let f(x)=1-x*2 and g(x)=1-x find (fg)(x)

Answers

Answer 1

(fg)(x) is the PRODUCT of functions f and g. If that's what you want, then:

(fg)(x) = (1-x^2)*(1-x) = 1 - x - x^2 + x^3 (answer)

Related Questions

Compare the functions shown below:

f(x) = −3x − 5
g(x)

cosine function with y intercept at 0, negative 3 h(x) = 2 cos(2x − π) + 4

Which function has the greatest y-intercept?

a. f(x)
b. g(x)
c. h(x)
d. all three functions have the same y-intercept

Answers

Find all y-intercepts:

1. For f(x): when x=0 you have that f(0)=-3·0-5=-5, then y-intercept is a point (0,-5).

2. For g(x): from the task conditions you have that g(x) is cosine function with y intercept at 0, negative 3, then y-intercept is a point (0,-3).

3. For h(x): when x=0 you have that h(0)=cos(2·0-π)+4=cos(-π)+4=-1+4=3, then y-intercept is a point (0,3).

As you can see the greatest y-intercept has function h(x).

Answer: correct choice is C.

Answer:

Step-by-step explanation:

I just took the test. :)

Evaluate the expression for = −3 and = 5.

r^{-4} s^2

Answers

If r = -3 and s = 5:
(r^-4)(s^2) = (-3^-4)(5^2) = (1/81)(25) = 25/81

If r = 5 and s = -3:
(r^-4)(s^2) = (5^-4)(3^2) = (1/625)(9) = 9/625

If r = -3 and s = 5:
(r^-4)(s^2) = (-3^-4)(5^2) = (1/81)(25) = 25/81

A bag contains 12 red marbles and 6 blue marbles. two marbles are drawn with replacement. find the probability.

Answers

248376203488451-5814-0395681-03581-403951-0958904680968590147514095714095714-5714578140587109p54

An empty box weighs 200g the box is filled with birthday party goozy bags and now weighs 6.2kg Each goody bag weighs 150Work out how many goody bags are inside the box

Answers

For this case, the first thing we are going to do is define variables.
We have then:
x: number of birthday party goozy bags
y: total weight
We then have the following equation:
y = 150x + 200
For y = 6200 we have:
6200 = 150x + 200
Clearing x:
x = (6200-200) / (150)
x = 40
Answer:
there are 40 goody bags inside the box

Answer:

Step-by-step explanation:

Solve 4x - 2= 86
thanks

Answers

4x-2=86
+2 +2 (-2 and +2 cancel each other out)
_______
4x=88 ( divide 4 on both sides)

x=22

x = 22

4x-2=86
+2 +2
_______
4x=88
4x/4=x
88/4=22

Eric plans to rent a car for a day from Easy Car Rental. He has a coupon for 25% off the daily base rate of $40. He will also have to pay an additional $0.15 for each mile he drives. Which expression represents the situation?

Answers

Let x represent the number of miles he drives

Base rate: 40 - (40 · 0.25) plus mileage: 0.15 · x
Total cost = 30 + 0.15x

Out of the 180 students at a summer camp, 72 signed up for canoeing. There were 23 students who signed up for trekking, and 13 of those students also signed up for canoeing.

Use a two-way table to organize the information and answer the following question:

Approximately what percentage of students signed up for neither canoeing nor trekking?

72%
40%
54%
98%

Answers

There are 72 students that signed up for canoeing, and 23 students that signed up for trekking. 13 of these 23 students also signed up for canoeing.

Use the following equation to find the amount of people that signed up for an activity:

[tex]72 + 23 - 13 = 82[/tex]

82 students signed up for canoeing or trekking.

Subtract this total from the total amount of students to find the total that did not sign up for an activity:

[tex]180 - 82 = 98[/tex]

Divide this number by the total amount of students in the camp:

[tex]98 \div 180 = 0.54[/tex]

Multiply this decimal by 100 to convert into a percentage:

[tex]0.54 * 100 = 54[/tex]

54% of students did not sign up for neither canoeing nor trekking.

Even though Kanest's answer is verified and correct, the attached picture is how the 2 way table should be set up:

A vegetable store sold 3 tons of vegetables less on the first day than on the second, and on the third day it sold 5/9 of the amount sold in the first two days. How many vegetables was the store selling every day if it sold altogether 98 tons of vegetables for the three days?

Answers

let
x---------> quantity (ton) of vegetables sold the first day
y---------> quantity (ton) of vegetables sold the second day
z---------> quantity (ton) of vegetables sold the third day

we know that
x=y-3---------> equation 1
z=(5/9)*(x+y)------> equation 2
x+y+z=98-----> equation 3
substitute equation 2 in equation 3
x+y+[(5/9)*(x+y)]=98----> multiply by 9----> 9x+9y+5x+5y=882
14x+14y=882-----> equation 4

to resolve the equations system formed by
x=y-3
14x+14y=882

using a graph tool
see the attached figure
the solution is
x=30
y=33
x+y+z=98----> z=98-(x+y)----> z=98-63---> 35

the answer is
vegetables sold the first day----> 30 ton
vegetables sold the second day----> 33 ton
vegetables sold the third day------> 35 ton

Answer:
amount sold on first day = 30 tons
amount sold on second day = 33 tons
amount sold in third day = 35 tons

Explanation:
Assume that the amount of vegetables sold on the second day is x.
We are given that:
Amount of vegetables sold on the first day is 3 tons less that sold on the second day.
This means that:
amount sold on first day = x - 3
Amount of vegetables sold on the third day is 5/9 the amount sold on the first two days.
This means that:
amount sold on third day = (5/9) (x + x - 3)
amount sold on third day = [tex] \frac{10}{9} x - \frac{5}{3} [/tex]

Now, we know that:
Total amount sold is 98 tons.
This means that:
98 = x - 3 + x + [tex] \frac{10}{9} x - \frac{5}{3} [/tex]

Now, we will solve for x as follows:
98 = [tex] \frac{28}{9} x - \frac{14}{3} [/tex]

882 = 28x - 42
882 + 42 = 28x
924 = 28x
x = 924/28
x = 33 tons

This means that:
amount sold on first day = x - 3 = 33 - 3 = 30 tons
amount sold on second day = x = 33 tons
amount sold on third day = [tex] \frac{10}{9} x - \frac{5}{3} [/tex] = [tex] \frac{10}{9} (33) - \frac{5}{3} [/tex] = 35 tons

Hope this helps :)

Simplify the expression 9xy + 6xy − 2xy. What is the coefficient of the simplified expression?

Answers

Hi there!

To find our answer we need to collect the terms of the expression.

[tex]9xy + 6xy - 2xy = \\ 15xy - 2xy = \\ 13xy[/tex]

The coefficient (which is the number just before the variable) of the simplified expression is 13.

9xy + 6xy - 2xy
13xy is the answer. THey are all like terms so just add then subtract.

The perimeter of a rectangular floor is 50 feet. find the dimensions of the floor if the length is four times the width.

Answers

length is 20
width is 5

let me know if you need more details

The dimensions of the rectangle are width = 5 feet and length = 20 feet.

What is the perimeter of the rectangle?

The perimeter of a rectangle is defined as the addition of the length and width.

The perimeter of a rectangle = 2(L + W)

Where W is the width of the rectangle and L is the length of the rectangle

We have been given that the perimeter of a rectangular floor is 50 feet.

The length is four times the width.

Let the width of the rectangle is x

So the length of the rectangle = 4x

The perimeter of a rectangle = 2(L + W)

50 = 2(4x + x)

50 = 2(5x)

50 = 10x

10x = 50

x = 50 /10

Apply the division operation,

x = 5

So the length of the rectangle = 4(5) = 20 feet

Therefore, the dimensions of the rectangle are width = 5 feet and length = 20 feet.

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What is the equation, in slope-intercept form, of the line that passes through (0, 3) and has a slope of −6?
y = 3x + 6
y = 3x − 6
y = −6x − 3
y = −6x + 3

Answers

Y = 3x - 6, slope is the last number in the equation.

Answer:

y=-6x+3

Step-by-step explanation:

Using the formula,

[tex](y-y_{1})=m(x-x_{1})\\(y-3)=(-6)(x-0)\\y-3=-6x\\y=-6x+3[/tex]

What’s the quadratic expression for this one

Answers

We have the following expression:
(2x + 5) * (7-4x)
Rewriting we have:
14x - 8x ^ 2 + 35 - 20x
Grouping terms with the same exponent:
-8x ^ 2 + x (14-20) + 35
Rewriting:
-8x ^ 2 - 6x + 35
Answer:
the quadratic expression for this is:
-8x ^ 2 - 6x + 35

In the ancient chinese proverb, there are more than how many different ways to breathe

Answers

Answer: 40

What we all know is that there is only one way to breath (inhaling and exhaling) For the ancient Chinese, as cited on ancient proverb there are forty (40) ways. These different ways promote relaxation thru breathing on the lower stomach.

ANOTHER FILL IN THE BLANKS QUESTION, MARKING BRAINLIEST FOR CORRECT ANSWER

Answers

Hi, again!
First blank: multiplication property of equality
Both sides of the equation were multiplied by (1/2).

Second blank: m<E
Angle E is an inscribed angle intercepting arc FGD, so by the inscribed angle theorem, its measure is half the measure of the arc.

Third blank: m<G
Same explanation as the prior blank

Fourth blank: substitution property of equality
Since angle E is equal to half the measure of arc FGD, we can replace that term. Likewise with angle G.

46 points for yall, i need math help.

Answers

Your answer would be the fourth choice, 6/13.

(4x-8)=(-9x-2)

4x= -9x+6

-5x= 6

x= -(6/5)

Please give an explanation with you answer, thank you :)

Answers

[tex]f(x)=2( \sqrt[3]{27})^{2x} [/tex]

Here 2 on left most side is the coefficient, 2x is the exponent and the of the function is cube root of 27.

So,

[tex]Base= \sqrt[3]{27} \\ \\ Base= \sqrt[3]{3^{3} } \\ \\ Base=3 [/tex]

Thus, the simplified base for the function is 3. So correct answer is option B

Find the dimensions of a rectangle whose width is 6 miles less than its length and whose area is 55 square miles.

Answers

let
x-----------> the length of a rectangle
y-----------> the width of a rectangle

we know that
area of a rectangle =length*width
area=55 mi²
55=x*y--------> equation 1
y=x-6-------> equation 2
substitute equation 2 in equation 1
55=x*[x-6]------> 55=x²-6x----------> x²-6x-55=0

using a graph tool-----> to resolve the second order equation
see the attached figure

the solution is
x=11 mi
y=x-6-----> y=11-6-----> y=5 mi

the answer is
the length of a rectangle is 11 miles
the width of a rectangle is 5 miles

Karen makes $5 per hour baby-sitting and $12 per hour giving music lessons. one weekend, she worked a total of 18 hours and made $139. how many hours did she spend baby-sitting?

Answers

Let the number of hours she spent in baby- sitting is x

and the number of hours she spent in music lessons is y.

Now, we have been given that she worked a total of 18 hours. Hence, we have

[tex]x+y=18\\ y=18-x...............................(1)[/tex]

And she made $139. Thus, we have

[tex]5x+12y=139..............................(2)[/tex]

Substituting the value of y from equation 1 in 2, we get

[tex]5x+12(18-x)=139\\ 5x+216-12x=139\\ -7x=-77\\ x=11[/tex]

Therefore, she spent 11 hours in baby-sitting.

Final answer:

Karen spent 11 hours baby-sitting and 7 hours giving music lessons.

Explanation:

Let x be the number of hours spent baby-sitting, and let y be the number of hours spent giving music lessons.

We are given the following information:

Karen makes $5 per hour baby-sitting, so she earned 5x dollars from baby-sitting.
Karen makes $12 per hour giving music lessons, so she earned 12y dollars from giving music lessons.
She worked a total of 18 hours, so x + y = 18.
She made a total of $139, so 5x + 12y = 139.

We can now set up a system of equations:

x + y = 18
5x + 12y = 139

To solve this system, we can use substitution or elimination method. Let's use the elimination method:

Multiply the first equation by 5 to make the coefficients of x the same: 5x + 5y = 90.
Subtract this new equation from the second equation: (5x + 12y) - (5x + 5y) = 139 - 90.
Simplify both sides of the equation: 7y = 49.
Divide both sides of the equation by 7: y = 7.
Substitute y = 7 into the first equation: x + 7 = 18.
Solve for x: x = 11.

Therefore, Karen spent 11 hours baby-sitting and 7 hours giving music lessons.

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Use the given information to match the answers.

ABC is a right triangle.

1. 2√13
2. √5
3. 3√3

1. If b = 2 and c = 3, then a =
2. If a = 3 and c = 6, then b =
3. If a = 4 and b = 6, then c =

Answers

using formula
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
1)
[tex] {3}^{2} = {a}^{2} + {2}^{2} \\ a = \sqrt{ {3}^{2} - {2}^{2} } \\ a = \sqrt{5} [/tex]
2)
[tex] {6}^{2} = {3}^{2} + {b}^{2} \\ b = \sqrt{ {6}^{2} - {3}^{2} } \\ b = \sqrt{27} \\ b = \sqrt{9} \sqrt{3} \\ b = 3 \sqrt{3} [/tex]
3)
[tex] {c}^{2} = {4}^{2} + {6}^{2} \\ c = \sqrt{ {4}^{2} + {6}^{2} } \\ c = \sqrt{52} \\ c = \sqrt{4} \sqrt{13} \\ c = 2 \sqrt{13} [/tex]

Hey there!

Solve them by using
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

1.
[tex] {a}^{2} + {2}^{2} = {3}^{2} \\ {a}^{2} + 4 = 9 \\ {a}^{2} = 9 - 4 \\ {a}^{2} = 5 \\ a = \sqrt{5} [/tex]

2.
[tex] {3}^{2} + {b}^{2} = {6}^{2} \\ 9 + {b}^{2} = 36 \\ {b}^{2} = 36 - 9 \\ {b}^{2} = 27 \\ b = \sqrt{9 \times 3} \\ b = 3 \sqrt{3} [/tex]

3.
[tex] {4}^{2} + {6}^{2} = {c}^{2} \\ 16 + 36 = {c}^{2} \\ {c}^{2} = 52 \\ c = \sqrt{13 \times 4} \\ c = 2 \sqrt{13} [/tex]

Hope this helps. - M

Assuming that one-pint is equal to 473 ml., how many pints can be found in one liter?

Answers

we know that
1 pint is equal to --------> 473 ml
1 liter is equal to--------> 1000 ml
so
1 pint is equal to --------> 473 ml
x pints------------------> 1000 ml
x=1000/473-----> 2.11 pints

the answer is
2.11 pints can be found in one liter

For this case we can make the following rule of three:
1 pint -------> 473 ml
x -------------> 1000 ml
Clearing x we have:
x = (1000/473) * (1)
x = 2.114164905
Rounding off we have:
x = 2
Answer:
can be found 2 pints in one liter

Find area of trapezoid using the Pythagorean theorem

Answers

You should either divide or add

This is a multistep problem. So, let's split it up.

Finding the height:
We need to look at the equation for find the diagonal of a triangle.
a²+b²=c²
We don't have leg one, but we have leg two. If we subtract the longer base by the shorter base, we have leg two.
11-7=4
a²+4²=5²
a²+16=25; let's subtract 16 from both sides.
a²=9
a=3

So, the height is 3.

Finding the area of the trapzoid:
Let's look at the formula for finding the area.
(b1+b2)(h÷2)=A; let's fill the variables in.
(7+11)(3÷2)=A
(18)(1.5)=A
27=A

So, the area of the trapezoid is 27 in²

Write an equation of the line that is parallel to 2x + 4y = 6 and passes through the point (6, 4).

Answers

2x + 4y = 6
4y = -2x + 6
y = -1/2x + 3/2
slope = -1/2

y = mx + b
y = -1/2x + b

At point (6, 4)
4 = -1/2(6) + b
4 = -3 + b
b = 7

Equation : y = -1/2x + 7

At 7 a.m. Gene left Austin and headed south at 10 miles per hour. At 8 a.m. Anne left from the same place and headed south on the same road. If Anne was 60 miles ahead by 3 p.m. on the same day, what was her speed?

Answers

The answer is 20 miles

Anne's speed is 20 miles per hour. If she returned home by the same path 7 hours and 30 minutes after she left, her average speed for the entire trip is 18.67 miles per hour while her average velocity is zero.

To answer this question, we need to calculate Anne's speed based on the information given. Gene started at 7 a.m. traveling at 10 miles per hour. By the time Anne starts at 8 a.m., Gene has already covered 10 miles (since he travels for 1 hour). The time from 8 a.m. to 3 p.m. is 7 hours. Both Anne and Gene travel the same path for these 7 hours, but Anne is 60 miles ahead of Gene by 3 p.m. Therefore, we need to calculate the total distance Gene traveled in 8 hours, add 60 miles to that distance, and then divide by 7 to find Anne's speed.

First, we determine Gene's total travel distance by 3 p.m., which is 10 miles/hour * 8 hours = 80 miles. Anne is 60 miles ahead, meaning she traveled 80 miles + 60 miles = 140 miles in 7 hours. Thus, Anne's speed is 140 miles \/ 7 hours = 20 miles per hour.

For part (c), if Anne returned home by the same path 7 hours and 30 minutes after she left, the total trip time would be 15 hours (7 hours to 3 p.m. and another 7 hours and 30 minutes back). Since the round trip distance is 140 miles out and 140 miles back, the total distance is 280 miles. Her average speed is total distance divided by total time, hence 280 miles / 15 hours = 18.67 miles per hour. The average velocity for the round trip is zero because she ends up at the starting point, so the overall displacement is zero.

A five question multiple choice quiz has five choices for each answer. Use the random number table provided, with 0’s representing incorrect answers, and 1’s representing correct answers to answer the following question: What is the experimental probability of correctly guessing at random exactly two correct answers?

Answers

Found a similar question online. Is the attached picture the same one as yours? Are these the choices also?
a. 5%
b. 65%
c. 45%
d. 25%

The answer is Letter D - 25%. Use the table and count the number of guesses that has two correct answers represented by 1. 01010, 10001, 11000, 01001, 00011 = a total of 5 numbers having 2 correct guesses out of 20 questions. Which means that there's twenty-five percent possibility of correctly guessing the answer out of 20 questions. 5/20 = 25%

Probability of correctly guessing at random exactly two correct answers is; 25%

How to find the experimental probability?

The table is missing but from the table shared by the first answer, we can count the number of guesses that has two correct answers.

Now, the ones that have two number of 1's are referred to as correct answers. Thus, counting them in the question, they are;01010, 10001, 11000, 01001, 00011.

Thus, there are 5 posssible correct answers out of 20. Thus;

Probability of correctly guessing at random exactly two correct answers is; 5/20 = 25%

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Paula caught a tarpon with a weight that was 11 times as great as the weight of a permit fish she caught. The total weight of the two fish was 180 pounds. How much did each fish weigh?

Answers

[tex]11 + 1 = 12 \\ 180 \div 12 = 15 \\ 15 \times 1 = 15 \\ 15 \times 11 = 165[/tex]
Tarpon=165
Permit=15

The weight of the permit fish will be 15 pounds and the weight of tarpon will be 165 pounds

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Assume that the weight of the permit fish is x pounds.

Then the weight of the tarpon would be 11x pounds.

According to the question, we can write equation as -

x + 11x = 180

12x = 180

x = 15

Weight of permit fish = 15 pounds

Weight of tarpon = 11 x 15 = 165 pounds

Therefore, the weight of the permit fish will be 15 pounds and the weight of tarpon will be 165 pounds.

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(05.07 mc) mandy needs to paint all the faces and the base of a model pyramid she made for her history project. the dimensions of the pyramid are shown here. what is the total surface area of the pyramid? a square pyramid is shown. the side of the square is 10 inches. the height of the triangular faces is 9 inches.

Answers

To find the area of the square pyramid you will consider the shapes that make up the net of the pyramid (what it looks like when it is unfolded).

There are 4 congruent (same size and shape) triangles and a square.

The area of the square is
A = bh
10 in x 10 in
A = 100 square inches.

The area of one triangle is
A = 1/2bh
1/2 x 10 in x 9 in
A = 45 square inches

45 square inches x 4 (for the 4 triangles)

180 square inches of triangles

180 + 100 = 280

The total surface area of the square pyramid is 280 square inches.

Answer:

280

Step-by-step explanation:

i n e e d p o i n t s

A painter places an 8.5 ft ladder against a wall. the bottom of the ladder is 4 ft from the base of the wall. how high up the wall does the ladder reach?

Answers

Use the Pythagorean Theorem:
a² + b² = c²
4² + b² = 8.5²
16 + b² = 72.25
b² = 56.25
b = 7.5

The ladder reaches a height of 7.5 ft on the wall

For Jack's birthday, his mom is taking him and 12 friends to the zoo. If she pays $11 for each ticket using her credit card, what impact will it have on the available credit left on her credit card?

Answers

The impact on Jack's mom's available credit after purchasing zoo tickets for Jack and 12 friends at $11 each will be a reduction of $143.

When Jack's mom pays $11 for each zoo ticket for him and his 12 friends, she will be purchasing a total of 13 tickets (one for Jack plus 12 for his friends). To calculate the total cost, multiply the number of tickets by the price per ticket:

Number of tickets: 13 (Jack + 12 friends)Price per ticket: $11Total cost: 13 tickets × $11 per ticket = $143

The total impact on her credit card's available credit will be a reduction of $143. If she had some available credit limit before this purchase, we just subtract this amount from her available credit to determine the new available credit.

x/3+6=9
what does x equal
x=___?

Answers

9514 1404 393

Answer:

Step-by-step explanation:

x/3 +6 = 9 . . . . . given

x/3 = 3 . . . . . . . subtract 6 from both sides

x = 9 . . . . . . . multiply both sides by 3

Now we have to,

find the required value of x.

→ x/3 + 6 = 9

→ x/3 = 9 - 6

→ x/3 = 3

→ x = 3 × 3

→ [x = 9]

Hence, 9 is the value of x.

Find the surface area of the following triangular prism

Answers

The surface area of the triangular prism is 144 ft³

How to find the surface area

The surface area of the prism is solved using the formula

= 2 * area of the base + Lateral surface area

Area of the base

= 2 * 1/2 * 6 * 8

= 48

Lateral surface area

= (10 + 6 + 8) * 4

= 24 * 4

= 96

Total surface area

= 48 + 96

= 144 ft³

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