Drag the tiles to the boxes to form correct pairs.
Match each operation involving Rx) and g(x) to its answer.
(t) = 1 - 22 and g(x) = V11 — 41
Answers
Answer:
[tex](g + f)(2) = \sqrt 3 - 3[/tex]
[tex](\frac{f}{g})(-1) = 0[/tex]
[tex](g + f)(-1) = \sqrt{15}[/tex]
[tex](g * f)(2) = -3\sqrt 3[/tex]
Step-by-step explanation:
Given
[tex]f(x) =1 - x^2[/tex]
[tex]g(x) = \sqrt{11 - 4x[/tex]
See attachment
Solving (a): (g + f)(2)
This is calculated as:
[tex](g + f)(2) = g(2) + f(2)[/tex]
Calculate g(2) and f(2)
[tex]g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}[/tex]
[tex]f(2) = 1 - 2^2 = -3[/tex]
So:
[tex](g + f)(2) = g(2) + f(2)[/tex]
[tex](g + f)(2) = \sqrt 3 - 3[/tex]
Solving (b): [tex](\frac{f}{g})(-1)[/tex]
This is calculated as:
[tex](\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}[/tex]
Calculate f(-1) and g(-1)
[tex]f(-1) = 1 - (-1)^2 = 0[/tex]
So:
[tex](\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}[/tex]
[tex](\frac{f}{g})(-1) = \frac{0}{g(-1)}[/tex]
[tex](\frac{f}{g})(-1) = 0[/tex]
Solving (c): (g - f)(-1)
This is calculated as:
[tex](g + f)(-1) = g(-1) - f(-1)[/tex]
Calculate g(-1) and f(-1)
[tex]g(-1) = \sqrt{11 - 4 * -1} = \sqrt{15}[/tex]
[tex]f(-1) = 1 - (-1)^2 = 0[/tex]
So:
[tex](g + f)(-1) = g(-1) - f(-1)[/tex]
[tex](g + f)(-1) = \sqrt{15} - 0[/tex]
[tex](g + f)(-1) = \sqrt{15}[/tex]
Solving (d): (g * f)(2)
This is calculated as:
[tex](g * f)(2) = g(2) * f(2)[/tex]
Calculate g(2) and f(2)
[tex]g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}[/tex]
[tex]f(2) = 1 - 2^2 = -3[/tex]
So:
[tex](g * f)(2) = g(2) * f(2)[/tex]
[tex](g * f)(2) = \sqrt 3 * -3[/tex]
[tex](g * f)(2) = -3\sqrt 3[/tex]
Related Questions
HELP ME ASAP PLS !!!
Answers
Answer:
64 degree
Step-by-step explanation:
The tangent is perpendicular to the normal. In case of circle the normal is the radius which passes from the center of the circle.
Here Angle BAC = 90 degree (as the angle between the tangent and normal)
Angle BAC = 26 degree,
The sum of all the angles in a triangle is 180 degree,
So,
angle BAC + angle ABC + angle ACB = 180 degree
26 degree + angle ABC + 90 degree = 180 degree
angle ABC = 64 degree
The number of birdhouses Ben can make varies directly with the amount of time he spends making the birdhouses. He can make 4 birdhouses in 1 1/2 hours. How many birdhouses can he make in 9 hours?
Answers
Answer:
24
Step-by-step explanation:
if he can make 4 birdhouses in 1 1/2 hours, 1 1/2 hours x 2 = 3. 8 birdhouses per 3 hours. 3 x 3 = 9 hours, 8 x 3 = 27
Answer:
24 birdhouses
Step-by-step explanation:
This is a proportional relationship. y = kx, where k is the constant of proportionality. We can determine k as follows:
4 birdhouses = k(1 1/2 hours), which leads to:
4 birdhouses
------------------------- = 8/3 birdhouses/hr
3/2 hours
In 9 hours, Ben can make (8/3)(9) birdhouses: 24 birdhouses
What is the slope of the line on the graph below?
Options:
A.-1/2
B.1/2
C.1
D.2
Answers
Answer:
2
Step-by-step explanation:
help meeee please thuis is due at 2
Answers
Answer:
the answer is 20
Step-by-step explanation:
because if you add all of it you get 20
Given the system of linear equations:
4x + 6y = 24
2x+y=8.
Which equations (select all) are a result from ADDING and/or SUBTRACTING the TWO
equations together?
6x + 7y = 32
2x + 6y = 16
2x + 5y = 16
63 - 6y = 32
Answers
if you add the two equations you get the first answer and if you subtract the two equations you get the second answer
What is the solution to the equation below?
Answers
Answer:
The solutions are (2,0) and (3,0)
Step-by-step explanation:
The common denominator is (x - 2)(x - 4) which comes to x^2 - 6x + 8 which is exactly what the denominator on the right hand side is.
2x (x - 4) - (x+3)(x - 2) = - 4x
============= ========
(x -2)(x - 4) x^2 - 6x - 8
Multiply both sides by x^2 -6x - 8
2x(x - 4) - (x^2 + x - 6 ) = - 4x Remove the brackets
2x^2 - 8x - x^2 - x + 6 = - 4x Combine like terms on the left
2x^2 - x^2 - 8x - x + 6 = - 4x
x^2 - 9x + 6 = - 4x Add 4x from both sides
x^2 - 9x + 4x + 6 = 0
x^2 - 5x + 6 = 0
This factors into
(x - 2) and (x - 3)
x - 2 = 0
x = 2
x - 3 = 0
x = 3
please help!!! due soon :)))) (look at my other questions too)
Answers
Which function describes the sequence 4, 12, 36, 108, ... for n = 1, 2, 3, 4...?
a) f(n) = 2" + 1
b) f(n) = 3n
c f(n) = (n − 1)2 + 3
d) f(n) = 4.3"-1
Answers
Answer:
d) f(n) = 4 . 3^(n-1)
______________
If you doubled joes age and added 10 years he would still be younger than his uncle. His uncle is 51. Use inequalities to find how old Joe is.
Answers
Answer:
He is 20 at oldest, or [tex]x\leq 20[/tex]
Step-by-step explanation:
The first step in finding a possible age is:
Subtract 10 from 51, and you get 41. Divide by 2, and you get about 20.5.
This means Joe is younger than or 20 years old.
Which of the following best describes the shape of the distribution below ?
A) Uniform
B) right skewed
C) bell shaped
D) left skewed
Answers
Answer:
Its right skewed
I ligit dont understad
Plz help asap!!
And explanation will get brainlyst
Find the equasion for the following parabola
Vertex (4,3)
Directrix x (6)
4
3
6
Answers
Answer:
(y - 3 )² = 8 ( x - 4 )
The given vertex of Parabola is ( 4 , 3)
And Directrix is X = 6
The equation of parabola is
( y - k )² = - 4 ( P) ( x - h )
Now p = 4 - x = 4 - 6 = - 2
And given value of ( k , h) = ( 4 , 3)
Or ( y - 3 )² = - 4 ( - 2) ( x - 4 )
Or, ( y - 3 )² = 8 ( x - 4 )
Hence The equation of parabola with directrix x = 6 And
vertex ( 4 , 3 ) is ( y - 3 )² = 8 ( x - 4 ) Answer
The answer is (y - 3 )² = 8 ( x - 4 ).
The given vertex of Parabola is ( 4 , 3)
And Directrix is X = 6
What is the equation of a parabola?The equation of a parabola is :
⇒ [tex]( y - k )^{2} = - 4 ( P) ( x - h )[/tex]
Now p = 4 - x = 4 - 6 = - 2,
And given value of ( k , h) = ( 4 , 3)
Or [tex]( y - 3 )^{2} = - 4 ( - 2) ( x - 4 )[/tex]
Or, [tex]( y - 3 )^{2} = 8 ( x - 4 )[/tex]
Hence, The equation of a parabola with directrix x = 6 and
vertex ( 4 , 3 ) is ( y - 3 )² = 8 ( x - 4 )
Learn more about the equation of a parabola here: brainly.com/question/4061870
#SPJ2
find the slope for me please (2, -5) (7, -5)
Answers
Answer:
slope=y2-y1/x2-x1
=-5+5/7-2
=0/5
=0
Step-by-step explanation:
Which choice is equivalent to the expression below?
√20 + √45
Answers
→ √20 + √45
→ 2√5 + 3√5
Taking √5 as common.→ (2 + 3)√5
→ 5√5
Therefore, option A is correct.
Find the area of the shape
Answers
I need help thank you!
(7x + 14)
(15x - 4)
Answers
Answer:
(7x + 14)° = 84°
(15x - 4)° = 146°
Step-by-step explanation:
62° + (7x + 14)° = (15x - 4)°
62° +7x + 14 = 15x - 4
15x - 7x = 62 + 14 + 4
8x = 80
x = 10
Therefore, exterior angle (15x - 4)° = 146°
interior angle (7x + 14)° = 84°
Aisha and some friends are going to the movies. At the theater, they sell a bag of
popcorn for $3.75 and a drink for $5. How much would it cost if they bought 5 bags of
popcorn and 8 drinks? How much would it cost if they bought p bags of popcorn and
d drinks?
Answers
Answer:
price of 5 bags of popcorn = 3.75 x 5 = 18.75
price of 8 drinks = 5 x 8 = 40
price of p bags of popcorn = 3.75 x p
price of d drinks = 5 x d
The tree diagram shows Leila's choices for dinner at a restaurant. How many possible dinner combinations exist?
Answers
Based on the tree diagram, there are a total of 12 possible dinner combinations for Leila.
Define combinations?
In mathematics, combinations are a way to count the number of ways to choose a subset of items from a larger set, where the order of the chosen items does not matter. The number of combinations is often denoted using the symbol "n choose k", where n is the total number of items and k is the number of items being chosen.
To see why, we can count the number of paths through the tree diagram. Starting at the top, there are 2 choices for the type of dips: Guacamole dip or Cheese dip. For each of these choices, there are 2 choices for the dessert : Burrito and Enchilada. Finally, for each main course, there are 2 choices for the main course: Chicken and Beef.
Multiplying the number of choices at each step, we get:
2 (choices for dips) x 2 (choices for dessert) x 2 (choices for main course) = 8 possible dinner combinations.
Therefore, there are 3 possible dinner combinations for Leila.
To learn more about subset from the given link :
https://brainly.com/question/23454979
#SPJ1
need help quickly please!
Answers
Answer:
86
Step-by-step explanation:
Considering that it is a triangle ABC which means AB = AC + BC AB = 48 + 38 = 86
I think that's it I hope it will help you
Jack bought 50 lbs of clay for his art projects. He used 13.2 lbs to make a sculpture, and 0.72 lbs for each mug. How many mugs did Jack make if he had 28.88 lbs of clay left over?
Please help me I really need the answer I have to do 6 more assignments and Helping me would really help me finishing.
Answers
Given :
Jack bought 50 lbs of clay for his art projects. He used 13.2 lbs to make a sculpture, and 0.72 lbs for each mug.
To Find :
How many mugs did Jack make if he had 28.88 lbs of clay left over.
Solution :
Clay required to make 1 mug, r = 0.72 lbs.
Amount of clay left after making sculpture is, T = 28.88 lbs.
Now, number of clay mug Jack can make is :
[tex]n = \dfrac{28.88}{0.72}\\\\n= 40.11[/tex]
Since, number of mug cannot be in decimal, so we take the floor value.
Therefore, number of mug that can be prepared is 40 .
Which set of shapes could be used to form a net for a square pyramid?
1 square and 4 triangles
2 squares and 4 triangles
1 square and 4 rectangles
2 squares and 4 rectangles
Answers
Answer:
1 square and 4 triangles
Step-by-step explanation:
Answer:
The answer is (A) or 1 square and 4 triangles .
Step-by-step explanation:
Looking at a picture of a square pyramid would help to answer this question. (Btw sorry if im late) Stay safe<3 .
What is the area of the shape?
Answers
Answer:
20 is the answer :))))
20
Find the exact value of sin 2pi/3
Answers
Answer:
2 x 3.14 = 6.28
6.28 divided by 3 = 2.093 around 2.1
The solid triangular prism shown below is made from metal . The prism is melted down and the metal is used to create a solid cube. Find the side length of the cube. For the triangle, the base is 9cm, Height is 4cm, and Length is 12cm.
Answers
Answer:
6 cm
Step-by-step explanation:
Given :
base is 9cm, Height is 4cm, and Length is 12cm.
Volume of triangular prism :
V = 1/2 * base * height * length
V = 1/2 * 9 * 4 * 12
V = 9 * 2 * 12
V = 216 cm³
Volume of a cube = a³
Where , a = side length
If 216cm³ is melted to form a cube
Then ;
a = 216^1/3
a = 6 cm
3. Three resistors with values of 3 Ω, 4 Ω and 5 Ω are connected to a 12 V battery.
a. Draw the circuit.
b. Calculate the equivalent resistance of the circuit.
c. Calculate the current through the battery.
d. How much current is passing through each resistor?
e. Calculate the voltage drop across each resistor.
f. How does the voltage drop across each resistor compare to the voltage of the battery?
4. Three resistors with values of 12 Ω, 24 Ω and 6 Ω are connected in series to one another and a 24 V power supply. Draw the circuit and fill in the data table.
Answers
Answer:
I think it's 4
Step-by-step explanation:
Three resistors with values of 12 Ω, 24 Ω and 6 Ω are connected in series to one another and a 24 V power supply. Draw the circuit and fill in the data table.
if r = 9 in., what are the volumes for the cone, cylinder, and sphere?
I NEED HELP WITH THIS IT'S DUE TOMORROW!!
Answers
Step-by-step explanation:
the volume of :
cone = ⅓π.r².r= ⅓π.r³
cylinder = π.r²r= π.r³
Sphere = 4/3 π.r³
for r = 9 in =>
the volume of:
14. cone = ⅓.π.9³= ⅓π × 729 = 243π in³
15. cylinder = π.9³ = 729π in³
16. Sphere = 4/3 π.9³ = 972π in³
17. the volume ratio among cone, cylinder and Sphere is : ⅓ : 1 : 4/3 =
1 : 3 : 4
how do i factor this problem?
Answers
do you know how to solve this?
Answers
Explanation:
According to the Pythagoras Theorem,
45^2 = 27^2 + a^2
2025 = 729 + a^2
2025 - 729 = a^2
1296 = a^2
a = sqrt 1296
a = 36
Answer:
a) 36yards
Step-by-step explanation:
I just took the test
You want to make five-letter codes that use the letters A, F, E, R, and without repeating any letter. What is the probability that a randomly chosen
code starts with Mand ends with E?
Answers
Answer:
Probability [chosen code starts with M and ends with E] = 0.05
Step-by-step explanation:
Given:
Total alphabet = A, F, E, R, and M
Creating name without repeat
Find:
Probability [chosen code starts with M and ends with E]
Computation:
Probability Name start with M = 1 / 5
Probability Name start with E = 1 / (5-1)
Probability Name start with E = 1 / 4
Probability [chosen code starts with M and ends with E] = Probability Name start with M x Probability Name start with E
Probability [chosen code starts with M and ends with E] = (1/5)(1/4)
Probability [chosen code starts with M and ends with E] = 1 / 20
Probability [chosen code starts with M and ends with E] = 0.05
Write a direct proportion equation
that shows the price (y) for any
number of posters (x) that are $2.50
each.
A. y = kx
B. 2.50x = y
C. $2.50 = yx
D. 2.50y = x
Answers
4d multiply 7d exponent is 4