A group of fitness club members lose a combined total of 28 kilograms in 1 week. There are approximately 2.2 pounds in 1 kilogram. Assuming the weight loss happened at a constant rate, about how many pounds did the group lose each day?​

Answer:

When I work with function composition, I usually convert "( f o g)(x)" to the more intuitive " f (g(x))" form. This is not required, but I certainly find it helpful. In this case, I get:

(g o f )(1) = g( f(1))

This means that, working from right to left (or from the inside out), I am plugging x = 1 into f(x), evaluating f(x), and then plugging the result into g(x). I can do the calculations bit by bit, like this: Since f(1) = 2(1) + 3 = 2 + 3 = 5, and since g(5) = –(5)2 + 5 = –25 + 5 = –20, then (g o f )(1) = g( f(1)) = g(5) = –20. Doing the calculations all together (which will be useful later on when we're doing things symbolically), it looks like this:

(g o f )(1) = g( f (1))

  = g(2(   ) + 3)   ... setting up to insert the original input

  = g(2(1) + 3)

  = g(2 + 3)

  = g(5)

  = –(   )2 + 5    ... setting up to insert the new input

  = –(5)2 + 5

  = –25 + 5

  = –20

Note how I wrote each function's rule clearly, leaving open parentheses for where the input (x or whatever) would go. This is a useful technique. Whichever method you use (bit-by-bit or all-in-one), the answer is:

(g o f )(1) = g( f (1)) = –20

I just computed (g o f )(1); the composition can also work in the other order

Step-by-step explanation:

The value of a is 4.

Hence, a = 4

Here,

[tex]f(x) = (5 - x)^3 and, g(x) = a + x^2,[/tex]

and [tex]f(g(x)) = (1 - x^{2} )^3[/tex]

We have to find the value of a.

What is composite function?

Function composition is an operation that takes two functions f and g and produces a function h such that h(x) = g(f(x)).

Now,

[tex]f(x) = (5 - x)^3 and, g(x) = a + x^2,[/tex]

and [tex]f(g(x)) = (1 - x^{2} )^3[/tex]

⇒ [tex]f(g(x)) = f ( a + x^{2} )[/tex]

⇒ [tex]f ( a + x^{2} ) = ( 5 - a - x^{2} )^3[/tex]

And,

[tex]f(g(x)) = (1 - x^{2} )^3[/tex]

[tex]( 5 - a - x^{2} )^3 = ( 1 - x^{2} )^3\\[/tex]

Taking cube root both sides,

[tex]( 5 - a - x^{2} ) = ( 1 - x^{2} )\\ 5 - a - x^{2} = 1 - x^{2} \\a = 4[/tex]

Hence, The value of a = 4.

Learn more about the composite function visit:

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Answer:

G. $9,200

Step-by-step explanation:

average depreciation = (amount of depreciation)/(number of years)

The amount of depreciation is the difference between the new cost and the current value.

amount of depreciation = $85,600 - $30,400 = $55,200

number of years = 6

average depreciation = (amount of depreciation)/(number of years)

average depreciation = ($55,200)/(6 years)

average depreciation = $9,200/year

Answer: G. $9,200

Answer:

what im thinking is $65

Step-by-step explanation:

Answer:

x > 1/5

Step-by-step explanation:

5 - 8x < 2x + 3

-8x < 2x -2

-8x -2x < -2

-10x < -2

x > 1/5

Answer:

C. Financing a brand new Car

Step-by-step explanation:

Financing a brand new car means that someone takes out a car loan that has to be paid over time, and that is something a spender would do because they are not saving money

Step-by-step explanation:

Notice it is not asking for an average rate, just her current rate. Approach this like this: say she is at the 29 mile "marker." In 3 hours, she gets to the 38th mile "marker." Therefore:

38-29 = 9, so in 3 hours, she went 9 miles.

9 miles/3 hours = 3 miles per hour, which would be equal to her current rate.

Answer:

31

Step-by-step explanation:

16(3)-3(-1)+5(-4)

48+3-20

51-21

31

Answer:

  b)  f(3) is defined, but is not equal to the limit

Step-by-step explanation:

The portion of the function defined by the rational expression is equivalent to x/(x+3), which has a value of 1/2 at x=3. This is the limit of f(x) from the left or right as x approaches 3. However, the function is not defined at that point as 1/2. Rather, it is defined to be f(3)=1.

So, the limits at f(3) exist and are 1/2, but the function is defined as a different value there.

The only applicable statement is the second one.

Answer:

-48

Step-by-step explanation:

Answer:

The vertical line test is used to determine if a graph of a relationship is a function or not. if you can draw any vertical line that intersects more than one point on the relationship, then it is not a function.

Answer:

z+7

Step-by-step explanation:

use PEMDAS!

1. divide 4/4, which is 1. (z-1+8)

2. combine like terms! -1 and 8 are like terms, so add them together. (z+7)

3. after that, you have the answer!! z+7!!

Answer:

Step-by-step explanation:

x + 3 = -x - 5

2x + 3 = -5

2x = -8

x = -4

Answer: x=-4

Step-by-step explanation: first add x from both sides to turn it into 2x+3=-5. then subtract 3 from both sides for it to turn to 2x=-8. finally divide both sides by to to find x=-4

Answer:

[tex]x = -\frac{2}{21}[/tex]

hope that helped ;w;

Answer:

[tex]27x - 15[/tex]

Step-by-step explanation:

When we apply the distributive property, we multiply all the terms inside the parentheses by the term directly outside of it.

So:

[tex]9x \cdot 3 = 27x[/tex]

[tex]-5 \cdot 3 = -15[/tex]

Putting these together, we get [tex]27x-15[/tex].

Hope this helped!

Answer: 1/2 power of 5 aight

1/2+1/2+1/2+1/2+1/2= 2 1/2

Step-by-step explanation:

1/2⁵ = 1/2 × 1/2 × 1/2 × 1/2 × 1/2 × 1/2

1/2⁵ = 1/64

Answer:

56/125

Step-by-step explanation:

Ok, so we know evaluate means to solve or to work out the situation. In this case we got 1.4•0.32. So, what we'll have to do is to solve this mathmatical equation 7/5 (1.4) • 8/25 (0.32) this in fractional form what we did is turnrf the decimal form of each reprecient of the problem into fractions. How to turn decimals in fractions is to simplify. Once, you've done that evaluate 7/5 and 8/25. This should get you 56/125.

Answer:

0.448

Step-by-step explanation:

Answer:

I hope the above pic will help you :)

Answer:

C

Step-by-step explanation:

It is a function because it passes the vertical line test and Xs do not repeat, then count out the Y-values which are the range.

Answer:

32 is composite and the rest are not. Hope this helps!

Step-by-step explanation:

Answer:

  examine the next digit and increase the number accordingly, before dropping the digits of no interest.

Step-by-step explanation:

You round any number by looking at the digit in the place to the right of the one you want to round to. If it is 5 or more, you add 1 to the number in the place you're rounding to, and drop (or zero) all digits to the right of that.

If you want to round this to tenths, you observe that the hundredths digit is 7, which is more than 4. So you add 1 tenth and drop the hundredths digit:

  99.87 ≈ 99.9 . . . . rounded to tenths

If you want to round this to units, you observe that the tenths digit is 8, which is more than 4. So you add 1 unit and drop the tenths and hundredths digits.

  99.86 ≈ 100 . . . . . rounded to nearest integer

Answer:

∠B = 52°.

Step-by-step explanation:

Given: m∠A=(8x-4)° and m∠B=(7x+3)°. ∠A and ∠B are vertical angles.

Since ∠A and ∠B are vertical angles. So, there measure are equal.

[tex]m\angle A=m\angle B[/tex]

[tex](8x-4)^{\circ}=(7x+3)^{\circ}[/tex]

[tex]8x-4=7x+3[/tex]

[tex]8x-7x=4+3[/tex]

[tex]x=7[/tex]

Now,

[tex]m\angle B=(7(7)+3)^{\circ}[/tex]

[tex]m\angle B=(49+3)^{\circ}[/tex]

[tex]m\angle B=52^{\circ}[/tex]

Therefore, the measure of ∠B is 52°.

Answer:

= and [tex]\leq[/tex] and [tex]\geq[/tex]

Step-by-step explanation:

Absolute value -9 is 9, but there is a negative sign so it is -9

-9=-9

Greater than or equal to works because of the equal sign.

Less than or equal to also works because of the equal sign.

Answer:

6 terms

Step-by-step explanation:

we have

[tex]2+8+32+..+2048[/tex]

we need to identify a pattern so

from 2 to 8 what could have happened?

well you could have added 6 and get 8

so that means that to 8 you have to add 6 and get 32

WRONG

so adding is not an option

what else could have happened?

well you could have multiplied by 4 and get 8

so that means that to 8 you have to multiply by 4 and get 32

which is true

so the geometric series is

[tex]2+4(2)+4(4(2))+4(4(4(2)))+...+[/tex] what?

you can see that in the 2nd term we have 1 four, in the 3rd we have 2 fours

so we can conclude in the nth term we have n-1 fours

so the formula is

[tex]2+8+32+...+4^{n-1} *2[/tex]

so we need to determine when

[tex]4^{n-1}*2=2048[/tex]

[tex]4^{n-1}*2*\frac{1}{2} =2048*\frac{1}{2} \\\\4^{n-1}=1024[/tex]

if we factorize 4 as [tex]2^2[/tex] and 1024 as [tex]2^{10}[/tex]

we have

[tex](2^2)^{n-1}=2^{10}\\\\2^{2(n-1)}=2^{10}\\\\2^{2n-2}=2^{10}[/tex]

so we see that the bases are equal, that must mean the exponents are equal

[tex]2n-2=10\\\\2n=10+2\\\\2n=12\\\\n=6[/tex]

so there are 6 terms

Answer:

x > 2

Step-by-step explanation:

5x +  1/3 * (3x + 6) > 14

5x + x + 2 > 14

6x + 2 > 14

6x > 12

x > 2

Answer:

x>2

Step-by-step explanation:

6x+2>14

6x>12

x>2

hope this helped a bit

Answer: 6 hours

Step-by-step explanation:

6.5x = 39

6=x

Answer:

20,136

Step-by-step explanation:

Follow My  -Tae.Nevacared 7777

Answer:

[tex]( - 4.6) + (3. - 7) = 0.6[/tex]

By the distance formula,

[tex]d = \sqrt{( x_2 - x_1) {}^{2} + (y_2 - y_1 {)}^{2} }[/tex]

Here,

[tex]x_1 = -4[/tex]

[tex]y_1 = 6[/tex]

[tex]x_2 = -7[/tex]

[tex]y_2 = 3[/tex]

Hence,

[tex]d = \sqrt{( {(-7 )+(- 4))}^{2} + {( 3 + 6)}^{2} } [/tex]

[tex]d = \sqrt{ {(-11)}^{2} + {9}^{2} } [/tex]

[tex]d = \sqrt{121+ 81} [/tex]

[tex]d = \sqrt{202} [/tex]

Answer:

Perimeter: 14a+2b

Tickets:7x+6

Step-by-step explanation:

Perimeter: Add all the functions together

Tickets: Subtract 15x+1 by 8x-5.