(x+5)(√ 1-x)
what is the product of this composite function?

Answers

Answer 1

Answer:

[tex]x\sqrt{1-x}+5\sqrt{1-x}[/tex]

Step-by-step explanation:

[tex](x+5)(\sqrt{1-x} )\\\\=\left(\sqrt{1-x}\right)\left(x+5\right)\\\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\\\a=\left(\sqrt{1-x}\right),\:b=x,\:c=5\\\\=\left(\sqrt{1-x}\right)x+\left(\sqrt{1-x}\right)\times\:5\\\\=x\left(\sqrt{1-x}\right)+5\left(\sqrt{1-x}\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\\\=x\sqrt{1-x}+5\sqrt{1-x}[/tex]


Related Questions


Which of the following lines is parallel to x = 7? (2 points)
a. 3y = 7
b. y = 7
c. X = y
d. X = 4

Answers

b. x=4
bc on a graph x=7 is a straight vertical line going through 7 on the x-axis, so the only other parallel line possible is x=4, which is also a straight vertical line going through the x-axis.
d. x=4
example is attached

what is the vertical line test and how is it used​

Answers

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.

A vertical line is a line that passes through no more than one point. Means only one point in one of the lines. The picture is an example :)

PLS HELP! THIS IS DUE IN 30 MINUTES!! I'LL GIVE BRAINLIEST AND 60 POINTS IN TOTAL IF U GET BRAINLIEST.

Answers

Answer:

Perimeter: 14a+2b

Tickets:7x+6

Step-by-step explanation:

Perimeter: Add all the functions together

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

How would you solve this problem: X + 3 = -x - 5

Answers

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

find the distance between the two points (-4,6) and (3,-7)

Answers

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]

List all the sets that the number -6 belongs to.

Answers

Answer:

Integers

Step-by-step explanation:

3x + 1/2y = 3 and 6x - y = 2 (use elimination with multiplication to solve)

Answers

Answer:

i prefer substitution methon for this one

i really prefer try using that

1 Which expressions are equivalent to 2 -36 +- ? Check all that apply 30+ + 1 + 2 + 3 + 4 +5 4 1 +30 5 2 O 2 + 3 + 4 1 275 +-+30​

Answers

Answer:

20,136

Step-by-step explanation:

Follow My  -Tae.Nevacared 7777

What is the missing steph in solving the inequality 5 - 8x < 2x + 3

Answers

Answer:

x > 1/5

Step-by-step explanation:

5 - 8x < 2x + 3

-8x < 2x -2

-8x -2x < -2

-10x < -2

x > 1/5

Which of these is an action by a person who chooses immediate spending over
saving?

Taking the bus
Opening a savings account
Financing a brand-new car
O Setting 10 percent of each paycheck aside

Answers

financing a brand new car

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

how do you round the decimal 99.87?

Answers

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

Write the integer that represents the situation.

Hilda spent $65 and now has no money left. She had
before her purchase.

Answers

Answer:

what im thinking is $65

Step-by-step explanation:

Suppose f(x) = (5 – x)3 and, g(x) = a + x2, and f(g(x)) = (1 – x2)3. What is the value of a? a = –6 a = –4 a = 4 a = 6

Answers

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:

https://brainly.in/question/14333427

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are 49 35 32 41 47 composite​

Answers

Answer:

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

Step-by-step explanation:

Solve the equation please I need help
1/3(3x-1)= -1/7-2/7

Answers

Answer:

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

hope that helped ;w;

Use the expression you wrote to predict the number of dreams that include people you know out of 28

Answers

Answer:

the number of dreams that include people you know out of 28 is 21

Step-by-step explanation:

Here is the complete question:

It is believed that about [tex]\frac{3}{4}[/tex] of our dreams  involve people that we know.

So the expression to describe the number of  dreams that feature people you know if you have "d" dreams is:

[tex]\frac{3}{4} d[/tex]

Now using the above expression we can predict number of dreams that include people you know out of 28. Here 28 represents number of dreams i.e. "d". So expression becomes:

[tex]\frac{3}{4} (28)[/tex]

Now simplify the above expression:

[tex]\frac{3}{4} (28)[/tex] = [tex]\frac{3*28}{4}[/tex] = [tex]\frac{84}{4}[/tex] = [tex]21[/tex]

Hence the number of dreams that include people you know out of 28 is 21

Before a chemist can combine a solution with other liquids in a laboratory, the temperature of the solution must be between 39⁰ C and 52⁰C. The chemist places the solution in a warmer that raises the temperature 6.5⁰C per hour. If the temperature is originally 0⁰C, how long will it take to raise the temperature to the necessary range values

Answers

Answer: 6 hours

Step-by-step explanation:

6.5x = 39

6=x

PLEASE HELP!!! i’ve been stuck on this for so long!!!

Determine the number of terms in the geometric series 2+8+32+...+2048

Answers

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

please answer asap.will mark you as brainliest

Answers

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.

Find the coordinates
of A' given a dilation
of 2
A(3,-6), B(0,9), C(2,-1)

Answers

Find the coordinates of A’ given a dilation of 2
A(3,-6), B(0,9), C(2,-1)

Simplify for a = 3, b= -4 and c=-1.
16a - 3c + 5b =

Answers

Answer:

31

Step-by-step explanation:

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

48+3-20

51-21

31

12(a−4) simplified I am confused with this question

Answers

Answer:

-48

Step-by-step explanation:

Grace read 9 books in 3 months what was her rate of reading Books per month​

Answers

Answer:

3 books per month

Step-by-step explanation:

9 books ÷ 3 months = 3 books per month :)

3 books a month because 9/3 is 3 :)

Simplify this algebraic expression.

z-4/4+8

Answers

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!!

help?? Thank u if you do help btw!

Answers

Answer:

10,000lbs

Step-by-step explanation:

There are 2000lbs in 1 ton

So

5 x 2000 = 10000lbs

Answer:

10,000 pounds is the the correct answer

Use the distributive property to simplify the expression
3(9x -5)

**ANYONE WHO ANSWERS WILL GET BRAINLIEST ANSWER!!!!!**

Answers

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: 3 x 9x + 3 x -5

On a bicycle, Adriana rides for 2 hours and is 22 miles from her house. After riding for 7 hours, she is 72 miles away. What is Adriana's rate?​

Answers

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.

∠A and \angle B∠B are vertical angles. If m\angle A=(8x-4)^{\circ}∠A=(8x−4) ∘ and m\angle B=(7x+3)^{\circ}∠B=(7x+3) ∘ , then find the measure of \angle B∠B.

Answers

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°.

Review the graph of function h(x). Which point is on the graph of the inverse function h–1(x)?
A. (2, 4)
B. (0, one-half)
C. (0, 1)
D. (–5, 1)

Answers

Answer:

C

Step-by-step explanation:

Point (0, 1) is on the graph of the inverse function h⁻¹(x).

What is an Inverse Function?If f(x) is an original function with output y, then we can get inverse of the original function by putting y in the inverse function to obtain x.The domain of original function becomes the range of its inverse function and the range of the original function becomes the domain of its inverse function.

Given: The graph of function y = h(x).

According to the graph, the function is a straight line:

y-intercept is (c) = 2

Consider two points on the graph, y = h(x).

Let (x₁, y₁) = (0, 2) and (x₂, y₂) = (2, -2).

Now, the slope (m) of the function will be calculated as:

⇒ m = (y₂ - y₁) / (x₂ - x₁)

⇒ m = (-2 - 2) / (2 - 0)

m = -2

Now, with c = 2 and m = -2 the equation of a given line will be calculated as:

The general equation of line is:

⇒ y = mx + c

y = -2x + 2

∴  y = h(x) = -2x + 2 is the given equation of line.

Now to find the h⁻¹(x), we have to interchange the values of x and y from the function h(x) and then obtain the relation for the general equation of line.

h⁻¹(x) will be calculated as:

⇒ x = -2y + 2

⇒ x - 2 = -2y

y = (2 - x)/2

∴ y = h⁻¹(x) = (2 - x)/2

Now, we will find which point is on the graph of h⁻¹(x).

Option (A): (2, 4)

put, x = 2 in the equation y = (2 - x)/2

⇒ y = 0

⇒ (2, 0) ≠ (2, 4)

∴ (2, 4) is not the point on h⁻¹(x).

Option (B): (0, 1/2)

put x = 0 in the equation y = (2 - x)/2

⇒ y = 1

⇒ (0, 1) ≠ (0, 1/2)

∴ (0, 1/2) is not the point on h⁻¹(x).

Option (C): (0, 1)

put x = 0 in the equation y = (2 - x)/2

⇒ y = 1

⇒ (0, 1) = (0, 1)

(0, 1) is the point on h⁻¹(x).

Option (D): (–5, 1)

put x = -5 in the equation y = (2 - x)/2

⇒ y = 3.5

⇒ (-5, 3.5) ≠ (–5, 1)

∴ (–5, 1) is not the point on h⁻¹(x).

Therefore, the point on the graph of the inverse function of h⁻¹(x) is (0, 1).

Learn about the Inverse Function here: https://brainly.com/question/16406473?referrer=searchResults

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Need help now please. what is 1/2 to the power of 5

Answers

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

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