\ &=\frac{0.1064}{0.0143}\\&\approx 7.41 \end

The P-value is the probability of getting a test statistic value  or a  more extreme value if the null hypothesis is true. Use the normal probability table in the appendix to determine the P-value.

P=P(Z<−7.41 or Z>7.41)

P=2P(Z>7.41)

P=2(0)

P=0

If the P-value is less than the significance level α,  the null hypothesis is rejected.

P<0.05⇒ Reject H₀

Therefore, there is ample evidence to support the claim that the proportion of vacant homes in the area is different from the proportion of vacant homes in the country.

Learn more about Standard normal distribution from here brainly.com/question/13383035

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