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3 years ago

Find the complete factorization of the expression. 15xz + 21yz

Mathematics

2 answers:

ss7ja [257]3 years ago

8 0

The answer would be 3z(5x + 7y)

Ivan3 years ago

7 0

Answer:

A) 3z(5x+7y)

Step-by-step explanation: This is the answer because if you distribute it right you get the answer.

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The function f(x) = x^3 has been transformed, resulting in function h.

Sholpan [36]

Answer:

To create function h, function f was translated 2 units to the right, translated 4 units down and reflected across the y-axis.

Step-by-step explanation:

Since f(x) = x^3 is transformed to h(x) = -(x+2)^3-4, by

1. Adding 2 to x in x³ to give f'(x) = f(x + 2) = (x + 2)³.

2. We now translate f(x + 2) down by subtracting 4 from f(x + 2) to give

f''(x) = f'(x) - 4 = f(x +2) - 4 = (x + 2)³ - 4.

3. We now reflect f'(x) across the y-axis by multiplying (x + 2)³ by -1 to get

h(x) = -(x + 2)³ - 4.

7 0

3 years ago

Read 2 more answers

An investment services company experienced dramatic growth in the last two decades. The following models for the company's reven

zlopas [31]

Answer: a) 138.32 and b) 35 years approx.

Step-by-step explanation:

Since we have given that

$R(t)=21.4e^{0.13t}\\\\C(t)=18.6e^{0.13t}$

So, Profit is given by

$Profit=R(t)-C(t)\\\\Profit=21.4e^{0.13t}-18.6e^{0.13t}\\\\Profit=e^{0.13t}(21.4-18.6)\\\\Profit=2.8e^{0.13t}$

Difference in years of 1990 and 2020=30

So, Profit becomes :

$P(30)=2.8e^{0.13\times 30}\\\\P(30)=2.8\times 49.40\\\\P(30)=138.32$

(b) How long before the profit found in part (a) is predicted to double? (Round your answer to the nearest whole number.) years after 1990.

So, profit doubles , we get :

$138.32\times 2=2.8e^{0.13t}\\\\276.65=2.8e^{0.13t}\\\\\dfrac{276.65}{2.8}=e^{0.13t}\\\\98.80=e^[0.13t}\\\\\ln 98.80=0.13t\\\\4.593=0.13t\\\\\dfrac{4..593}{0.13}=t\\\\35.33=t$

Hence, a) 138.32 and b) 35 years approx.

6 0

3 years ago

I need help with this problem, if you could describe how to do it thats fine aswell, but im a little confused with this

iVinArrow [24]

The slope is 5/1 because u find a point (4,20) and then like “simplify” it, 1/

he would charge $4 for half a gallon of milk

7 0

2 years ago

Read 2 more answers

Which operation should you perform first when evaluating the expression:

nevsk [136]

Answer: the power so ans should be 81

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

In Pennsylvania the average IQ score is 101.5 The variable is normally distributed and the population standard deviation is know

elena-14-01-66 [18.8K]

Answer:

P-value = 0.0368

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 101.5

Sample mean, $\bar{x}$ = 106.4

Sample size, n = 30

Alpha, α = 0.05

Population standard deviation, σ = 15

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 101.5\\H_A: \mu> 101.5$

We use One-tailed(right) z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{106.4 - 101.5}{\frac{15}{\sqrt{30}} } = 1.789$

Now, $z_{critical} \text{ at 0.05 level of significance } = 1.64$

Since,

$z_{stat} > z_{critical}$

We reject the null hypothesis and accept the alternate hypothesis. Thus, students in Pennsylvania have an IQ that is significantly greater than the state average.

P-value can be calculated with the standard normal table.

P-value = 0.0368

P-value is lower than the significance level.

4 0

3 years ago