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Usimov [2.4K]
3 years ago
13

Please help! It is college algebra

Mathematics
2 answers:
uranmaximum [27]3 years ago
4 0

Answer:  x = 5 , \frac{-1}{3}

Step-by-step explanation:

8(^{x^{2}-\frac{14}{3}x}) = 32

This could be written in index form as :

2^{3}( ^{x^{2}-\frac{14}{3}x})=2^{5}

By laws of indices , we will equate their power , that is :

3(x^{2} -\frac{14}{3}x) = 5

Expanding , we have :

3x^{2} -14x=5

3x^{2} -14x-5=0

factorising the Quadratic equation , we have :

3x^{2} -15x + x -5=0

3x(x-5)+1(x-5)=0

(x-5)(3x+1) = 0

Therefore:

x-5 = 0      or 3x+1=0

x = 5 , \frac{-1}{3}

beks73 [17]3 years ago
4 0

Answer:

x = 4 2/3

Step-by-step explanation:

8(x^2 -14/3 *x) = 32

Rearrange:

Rearrange the equation by subtracting or addition what is to the right of the equal sign from both sides of the equation :

We have done the opposite and added as it was subtraction sign:

8x + 16 -14/3 * x = 32 + 14/3

Step  1  :

Equation at the end of step  1  seen here below : 32+14/3 -16

+ 16 * x = 32+14/3 -16

Pulling out like terms :  Pull out like factors :  ( + )  ( + )

= 8x + 8x =16 +14/3     : Note :  AB = BA  : property of multiplication.

  x = 14/3  x = 4 2/3    

                               or

2 is the square of 8

Two solutions were found :

x = 14/3

x = 4 2/3

Trying to factor as a Difference of Squares :

3.2      Factoring:  8x + 8x = 2 *2 = 4 * 2/3

                                 x = 14/3  x = 4 √2.66

This cannot be done as it is creates a new fraction 2 33/50

We find x = 4 2/3 is the answer.

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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

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3 years ago
Twelve less than a third of a number is -10
jolli1 [7]
I believe that number would be 6.
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Answer:

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Step-by-step explanation:

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Width of room :

Using Pythagoras rule:

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Answer:

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Step-by-step explanation:

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x = 2i

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4 0
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