Plz help me and explain it.

In the expression below, a is an integer. 12^3+ax-20 if 3x+4 is a factor of the expession above, what is the value of a

SVEN [57.7K]

Our function is:

$f(x)=12^3+ax-20$

Now, if $3x+4$ is a factor of $f(x)$ then $x=\frac{-4}{3}$ must satisfy the equation:

So, $f(\frac{-4}{3} )=0$

Putting $x=\frac{-4}{3}$

We get,

$f(\frac{-4}{3} )=12^3+a(\frac{-4}{3} )-20=0$

$12^3+\frac{-4}{3} a-20=0$

$\frac{-4}{3} a=20-12^3=20-1708$

$a=-1708 \times \frac{-3}{4} =1281$

So, the value of 'a' for the given expression is 1281.

4 0

2 years ago

Reuben says, "two days ago i was 20 years old. later next year, i will be 23 years old." how is this possible?

Aneli [31]

Let us always base on the present age. We denote this by x. Now, the age he had 2 years ago would then be denoted as (x-2). Let's equate this to 20 years old.

x - 2 = 20
x = 20 + 2
x = 22 years old
He should be 22 years old now.

Let's check the other condition. After 1 year, his age should be (x+1). Let's equate this to 23 years old.

x + 1 = 23
x = 23 - 1
x = 22

Thus, this is possible if Reuben is 22 years old as of the present.

7 0

2 years ago

A local high school held a two-day fundraiser selling lunches. The equations shown represent the amount of money the school coll

Over [174]

Answer:

11

Step-by-step explanation:

The two equations appear to be ...

12x +4y = 152
32x +12y = 420

These can be solved for y using Cramer's rule:

y = (152(32) -420(12))/(4(32) -12(12)) = -176/-16 = 11

The cost of the vegetarian lunch is 11.

_____

<em>Comment on Cramer's Rule</em>

For equations ...

ax +by =c

dx +ey = f

The solutions are ...

x = (bf -ey)/(bd -ea)

y = (cd -fa)/(bd -ea) . . . . note the denominators are the same expression

Once you memorize the pattern of products, this can be the simplest way to solve a pair of equations--especially if you only need one of the variable values.

6 0

2 years ago

Write an inequality. Thank you!<br><br> PLEASE ANSWER IMMEDIATELY!

guapka [62]

Answer:

m > 2

Step-by-step explanation:

Since it is an open dot, it is not greater than or equal to, but rather just greater than.

Then, since the arrow goes to the right, the equation is greater than.

8 0

2 years ago

There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote f

Ann [662]

Answer:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The estimated population proportion for this case is:

$\hat p = \frac{350}{500}=0.7$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

7 0

2 years ago