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3 years ago

15

The quadratic equation: y=x^2+2x-8 is in standard form. What is the vertex and factored form equivalent to this? Also solve for

X

1 answer:

Valentin [98]3 years ago

7 0

V (-1,-9)
Y=1(x+1)^2-9
If you’re talking about the value of x in the quadratic equation then it is x=-4 &x=2

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Luke is going to repaint both sides of the door of his room. The door is 36 inches long by 80 inches high. His options at the pa

earnstyle [38]

$26.20 minimum cost of option 1
$36.68 minimum cost of option 2

Area₁ = Length x Width
A₁ = 80 x 36
A₁ = 2880 in² * this in only one side of the door.

Total Area = A₁ x 2 sides = 2880 = 5760 in² * only good for 1 coating of paint
Total Area to be coated = 5760 x 2 coats of paint = 11,520 in²

1st option - $10 / gallon and 4400 sq. in.
2nd option - $ 7 / gallon and 2200 sq. in

11,520 / 4400 = 2.62 x $10 = $26.20 minimum cost of option 1
11,520 / 2200 = 5.24 x $ 7 = $36.68 minimum cost of option 2

8 0

4 years ago

What is the volume of the cube when one side is 2 1/2 in

oksian1 [2.3K]

Answer:

15 5/8 in³ (=15.625 in³)

Step-by-step explanation:

recall

volume of cube = length ³

given length = 2 1/2 = 5/2 inches

volume of cube,

= (5/2) ³

= 5³ / 2³

= 125 / 8

= 15 5/8 in³

8 0

4 years ago

Simplify (7x^2 + 3y-4)+(5x^2+5y)

Alex Ar [27]

\left[x _{2}\right] = \left[ \left( \frac{1}{6}\,i \right) \,\sqrt{3}\,\sqrt{\left( -4+8\,y\right) }\right][x2]=[(61i)√3√(−4+8y)] totally answer

5 0

3 years ago

Find all solutions of the equation in the interval [0,2pi).<br> 3csc^2x-4=0

nikdorinn [45]

The answer is going to be 2x-91/61 (18) because of the length of the interval the interval will be bisected

3 0

3 years ago

g PROBLEM 3. Based on data from Consumer Reports, replacement times of TVs is on average 3.75 years with the standard deviation

Aleksandr [31]

Answer:

29.81% probability that their average replacement time is less than 3.5 years

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 3.75, \sigma = 2.5, n = 28, s = \frac{2.5}{\sqrt{28}} = 0.47$

What is the probability that their average replacement time is less than 3.5 years

This is the pvalue of Z when X = 3.5. So

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

By the Central Limit Theorem

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

$Z = \frac{3.5 - 3.75}{0.45}$

$Z = -0.53$

$Z = -0.53$ has a pvalue of 0.2981

29.81% probability that their average replacement time is less than 3.5 years

4 0

3 years ago