All categories

3 years ago

The product of some negative number and 4 less than twice that number is 286 find the number

1 answer:

5 0

Let's say that number is hmmm "a"

now.. twice "a" is 2*a or 2a
4 less than that is " 2a - 4"

now, the product of those two fellows is 286, well ok

a( 2a - 4) = 286

thus

$\bf a(2a-4)=286\implies 2a^2-4a^2=286\implies a^2-2a^2=143
\\\\\\
a^2-2a^2-143=0\implies (a-13)(a+11)=0
\\\\\\
\begin{cases}
a-13=0\implies &a=13\\
a+11=0\implies &\boxed{a=-11}
\end{cases}$

You might be interested in

21 and 22 are complementary angles. The measure of Z1 is 45 The measure of Z2 is 3x°. Find the value of x. The figure is not dra

Alex

9514 1404 393

Answer:

x = 15

Step-by-step explanation:

Given:

∠1 + ∠2 = 90°

∠1 = 45°

∠2 = 3x°

Find:

Solution:

Using the given values in the given equation, we have ...

45° +3x° = 90°

15 + x = 30 . . . . . . divide by 3°

x = 15 . . . . . . . . . . . subtract 15

6 0

2 years ago

Please help asap !!!!

Allisa [31]

No solution
This will help I hope

8 0

2 years ago

In ABC, what is the measure of angle B?

NeX [460]

Answer:

Step-by-step explanation:

The sum of two remote interior angles (a remote interior angle is the interior angle that is not supplementary to the exterior angle given -- in this case A and B are remote angles) equals the exterior angle.

In This case A + B = 140

A = x + 2

B = 2x

x +2 + 2x = 140

3x + 2 = 140 Subtract 2 from both sides

3x = 138 Divide by 3

x = 138/3

x = 46

<B = 2x

<B = 2*46

<B = 92

6 0

2 years ago

The measure of an angle is 164°. What is the measure of its supplementary angle?

storchak [24]

Answer:

Step-by-step explanation:

180-164=16 do the answer is 16

3 0

1 year ago

A sociologist was investigating the ages of grandparents of high school students. From a random sample of 10 high school student

umka2103 [35]

Answer:

$(69.8-71.6) -2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= -8.908$

$(69.8-71.6) +2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= 5.308$

So then the confidence interval for the difference of means is given by:

$-8.908 \leq \mu_M -\mu_F \leq 5.308$

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".

$\bar X_{M}= 69.8$ represent the mean for the age of grandmother

$\bar X_{F}= 71.6$ represent the mean for the age of grandfather

$s_{M}= 8.38$ represent the sample deviation for the age of grandmother

$s_{F}= 6.65$ represent the sample deviation for the age of grandfather

$n_M = n_F= 10$

Solution to the problem

For this case the confidence interval is given by:

$(\bar X_{M} -\bar X_F) \pm t_{\alpha/2} \sqrt{\frac{s^2_M}{n_M} +\frac{s^2_F}{n_F}}$

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

$df=n_M +n_F-2=10+10-2=18$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,18)".And we see that $t_{\alpha/2}=2.101$

And replacing we got:

$(69.8-71.6) -2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= -8.908$

$(69.8-71.6) +2.101 \sqrt{\frac{8.38^2}{10} +\frac{6.65^2}{10}}= 5.308$

So then the confidence interval for the difference of means is given by:

$-8.908 \leq \mu_M -\mu_F \leq 5.308$

5 0

3 years ago