need help ! please give a answer :)

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:

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:

The Answer is D.

Step-by-step explanation:

You just need to plug in x for the first few, if it doesn't match go to the next option.

I tried this and figured out it's d in less than a minute.

Answer:

Step-by-step explanation:

Answer:

[tex]V=471\ \text{units}^3[/tex]

Step-by-step explanation:

Given that,

Radius of the cone, r = 5 units

Height of the cone, h = 6 units

We need to find the volume of the cone. The formula for the volume of the cone is given by :

[tex]V=\pi r^2 h[/tex]

Substitute all the values,

[tex]V=3.14\times 5^2\times 6\\\\V=471\ \text{units}^3[/tex]

So, the volume of the cone is [tex]471\ \text{units}^3[/tex].

Answer:

16/5

Step-by-step explanation:

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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!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: 9

Step-by-step explanation:

If 19 students take history, 12 take economics and 5 take both:

19-5 = 14 students that take only history

12-5 = 7 students that take only economics

Therefore total number of students who either history, economics or history and economics: 14 + 7 + 5 = 26

Therefore students who take neither: 35 - 26 = 9

students who take neither: 35 - 26 = 9.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

In a class of 35 students, 19 take history and

12 take economics. If 5 take both subjects,

now,

If 19 students take history, 12 take economics and 5 take both:

19-5 = 14 students that take only history

12-5 = 7 students that take only economics

Therefore total number of students who either history, economics or history and economics: 14 + 7 + 5 = 26

Therefore students who take neither: 35 - 26 = 9

To learn more on subtraction click:

brainly.com/question/2346316

#SPJ2

Answer:

2/1

Step-by-step explanation:

Use the equation m=[tex]\frac{y2-y1}{x2-x1}[/tex]

Answer:

20ml : 6ml: 15ml

Step-by-step explanation:

1000 milliters is 1 liter, so we would have to convert it to the ml so that it will all be in proportion. To simplify a ratio, divide by a number they can all be divided by. In this case, it was 10 first, so it made it 100: 30: 75. Then, to simplify it more, they can all be divided by 5, which is the lowest it can be since 20: 6: 15 have no numbers in common to be divided by.

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:

a because 5 or less than 5 equals almost or less than 10

110 - 1 = 109

1 x 109 = 109

Answer:

[tex]110 - 1 = 109 \\ 200 - 91 = 109 \\ thank \: you[/tex]

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:

[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:

$21847

Step-by-step explanation:

Answer:

10=Z and 10=Y

Step-by-step explanation:

since it is a 45, 45, 90 triangle

both Z and Y will be the same length

the hypotenuse has a length of [tex]x\sqrt{2}[/tex] with x being the length of the legs

Since the length of this triangle's hypotenuse is [tex]10\sqrt{2}[/tex] the side length would be 10

Hope that helps :)

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:

Answer:

5 kg flour remains

Step-by-step explanation:

80% of the original 25 kg comes to 0.80(25 kg), or 20 kg.  We convert 80% to its decimal equivalent, 0.80, to get this result  

The amount of flour remaing is then (1.00 - 0.80)(25 kg), or 0.20(25 kg) = 5 kg.

5 kg flour remains.

Answer:

25 - 20 = 5 kg

Steps:

25×80/100 = 25×8/10 = 200/10 = 20 kg

25 - 20 = 5 kg

Answer:

Diameter = 54 units

Step-by-step explanation:

Given:

Angle θ = 80'

Length of arc TV = 12π

Find:

Diameter

Computation:

Length of arc = [θ/360][2πr]

So,

12π = [80/360][2πr]

54 = 2r

r = 27

Diameter = 2r

So,

Diameter = 54 units

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:

Output, y = -1 when input, x = 30

Step-by-step explanation:

Given equation:

y = 14 - 0.5x

Where,

y = output

x = input

Find the output, y, when the input, x, is 30

y = 14 - 0.5x

y = 14 - 0.5(30)

y = 14 - 15

y = -1

Therefore,

Output, y = -1 when input, x = 30

Answer:

-1

Step-by-step explanation:

KHAN ACADEMY :)

I CAN FIND AN EXPLANATION IF NEEDED

Answer: $6.40

Step-by-step explanation: im just way too big brained

Answer:

$40

Step-by-step explanation:

32/(1-.2)=32/.80=40

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:

S=(8*5*3)m3

=120mcube

Answer:

AB = 9.5 units

Step-by-step explanation:

Here, we want to find the measure of AB

To do this, we are going to make use of the sine rule

for the sine rule, the ratio of the measure of a side and the sine of the angle that faces the side is a constant value for a triangle

Thus, we have it that; in a triangle ABC

a/sin A = b/sin B = c/sin C

using the triangle given;

we need the measure of the angle at C

The sum of angles in a triangle is 180

thus;

C + 93 + 48 = 180

C = 180 - 93 -48

C = 39 degrees

Now, to get the value of AB;

AB/sin 39 = 15/sin 93

AB = (15 * sin 39)/sin 93

AB = 9.5 units

Answer:

16

Step-by-step explanation:

sin = adjacent ÷ hypotenuse.

sin 45 = x ÷ 23

0.71 = x ÷ 23

0.71 × 23 = x

x = 16.26

~ 16.

Answer:

Step-by-step explanation:

using the Pythagorean theorem     a² + b² = c²

in this triangle a = x and b = x  so   x² + x²  = c²       c is the hypotenuse

                 x² + x²  = c²

                   2x² = c²             since c = 23 solve for x

                     x² =  c² / 2

                     x   =  ± √(c² / 2)

                     x   =  ± √(23² /2)

                          = ± √(529 /2)            

                          = ± √(264.5)            

                          =  16.26          x can't be negative

        That is correct but it doesn't answer the question

                 x = ??? / √xx

           sin 45  = √2 / 2  which equals    x / 23

                      √2 / 2  =    x / 23

                       x =  23 (√2 / 2)

                          =  23 (√2)  / 2             divide the √2 numerator and demenator

                          =  23 (√2)/√2 / (2 / √2)

                           = 23 / (2 / √2)

Sorry I have no idea what goes in the green box