what is the value of x?

Answer:

[tex]log_{2\sqrt 2} X = \frac{1}{3}k[/tex]

Step-by-step explanation:

Given

Let the number be X

From the first statement, we have:

[tex]log_{\sqrt 2} X = k[/tex]

Required

Find [tex]log_{2\sqrt 2} X[/tex]

[tex]log_{\sqrt 2} X = k[/tex]

using the following law of logarithm

[tex]log_ab = n, b=a^n[/tex]

So:

[tex]log_{\sqrt 2} X = k[/tex]

[tex]X = \sqrt{2}^k[/tex]

Substitute: [tex]X = \sqrt{2}^k[/tex] in [tex]log_{2\sqrt 2} X[/tex]

[tex]log_{2\sqrt 2} X = log_{2\sqrt 2} ( \sqrt{2}^k)[/tex]

[tex]log_{2\sqrt 2} X = klog_{2\sqrt 2} \sqrt{2}[/tex]

Apply the following law:

[tex]log_ab = \frac{log\ b}{log\ a}[/tex]

[tex]log_{2\sqrt 2} X = k\frac{log\ \sqrt 2}{log\ {2\sqrt 2}}[/tex]

Express the square roots as power

[tex]log_{2\sqrt 2} X = k\frac{log\ 2^\frac{1}{2}}{log\ {2 * 2^\frac{1}{2}}}[/tex]

[tex]log_{2\sqrt 2} X = k\frac{log\ 2^\frac{1}{2}}{log\ {2^\frac{3}{2}}}[/tex]

using the following law of logarithm

[tex]log_ab = n, b=a^n[/tex]

[tex]log_{2\sqrt 2} X = k\frac{\frac{1}{2}log\ 2}{\frac{3}{2}log\ 2}}[/tex]

[tex]log_{2\sqrt 2} X = k\frac{\frac{1}{2}}{\frac{3}{2}}}[/tex]

Rewrite as:

[tex]log_{2\sqrt 2} X = k * \frac{1}{2} \div\frac{3}{2}[/tex]

[tex]log_{2\sqrt 2} X = k * \frac{1}{2} *\frac{2}{3}[/tex]

[tex]log_{2\sqrt 2} X = k * \frac{1}{1} *\frac{1}{3}[/tex]

[tex]log_{2\sqrt 2} X = \frac{1}{3}k[/tex]

Answer:60 percent

Step-by-step explanation: You have fraction the two numbers which will be 12/20 them you times it by 100 which equals 60 oranges.

Answer:

D, -42 multiply 6 on both sides

D. because when it is multiplied, the inequality is no longer true.

Answer:

2/1 of a family

Step-by-step explanation:

Answer:

24.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

The triangles are similar.

x/(x+4) = 7.2/12

x/(x+4) = 0.6

x = 0.6(x+4)

0.4x + 2.4

x = 6

Answer:

Explanation:

f  (  − 3 )  basically means substitute  − 3  for  x  in the function  − 5 x

f

(

−

3

)

=

−

5

(

−

3

)

−

7

f

(

−

3

)

=

15

−

7

f

(

−

3

)

=8

Step-by-step explanation:

? + 31° + 94° = 180°

? + 125° = 180°

? = 180° - 125°

? = 55°

Answer: 52°

Step-by-step explanation:

Angles in a triangle always add up to 180°.

So to work out what the missing angle is, you would have to add 34 and 94 together.

34+94=128

Then you would have to take 128 away from 180.

180-128=52°

Hope this helps :)

Answer:

90

Step-by-step explanation:

The average of a set of numbers is the sum of the numbers, divided by the count of the numbers.

Thus, the average of 85, 88 and 97 is

85 + 88 + 97

------------------- = 270/3, or 90

         3

Answer:

90

Step-by-step explanation:

Answer:

I dont see the question...

Step-by-step explanation:

Answer:

5.42

Step-by-step explanation:

hope this helped!! :)

Answer:

7 is the answer

Step-by-step explanation:

Answer:

This equals 7

Step-by-step explanation:

I used a calculator

Can I have brainliest pls

Answer:

63

Step-by-step explanation:

To find the area of a trapezoid you have to use the formula

a+b/2 h

So we would substitute them

3 + 15 / 2 x 7

Which would equal

63

Hope this helps :)

Answer:

The doomsday is 146 days

Step-by-step explanation:

Given

[tex]\frac{dy}{dt} = ky^{1 +c}[/tex]

First, we calculate the solution that satisfies the initial solution

Multiply both sides by

[tex]\frac{dt}{y^{1+c}}[/tex]

[tex]\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}[/tex]

[tex]\frac{dy}{y^{1+c}} = k\ dt[/tex]

Take integral of both sides

[tex]\int \frac{dy}{y^{1+c}} = \int k\ dt[/tex]

[tex]\int y^{-1-c}\ dy = \int k\ dt[/tex]

[tex]\int y^{-1-c}\ dy = k\int\ dt[/tex]

Integrate

[tex]\frac{y^{-1-c+1}}{-1-c+1} = kt+C[/tex]

[tex]-\frac{y^{-c}}{c} = kt+C[/tex]

To find c; let t= 0

[tex]-\frac{y_0^{-c}}{c} = k*0+C[/tex]

[tex]-\frac{y_0^{-c}}{c} = C[/tex]

[tex]C =-\frac{y_0^{-c}}{c}[/tex]

Substitute [tex]C =-\frac{y_0^{-c}}{c}[/tex] in [tex]-\frac{y^{-c}}{c} = kt+C[/tex]

[tex]-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}[/tex]

Multiply through by -c

[tex]y^{-c} = -ckt+y_0^{-c}[/tex]

Take exponents of [tex]-c^{-1[/tex]

[tex]y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]

[tex]y = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]

[tex]y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]

i.e.

[tex]y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]

Next:

[tex]t= 3[/tex] i.e. 3 months

[tex]y_0 = 2[/tex] --- initial number of breeds

So, we have:

[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]

-----------------------------------------------------------------------------

We have the growth term to be: [tex]ky^{1.01}[/tex]

This implies that:

[tex]ky^{1.01} = ky^{1+c}[/tex]

By comparison:

[tex]1.01 = 1 + c[/tex]

[tex]c = 1.01 - 1 = 0.01[/tex]

[tex]y(3) = 16[/tex] --- 16 rabbits after 3 months:

-----------------------------------------------------------------------------

[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]

[tex]16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}[/tex]

[tex]16 = [-0.03 * k + 2^{-0.01}]^{-100}[/tex]

[tex]16 = [-0.03 k + 0.9931]^{-100}[/tex]

Take -1/100th root of both sides

[tex]16^{-1/100} = -0.03k + 0.9931[/tex]

[tex]0.9727 = -0.03k + 0.9931[/tex]

[tex]0.03k= - 0.9727 + 0.9931[/tex]

[tex]0.03k= 0.0204[/tex]

[tex]k= \frac{0.0204}{0.03}[/tex]

[tex]k= 0.68[/tex]

Recall that:

[tex]-\frac{y^{-c}}{c} = kt+C[/tex]

This implies that:

[tex]\frac{y_0^{-c}}{c} = kT[/tex]

Make T the subject

[tex]T = \frac{y_0^{-c}}{kc}[/tex]

Substitute: [tex]k= 0.68[/tex], [tex]c = 0.01[/tex] and [tex]y_0 = 2[/tex]

[tex]T = \frac{2^{-0.01}}{0.68 * 0.01}[/tex]

[tex]T = \frac{2^{-0.01}}{0.0068}[/tex]

[tex]T = \frac{0.9931}{0.0068}[/tex]

[tex]T = 146.04[/tex]

The doomsday is 146 days

Answer: 20790

Step-by-step explanation:

Answer:

2.0986814e+29

Step-by-step explanation:

Answer:

what

Step-by-step explanation:

punch your calculator to find out

even the calculator might not give u the exact value

Answer:

-1/2

Step-by-step explanation:

Answer:

the answer is the slope is -1/2

Answer: 4, 800

Step-by-step explanation:

Answer:

the answer is

x=22..........

Answer:

ANSWER

Step-by-step explanation:

Answer:

if you pit the shape in a straight line it would be 180 degrees now take 180 take 130 and 100 and subtract those add that to the other 30 then take 180 divided by 60

Answer:

x = 50°

Step-by-step explanation:

sum of exterior angles is always equal to 360°

so, we can add all the given numbers and set them equal to 360° to find x:

130° + 30° + 100° + x° + x° = 360°

260° + 2x = 360°

2x = 100°

x = 50°

Answer:

w = [tex]l + \frac{25 - l^{2}}{l - 5}[/tex]

(Anyone can correct me if I'm wrong)

Step-by-step explanation:

Before we start the solving, we can make the following statements:

Area = l x w

Area = 5x + 25

therefore,

l x w = 5x + 25

Since the question states that the length is x more than the width, so we can make the following statement:

w = l + x

With this, we can substitute it to the first statement we made, l x w = 5x + 25,

l x (l + x) = 5x + 25

[tex]l^{2}[/tex] + lx = 5x + 25

lx - 5x = 25 - [tex]l^{2}[/tex]

x(l - 5) = 25 - [tex]l^{2}[/tex]

x = [tex]\frac{25 - l^{2}}{l - 5}[/tex]

From this, we can find w by substituting it in the statement we made earlier, w = l + x,

w = [tex]l + \frac{25 - l^{2}}{l - 5}[/tex]

Answer: D

Step-by-step explanation:

Answer:

x = 14

y = 18

Step-by-step explanation:

By the property of similar triangles,

If two triangles are similar their corresponding sides will be proportional.

[tex]\frac{AB}{EF}= \frac{AC}{GE}[/tex]

[tex]\frac{5}{10}=\frac{7}{x}[/tex]

x = [tex]\frac{70}{5}[/tex]

x = 14

Similarly, [tex]\frac{AB}{EF}= \frac{CB}{GF}[/tex]

[tex]\frac{5}{10}=\frac{9}{y}[/tex]

y = [tex]\frac{90}{5}[/tex]

y = 18

Answer:

111

Step-by-step explanation:

Answer:

Cost of one bundle of shingles is $20 and cost of one roll of roofing paper is $110.

Step-by-step explanation:

Let the cost of each bundle of shingles = x

And cost of the roofing paper = y

Contractor buys 30 bundles of shingles and 4 rolls of roofing paper for $1040.

30x + 4y = 1040

15x + 2y = 520 -----(1)

In a second purchase contractor buys 12 bundles of shingles and 16 rolls of roofing paper for $2000

12x + 16y = 2000

3x + 4y = 500 --- (2)

Equation (1) multiplied by 2 then subtracted from equation (2)

(3x + 4y) - 2(15x + 2y) = 500 - 1040

(3x - 30x) + (4y - 4y) = -540

-27x = -540

x = 20

From equation (1)

15(20) + 2y = 520

300 + 2y = 520

2y = 220

y = 110

Therefore, cost of one bundle of shingles is $20 and cost of one roll of roofing paper is $110.

Answer:

(g o f)(5) = 47

Step-by-step explanation:

We are given a composite function:

g(x) = 4x + 3

f(x) = 3x - 4

We are supposed to find (g o f)(5), which really means g( f(x) ). So, we put the function of f(x) for every x in g(x), like this:

g(x) = 4x + 3

g( f(x) ) = 4(3x - 4) + 3

g( f(x) ) = 12x - 16 + 3

g( f(x) ) = 12x - 13

Now, we also need to evaluate for x = 5, like this:

g( f(5) ) = 12(5) - 13

g( f(5) ) = 47