Hello please solve this question I hope you have a great day! SHOW YOUR WORK PLEASE!

Answer:

Step-by-step explanation:

we are given a equation

[tex] \sf \displaystyle \: \log_{4}( - x) + \log_{4}( 6 - x) = 2[/tex]

to solve so

recall logarithm multiplication law:

[tex] \sf \displaystyle \: \log_{4}( - x \times (6 - x)) = 2[/tex]

simplify multiplication:

[tex] \sf \displaystyle \: \log_{4}( - 6 x + {x}^{2} ) = 2[/tex]

remember [tex]\displaystyle \log_{4}(4^2)=2[/tex]

so

[tex] \sf \displaystyle \: \log_{4}( - 6 x + {x}^{2} ) = \log_{4}( {4}^{2} ) [/tex]

cancel out [tex]\log_4[/tex] from both sides:

[tex] \sf \displaystyle \: - 6 x + {x}^{2} = {4}^{2} [/tex]

simplify squares:

[tex] \sf \displaystyle \: - 6 x + {x}^{2} = 16[/tex]

move left hand side expression to right hand side and change its sign:

since we are moving left hand side expression to right hand side there'll be only 0 left in the left hand side

[tex] \sf \displaystyle \: - 6 x + {x}^{2} - 16 = 0[/tex]

rewrite it to standard form i.e ax²+bx+c=0

[tex] \sf \displaystyle \: {x}^{2} - 6x - 16 = 0[/tex]

rewrite -6x as 2x-8x:

[tex] \sf \displaystyle \: {x}^{2} + 2x - 8x - 16 = 0[/tex]

factor out x and 8:

[tex] \sf \displaystyle \: x {(x}^{} + 2) - 8(x + 2) = 0[/tex]

group:

[tex] \sf \displaystyle \: (x - 8){(x}^{} + 2) = 0[/tex]

[tex] \displaystyle \: x = 8 \\ x = - 2 [/tex]

[tex] \therefore \: x = - 2[/tex]

move left hand side log to right hand side:

[tex] \displaystyle \: \log(x ) + \log(x - 21) = 2 [/tex]

use mutilation logarithm rule;

[tex] \displaystyle \: \log( {x}^{2} - 21x) = 2 [/tex]

[tex]\log(10^2)=2[/tex] so

[tex] \displaystyle \: \log( {x}^{2} - 21x) = \log({10}^{2} )[/tex]

cancel out log from both sides:

[tex] \displaystyle \: {x}^{2} - 21x = 100[/tex]

make it standard form:

[tex] \displaystyle \: {x}^{2} - 21x - 100= 0[/tex]

factor:

[tex] \displaystyle \: {(x} + 4)(x - 25)= 0[/tex]

so

[tex] \displaystyle \: x = 25[/tex]

Answer:

$810 and the other is $730

$80 more

Step-by-step explanation:

.02 x 8000 = 160

160 + 650 = 810

.06 x 8000 = 480

480 + 250 = 730

810-730 = 80

Answer:

a)32500

b)0.00604

c)2.4×10^6

d)1.47x10-³

Step-by-step explanation:

plz can i get brainliest:)

Answer:

to find the area to the right positive z-score begin by reading off the area in the standard mormal distribution table, since the total area under the bell curve is 1 we subtract the area from the table from 1. for example the area to the left of z=1.02 is given in the table as 0.846

Step-by-step explanation:

right answer

Answer:

C, 40

Step-by-step explanation:

If there are 12 seats in each row, and 486 hamsters total, then we can safely assume one hamster takes up one seat.

To find out how many rows they can take, we need to divide the number of hamsters by the number of seats to get 486 / 12 approximately equals 40.

Answer:

C.

Step-by-step explanation:

Take the first two numbers of 486.

How many times does 12 fit into 48?

4 times.

Since all of the estimations do not have any form of individual single digits (as they do normally), we would dismiss the 6 and use its place just as a '0.'

40.

Hope this helped!

Answer:

s(r(2)) = 6

Step-by-step explanation:

You would first solve for r(2). You then input r(2) which equals -2 into s(r(2)).

r(x)= -2x + 2

r(2)= -2(2) + 2

r(2)= -4 +2

r(2)= -2

s(x)=x² + 2

s(r(2)) = (-2)² +2

s(r(2)) = 6

Answer:

BC =De is incorect

Step-by-step explanation:

De would be equal to Ab not Bc

Answer:

x = 27

Step-by-step explanation:

1/3 x +9 = 18

1/3 x = 18 - 9

1/3 x =9

3* 1/3 x = 9*3

x= 27

Answer:

(351.04, 368.96)

range values of 1.96 standard deviation are 352.16 to 367.84

answer is 367

Step-by-step explanation:

The selection of r objects out of n is done in

many ways.

The total number of selections 10 that we can make from 6+7=13 students is  

thus, the sample space of the experiment is 286

A.  

"The probability that a randomly chosen team includes all 6 girls in the class."

total number of group of 10 which include all girls is C(7, 4), because the girls are fixed, and the remaining 4 is to be completed from the 7 boys, which can be done in C(7, 4) many ways.

P(all 6 girls chosen)=35/286=0.12

B.

"The probability that a randomly chosen team has 3 girls and 7 boys."

with the same logic as in A, the number of groups were all 7 boys are in, is  

so the probability is 20/286=0.07

C.

"The probability that a randomly chosen team has either 4 or 6 boys."

case 1: the team has 4 boys and 6 girls

this was already calculated in part A, it is 0.12.

case 2, the team has 6 boys and 4 girls.

there C(7, 6)*C(6, 4) ,many ways of doing this, because any selection of the boys which can be done in C(7, 6) ways, can be combined with any selection of the girls.  

the probability is 105/286=0.367

since  case 1 and case 2 are disjoint, that is either one or the other happen, then we add the probabilities:

0.12+0.367=0.487 (approximately = 0.49)

D.

"The probability that a randomly chosen team has 5 girls and 5 boys."

selecting 5 boys and 5 girls can be done in  

many ways,

so the probability is 126/286=0.44

Did this help??

Answer:

It was right!

Step-by-step explanation:

Answer:

A is 360

Step-by-step explanation:

Answer:

Step-by-step explanation:

Multiply $30 by .25 you get, it's $7.50so you subtract $7.50 from $30 and you get $22.50. Then multiply 2 (sweaters) by $22.50 and you get $45,but wait you still have to multiply that sales tax so you multiply .04 by $45 and you get $1.80, later you subtract $1.80 from $45 and you get $43.20(the cost of the two sweaters) I did part1 only cuz' no I have no time left Sorry for the inconvenience

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Answer: x = 2.5

Explanation:

5.2 * 9.3 * x = 120.9

120.9 / 5.2 = 9.3 * x

23.25 = 9.3 * x

23.25 / 9.3 = x

x = 2.5

I hope this helped!

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- Zack Slocum

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Step-by-step explanation:

5.80×0.725= 4.205

5.80+4.205

= 10 .005

Answer:

y = 150x

Step-by-step explanation:

There is a proportional relationship between number of computers sold (x) and profit generated (y)

y ∝ x

y = kx

Here, k = proportionality constant

From the table given,

At y = 450 and x = 3,

450 = k(3)

k = 150

Therefore, expression that represents the proportional relationship will be,

y = 150x

Answer:

[tex]4\frac{19}{24}[/tex]

Step-by-step explanation:

I hope I did this right:

So first thing to do is set up the equation.

[tex]K + \frac{1}{3} = 5\frac{1}{8}[/tex]

Next thing to to is subtract 1/3 from both sides to get:

[tex]K = 5\frac{1}{8} - \frac{1}{3}[/tex]

Next up, you will multiply each of the fractions by the opposing value

(multiply 1/8 by 3 and 1/3 by 8)

[tex]K = 5\frac{3}{24}[/tex][tex]-\frac{8}{24}[/tex]

Alright almost done, by multiplying 24 by 5 you get 120, that will go in the numerator to make the math a lot easier.

K = [tex]\frac{123}{24}[/tex][tex]-\frac{8}{24}[/tex]

Finally, you subtract 123 over 24 by 8 over 24.

K = [tex]\frac{123}{24} - \frac{8}{24} = \frac{115}{24}[/tex]

Then just simplfy the 115/24 to get

[tex]4\frac{19}{24}[/tex]

Answer:

The radius is 4.5

Step-by-step explanation:

Well circumfrence is basically

2πr=Circumference

In this case

2πr= 28.26

π is about 3.14

2*3.14*r=28.26

Now combine

6.28r=28.26

Now solve

r=4.5

9514 1404 393

Answer:

  b = 6

Step-by-step explanation:

The area is given by the formula ...

  Area = 1/2·ab·sin(C)

  12 = (1/2)(8)b·(1/2) . . . . . fill in the given values

  12 = 2b . . . . . . . . . . . simplify

  6 = b . . . . . . . . . . . divide by 2

The length of side b is 6 units.

Answer:

x=30

Step-by-step explanation:

4x+2x+3x +3x=360. .... (angles of the quadrilateral add up to 360)

12x=360

12x/12=360/12

x=30

Answer:

It would be C, hopefully you still have time! y = 4x + 3

Step-by-step explanation:

Answer: D

Step-by-step explanation:

right on edge

Answer:

it would make most sense as the second answer or the one with the yellow dot next to it

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

AB is parallel to CD because neither lines cross

Answer: please help me with this, I will do whatever you want but please help me please!

Step-by-step explanation:

Answer: 28

Step-by-step explanation:

there are 3 boys for every 4 girls, so 4 times 4 is equal to 16. Now just multiply 3 times 4. 16 + 12 = 28.

Based on the linear pair postulate, the statement that is true is: D. m∠SWX = 108°.

According to the linear pair postulate, the sum of angles that form a linear pair equals 180 degrees.

72° and ∠SWX are a linear pair. Therefore:

m∠SWX = 180 - 72

m∠SWX = 108°

The statement that is true is: D. m∠SWX = 108°

Learn more about the linear pair postulate on:

https://brainly.com/question/13890989

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Answer:

it is not factorable

Step-by-step explanation:

it is not factorable

Answer:

63 for the whole figure, for the different shaded regions it goes as follows, 17.5 for the white area and 45.5 for the grey area

Step-by-step explanation: