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3 years ago

Algebra- Factoring by Grouping Need help ASAP

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

6 0

Answer:

The answer to your question is 2r²

Step-by-step explanation:

Data

2r³ + 4r² + 5r + 10

-Process

1.- Find the GCF of the first two terms

2r³ + 4r²

-Find the GCF of the coefficients

2 4 2

1 2 2

-The GCF is 2 because it divided both numbers

2.- Find the GCF of the variable

r³ r² the GCF is the highest power that both "r's" has.

then GCF = r²

3.- Group the GCF(point 1 and 2) = 2r²

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UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each

grigory [225]

Answer:

1. 20 pounds

2. $11

Step-by-step explanation:

To set this up, you have to use a system of equations. It would look like this, where $p$ is pounds and $t$ is total cost:

UPS: $t=7+0.20p$

FedEx: $t=5+0.30p$

In order to solve a system of equations you must either a.) graph it, or b.) set them equal to each other.

If you graph it, the answer is where the two lines intersect.

If you set them equal to each other, solve it.

I will set them equal to each other in this:

$7+0.20p=5+0.30p$

The first step in a problem like this, where there's the same variable on both sides, is to subtract the smaller variable from both sides. In this case, it is $0.20x$ . That would turn the equation into:

$7=5+0.10p$

After that, you must solve it like a regular two-step equation.

Start by subtracting 5 from both sides:

$2=0.10p$

Now, you must divide both sides by $0.10$ .

$\frac{2}{0.10}=\frac{0.10p}{0.10}$

That would give us:

$20=p$

This means that in order for the prices to be the same, the package must be 20 pounds.

Now in order to find the total cost, you must plug 20 into one of the equations. It doesn't matter which, since they both equal the same. I will plug it into the FedEx equation:

$t=5+0.30(20)$

Now you can just use a calculator and solve that or do it by hand. Multiply 0.30 by 20, to get 6, then add 5, which equals 11.

You should get: $t=11$ .

This means that the total cost, when the costs are the same for both FedEx and UPS, is $11.

3 0

4 years ago

Square root of 79 rounded to the nearest hundredth?

34kurt

8.88 I think. Hope this helps :)

5 0

3 years ago

Read 2 more answers

David and Peter had $90 and $200 respectively. They were each given an equal amount of money. Then Peter had twice as much money

Aleksandr [31]

20 dollars each! hope it helps.

4 0

3 years ago

A coffee packaging plant claims that the mean weight of coffee in its containers is at least 32 ounces. A random sample of 15 co

Luda [366]

Answer:

We conclude that the mean weight of coffee in its containers is at least 32 ounces which means that the data support the claim.

Step-by-step explanation:

We are given that a coffee packaging plant claims that the mean weight of coffee in its containers is at least 32 ounces.

A random sample of 15 containers were weighed and the mean weight was 31.8 ounces with a sample standard deviation of 0.48 ounces.

Let $\mu$ = mean weight of coffee in its containers.

SO, Null Hypothesis, $H_0$ : $\mu \geq$ 32 ounces {means that the mean weight of coffee in its containers is at least 32 ounces}

Alternate Hypothesis, $H_A$ : $\mu$ < 32 ounces {means that the mean weight of coffee in its containers is less than 32 ounces}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean weight = 31.8 ounces

s = sample standard deviation = 0.48 ounces

n = sample of containers = 15

So, the test statistics = $\frac{31.8 -32}{\frac{0.48}{\sqrt{15} } }$ ~ $t_1_4$

= -1.614

The value of t test statistics is -1.614.

Now, at 0.01 significance level the t table gives critical value of -2.624 at 14 degree of freedom for left-tailed test.

Since our test statistic is more than the critical value of t as -1.614 > -2.624, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean weight of coffee in its containers is at least 32 ounces which means that the data support the claim.

8 0

4 years ago

Are either of these linear?

sesenic [268]

The 2nd one is linear

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4 years ago