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Veseljchak [2.6K]
3 years ago
14

Which linear function represents the line given by the point-slope equation y – 2 = 4(x – 3)?

Mathematics
1 answer:
patriot [66]3 years ago
8 0

y = 4x - 10. The linear functions y = 4x - 10 represent the line given by the point-slope equation y - 2 = 4(x - 3).

In order to solve this problem, we have to take the point-slope equation y - 2 = 4(x - 3) and convert it to the linear function form y = mx + b as follow:

y - 2 = 4(x - 3)

y - 2 = 4(x) - (4)(3)

y - 2 = 4x - 12

y - 2 + 2 = 4x -12 +2

y = 4x - 10 (Linear function)

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(2a-b)2-(a-2b)2 factorial
kvasek [131]

Hello, we know that for a and b real numbers

a^2-b^2=(a-b)(a+b)

So,

(2a-b)^2-(a-2b)^2=(2a-b-a+2b)(2a-b+a-2b)\\\\=(a+b)(3a-3b)\\\\\boxed{=3(a+b)(a-b)}

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7 0
3 years ago
What is the value of this expression when d = 4 7/8 and f = 3 1/2<br> 6 (d - f) + f
ioda

7+(10−4)2:4⋅231=7+62:4⋅81=7+36:4⋅81=7+9⋅81=7+89=7+181=881

4 0
2 years ago
A bucket can hold a total of 5 gallons. If the bucket is 45% full, how much water is in the bucket?
kirill [66]

The question is an illustration of volume, and the amount of water in the bucket at 45% full is 2.25 gallons

<h3>How to determine the amount of water?</h3>

The capacity of the bucket is given as:

Bucket = 5 gallons

At 45% full, we have:

Capacity = 45% * 5 gallons

Evaluate the product

Capacity = 2.25 gallons

Hence, the amount of water in the bucket at 45% full is 2.25 gallons

Read more about volumes at:

brainly.com/question/1972490

#SPJ1

3 0
2 years ago
Suppose that a company prints baseball cards. They claim that 30% of the cards feature rookies, 60% feature veterans, and 10% fe
liraira [26]

Answer:

H0: The distribution of players featured on the cards is 0.30 rookies, 0.60 veterans, and 0.10 All-Stars.

Ha: At least one of the proportions in the null hypothesis is false.

Step-by-step explanation:

On this case we need to apply a Chi squared goodness of fit test, and the correct system of hypothesis would be:

H0: The distribution of players featured on the cards is 0.30 rookies, 0.60 veterans, and 0.10 All-Stars.

Ha: At least one of the proportions in the null hypothesis is false.

And in order to test it we need to have observed and expected values. On this case we  can calculate the Expected values like this

E_{rookies}=50*0.3=15

E_{veterans}=50*0.6=30

E_{All stars}=50*0.1=5

The observed values are not provided. The statistic on this case is given by:

\chi^2 =\sum_{i=1}^n \frac{(O_i) -E_i}{E_i}

And this statistic follows a chi square distribution with k-1 degrees of freedom on this case k=3, since we have 3 groups.

We can calculate the p valu like this:

P(\chi^2 > \chi^2_{calculated})=p_v

And if the p value it's higher than the significance level we FAIL to reject the null hypothesis. In other case we reject the null hypothesis.

5 0
3 years ago
Triangle ABC has vertices A(1,4), B(−2,4) , and C(−1,−1) . A dilation with a scale factor of 0.25 and center at the origin is ap
zloy xaker [14]
So multiply to get answer.

B' is (-2*.25, 4*.25), or (-0.5, 1)

Answer: (-0.5, 1)
6 0
3 years ago
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