Answers
Answer:
(a) (f o g)(x) = x^2 - 15x + 54
(b) (g o f)(x) = x^2 + 3x - 9
(c) (f o f)(x) = x^4 + 6x^3 + 12x^2 + 9x
(d) (g o g)(x) = x - 18
Step-by-step explanation:
f(x) = x^2 + 3x
g(x) = x - 9
(a)
(f o g)(x) = f(g(x)) = (g(x))^2 + 3(g(x)) = (x - 9)^2 + 3(x - 9)
(f o g)(x) = x^2 - 18x + 81 + 3x - 27
(f o g)(x) = x^2 - 15x + 54
(b)
(g o f)(x) = g(f(x)) = f(x) - 9 = x^2 + 3x - 9
(c)
(f o f)(x) = f(f(x)) = (x^2 + 3x)^2 + 3(x^2 + 3x)
(f o f)(x) = x^4 + 6x^3 + 9x^2 + 3x^2 + 9x
(f o f)(x) = x^4 + 6x^3 + 12x^2 + 9x
(d)
(g o g)(x) = g(g(x)) = x - 9 - 9 = x - 18
Related Questions
I WILL GIVE BRAINLEST PLEASE HELP
Which of the following is an example of the difference of two squares?
A x2−9
B x3−9
C (x+9)2
D (x−9)2
I know the answer is either A or B i might be wrong tho pls help im not sure.
Answers
Answer:
A
Step-by-step explanation:
In this question, we are concerned with selecting which of the options best represents the difference of two squares.
Let’s have an exposition below as follows;
Consider two numbers, which are perfect squares and can be expressed as a square of their square roots;
a^2 and b^2
where a and b represents the square roots of the numbers respectively.
Inserting a difference between the two, we have;
a^2 - b^2
Now by applying the difference of two squares, these numbers will become;
a^2 - b^2 = (a + b)(a-b)
So our answer out of the options will be that option that could be expressed as above.
The correct answer to this is option A
Kindly note that;
x^2 -9 can be expressed as x^2 - 3^2 and consequently, this can be written as;
(x-3)(x + 3)
Answer the question below. Type your response in the space provided. Then compare your answer to the sample answer.
Point B(-2,4) lies on a circle centered at A(1, 3). Write a paragraph proof to determine whether C(4, 2) also lies on the circle.
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x x
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Characters used: 0/15000
Submit
Answers
Answer: see proof below
Step-by-step explanation:
The standard equation of a circle is (x - h)² + (y - k)² = r² where (h. k) is the center of the circle and r is the radius. It is given that A (h, k) = (1, 3) and point B (x, y) = (-2,4) is on the circle. Substitute the center (h, k) and point B(x, y) = (-2,4) into the standard equation of a circle to get r² = 10. To prove that C(x, y) = (4, 2) is also a point on the circle, substitute the center (h, k) and the point C(x, y) = (4, 2) into the standard equation of a circle to get r² = 10. Since the radius is the same for both point B and point C and it is given that point B is on the circle, then we must conclude that point C is also on the circle.
Answer:
I am given that the center of a circle is at A(1, 3) and that point B(-2, 4) lies on the circle. Applying the distance formula to A and B, I get the following:
AB=Square Root ( (-2 - 1 )^2 + (4 - 3 )^2 ) = Square root ( 9 + 1 )
AB = Square root (10)
Since B lies on the circle, this length is the length of the radius of the circle. Applying the distance formula to A and C(4, 2), I get the following:
AC = Square Root ( ( 4 - 1 )^2 + (2 - 3 )^2 ) = Square root ( 9 + 1 )
AC = Square root (10)
Thus, the distance to C from the center A is equal to the length of the radius of the circle. Any point whose distance from the center is equal to the length of the radius lies on the circle. Therefore, point C lies on the circle.
Step-by-step explanation:
Which of the following is a point-slope equation of a line that passes through the points (-1,4) and (8,2)
Answers
Answer:
y - 2 = -2/9( x - 8)
Step-by-step explanation:
hope this helps
let me know if u need more help
Answer:
y - 2 = -2/9(x - 8) or y - 4 = -2/9(x + 1)
Step-by-step explanation:
find slope first
(2 - 4)/(8 - -1) = -2/9
y - 2 = -2/9(x - 8)
sandra is playing a trivia game.on her first turn she lost 75 points. on her second turn,she lost 35 points. on her third turn,she scored 100 points. What is sandras score after three turns?
Answers
Answer: -10 points
Step-by-step explanation:
She lost 110,so that loss -the gain(100) is the total score at the end of three games
Which of the following functions is neither even nor odd? A. f(x)=x6−3x4−4x2 B. f(x)=2x3−3x2−4x+4 C. f(x)=x5−2x3−3x D. f(x)=6x5−x3
Answers
even function : [tex] f(x)=f(-x)[/tex] , odd function: $f(x)=-f(-x)$
it is neither odd nor event when both condition don't hold.
See option B.
$f(x)=2x^3-3x^2-4x+4$
$f(-x)=-2x^3-3x^2+4x+4=-(2x^3+3x^2-4x-4)$
clearly, it is neither odd nor even.
A daycare facility is enclosing a rectangular area along the side of their building for the children to play outdoors. They need to maximize the area using 180ft of fencing on three sides of the yard. The quadratic equation A=−2x2+180x gives the area, A, of the yard for the length, x, of the building that will border the yard. Find the length of the building that should border the yard to maximize the area, and then find the maximum area.
Answers
Answer:
a) length x = 45ftb) maximum area = 4050 ft²Step-by-step explanation:
Given the quadratic equation A=−2x2+180x that gives the area A of the yard for the length x, to maximize the area of the yard then dA/dx must be equal to zero i.e dA/dx = 0
If A=−2x²+180x
dA/dx = -4x + 180 = 0
-4x + 180 = 0
Add 4x to both sides
-4x + 180 + 4x = 0 + 4x
180 = 4x
x = 180/4
x = 45
Hence the length of the building that should border the yard to maximize the area is 45 ft
To find the maximum area, we will substitute x = 45 into the modelled equation of the area i.e A=−2x²+180x
A = -2(45)²+180(45)
A = -2(2025)+8100
A = -4050 + 8100
A = 4050 ft²
Hence the maximum area of the yard is equal to 4050 ft²
At a potluck, Agatha brings four dishes, Bertha brings three dishes, and five other friends bring no dishes but instead money to help pay for the food. If all the dishes are eaten up, and everyone eats the same amount, what fraction of the money should go to Bertha?
Answers
Answer:
3/7
Step-by-step explanation:
Agatha brings four dishes, Bertha brings three dishes. The total number of dishes brought = dishes brought by Agatha + dishes brought by Bertha.
Total dishes = 4 + 3 = 7 dishes
The remaining five friends brought money for the dishes. Therefore the fraction of money going to Bertha is the ratio of dishes brought to Bertha to the total number of dishes multiplied by the money. Therefore:
Fraction of the money should go to Bertha = dishes brought by Bertha/total dishes
Fraction of the money should go to Bertha = 3/7 × money
Please help asap. I will give a thanks, rate your answer and mark the brainliest one too!
The formula v^2 - u^2 = 2as is used to model a moving object, where: u= starting speed (m/s) v = final speed (m/s) a = acceleration (m/s²) s = distance travelled (m) A car stops at some traffic lights. It then accelerates at 2.3 m/s² until it reaches a speed of 13.6 m/s. Find the distance, s, that it has travelled since stopping at the lights. Give your answer correct to 1 decimal place.
Answers
Answer:
s = 40.2 m
Step-by-step explanation:
It is given that,
Initial speed of the car, u = 0 m/s
Final speed of the car, v = 13.6 m/s
Acceleration of the car, a = 2.3 m/s²
We need to find the distance, s, that it has travelled since stopping at the lights. For this, we will use third equation of motion as :
[tex]v^2-u^2=2as[/tex]
s is distance
[tex]s=\dfrac{v^2-u^2}{2a}\\\\s=\dfrac{(13.6)^2-0}{2\times 2.3}\\\\s=40.2\ m[/tex]
So, the distance covered by the car is 40.2 meters.
What collateral secures a mortgage?
O A.
5% of the purchase price of the house
B.
the house itself
C.
10% of the purchase price of the house
D.
none
Answers
Answer:
The House
Step-by-step explanation:
I need 51-55 Thanks You :D no
Answers
Answer:
Below
Step-by-step explanation:
All figures are squares. The area of a square is the side times itself
Let A be the area of the big square and A' the area of the small one in all the 5 exercices
51)
● (a) = A - A'
A = c^2 and A' = d^2
● (a) = c^2 - d^2
We can express this expression as a product.
● (b) = (c-d) (c+d)
■■■■■■■■■■■■■■■■■■■■■■■■■■
52)
● (a) = A-A'
A = (2x)^2 = 4x^2 and A'= y^2
● (a) = 4x^2 - y^2
● (b) = (2x-y) ( 2x+y)
■■■■■■■■■■■■■■■■■■■■■■■■■■
53)
● (a) = A-A'
A = x^2 and A' = y^2
● (a) = x^2-y^2
● (b) = (x+y) (x-y)
■■■■■■■■■■■■■■■■■■■■■■■■■■
54)
● (a) = A-A'
A = (5a)^2 = 25a^2 and A' =(2b)^2= 4b^2
● (a) = 25a^2 - 4b^2
● (a) = (5a-2b) (5a+2b)
■■■■■■■■■■■■■■■■■■■■■■■■■■
55)
● (a) = A - 4A'
A = (3x)^2 = 9x^2 and A'= (2y)^2 = 4y^2
● (a) = 9x^2 - 4 × 4y^2
● (a) = 9x^2 - 16y^2
● (a) = (3x - 4y) (3x + 4y)
The area of a trapezium is 31.5 cm². If the parallel sides are of length 7.5 cm and 5.3 cm, calculate the perpendicular distance between them
Answers
Answer:
The answer is 4.9cmStep-by-step explanation:
To find the perpendicular distance between them that's the height we use the formula
[tex]Area \: \: of \: \: a \: \: trapezium = \frac{1}{2} (a + b) \times h[/tex]
where
a and b are the parallel sides of the trapezium
h is the perpendicular distance
From the question
Area = 31.5cm²
a = 7.5 cm
b = 5.3 cm
Substituting the values into the above formula we have
[tex]31 .5 = \frac{1}{2} (7.5 + 5.3) \times h[/tex]
[tex]31.5 = \frac{1}{2} \times 12.8h[/tex]
[tex]31.5 = 6.4h[/tex]
Divide both sides by 6.4
[tex]h = \frac{31.5}{6.4} [/tex]
h = 4.921875
We have the final answer
h = 4.9cmHope this helps you
A jar contains only red, white and blue marbles. The number of red marbles is 4/5 the number of white ones, and the number of white ones is 3/4 the number of blue ones. If there are 470 marbles in all, how any of them are blue?
•120
•200
•150
•184
Answers
Answer:
200
Step-by-step explanation:
i multiplied the answer choices by the fractions and 200 was the one that checked out
Fogoh!! Plz HELPi suck at math haha
Answers
Answer:
f(g(h(x))) = (sqrt(x) - 1)^4 + 4
Step-by-step explanation:
f(x) = x^4 + 4
g(x) = x - 1
h(x) = sqrt(x)
g(h(x)) = sqrt(x) - 1
f(g(h(x))) = (sqrt(x) - 1)^4 + 4
how do you find the surface area of this triangular prism?
Answers
To find the area of a triangular prism you have to do A 1/2 bh or A bh/2 which means you have to multiply those two fractions and reduce them
Answer:
Find the area of the 2 triangle faces first and then find the area of the 3 rectangle faces and add them together to get [tex]159cm^{2}\\[/tex]
Step-by-step explanation:Step 1: Find the surface area of the 2 triangles
[tex]\frac{(6)(5.5)}{2}[/tex] x2 = [tex]33cm^2\\[/tex]
Step 2: Find the surface area of the 3 rectangles
(6x7) x 3 = [tex]126cm^2[/tex]
Step 3: Add the 2 surface areas together
[tex]33cm^2\\[/tex] + [tex]126cm^2[/tex] = [tex]159cm^2[/tex]
Therefore the surface area of the prism is [tex]159cm^{2}[/tex]
i need help :( please answer
Answers
Answer:
[tex] = - ( \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} )[/tex]
Step-by-step explanation:
[tex] - {(3)}^{ - 4} = \\ - ( { 3}^{ - 4} )= \\ - (\frac{1}{ {3}^{4} } )[/tex]
[tex] = - ( \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} )[/tex]
[tex] = - \frac{1}{81} [/tex]
I hope it helps
For all x, 5-3(x-4)=?
Answers
Answer:
the answer that i find is 17-3x
Kameryn flips a coin, rolls a 6-sided die, and then spins an 8-section
spinner. How many possible outcomes are there?
Answers
Answer:
96 possible outcomes
Step-by-step explanation:
2 x 6 x 8 = 96
Half the marbles in a bag are red, 1/6 of the marbles are blue, and the remaining 8 marbles are white how many total marbles are in the bag
Answers
Hey there! I'm happy to help!
Let's represent the total number of marbles with the variable t. We have the following information.
1/2t+1/6t+8=t (1/2 of total are red, 1/6 of total are blue, 8 are white, add them up to get total)
Now, we solve for t.
1/2t+1/6t+8=t
We combine like terms.
2/3t+8=t
We subtract t from both sides.
-1/3t+8=0
We subtract 8 from both sides.
-1/3t=-8
We divide both sides by -1/3.
t=24
Therefore, there ae 24 total marbles in the bag.
Have a wonderful day! :D
The total number of marbles will be 7/2.
What is Addition?
A process of combining two or more numbers is called addition.
Given that;
Half the marbles in a bag are red, 1/6 of the marbles are blue, and the remaining 8 marbles are white.
Now,
Since, Half the marbles in a bag are red, 1/6 of the marbles are blue, and the remaining 8 marbles are white.
Hence, Total number of marbles = 1/2 + 1/6 + 8
= 8 / 12 + 8
= 4 / 3 + 8
= 28/8
= 7/2
Thus, The total number of marbles will be 7/2.
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8) There are 2116 students in a school .In how many equal rows and columns can they be arranged for a drill display?
Answers
Answer:
46
Explanation:
root of 2116
=46×46
Therefore 46 columns and 46 rows
Answer:
46 rows, 46 columns.
Step-by-step explanation:
First factor 2116:
2) 2116
2 } 2058
23 ) 529
23
2116 = 2*2*23*23
= 46 * 46
Please answer question now
Answers
Answer:
90
Step-by-step explanation:
Tangents drawn to a circle from an external point are equal, thus
IH = IJ = 7
ON = OH = 19 - 7 = 12
MN = ML = 26 - 7 = 19
Summing the 4 sides for perimeter (P)
P = 26 + 19 + 7 + 7 + 12 + 19 = 90
How many times larger is the value of
86,000,000 than 8,600?
Answers
Answer:
a 1000 times// just divide them
Answer:
10,000 times Larger
Step-by-step explanation:
To determine the multiple larger for 86,000,000 than 8,600, we simply will use the division operation and the result will be the multiple.
86,000,000 / 8,600 = 10,000
Hence, the number 86,000,000, is 10,000 times larger than 8,600.
Another method is simply to look at the additional zeroes that 86,000,000 has in comparison to 8,600. Since we can see that 86 is the only non-zero digit within the two numbers, we can use the properties of the decimal system to compare. Note that 86,000,000 has 6 zeroes, while 8,600 has two zeros. This means that we will need 4 zeroes as part of our tens multiple, so we can say that 10,000 is the multiple. Once again, we see that 86,000,000 is 10,000 times larger than 8,600.
Cheers.
Complete the square.
3x^2-12x=96
Answers
Answer:
x = 8 and -4
Step-by-step explanation:
3x² - 12x = 96
3(x² - 4x + 4 = 32 + 4)
3[(x - 2)² = 6²]
x - 2 = +/- 6
x = 8
x = -4
x=8
x=-4
Dos secretarias deben escribir el mismo número de cartas. La primera escribe 2 cartas por hora y la otra, 5 cartas por hora. Si la primera ha empezado 6 horas antes que la segunda. ¿Cuántas horas
trabajó la primera?
Ayuden!!
Answers
Answer:
El número de horas que trabajó la primera secretaria es de 10 horas
Step-by-step explanation:
Los parámetros dados son;
El número de letras que la primera secretaria puede escribir por hora = 2 letras
El número de letras que el segundo secretario puede escribir por hora = 5 letras
Dado que la primera secretaria comenzó 6 horas antes que la segunda secretaria, tenemos;
Sea el tiempo en horas en que ambas secretarias habrán escrito el mismo número de letras = [tex]t_e[/tex]
2 × [tex]t_e[/tex] + 2 × 6 = 5 × [tex]t_e[/tex]
2 × [tex]t_e[/tex] + 12 = 5 × [tex]t_e[/tex]
12 = 5 × [tex]t_e[/tex] - 2 × [tex]t_e[/tex] = 3 × [tex]t_e[/tex]
12 = 3 × [tex]t_e[/tex]
3 × [tex]t_e[/tex] = 12
[tex]t_e[/tex] = 12/3 = 4 horas
El número de horas que trabajó la primera secretaria = Tiempo de inicio anticipado + Tiempo que le toma a la segunda secretaria que comenzó 6 horas más tarde y a la primera secretaria que había estado escribiendo durante 6 horas (inicio anticipado) escribir la misma cantidad de cartas
El número de horas que trabajó la primera secretaria = 6 + 4 = 10 horas.
Por lo tanto, el número de horas que trabajó la primera secretaria = 10 horas.
what is the correct symbol?
Answers
Answer:
Since 10/9 is greater than 1, multiplying by 10/9 makes the value larger
Step-by-step explanation:
Step 1: Solve the fraction
10/9 = 1.1112
Therefore 10/9 > 1
Step 2: Multiple the fraction by itself
10/9 x 10/9 = 100/81
Convert fraction to decimals
100/81 = 1.2345678901.....
1.234567901 > 1.1112
Therefore 10/9 x 10/9 is bigger than 10/9
HELPP NEEDED ASAP PLEASE.
There are 20n members in the Trumpington marching band, and when they line up in rows of 26, there are 4 band members left over. If n is an integer and there are fewer than 1000 band members, what is the maximum number of people that could be in the Trumpington marching band?
Answers
Answer:
The maximum number of people that can be in the Trumpington marching band is 940 people
Step-by-step explanation:
The number of members = 20·n
The number per row = 26
The number left = 4
Therefore, we have;
If there are x rows of 26, we have;
26 × x = 20·n - 4
We have;
26 × x < 996
26 × x < 20·n
20·n < 996 therefore, 20·n ≤ 980
We check that 980/26 = 37 and some fractions
26 × 37 = 962 which will leave a remainder of 2
Therefore, we note that for 26 to have a remainder of 4, the last digit of the factor x must be 6 so has to get the last digit of the product 26 × x to be 6 while the digit of the product 20×n is 0 which will live 4 members out to get to the next 10 as follows;
26 × 36 = 936 while 20 × 47 = 940
We get 940 - 936 = 4 members
Therefore, the maximum number of people that can be in the Trumpington marching band = 940.
A man gave his 8000$ as pocket money and his son 1000$ less.Express the girls money as a percentage of the total sum of money.
Answers
Answer:
About 89%
Step-by-step explanation:
8000 + 1000 = 9000.
To find the girls money as a percentage of the total sum of money, you must take 8000 and divide it by 9000.
8000/9000 = .8888 = 88.88 = 88.9% or about 89%.
please please answer this question now
با )
Answers
Answer:
43/90
Step-by-step explanation:
We want to express 0.47777... as a ratio of two integers. To do so, we need to multiply by 10^n, where n is the number of repeating decimals. Only 7 is repeating so we multiply 0.47777... by 10. The trick to do this is to let x=0.47777... In other words, what we are doing is the following:
[tex]x=0.47777...\\10x=4.7777....\\\text{Subtract x}\\10x-x=4.7777...-x\\9x=4.7777...-0.4777...\\9x=4.3\\x=4.3/9=43/90=0.4\overline{7}[/tex]
1: The best statement for reason 6 of this proof is -∠A ≅ ∠C
-∠B ≅ ∠D
-∠B and ∠D are supplements
-∠B ≅ ∠B
2.The best reason for statements 3.5. and 7 in this proof is
- Alternate interior angles are congruent.
-Corresponding angles are congruent.
-Alternate exterior angles are congruent.
-Interior angles on the same sides of a transversal are supplements.
3. The best statement for reason 8 of this proof is
-∠B ≅ ∠B -∠A and ∠C are supplements.
-∠B ≅ ∠D
-∠A ≅ ∠C
Answers
Answer:
1) -∠B ≅ ∠D
2) -Interior angles on the same side of a transversal are supplementary
3) -∠A ≅ ∠C
Step-by-step explanation:
1) Given that ∠A and ∠B are supplements and ∠A and ∠D are supplements, we have; ∠B ≅ ∠D
2) Given that ABCD is a parallelogram, therefore ∠A and ∠B, ∠A and ∠D and ∠B and ∠C are interior angles on the same side of a transversal and are therefore supplementary
3) Given that ∠A and ∠B and ∠B and ∠C are supplementary, therefore, ∠A ≅ ∠C.
Help me figure this out, I don’t understand
Answers
Answer:
0,3
1,1
-1,1
-2.55, -10
2.55, -10
Step-by-step explanation:
It's asking for you to graph it and figure out points from the equation.
What you can do is subsitute values for X and solve for Y or use a graphing calculator. I used desmos, an online calculator and looked for coordinates. Also the +3 is the y intercept, which means y is 3 when x is 0.
Becky is buying fabric to make new pillows for her couch. She spends $71.50 on striped fabric and $52.25 on checkered fabric. If both fabrics cost $5.50 per yard, how many total yards of fabric does she buy?
Answers
Answer:
22.5
Step-by-step explanation:
im smart
Beaky bought 13 yards of striped fabric and 9.5 yards of checkered fabric.
Given that,
Becky is buying fabric to make new pillows for her couch. She spends $71.50 on striped fabric and $52.25 on checkered fabric.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Both fabrics cost $5.50 per yard, how many total yards of fabric she buys is to be determined so,
Divide the total cost of the fabric by the cost per yard of $5.50,
Striped fabric = 71.50 / 5.50 = 13 yards
checkered fabric = 52.25/71.50 = 9.5 yards
Thus, beaky bought 13 yards of striped fabric and 9.5 yards of checkered fabric.
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