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Paul [167]
3 years ago
15

It takes four steps to factor 48 – 3y 4 completely. Using complete sentences and the appropriate vocabulary, explain each of the

four steps.
Mathematics
1 answer:
Nezavi [6.7K]3 years ago
8 0

Answer:

3(2 - y)(2 + y)(4 + y²)

Step-by-step explanation:

48 - 3y⁴

Take 3 common:

3(16 - y⁴)

16 is 4² and y⁴ is (y²)²

3(4² - (y²)²)

Using a² - b² = (a - b)(a + b)

3(4 - y²)(4 + y²)

Again, 4 = 2²

3(2² - y²)(4 + y²)

3(2 - y)(2 + y)(4 + y²)

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((–7) + (3 + i)) - (2 - (6 + i)) =-9 + 9 i
3 0
4 years ago
The relation R is shown below as a list of ordered
Dmitrij [34]

Answer:

(1, 4) and (1,3), because they have the same x-value

Step-by-step explanation:

For a relation to be regarded as a function, there should be no two y-values assigned to an x-value. However, two different x-values can have the same y-values.

In the relation given in the equation, the ordered pairs (1,4) and (1,3), prevent the relation from being a function because, two y-values were assigned to the same x-value. x = 1, is having y = 4, and 3 respectively.

Therefore, the relation is not a function anymore if both ordered pairs are included.

<em>The ordered pairs which make the relation not to be a function are: "(1, 4) and (1,3), because they have the same x-value".</em>

7 0
3 years ago
True or false? The quadratic equation 10p2 - 5p = -8 has one solution.
pav-90 [236]

Answer: False

=============================================

Explanation:

I'll use x in place of p.

The original equation 10x^2-5x = -8 becomes 10x^2-5x+8 = 0 after moving everything to one side.

Compare this to ax^2+bx+c = 0

We have

  • a = 10
  • b = -5
  • c = 8

Plug those three values into the discriminant formula below

d = b^2 - 4ac

d = (-5)^2 - 4(10)(8)

d = 25 - 40*8

d = 25 - 320

d = -295

The discriminant is negative, which means we have no real solutions. If your teacher has covered complex or imaginary numbers, then you would say that the quadratic has 2 complex roots. If your teacher hasn't covered this topic yet, then you'd simply say "no real solutions".

Either way, this quadratic doesn't have exactly one solution. That only occurs when d = 0. Therefore, the original statement is false.

6 0
2 years ago
A rectangle garden is 6 feet long and 4 feet wide a second rectangular garden has dimensions that are doubled the dimensions of
OLga [1]
I do not know this one but the first garden is 24 and the second one is 576.
8 0
3 years ago
Suppose you are the manager of Speedy Oil Change which claims that it will change the oil in​ customers’ cars in less than 30 mi
Veronika [31]

Answer:

Explained below.

Step-by-step explanation:

(1)

The hypothesis can be defined as follows:

<em>H</em>₀: The Speedy Oil Change will change the oil in​ customers’ cars in more than 30 minutes on average, i.e. <em>μ</em> > 30.

<em>H</em>ₐ: The Speedy Oil Change will change the oil in​ customers’ cars in less than 30 minutes on average, i.e. <em>μ</em> ≤ 30.

(2)

Use Excel to compute the sample mean and standard deviation as follows:

\bar x=\text{AVERAGE(array)}=24.917\\\\s=\text{STDEV.S(array)}=8.683

Compute the test statistic as follows:

t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{24.917-30}{8.683/\sqrt{36}}=-3.51

The degrees of freedom is:

df = n - 1

   = 36 - 1

   = 35

Compute the p-value as follows:

p-value=P(t_{35}

(3)

The <em>p</em>-value = 0.0006 is very small.

The null hypothesis will be rejected at any of the commonly used significance level.

(4)

There is sufficient evidence to support the claim that the Speedy Oil Change will change the oil in​ customers’ cars in less than 30 minutes on average.

3 0
3 years ago
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