If g(x) is the inverse of f(x), what is the value of f(g(2)?
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Explanation:
g(x) is the inverse of f(x), which tells us that g undoes everything f(x) does.
If we input x = -6 then f(x) outputs 1
g(x) then reverses this to say that g(1) = -6. The inputs and outputs swap roles.
Moving to row 2, we see that f(-3) = 2 which reverses to g(2) = -3
We'll replace the g(2) with -3 to go from
f( g(2) )
to
f( -3 )
-3 isn't the answer, but I wanted to put it in bold to show how the replacement is happening.
From the table, we see that f(-3) = 2 which is the final answer
In other words, f(g(2)) = 2
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Side note:
We can say that f(g(x)) = x for any number x in the domain of g(x).
As another example, g(3) = 5 and f(g(3)) = f(5) = 3.
The same works the other way around meaning that g(f(x)) = x.
A local water park has two types of season passes. Plan A costs a one-time fee of $144 for admission plus $10 for parking every trip. Plan B costs a one-time fee of $48 for parking plus $22 for admission every trip. How many visits must a person make for plan A and plan B to be equal in value?
The person must make 8 trips for Plan A and B to be equal.
Plan A will cost $144 and then $10 for every parking. Assuming the number of trips is x, the expression would be:
= One time fee + (Fee per parking x number of trips)
= 144 + 10x
Plan B will cost $48 then parking of $22. Expression will be:
= 48 + 22x
To find out the number of trips where the cost will be equal, equate the two:
144 + 10x = 48 + 22x
144 - 48 = 22x - 10x
96 = 12x
x = 96 / 12
x = 8 trips
The person must therefore make 8 trips for Plan A and B to be equal.
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Question 1
Researchers want to find a way to increase the growth rate of corn so it can be harvested more often. To test the effectiveness of a new type of spray fertilizer, plants grown from 200 corn seeds were divided equally into two groups: a treatment group and a control group. The treatment group was frequently sprayed with the new type of fertilizer. The growth in centimeters of each corn plant was noted before and after the treatment.
The results showed that the mean change in the growth rate by the treatment group is 8 points more than that of the control group. To test whether the results could be explained by random chance, researchers created a table that summarizes the results of 1,000 re-randomizations of the data with differences of means rounded to the nearest 2 points.
Consider the significance level to be set at 5%, so results less than 5% can be considered statistically significant.
Part B
Question
Which statement is true about the result considering a significance level of 5%?
The result is not statistically significant, which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.
The result is statistically significant, which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.
The result is statistically significant, which implies that spraying the corn plants with the new type of fertilizer does not increase the growth rate.
The result is not statistically significant, which implies that this result could be due to random chance.
Answer:
So what are you asking me to do
Answer:
A.
Step-by-step explanation:
Find the value of x.
A. 12
B. 5
C. 16
D. 4
Answer:
According to intersecting chard theorem:-
[tex]12(x)=8(x+2)[/tex]
[tex]12x=8x+16[/tex]
[tex]12x-8x=16[/tex]
[tex]4x=16[/tex]
[tex]x=16/4[/tex]
[tex]x=4[/tex]
So, your answer is D) 4
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hope this helps you!!
The required value of the x is 4 for the given circle. Option D is correct.
A figure is shown of a circle with two intersecting cords fractions 12+x and x+2+8. The value of the x is to determine.
The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²,
where h, k is the coordinate of the circle's center on the coordinate plane and r is the circle's radius.
The chords of the circle is the lines that bisect the circles in two parts, Longest chord of the circle is the Diameter.
Now.
x+2/x=8/12
12x = 8x+16
12x-8x=16
4x = 16
x = 4
Thus the required value of x is 4 for a given circle.
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If there are 28 girls and 32 boys in the school’s band, what is the ratio of boys to to total students?
If it takes 2 cups of flour to make 45 cookies, how many cups of flour will it take to make 135 cookies? (hint: set up a proportion.)
A factory makes 12 bikes in 3 hours. If it keeps making bikes at the same rate, how many bikes will it have made in 8 hours? (hint: set up a proportion.)
On a map, two cities measure 6.2 cm apart. If the scale of the map is 5 cm per 10 miles, then how many miles apart are the cities? (hint: set up a proportion.)
4 questions will mark brainliest 1st to answer them in order
Answer:
1. 8:15
2. 6
3. 32
4. 12.4
What is the slope of the line represented by the equation y=-1/2-5x
Answer:
m = -5
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Identify
y = -1/2 - 5x
Compare:
y-intercept b = -1/2
slope m = -5
Answer:
The slope is -5 and the y intercept is -1/2
Step-by-step explanation:
This equation is written in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = -5x-1/2
The slope is -5 and the y intercept is -1/2
Evaluate the expression c5 when c = 3.
Replace c with 3:
3^5 = 3 x 3 x 3 x 3 x 3 = 243
The answer is 243
Answer:
15
Step-by-step explanation:
c5
3(5)
3 x 5
15
hi please answer me asap I will mark brainlist
Answer:
1) c
2) b
3) d
4) b
5) c
6) b
7) b
8) d
9) c
What is the solution to this equation? X/4 =-12
A. x = 48
B. X= -3
C. x = -48
D. X= 3
Answer:
C. x=-48
Step-by-step explanation:
x/4=-12
multiply both sides by 4
4x/4=4 (-12)
simplify
x=-48
Analyze the diagram below and complete the instructions that follow. find tan
PLZZ HELP ASAP AND SHOW WORK PLZ
Answer:
39 acute isoceleleellsllelsls
Step-by-step explanation:
The angles of triangle always add to 180 degrees. So that angle on the bottom already takes up 102 so 180-102=78 and there are 2 angles left so both of those are 39 because 78/2=39 and 39 is an acute angle since its less than 90 degrees so ya
helppp me i need help plzzzzz
Answer:
x+3y -10 =0
Step-by-step explanation:
In slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = -1/3x +10/3
We want it in the general form ax+by +c =0 where a,b,c are integers and a>0
Multiply by 3 on each side
3*y = 3(-1/3x +10/3)
3y = -x +10
Add x to each side
x+3y = -x+10 +x
x+3y = 10
Subtract 10 from each side
x+3y -10 = 10-10
x+3y -10 =0
The slope of a line is [tex] - \frac{1}{3} [/tex] and the y-intercept is [tex] \frac{10}{3} [/tex]. What is the equation of the line written in general form?
Choices:○ 10x + 3y - 1 = 0
○ x + 3y + 10 = 0
○ x + 3y - 10 = 0
Remember to use this formula:[tex] \quad \quad\quad\quad\boxed{\tt{y = mx + b}}[/tex]
Given that:[tex]\quad \quad\quad\quad\boxed{\tt{Slope (m) = \frac{1}{3} }}[/tex]
[tex]\quad \quad\quad\quad\boxed{\tt{y \: intercept(b) = \frac{10}{3} }}[/tex]
Lets try![tex] \quad \quad\quad\quad\boxed{\tt{y = - \frac{ 1}{3}x + \frac{10}{3} }}[/tex]
Then convert it in general form using this formula:[tex] \quad \quad\quad\quad\boxed{\tt{ax + by + c = 0}}[/tex]
Each side will be multiply by 3[tex] \quad \quad\quad\quad\boxed{\tt{ (3)y = 3(- \frac{ 1}{3}x + \frac{10}{3} )}}[/tex]
[tex] \quad \quad\quad\quad\boxed{\tt{ 3y = \cancel{ \color{red}3}(- \frac{ 1}{ \cancel{ \color{red}3}}x + \frac{10}{ \cancel{ \color{red}3}} )}}[/tex]
[tex] \quad \quad\quad\quad\boxed{\tt{3y = - x + 10}}[/tex]
Let's convert "x" like this.[tex] \quad\quad\quad\boxed{\tt{3y = - x + 10}} \: ➡ \: \boxed{\tt{x + 3y = 10}}[/tex]
Convert "10" like this.[tex] \quad\quad\quad \boxed{\tt{x + 3y = 10}} \: ➡ \: \boxed{ \tt{x + 3y - 10 = 0}}[/tex]
Hence, the answer is:[tex]\quad \quad\quad\quad \boxed{ \color{green}{ \tt{x + 3y - 10 = 0}}}[/tex]
_________
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Wilt Chamberlain scored 100 points in a single basketball game on March 2, 1962. In that game, he made 36 field goals (baskets) in 63 attempts. Find the ratio of field goals to attempts
Answer:
Field goals: No. of attempts
36:63
4:7 (simplest form)
Hence, the answer is 4:7.
Find the value of the y-intercept of the line whose equation is 5x - 3y = -12.
A. -12/5
B. -4
C. 4
Answer:
C. 4 is the right answer!
Step-by-step explanation:
4. Meg uses 1/2 of her supply of raisins
to make trail
mix and 3/10 of her supply of raisins to make
cookies. If Meg uses 8 pounds of raisins, how many
pounds of raising are in her supply
Answer:
10 pounds
Step-by-step explanation:
Let x represent the amount of raisins Meg have in her supply. She uses 1/2 of her supply of raisins to make trail mix and 3/10 of her supply of raisins to make cookies which gives a total of 8 pounds of raisins being used. To find the amount of raisins she has in her supply, we use the equation:
(1/2)x + (3/10)x = 8
multiply through by 20:
(1/2)x * 20 + (3/10)x * 20 = 8 * 20
10x + 6x = 160
16x = 160
Divide both sides of the equation by 16:
16x/16 = 160/16
x = 10 pounds
Therefore she have 10 pounds of raisins in her supply
The triangles below are similar. Find the length of ED.
Answer:
ED = 6
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{ED}{BA}[/tex] = [tex]\frac{EF}{BC}[/tex] , substitute values
[tex]\frac{ED}{9}[/tex] = [tex]\frac{12}{18}[/tex] ( cross- multiply )
18 ED = 108 ( divide both sides by 18 )
ED = 6
F is proportional to a If F = 36 when a = 9 find, a when F = 32
Answer:
a = 8
Step-by-step explanation:
Given F is proportional to a then the equation relating them is
F = ka ← k is the constant of proportion
To find k use the condition F = 36 when a = 9
36 = 9k ( divide both sides by 9 )
4 = k
F= 4a ← equation of proportion
When F = 32 , then
32 = 4a ( divide both sides by 4 )
8 = a
Evaluate the function
f(8) + g(-1) for the functions f(x) = -2x + 9 and g(x) = x²-2
Answer:
- 8
Step-by-step explanation:
To evaluate f(8) substitute x = 8 into f(x)
f(8) = - 2(8) + 9 = - 16 + 9 = - 7
Similarly for g(- 1)
g(- 1) = (- 1)² - 2 = 1 - 2 = - 1
Then
f(8) + g(- 1) = - 7 + (- 1) = - 7 - 1 = - 8
Tony is building a new silo to store corn as animal feed. It will be a cylinder
topped with a half-sphere, and must store 21 000 t of corn. The entire silo can be
filled with corn. Tony wants to minimize the surface area of the silo to reduce
materials and paint costs. He has the following information:
• 1 cubic m of corn has a mass of 700 kg.
• Building costs are $8/m2, taxes included.
• Paint comes in 3.8 L cans.
Each can covers 40 sq m and costs $35,
taxes included.
• Corn costs $140 per tonne ($140/t), taxes
included.
02
Recall that 1 ton = 1000kg
What is the total cost to build, paint, and fill a silo with the least surface area?
Answer:
its $2,400
Step-by-step explanation:
if this helps please mark brainliest
PLSS HELP NEED ANSWER RIGHT NOW BEFORE THE TIME ENDS!
THANK YOU!!
Answer:
third box
first box
second box
Step-by-step explanation:
1/3x + 1/4 -2/3x; combine like terms
-1/3x + 1/4 (third box)
1/3x + 1/4 + 2/3x; combine like terms
(3/3)x +1/4 (first box)
3/3 is 1, so we don't have to write it
2/3 + 3/4x -1/3; combine like terms
1/3 + 3/4x (swap, and is second box)
A certain word game contains a large 20-sided die with letters instead of numbers on the sides. If all of the vowels (a, e, i, o, and u) are on the die, then what is the probability of rolling a vowel?
Answer:
The probability to get the vowel is 1/4.
Step-by-step explanation:
The number of elements in sample space, n(S) = 20
The number of elements in event, n (E) = 5
The probability to get the vowel is
[tex]P(E) =\frac{n(E)}{n(S)}\\\\P(E)=\frac{5}{20}\\\\P(E) = \frac{1}{4}[/tex]
The perimeter of a rectangle is 80x. The base is 7 times the height. In terms of x, what are the dimensions of the rectangle?
a.
h = 10x, b = 10x
c.
h = 3x, b = 5x
b.
h = 5x, b = 35x
d.
h = 5x, b = 25x
is due today !! need help (show work/explanation)
Answer:
Step-by-step explanation:
radius=diameter/2
=8/2
=4 m
volume of a cylinder =πr^2h
=3.14*(4)^2*13
=40.82*16
=653.12 m^3
Please help I’ll give brainliest
Answer:
3675
Step-by-step explanation:
3500x.05 (5%)=175 GCT
3500+175=3675.
What is the length of bc in the right triangle below?
Which of the following is a factor of 8x2– 10x– 3?
Answer:
8x2- 10x- 3 = 46
Step-by-step explanation:
Solve the equation for a.
K = 4a + 9ab
a = K(4 + 9b)
a = 4(K + 9b)
a = a equals StartFraction 4 plus 9 b Over K EndFraction equals h.
a = a equals StartFraction K Over 4 plus 9 b EndFraction equals h.
Answer:
a = k/(4 + 9b)
Step-by-step explanation:
Here, we want to make a the formula subject
We have this as;
k = a(4 + 9b)
a = k/(4 + 9b)
The expression for a fom the give expression is a = k/(4 + 9b)
Subject of formulaGiven the following equation
K = 4a + 9ab
Factor out the GCF
K = a(4 + 9b)
Divide both sides by 4 + 9b
k/4+9b = a(4 + 9b)/4+9b
k/(4 + 9b) = a
Hence the expression for a fom the give expression is a = k/(4 + 9b)
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Calcula el porcentaje de sal de mesa o cloruro de sodio que contiene una disolución que se preparó con 5 gramos de cloruro de sodio y 95 gramos de agua.
Answer:
inglese please
Step-by-step explanation:
A circular table has a radius of 5cm. Decorative trim is placed along the outside edge. How
long is the trim?
in a cave, a stalactite gets 4 millimeters longer each year. This year it is 72 centimeters long. How many years until it is 1 meter long?