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3 years ago

Sketxh the graph of y=(x+3)^3 and state the points where the graph crosses the axes

Mathematics

1 answer:

gtnhenbr [62]3 years ago

6 0

Answer: the graph crosses the x-axis at x = -3

Step-by-step explanation:

y = (x + 3)³

To find where the graph crosses the x-axis, let y = 0 and solve for x:

0 = (x + 3)³

0 = (x + 3) with a multiplicity of 3

-3 = x with a multiplicity of 3.

Since multiplicity is an ODD number, the graph CROSSES the x-axis at x = -3

Graph:

Leading coefficient is POSITIVE so right side goes to +∞
Degree of polynomial is ODD so left side goes to -∞

graph is attached

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. Mrs. Huang operates a soybean farm. She buys many supplies in bulk. Often the bulk products need to be custom mixed before Mrs

dimulka [17.4K]

Answer:

18 L

Step-by-step explanation:

Given : she must mix a solution of 67% herbicide with a solution of 46% herbicide to form 42 liters of a 55% solution.

To Find: How much of the 67% solution must she use?

Let x = amount of 67% solution needed

Then 42-x=amount of 46% solution needed

Now we know that the pure herbicide in the 67% solution

So, pure herbicide = (0.67x)

The amount of pure herbicide in the 46% solution (0.46(42-x))

Now 42 liters of a 55% solution = (0.46(42-x))

So,

Amount of 67% solution + Amount of 46% solution = 42 liters of a 55% solution

⇒0.67x+0.46(42-x)=0.55*42

⇒0.67x+19.32-0.46x=23.1

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⇒ $x=\frac{3.78}{0.21}$

⇒x = 18 liters

Hence she use 18 liters of the 67% solution

5 0

3 years ago

Read 2 more answers

PLEASE HELP ME IT WOULD MEAN A LOT

arlik [135]

Answer:

12x³ - 3x

Step-by-step explanation:

Given 

f(x) = x and g(x) = 4x² - 1

Now, 

3 f(x) * g(x) 

= 3 * x (4x² - 1)

= 3x ( 4x² - 1 )

= 12x³ - 3x 

Hope it will help :)

4 0

3 years ago

A researcher reports survey results by stating that the standard error of the mean is 25 the population standard deviation is 40

bezimeni [28]

Answer:

a) A sample of 256 was used in this survey.

b) 45.14% probability that the point estimate was within ±15 of the population mean

Step-by-step explanation:

This question is solved using the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

a. How large was the sample used in this survey?

We have that $s = 25, \sigma = 400$ . We want to find n, so:

$s = \frac{\sigma}{\sqrt{n}}$

$25 = \frac{400}{\sqrt{n}}$

$25\sqrt{n} = 400$

$\sqrt{n} = \frac{400}{25}$

$\sqrt{n} = 16$

$(\sqrt{n})^2 = 16^2[tex][tex]n = 256$

A sample of 256 was used in this survey.

b. What is the probability that the point estimate was within ±15 of the population mean?

15 is the bounds with want, 25 is the standard error. So

Z = 15/25 = 0.6 has a pvalue of 0.7257

Z = -15/25 = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

45.14% probability that the point estimate was within ±15 of the population mean

3 0

3 years ago

A video game costs $45.99. It is 45% off today at the store. What is the sale price of the video game?

stepan [7]

Answer:

the sale price of the video game after discount is 25.29

hope this helps have a nice day please give me brainliest:)

Step-by-step explanation:

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3 years ago

Is an estimate for the percent of a number always,sometimes or never greater than actual percent of the number

posledela

It would be sometimes because it can be 82.2% but if you round it the closest one would be 80% if it was 84.7% its closer to 85 so it would be 85% I hope I helped you out rate the answer if I got it right thanks!

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3 years ago

Sketxh the graph of y=(x+3)^3 and state the points where the graph crosses the axes​

Sketxh the graph of y=(x+3)^3 and state the points where the graph crosses the axes