Answer:
Step-by-step explanation:
B 4C and log 625
A function is given:
f(x) = 3x + 12
a. Determine the inverse of this function and name it g(x).
b. Use composite functions to show that these functions are inverses.
c. Evaluate f(g(–2)). Explain: What is the domain?
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100 POINTS
Answer:
Step-by-step explanation:
hello :
a)
let f(x) = y so : x = g(y)
in expression = f(x) =3x+12
means : y = 3x +12 calculate : x
3x = y -12
x = (1/3)y - 4
the inverse is : g(x) = (1/3)x - 4
b)f(g(-2) = f(-14/3)
because: g(-2) = (1/3)(-2)-4 = -2/3-4 = -14/3
so : f(g(-2) = f(-14/3)=3(-14/3)+12 = - 2
1. The inverse of the function is g(x) = (1/3)x - 4.
3. The value of f(g(–2)) is -2.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x)= 3x+ 12
1. let f(x) = y then x = g(y)
y = 3x+ 12
y- 12 = 3x
x= y/3 + 4
So, the inverse of the function is g(x) = (1/3)x - 4.
2. For showing the function are inverse we have to that
(fog)(x) = f(g(x)) =x and (gof)(x) =g(f(x)) = x
Take (fog)(x) = f(g(x))
= f( (1/3)x - 4.)
= 3 ((1/3)x - 4) 12
= x - 12 + 12
= x
Now, (gof)(x)
=g(f(x))
= g(3x+ 12)
= (1/3) ( 3x+ 12) -4
= x + 4 - 4
= x
3. f(g(-2))
So, g(-2)
= (1/3)(-2)-4
= -2/3-4
= -14/3
Then, f(g(-2)) = f(-14/3)
=3(-14/3)+12
= - 2
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It takes 1 and 1 4th cups of milk to make 8 pancakes, how many cups of milk is needed to make 20
What is the value of the expression below?
7 divided by 2 minus 4.5 x times 3 + 8
Answer:
-2
Step-by-step explanation:
7. Two shoppers bought meat at a
supermarket deli. The first bought 3
pounds of meat for $9.87. The second
bought 4 pounds of meat for $16.76.
Neither of the shoppers had a coupon or
a discount card. Can you tell if both
shoppers bought the same kind of meat?
Explain why or why not.
s?
Final answer:
By calculating and comparing the price per pound of meat for each shopper, it is clear that they paid different prices per pound ($3.29 and $4.19), indicating they did not buy the same kind of meat.
Explanation:
To determine if both shoppers bought the same kind of meat, we need to calculate the price per pound that each shopper paid and compare the results. The first shopper bought 3 pounds for $9.87. To find the price per pound, we divide $9.87 by 3 pounds, which gives us $3.29 per pound.
The second shopper bought 4 pounds for $16.76. Similarly, we divide $16.76 by 4 pounds to get $4.19 per pound. Since the price per pound for each shopper is different, we can deduce that they did not buy the same kind of meat.
1/2x-1/3y=5
X=2/3y+10
What is the y and the x
Answer:
The system has infinite solutions
Is a consistent dependent system
Step-by-step explanation:
we have
First equation
[tex]\frac{1}{2}x-\frac{1}{3}y=5[/tex]
Isolate the variable y
[tex]\frac{1}{3}y=\frac{1}{2}x-5[/tex]
Multiply by 3 both sides
[tex]y=\frac{3}{2}x-15[/tex] ----> equation A
Second equation
[tex]x=\frac{2}{3}y+10[/tex] -
Isolate the variable y
[tex]\frac{2}{3}y=x-10[/tex]
Multiply by 3/2 both sides
[tex]y=\frac{3}{2}x-15[/tex] ---> equation B
Compare equation A and equation B
The equations are identical
therefore
The system has infinite solutions
Is a consistent dependent system
Find the area of a square Park whose perimeter is 320m.
Answer:
Step-by-step explanation:
A square is equal on each side. There are a total of 4 sides so we would take 320 and divide it by four to find the size of one side.
320/4
80
A = lw
A = 80 x 80
A = 6400 m^2
3(p-3) – 5p>-3p- 6
How do u solve?
Answer:
p>3
Step-by-step explanation:
<=> 3p - 9 - 5p > -3p - 6
<=> -2p + 3p > -6 + 9
<=> p > 3
To solve the inequality 3(p-3) - 5p > -3p - 6:
Simplify and combine like terms to get p > 3 as the solution.
An inequality is a mathematical statement that uses the inequality symbol to indicate the relationship between two expressions. Both sides of an inequality sign have different expressions.
The given expression is:
3(p-3) – 5p>-3p- 6
Distribute the 3 to the terms inside the parentheses:
3p - 9 - 5p > -3p - 6
Combine like terms on both sides of the inequality:
-2p - 9 > -3p - 6
Move all the terms containing p to one side by adding 3p to both sides: -2p + 3p - 9 > -6
Simplify:
p - 9 > -6
Move the constant term to the other side by adding 9 to both sides:
p - 9 + 9 > -6 + 9
Simplify: p > 3
Hence,
The solution of the given inequality is p > 3.
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6,000(1-(1+0.06)‐³²)/0.06(1+0.06)
Answer:
79716.98
Step-by-step explanation:
Woahhhhhh numbers
Step-by-step explanation:
I don’t know.
A jar contains 12 caramels, 7 mints and 16
dark chocolates. What is the probability of
selecting a mint expressed as a fraction?
Answer:
Step-by-step explanation:
Add the three digits together:
12+7+16=35
7/35, or 1/5.
a cheetah runs at a rate of 75 miles per hour about how many leaders can it run in 5 seconds
Answer:
Distance in meters D = 167.75 meters
Step-by-step explanation:
Distance covered in 5 seconds is given by:
Distance, D = Speed (S) X Time (T)
Where,
Distance = ?
Speed = 75mph
Time = 5s
Since we are calculating distance in meters, we have to convert 75miles per hour to meters per second
75mph = 75miles/1hr X 1km/0.621miles X 1000m/1km X 1hr/60mins X 1min/60s
= (75X1000) / (0.621X60X60) meter per second
= 75000/2235.6 meter per second
= 33.55 meter per second
∴ Distance D = 33.55 meter per second X 5 seconds
= 167.75 meters
Find the slope of the following and then write the equation
Answer:
See explanation
Step-by-step explanation:
Assuming we want to find the slope and equation of the line going through:
(0,1) and (1,2).
Then the slope is given by:
[tex]m = \frac{2 - 1}{1 - 0} [/tex]
This implies that:
[tex]m = 1[/tex]
The equation is given by:
[tex]y = mx + b[/tex]
Where b=1 is the y-intercept since the line passes through (0,1).
Hence the equation is:
[tex]y = x + 1[/tex]
$239 television; 10% discount
answer: $215.10
the TV's original price is $239, but with 10% off, it is now 90% of the original price. therefore we have to find 90% of 239:
0.90*239=215.10
Answer:
215.10 here ya go
There are 95 students who have applied for a scholarship.
If there are 41 men and 36 minorities, 19 of whom are
women, how many women applied for the scholarship?
Answer:
37
Step-by-step explanation:
Students who applied or a scholarship=95
Of that:
Men= 41
Minorities= 36
Minorities who are women= 19
Minorities who are men = 36-19=17
Women+ Minorities who are women=Students who applied or a scholarship-(Men+Minorities who are men)
x + 19=95-(41+17)
x+19=95-58
x+19=37
x= 37-19
x=18
Women who are NOT minority=18
Total women=Minorities who are women+Women who are NOT minority
Total women=18+19
Total women=37
By understanding the problem as a basic arithmetic problem, we determine there are 54 women who applied for the scholarship by subtracting the number of men (41) from the total number of students (95).
Explanation:To resolve the question, 'how many women applied for the scholarship', it's essential to understand the problem as a basic addition and subtraction problem. The numbers provided in the question give us initial points. It's stated that there are 41 men who applied, and if there are 95 students in total, we can calculate the total women by subtracting the number of men from the total. So, 95 total students - 41 men = 54 women. This calculation gives us the number of women that applied for the scholarship.
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Y=5x+39
Y=3.5x+60
Solve the following system
x=14 and y=109
Step-by-step explanation:
Given
y= 5x +39
y= 3.5x +60
5x+39 = 3.5 x+60
5x-3.5x = 60-39
1.5x =21
x= 21/1.5 = 14
Use the value of x = 14 in equation y=5x+39
y=5*14 +39
y=109
Hence, x=14 and y=109
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Final answer:
To solve the given system of linear equations, we use the elimination method to find the intersection point (14, 109), which is where the two lines represented by the equations meet.
Explanation:
To solve the system of equations:
y = 5x + 39
y = 3.5x + 60
We can use the method of substitution or elimination. In this case, elimination is the straight-forward choice. Since both equations are already solved for y, set them equal to each other and solve for x:
5x + 39 = 3.5x + 60
Now, subtract 3.5x from both sides:
1.5x + 39 = 60
Subtract 39 from both sides:
1.5x = 21
Divide both sides by 1.5:
x = 14
Now, plug the value of x into one of the original equations to solve for y:
y = 5(14) + 39
y = 70 + 39
y = 109
The solution to the system is (14, 109). This represents the point where the two lines intersect on a graph.
a line with a slope of -3 and an x-intercept of 15 passes through wich of the following points
A. (0,30)
B. (5,15)
C. (10,10)
D. (−5,60)
The Answer is D) because it is
How many different triangles can you make if you’re giving the measurements for two sides and the angle between those sides
Answer:
1
Step-by-step explanation:
Ashley is deciding between two jobs. Job A pays $2000 per month with a monthly raise of $85. Job B pays $2000 per month with a monthly raise of 4%. Write a function to represent the monthly salary for Job B after x months.
The monthly salary for Job B after x months, which includes a 4% monthly raise, can be represented by the exponential function S(x) = 2000 * (1 + 0.04)^x, where S(x) is the salary and x is the number of months.
Explanation:To represent the monthly salary for Job B after x months, we need to account for the 4% raise each month. Since the starting salary is $2000, and the raise is 4% (or 0.04 in decimal form) of the previous month's salary, the function to represent the monthly salary can be written using a geometric sequence formula.
Let S(x) be the salary at month x. The function will be an exponential function in the form:
S(x) = 2000 * (1 + 0.04)^x
Here, 2000 is the initial salary, 0.04 represents the 4% raise, and x is the number of months that have passed.
What is the first step when solving the equation below for x 4x - 0.2 = 1.9
A. Add 1.9 to both sides of the equation
B. Subtract 0.3 from both sides of the equation
C. Divide each side of the equation by 4
D. Add 0.3 to both sides of the equation
Answer:
First add 0.2 to both sides
x = 0.53
Step-by-step explanation:
4x - 0.2 = 1.9
4x - 0.2 + 0.2 = 1.9 + 0.2
4x = 2.1
Divide both sides by 4
4x/4 = 2.1/4
x =0.53
If it is 12:50, what will the time be 5 hours and 20 minutes later?
Lets first make it easier.
If you add the 20 minutes to 12:50 it will turn to 1:10.
After this you add the 5 hours.
This will turn 1:10 into 6:10.
Hope this helps :)
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Finley's pumpkin had a mass of 6.5 (kg) before he carved it. After carving it, the pumpkin had a mass of 3.9 kg
What was the percent decrease in the mass of the pumpkin?
Answer:
40% decrease
Step-by-step explanation:
6.5*40%=2.6
6.5-2.6=3.9
Answer:
40%
Step-by-step explanation:
Original Mass of the pumpkin = 6.5kg
After carving, the mass of the pumpkin became = 3.9 kg
Decrease in mass = 6.5 — 3.9 = 2.6kg
Therefore, the percentage decrease in mass of the pumpkin = (2.6/6.5)x100 = 40%
Which statement correctly compares the constants of variation for the graph and the equation below?
On a coordinate plane, a line goes through points (0, 0) and (1, 3).
StartFraction 10 x Over 3 y EndFraction = 1
The graph has a greater constant of variation.
The equation has a greater constant of variation.
The constant of variation is the same for the graph and the equation.
The constant of variation cannot be compared because the equation is nonproportional.
Answer:
The equation has a greater constant of variation
Step-by-step explanation:
The graph is of a line through point (0, 0) can be represented by the equation ...
y = kx
Using the given values for x and y, we see that ...
3 = k·1
k = 3 . . . . . the constant of variation for the graph
__
The given fraction can be rewritten as ...
y = (10/3)x = (3 1/3)x
In this form, the constant of variation is 3 1/3, greater than that of the graph.
Answer:
The equation has a greater constant of variation
Step-by-step explanation:The equation has a greater constant of variation
A balance scale was in perfect balance when Jane placed a box of candy on one pane of the balance and 3/4 of the same sized candy box together with 3/4 pound weight on the other pane. How much did the full box of candy weight.
Answer:
Step-by-step explanation:
i'm pretty sure that you will have to add it.
so, when we add two fractions such as 3/4 + 3/4, we make sure that the denominators (the bottom numbers) are the same and then we simply add the numerators (the top numbers).
in this problem, the denominators are the same so we will simply add 3+3 which equals to 6/4. the denominator will remain the same.
answer:
3/4 + 3/4 = 6/4
i hope this is helpful.
The required weight of the candy box is 3 pounds.
Given that,
A balance scale was in perfect balance when Jane placed a box of candy on one pane of the balance and 3/4 of the same-sized candy box together with 3/4 pound weight on the other pane.
To determine how much the full box of candy weighs.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Let the weight of the candy box be x,
3/4 of the same-sized candy box
weight = 3/4 pound
x = 3/4x + 3/4
x / 4 = 3/4
x = 3
Thus, the required weight of the candy box is 3 pounds.
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Using the values from the graph, compute the values for the terms given in the problem. Choose the correct answer.
Percentage of
Market Value
of Car
(solid line)
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Maintenance and Repair Costs
as Percentage of Car's Value
(dashed line)
-
-
-
0
1st
yr.
2nd
yr.
3rd
yr.
4th
yr.
5th
yr.
6th
yr.
7th
yr.
8th
YT.
9th
yr.
10th
yr.
Age of car = 6 years.
Original cost = $12,995.
The current market value is $
Answer:
$1299.50
Step-by-step explanation:
It appears that the graph shows the percentage of market value of a 6-year-old car is about 10%. So the value of such a car with an original value of $12,995 would be ...
$12,995 × 0.10 = $1299.50
The current market value is $1299.50.
The current market value of the car is $1299.50
How to determine the current market valueThe original cost is given as:
Original = $12,995.
From the graph, the worth of the car after 6 years is
Rate = 10%
So, the current market value of the car is:
Value = $12,995 * 10%
Evaluate the product
Value = $1299.50
Hence, the current market value of the car is $1299.50
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What is the LCM (least common multiple) of 2 and 7?
Answer:
14
Explanation:
2 l 7
4 l 14
6 l 21
8 l 28
10 l 35
12 l 42
14 l 49
If you noticed the italized, bold, and underlined number fourteen, you would notice that 2 and 7 both have number fourteen as a multiple and it is also the least common multiple.
Write the equation y-2=6x+3 in y=mx+b form
Answer:
y=6x+5
Step-by-step explanation:
y-2=6x+3
y=6x+3+2
y=6x+5
When is a zero not significant?
O
A. When it comes after the decimal point, as in 4.000
O
B. When it is included in scientific notation, as in 3.04 x 10-2
O
C. When it precedes a non-zero digit but falls after a decimal point,
as in 0.0004
O
D. When it falls between two non-zero digits, as in 4.09
Answer: A. When it comes after the decimal point, as in 4.000
Step-by-step explanation: If there are no other numbers after the zeros, there is no reason for them to be place holders. Zeros in decimals act as place holders such as in 4.09 or 4.0009. This actually does change the value of the decimal but 4.000 is just the same as a regular old 4. Hope this helps!
How do you write nine and two hundred thirty five thousandths?
Answer:
9.235
Step-by-step explanation: There you g. Hope it helps!
Kate wants to build a fence around her garden to prevent her rabbits from eating her vegetables. The rabbit fencing costs $7.50 per metre. How much will it cost to enclose a square garden with an area of 144m^?
Solution:
Given that,
Kate wants to build a fence around her garden to prevent her rabbits from eating her vegetables
Given is a square garden
Area = 144 square meter
The area of square is given as:[tex]Area = (side)^2\\\\144 = (side)^2\\\\Take\ square\ root\ on\ both\ sides\\\\side = 12[/tex]
Thus length of side of square is 12 meter
Find the perimeter of square garden:Perimeter = 4(side)
Perimeter = 4(12)
Perimeter = 48 meter
The rabbit fencing costs $7.50 per meter[tex]Cost = perimeter \times 7.50\\\\Cost = 48 \times 7.50\\\\Cost = 360[/tex]
Thus it costs $ 360 to enclose a square garden with an area of 144 square meter
What was the origin of the territorial dispute over Taiwan
Answer:
The territorial dispute over Taiwan originated in 1949 when the Chinese people fled to Taiwan due to the complete control of Communists in Mainland China.
Explanation:
The event happened after the "Chinese Civil War," a war between the Kuomintang and the Communist Party of China (CPR). This resulted to many Chinese people fleeing from Southern China to Taiwan in order to prevent the advances of the Communist Party. This was also a sign of retreat from the war.
Moving to Taiwan from China took 4 months and this was meant to be a temporary solution rather than being permanent. However, the plan could not be realized thus, resulting to many Chinese people living in Taiwan until today.
So, this led to the controversial issue that Taiwan is, somehow, part of China. In connection with this, territorial disputes arose whether Taiwan should be unified with Mainland China.
what is 17½ divided by ⅚
Answer:
Step-by-step explanation:
(17 1/2) / (5/6) =
(35/2) / (5/6) =
35/2 * 6/5 =
105/5 =
21 <===