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1 year ago

Write g(x) = 4x2 + 88x in vertex form. The function written in vertex form is g(x) = _ (x +11)2 +__.

Mathematics

2 answers:

wel1 year ago

5 0

$The\ vertex\ form:\\\\f(x)=a(x-h)^2+k$

$\text{Use}\ (a+b)^2=a^2+2ab+b^2\qquad(*)$

$g(x)=4x^2+88x=4(x^2+22x)=4(x^2+2\cdot x\cdot11)\\\\=4(\underbrace{x^2+2\cdot x\cdot11+11^2}_{(*)}-11^2)=4[(x+11)^2-121]=4(x+11)^2+(4)(-121)=4(x+11)^2-484$

klio [65]1 year ago

4 0

Answer:

To keep it simple the answer is g(x) = 4 (x+11) ^2 + -484

The 4 stays the same and then the -484 is 88 multiply by -5.5.

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Given that line s is perpendicular to line t, which statements must be true of the two lines? Check all that apply.

artcher [175]

The basis to respond this question are:

1) Perpedicular lines form a 90° angle between them.

2) The product of the slopes of two any perpendicular lines is - 1.

So, from that basic knowledge you can analyze each option:

<span>a.Lines s and t have slopes that are opposite reciprocals.

TRUE. Tha comes the number 2 basic condition for the perpendicular lines.

slope_1 * slope_2 = - 1 => slope_1 = - 1 / slope_2, which is what opposite reciprocals means.

b.Lines s and t have the same slope.

FALSE. We have already stated the the slopes are opposite reciprocals.

c.The product of the slopes of s and t is equal to -1

TRUE: that is one of the basic statements that you need to know and handle.

d.The lines have the same steepness.

FALSE: the slope is a measure of steepness, so they have different steepness.

e.The lines have different y intercepts.

FALSE: the y intercepts may be equal or different. For example y = x + 2 and y = -x + 2 are perpendicular and both have the same y intercept, 2.

f.The lines never intersect.

FALSE: perpendicular lines always intersept (in a 90° angle).

g.The intersection of s and t forms right angle.

TRUE: right angle = 90°.

h.If the slope of s is 6, the slope of t is -6

FALSE. - 6 is not the opposite reciprocal of 6. The opposite reciprocal of 6 is - 1/6.

So, the right choices are a, c and g.
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1 year ago

Read 2 more answers

Sarah received \$55$55dollar sign, 55 for her birthday. She used some of that money to buy 333 shirts priced at mmm dollars each

satela [25.4K]

Answer:

$(55-3m) is the amount of money she has left

Step-by-step explanation:

In this question, we are asked to give an expression to represent how much money was left after Sarah had bought some certain stuffs at some prices using the money she received at her birthday.

Firstly, we identify that the total amount of money she has to spend is $55.

Now let’s project her total spendings. She bought 3 shirts with each shirt costing $m.

The total amount spent on the shirts is thus; 3 * $m = $3m

The amount of money she has left is the difference.

Mathematically, this is equal to $55 - $3m

4 0

1 year ago

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The XO Group Inc. conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of

slavikrds [6]

Answer:

a) 0.0392

b) 0.4688

c) At least $39,070 to be among the 5% most expensive.

Step-by-step explanation:

Problems of normally distributed samples can be 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 problem, we have that:

$\mu = 29858, \sigma = 5600$

a. What is the probability that a wedding costs less than $20,000 (to 4 decimals)?

This is the pvalue of Z when X = 20000. So

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

$Z = \frac{20000 - 29858}{5600}$

$Z = -1.76$

$Z = -1.76$ has a pvalue of 0.0392.

So this probability is 0.0392.

b. What is the probability that a wedding costs between $20,000 and $30,000 (to 4 decimals)?

This is the pvalue of Z when X = 30000 subtracted by the pvalue of Z when X = 20000.

X = 30000

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

$Z = \frac{30000 - 29858}{5600}$

$Z = 0.02$

$Z = 0.02$ has a pvalue of 0.5080.

X = 20000

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

$Z = \frac{20000 - 29858}{5600}$

$Z = -1.76$

$Z = -1.76$ has a pvalue of 0.0392.

So this probability is 0.5080 - 0.0392 = 0.4688

c. For a wedding to be among the 5% most expensive, how much would it have to cost (to the nearest whole number)?

This is the value of X when Z has a pvalue of 0.95. So this is X when Z = 1.645.

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

$1.645 = \frac{X - 29858}{5600}$

$X - 29858 = 5600*1.645$

$X = 39070$

The wedding would have to cost at least $39,070 to be among the 5% most expensive.

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1 year ago

A yard is equal in length to three feet. The function f(x) takes a measurement in yards (as input) and returns a measurement in

Grace [21]

If it takes yards and turns it into feet then it just multiplies it by 3

so if the input is 10.5 then you just multiply it by three

31.5 feet is the imput

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1 year ago

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Whats another way to write 300 70 5/10 8/100?

Aloiza [94]

I don't understand what you mean by 300 and 70, unless you meant 300/70 (in that case it would be 30/7).

5/10 would be 1/5

8/100 would be 2/25.

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2 years ago

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Write g(x) = 4x2 + 88x in vertex form. The function written in vertex form is g(x) = ___ (x +11)2 +____.

Write g(x) = 4x2 + 88x in vertex form. The function written in vertex form is g(x) = _ (x +11)2 +__.