Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.)
ln z(z − 1)^8, z > 1

Answer:

George : Carl : Alex = 1 : 12 : 4

Step-by-step explanation:

let a = Alex's age in years

let g = George's age in years

let c = Carl's age in years

Given:

⇒ a = 12 + g

⇒ g = a - 12

Given:

⇒ c = 3a

Given:

⇒ a + g + c = 68

Substitute the first two equations in the last equation and solve for a:

⇒ a + (a - 12) + 3a = 68

⇒ 5a - 12 = 68

⇒ 5a = 80

⇒ a = 16

Substitute the found value of a into the other equations to find g and c:

⇒ g = 16 - 12 = 4

⇒ c = 3(16) = 48

Therefore:

Ratio

George : Carl : Alex = 4 : 48 : 16

Reduce by dividing by 4 → 1 : 12 : 4

Answer: C) (12, -14)

Step-by-step explanation:

I am going to solve by elimination.

Start by subtracting one equation from the other

[tex]y=-x-2\\-(y=-\frac{1}{2} x-8)\\0=-\frac{1}{2} x+6[/tex]

Now solve for x

[tex]0=-\frac{1}{2} x+6\\0-6=-\frac{1}{2} x+6-6\\-6=-\frac{1}{2} x\\(-6)(-2)=(-2)(-\frac{1}{2} x)\\12=x[/tex]

Now sub in x into one of the equations to find the value of y

[tex]y=-(12)-2\\y=-14[/tex]

Answer:

Yo espero yo ayuda tu résolve estes équations

Step-by-step explanation:

a) x=8

b) x=-7

c) x=5,1

d) x=5/4

e) x=-3

f) x=5

Lo siento, mi español no son muy bien.

Answer:

Step-by-step explanation:

Answer:

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

option ( c ) [tex]\huge\pink{1 \frac{2}{5} }[/tex]

step by step explanation -

well , the question asks us to find the difference between the two terms given as mixed fractions ~

tho it's not that difficult to simplify a problem in mixed fraction , but solving the problem by first converting it to an improper fraction reduces the risk of mistakes ! so let's do the question by that way ~

[tex]4 \frac{4}{5} - 3 \frac{2}{5} \\ \\ converting \: into \: improper \: fraction \: we \: get \\ \\ \implies \: \frac{5 \times 4 + 4}{5} \: \: - \: \: \frac{5 \times 3 + 2}{5} \\ \\ \implies \: \frac{24}{5} \: \: - \: \: \frac{17}{5} \\ \\ since \: the \: denominators \: are \: same \: we \: can \: simply \: subtract \: the \: terms \\ \\ \implies \: \frac{7}{5} [/tex]

we're done with our solution tho , but since the options given are in mixed fraction , so let's convert the improper fraction , obtained as the answer , into a mixed fraction !

[tex] \frac{7}{5} = 1 \frac{2}{5} \\ [/tex]

hope helpful :D

Answer:

1 2/5

Step-by-step explanation:

subtract it and then add it and u will have your answer

Answer:

40/3

Step-by-step explanation:

-0.6X=-8

X=-8/-06

X=40/3

Answer:

c=3a=180

Step-by-step explanation:

c=3a,t=c+10 and a +t=430

a+3a+3a+10=430

7a=420

a=60

c=3a=180

The total amount of deduction in percentage is 22%. Then the correct option is B.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

The total amount of deductions from an employee’s gross pay is $83.20. if the gross pay is $378.18.

Then the percentage will be given as

[tex]\rm P = \dfrac{83.20}{378.18}\times 100\\\\P = 0.220 \ or \ 22\%[/tex]

More about the percentage link is given below.

https://brainly.com/question/8011401

[tex]-4x-4y = 24~~...(i)\\\\3x +10 = y~~....(ii)\\\\\text{Substitute}~ y = 3x +10~ \text{in eq (i):}\\\\-4x -4(3x+10) = 24\\\\\implies -4x -12x -40=24\\\\\implies -16x =24+40\\\\\implies -16x = 64\\\\\implies x =- \dfrac{64}{16}\\\\\implies x = -4\\\\\text{Substitute}~ x = -4 ~ \text{in equation (ii) to find y:} \\\\y=3(-4) +10 = -12 +10 = -2\\\\\text{Hence,}~(x,y) = (-4,-2)[/tex]

Answer:

2

Step-by-step explanation:

2 is 2 away from 0

Answer

The area will be 484 square centimeters.

Answer:

anwer 9$ and hour

Step-by-step explanation:

9×8=72

9+5=14

14×3=42

42+72=114

Answer:

357.5ft^3

Step-by-step explanation:

solve for bottom reticular prism

8 * 10 * 4

320ft^3

solve for top triangular prism

((3*5)/2)*5

37.5ft^3

add top and bottom  

320+37.5

357.5ft^3

Answer: 268ft^3

Step-by-step explanation: To solve, find the area of each side and add them all together.

8*4=32*2=64

10*4=40*2=80

10*5=50*2=100

8*3/2=12*2=24

64+80+100+24=268

Hope I helped <3

Answer:

y-6=(3/2)(x+6)

Step-by-step explanation:

Given:

Point-Slope:

[tex]\displaystyle \large{y-y_1=m(x-x_1)}[/tex]

Substitute m = 3/2, x1 = -6 and y1 = 6:

[tex]\displaystyle \large{y-6=\dfrac{3}{2}[x-(-6)]}\\\displaystyle \large{y-6=\dfrac{3}{2}(x+6)}[/tex]

Therefore, the equation is y-6=3/2(x+6)

Answer:

1. 27.5

2.32.5

3.30

6.22.5

11. 17.5

16.12.5

21. 7.5

7.27.5

12.22.5

17.17.5

22.12.5

8.25

13.20

18.15

23.10

Answer:

lawer, Police officer criminal justice

Answer:

L=93

Step-by-step explanation:

So basically you need to know the formula beforehand the formula to find the length of a rectangle what is P=2(l+w) so to find for L the equation will be L=P/2-W=294-54=93 Therefore 93 is L

Answer:

3.5555555555556

Step-by-step explanation:

you cannot find the Mean Absolute Deviation of one number. This answer is the data set 2, 9, and 0. 3.5555555555556 is the Mean Absolute Deviation of 2, 9, 0.

Answer:

x^2 + 14x + 57 = 0

Step-by-step explanation:

(x+5)^2+4(x+5)+12 = 0

x^2 +10x + 25 + 4x + 20 + 12 = 0

x^2 + 14x + 57 = 0

The expression for y is y = 2x +20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

We're given that:

Then we have:

y = time on math homework + history homework

y = 2 +2 +2 ... (x times) + 20 minutes

[tex]y = 2x + 20[/tex]

x is "number of math problems". Thus, x can be 0,1,2,... These numbers are called non-negative integers(or integers greater or equal to 0) or whole numbers.

y is the time taken, but we see that

y = 2 times (non-negative integer) + 20

y = positive integer times non-negative integer + positive integer

Thus, we have:

y = non-negative integer + positive integer = positive integer

Thus, y assumes positive integral values only (in minutes).

Also, y is always going to be at least 20 (as history homework is going to take 20 minutes, even if math homework is nill ).

Thus, the expression for y is y = 2x +20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20

Learn more about domain here:

https://brainly.com/question/20073127

Answer:

The answer is c3 or c x 3.

Step-by-step explanation:

Because the product in math is multiplication, the product of c and 3 would be c x 3.

Answer:

Then the vertex is at (h, k) = (2, –3) and the value of p is –3. Since y is squared and p is negative, then this is a sideways parabola that opens to the left. This puts the focus 3 units to the left of the vertex.

vertex: (2, –3); focus: (–1, –3)

Step-by-step explanation:

Answer:

16π

Step-by-step explanation:

Given:

[tex]\text{Radius of circle}: 4 \ \text{m}[/tex]

Formula:

[tex]\text{Area of circle} = \pi r^{2}[/tex]

Replace the radius in the formula:

[tex]\implies \text{Area of circle} = \pi (4)^{2}[/tex]

Evaluate the area:

[tex]\implies \text{Area of circle} = \pi (4)(4)[/tex]

[tex]\implies \text{Area of circle} = 16\pi[/tex]

Since the question says to determine the area in terms of π, the final answer is 16π.

Answer:

4/12  2/3 5/6 5/6

Step-by-step explanation:

Answer:

The surface area of a figure is the sum of all the sides that consist of it.

Let's first find the base's area, using the formula for the area of a rectangle, L · W:

9(6)

= 54 is the area of the base.

Now let's find the entire front side of this figure's area and double it so we get both the areas of the front and back side (using the formula for the area of a rectangle):

4(9)[bottom front rectangle] + 4(5)[upper front rectangle]

36 + 20

= 56, now double that area to get the area of both the front and back side:

56(2)

= 112 is the area of both the entire front and back side of this figure.

Now let's figure out the area of the right whole side of this figure then double it so we get both the areas for the left and right sides.

But, if we look at the middle rectangle to the right and left sides, we can see that there is no value, so let's find the value first.

The total length across the figure is 9 inches.

And we are given that the rectangle above intersects with the total length, so let's exclude that from 9 inches.

9 - 4 = 5, so now the total length of the two rectangles beside the above rectangle is 5.

But we want to find the value of one side, so divide 5 by 2.

5/2 = 2.5 inches.

Now let's find the whole entire area of the right side to this figure.

5(6)[upper right rectangle] + 2.5(5)[flat middle right rectangle] + 6(4)[bottom right rectangle)

30 + 12.5 + 24

= 66.5, now double that area to get both the area of the right and left side.

66.5(2)

= 133, is the area of both the right and left side of this entire figure.

Finally, we add all those areas together to get the surface area:-

54 + 112 + 133

= 299 inches is the surface area for this figure.

Answer:The surface area of a figure is the sum of all the sides that consist of it.

Let's first find the base's area, using the formula for the area of a rectangle, L · W:

9(6)

= 54 is the area of the base.

Now let's find the entire front side of this figure's area and double it so we get both the areas of the front and back side (using the formula for the area of a rectangle):

4(9)[bottom front rectangle] + 4(5)[upper front rectangle]

36 + 20

= 56, now double that area to get the area of both the front and back side:

56(2)

= 112 is the area of both the entire front and back side of this figure.

Now let's figure out the area of the right whole side of this figure then double it so we get both the areas for the left and right sides.

But, if we look at the middle rectangle to the right and left sides, we can see that there is no value, so let's find the value first.

The total length across the figure is 9 inches.

And we are given that the rectangle above intersects with the total length, so let's exclude that from 9 inches.

9 - 4 = 5, so now the total length of the two rectangles beside the above rectangle is 5.

But we want to find the value of one side, so divide 5 by 2.

5/2 = 2.5 inches.

Now let's find the whole entire area of the right side to this figure.

5(6)[upper right rectangle] + 2.5(5)[flat middle right rectangle] + 6(4)[bottom right rectangle)

30 + 12.5 + 24

= 66.5, now double that area to get both the area of the right and left side.

66.5(2)

= 133, is the area of both the right and left side of this entire figure.

Finally, we add all those areas together to get the surface area:-

54 + 112 + 133

= 299 inches is the surface area for this figure.

Step-by-step explanation:

Answer:

i got you explain

Step-by-step explanation:

Two rational numbers between -2 and 2 are : 0 and 1.

or The two rational no are -1 and +1

[tex]\qquad \qquad \huge \pink {\sf{☁Answer☁}} \\ \\ [/tex]

→ first rational number

[tex] \tt{⇒ \frac{ ( { \cancel{-2}}+{ \cancel 2)}} {\cancel{2}}} \\ \\ \tt{⇒ \frac{ 0}{2} }\\ \\ \tt{⇒0} [/tex]

[tex] \pink{ \rule{60mm}{2.2pt}}[/tex]

→ Second rational number

[tex]\\ \tt{⇒ \frac{(-2+0)}{2}} \\ \\ \tt{⇒ \frac{ \cancel{-2}}{ \cancel{2}} }\\ \\ \tt{⇒-1} [/tex]

[tex]\rule{70mm}{3.9pt}[/tex]

[tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]

Answer:

The first one is blinded. I didn't get the other one though. The one that says "neither the subjects nor the researchers" is wrong.

Step-by-step explanation:

I use Plato.

The experiment is blindeded because the scientist know which treatment group each subject is in.

Experiment is the scientific approach to determine the properties of some sample by doing some research on it eg. By adding another material, or determination of hypothesis.

Hypothesis is the assumption which is made under some evidence which can be proceed further verification or by doing experiment on it.

From the question it is clear that the scientist wants to meassure the effect of apple cider vinegar subject on the blood sugar level.

So here the effect of apple cider vinegar subject on the blood sugar level is hypothesis.

From 200 randomly choosen young groups one half have taken apple cider where other half have taken placebo in order to clarify and study which group has taken which treatment and their effect in their blood sugar level.

Learn more about experiment

Here : https://brainly.com/question/5397388

#SPJ2

passenger cars = 36

total no. of cars = 36 + 8 = 44

hope it helps...!!!