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3 years ago

A(x) = 2 (3x - 2)(x - 5)

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

7 0

Answer:

Quadratic polynomial can be factored using the transformation ax

+bx+c=a(x−x

)(x−x

), where x

and x

are the solutions of the quadratic equation ax

+bx+c=0.

−x

−3x+5=0

All equations of the form ax

+bx+c=0 can be solved using the quadratic formula:

−b±

−4ac

. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

2(−1)

−(−3)±

(−3)

−4(−1)×5

Square −3.

2(−1)

−(−3)±

9−4(−1)×5

Multiply −4 times −1.

2(−1)

−(−3)±

9+4×5

Multiply 4 times 5.

2(−1)

−(−3)±

9+20

Add 9 to 20.

2(−1)

−(−3)±

The opposite of −3 is 3.

2(−1)

3±

Multiply 2 times −1.

−2

3±

Now solve the equation x=

−2

3±

when ± is plus. Add 3 to

−2

Divide 3+

by −2.

−

−3

Now solve the equation x=

−2

3±

when ± is minus. Subtract

from 3.

−2

3−

Divide 3−

by −2.

−3

Factor the original expression using ax

+bx+c=a(x−x

)(x−x

). Substitute

−3−

for x

and

−3+

for x

−x

−3x+5=−(x−

−

−3

)(x−

−3

)

EVALUATE

5−3x−x

2Quadratic polynomial can be factored using the transformation ax

+bx+c=a(x−x

)(x−x

), where x

and x

are the solutions of the quadratic equation ax

+bx+c=0.

−x

−3x+5=0

All equations of the form ax

+bx+c=0 can be solved using the quadratic formula:

−b±

−4ac

. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

2(−1)

−(−3)±

(−3)

−4(−1)×5

Square −3.

2(−1)

−(−3)±

9−4(−1)×5

Multiply −4 times −1.

2(−1)

−(−3)±

9+4×5

Multiply 4 times 5.

2(−1)

−(−3)±

9+20

Add 9 to 20.

2(−1)

−(−3)±

The opposite of −3 is 3.

2(−1)

3±

Multiply 2 times −1.

−2

3±

Now solve the equation x=

−2

3±

when ± is plus. Add 3 to

−2

Divide 3+

by −2.

−

−3

Now solve the equation x=

−2

3±

when ± is minus. Subtract

from 3.

−2

3−

Divide 3−

by −2.

−3

Factor the original expression using ax

+bx+c=a(x−x

)(x−x

). Substitute

−3−

for x

and

−3+

for x

−x

−3x+5=−(x−

−

−3

)(x−

−3

)

EVALUATE

5−3x−x

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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4 years ago

Solve and explain please

Leokris [45]

Therefore the inequality is x≤11

and maximum I can withdraw 11 bills.

Step-by-step explanation:

Given ,

Current balance $320

Minimum balance $100

I could spent =$(320-100) = $220

Let the number of bills be x.

Total amount of x bills = $20x

According to the problem,

20x≤ 220

⇔x ≤ $\frac{220}{20}$

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Therefore the inequality is x≤11

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6 0

3 years ago

You go to a local mechanic to get your tires changed. The tires cost $300. There is a 6% sales tax, but you get a 10% discount.

Romashka-Z-Leto [24]

Answer:

a) $T(x)=300x+18x=318x$

b) $D(x)=318x-(0.1)(318)+10x\\=296.2x$

c) Yes.

Step-by-step explanation:

We have that:

$Tires=$300\\Tax=0.006\\Discount=0.1\\$

And we have $10 free of taxes.

Making x= number of tires to buy, then we have that the total cost of tires is:

$Total_{Tires}=300x$

So, what we pay for taxes is given by:

$Taxes=(300x)(0.06)=18x$

a) Then, according to the above, we can write down the total cost before the discount as:

$T(x)=300x+18x=318x$

b) And the total cost after discounts, is then given by:

$D(x)=318x-(0.1)(318)+10x\\=296.2x$

c) If the discount is added first, then less tax will be paid because the amount on which it is paid is lower. If the discount is added later, then the taxes will have been taxed on a higher amount, so it does matter whether they are added first or later.

6 0

4 years ago

A random sample of ten 2011 sports cars is taken and their city mileage is recorded. The results are as follows: 20 21 25 21 21

serious [3.7K]

Answer:

$ME = 1.833 * \frac{4.367}{\sqrt{10}}= 2.531$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=24.8$

The sample deviation calculated $s=4.367$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=10-1=9$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,9)".And we see that $t_{\alpha/2}=1.833$

And the margin of error would be given by:

$ME = 1.833 * \frac{4.367}{\sqrt{10}}= 2.531$

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4 years ago

If we reject the null hypothesis, can we claim to have proved that the null hypothesis is false? why or why not?

sp2606 [1]

Yes, you can claim that the null hypothesis. But you must pay attention the p-value. If the p-value is higher than the significant value the null hypothesis can't be rejected.

7 0

3 years ago