Find the inverse function in slope-intercept form (mx+b): f(x)= -3x+3
Answers
The inverse function of f(x) = -3x + 3 in slope-intercept form is g(y) = (-1/3)y + 1.
What is the inverse function?
The inverse function of a function f(x) is a function g(x) such that g(f(x)) = x for all x in the domain of f.
The given function is f(x) = -3x + 3. To find the inverse function, we can solve for x in terms of y:
y = -3x + 3
0 = -3x + y + 3
-y = -3x + 3
x = (-y + 3) / -3
The inverse function is then g(y) = (-y + 3) / -3. Rewriting this in slope-intercept form gives:
g(y) = (-1/3)y + 1
Hence, the inverse function of f(x) = -3x + 3 in slope-intercept form is g(y) = (-1/3)y + 1.
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Related Questions
Please explain your answer to the question in the picture with steps.
Answers
HELP ME PLEASE will give brainliest
Answers
Answer:
a
Step-by-step explanation:
At an assembly, 180 students sit in 9 equal rows. How many students sit in each row?
Answers
Answer:
20 students per row
Step-by-step explanation:
person per each row=180/9=20
Answer:
20
Step-by-step explanation:
Take the number of students and divide by the number of students
180/9
20
There are 20 students in each row
On the day you were born, Uncle Peyton gave your parents a piece of sports memorabilia valued at
$75. If past trends continue, it should appreciate in value 12% per year. If you sell it on your 18th
birthday, what can you expect the sale price to be?
Answers
Answer:
$162
Step-by-step explanation:
12% of $75 is $9 Therefore,
$9 x 18 = 162 ( 18 being the years )
Hope this helps!!!
-Conrad
What is the domain of the square root function graphed below?
On a coordinate plane, a curve open up to the right in quadrant 4. It starts at (0, negative 1) and goes through (1, negative 2) and (4, negative 3).
x less-than-or-equal-to negative 1
x greater-than-or-equal-to negative 1
x less-than-or-equal-to 0
x greater-than-or-equal-to 0
Mark this and return
Answers
The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.
The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.
From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).
The x-values of these points are 0, 1, and 4.
Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.
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What is the slope of the line
Answers
Step-by-step explanation:
Look at the points (0,-3) and ( 3,0)
slope, m = rise / run = 3 / 3 = 1
Answer:
1
Step-by-step explanation:
y=x+3
One month Eric rented 3 movies and 5 video games for a total of $34. The next month he rented 9 movies and 7 video games for a total of $56. Find the rental
cost for each movie and each video game.
Rental cost for each movie:
Rental cost for each video game:
G
O
G
Answers
movies 1.75 each
games 5.75 each
What is 2251 rounded to the nearest hundred
Answers
30x + 40y =
what is the answer please help me
Answers
Answer:
10(3x + 4y)
Step-by-step explanation:
Can anyone help please?
Answers
Answer:
h(t) = -16t(t-6)
h(2) = 128
Step-by-step explanation:
h(t) = -16t² + 96t
h(t) = -16t(t-6)
t = 3
h(2) = -16(2)(2 - 6)
h(2) = 128
Find the slope and the y-intercept of the line.
Answers
Answer:
slope=-1/5
y intercept=8
Hope this helps
Step-by-step explanation:
Answer:
Slope = -1/5
y-intercept: 8
Step-by-step explanation:
The line equation is y = mx + b, where m is the slope and b is the y-intercept.
We see that m is replaced by -1/5 and that b is replaced by 8.
Hope this helps!
Question 1
Mathematical thinking is making rational __________________ with your own thoughts using only definitions, properties, theorems, and postulates.
Question 2
A regular polygon has the same number of lines of symmetry as the number of sides. For example, a pentagon has 5 sides and 5 lines of symmetry. The number of degrees apart each line of symmetry is equals 360 degrees divided by the number of sides. The pentagon's lines of symmetry are 360/5 degrees apart, or 72 degrees apart. How many degrees apart are the triangle's lines of symmetry?
60 degrees
180 degrees
90 degrees
120 degrees
Answers
The triangle lines of symmetry are 60 degrees apart option (A) 60 degrees is correct.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
As we know,
The act of using mathematics to address issues in the actual world is known as mathematical thinking.
As the pentagon has 5 sides and 5 lines of symmetry.
The pentagon's lines of symmetry are apart 72(360/5) degrees apart.
Similarly in the triangle, the sum of the interior angle is 180 degrees
The triangle lines of symmetry are 60(180/3) degrees apart.
Thus, the triangle lines of symmetry are 60 degrees apart option (A) 60 degrees is correct.
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What is the quotient of the expression (5.04 × 10¹2) (6.3 × 109) written in scientific notation?
O 0.8 x 10³
0 8 x 10³
0 8 x 10²
O 0.8 x 1021
Answers
The quotient of the expression is 8 × 10² and option C is the correct answer.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
Adding exponents while maintaining the same base is the rule for multiplying like bases.
Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.
Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.
Rewrite as fraction:
\(\frac{(5.04) (10^{12})}{(6.3)(10^9)}\)
Simplify using exponent rule with same base \(\frac{a^n}{a^m} = a^{(n-m)}\):
\(\frac{(5.04) (10^{12-9})}{(6.3)}\)
Calculate the sum or difference:
\(\frac{(5.04) (10^{3})}{(6.3)}\)
Convert fraction into decimal: 0. 8 × 10³ = 8 × 10².
Hence, the quotient of the expression is 8 × 10² and option C is the correct answer.
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Researchers are studying the distribution of subscribers to a certain streaming service in different populations. From a random sample of 200 people in City C, 34 were found to subscribe to the streaming service. From a random sample of 200 people in City K, 54 were found to subscribe to the streaming service. Assuming all conditions for inference are met, which of the following is a 90% confidence interval for the difference in population proportions (City C minus City K) who subscribe to the streaming service?
A. (0.17 – 0.27) + or - 1.65 underroot 0.17/200 + 0.27/200.
B. 0.17 – 0.27) + or -1.96 underroot (0.17)(0.83) + (0.27)(0.73)/400
C. 0.17 – 0.27) + or - 1.65 underroot (0.17)(0.83) + (0.27)(0.73)/400
D. (0.17 – 0.27) + or - 1.96 underroot (0.17)(0.83) + (0.27)(0.73)/200
E. (0.17 – 0.27) + or - 1.65 underroot (0.17)(0.83) + 0.27)(0.73)/200
Answers
Answer:
\((0.17 - 0.27) \pm 1.65\sqrt{\frac{0.17*0.83 + 0.27*0.73}{200}}\), that is, option C
Step-by-step explanation:
From a random sample of 200 people in City C, 34 were found to subscribe to the streaming service. From a random sample of 200 people in City K, 54 were found to subscribe to the streaming service.
This means that the proportions are:
\(p_C = \frac{34}{200} = 0.17\)
\(p_K = \frac{54}{200} = 0.27\)
Subtraction of proportions:
In the confidence interval, we subtract the proportions. So:
\(p = p_C - p_K = 0.17 - 0.27\)
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).
Standard error:
For a subtraction, as the standard deviation of the distribution is the square root of the sum of the variances, we have that:
\(\sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.17*0.83 + 0.27*0.73}{200}}\)
90% confidence level
So \(\alpha = 0.1\), z is the value of Z that has a pvalue of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).
So the confidence interval is:
\((0.17 - 0.27) \pm 1.65\sqrt{\frac{0.17*0.83 + 0.27*0.73}{200}}\), that is, option C
You determine the percent abundance of
each length of nail and record it in the data
table below.
Sample
Type
Short nail
Medium nail
Long nail
Number Abundance
of Nails
(%)
67
18
10
70.5
19.0
10.5
Nail Length
(cm)
2.5
5.0
7.5
What is the weighted average length, in cm,
of a nail from the carpenter's box?
Answers
The weighted average length of a nail from the carpenter's box is 3.5 centimeters.
How to calculate the weighted average length?Different from calculating the average, the weighted average implies considering the frequency or abundance percentage. Now, to calculate the average weighted we will need to multiply the length of each type of nail by the abundance and finally, we will need to add the results obtained. The process is shown below:
Short nail: 2.5 cm x 70.5%= 1.7625 cm
Medium nail: 5.0 cm x (19% = 0.95 cm
Long nail: 7.5 cm x 10.5% = 0.7875 cm
1.7625 cm + 0.95 cm + 0.7875 cm = 3.5 cm
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Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
labor-hours and its standard cost card per unit is as follows:
Direct material: $ pounds at $11.00 per pound
Direct labor: 3 hours at $12 per hour
Variable overhead: 3 hours at $7 per hour
Total standard variable cost per unit
The company also established the following cost formulas for its selling expenses:
sales salaries and commissions
shipping expenses
Fixed Cost per
Month
$ 280,000
$ 260,000
$ 55.00
36.00
$112.00
Variable
Cost per
Unit Sold
$ 20.00
$ 11.00
The planning budget for March was based on producing and selling 21,000 units. However, during March the company
actually produced and sold 26.600 units and incurred the following costs:
a Purchased 154.000 pounds of raw materials at a cost of $9.50 per pound. All of this material was used in production.
b. Direct laborers worked 63,000 hours at a rate of $13.00 per hour
e Total variable manufacturing overhead for the month was $510,930
d Total advertising sales salaries and commissions, and shipping expenses were $286,000, $495,000, and $195,000,
respectively
6 What direct labor cost would be included in the company's flexible budget for March?
Answers
The direct labor cost included in the Preble Company's flexible budget for March is $819,000.
How to compute Preble Company's direct labor cost?To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.
Given:
Actual production and sales =n26,600 units
Actual direct labor rate = $13.00 per hour
Actual direct labor hours worked = 63,000 hours
Direct labor cost = Actual direct labor rate × Actual direct labor hours worked
Direct labor cost = $13.00/hour × 63,000 hours
Direct labor cost = $819,000
Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.
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3 to the power of 5 = 243. Explain how to use that fact to quickly evaluate 3 to the power of 6
Answers
Step-by-step explanation:
3^6 = 3 * 3^5
= 3 * 243 = 729
Which linear function represents the line given by the point-slope equation y - 8 = % (x - 4)?
?? Pls help :0
Answers
Answer:
option 2
Step-by-step explanation:
\(y - 8 = \frac{1}{2} (x - 4)\\\\y = \frac{1}{2}x - 2 + 8\\\\y = \frac{1}{2}x + 6\\\\)
Kenny recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-x-4 = 0 and calculate its properties
hope this helps!
3. Given f ( x ) = x2 + 1 and g ( x ) = x – 4 , find ( f g ) ( x ) and ( f g ) ( 3 ).
Answers
Answer: = -10
Step-by-step explanation:
Step 1. Solve for ( f g ) ( x ).
\(Since ( f g ) ( x ) = f ( x ) * g ( x ) , then\)
\(= (x^2 + 1 ) ( x - 4 )\\= x^3 - 4 x^2 + x - 4\)
Step 2. Find ( f g ) ( 3 )
\(Since ( f g ) ( x ) = x^3 -4 x^2 + x -4, then\)
\(\\( f g ) ( 3 ) = (3)^3 -4 (3)^2 + (3) -4\\= 27 -36 + 3 -4\\ = -10\)
Answer:
=19 !!!!!!!!!!!!!!
Step-by-step explanation:
help me please please please
Answers
The angle measures for this problem are given as follows:
a = 62º.b = 118º.c = 62º.d = 62º.How to obtain the angle measures?The sum of the measures of the internal angles of a triangle is of 180º.
The triangle in this problem is ABC, hence the measure of a is obtained as follows:
a + 68 + 50 = 180
a = 180 - (68 + 50)
a = 62º.
c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:
c = 62º.d = 62º.Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:
a + b = 180
62 + b = 180
b = 118º.
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if a man walks 16 km in 5 hours, how long would he take to walk 11.2km
Answers
Answer:
Time taken to walk 16 km =5hrs
Time taken to walk 1km =5/16 hr
Time taken to walk 11.2km =(5/16)×(112/10) = 3.5hrs
HOPE IT WILL HELP U..
PLZ MARK IT AS BRAINLIEST ANSWER..
Add the number that would make the expression a perfect square. Next write an equivalent expression in factored form (as a perfect square).a. x^2 - 6x
Answers
The number that would make the expression a perfect square as calculated from the given data is 9.
To get the number which should be added to make the given equation as a perfect square is ,
we will add the half of the coefficient of x to x²
i.e.,
(1/2 x 5 )² = 3²
=9
Therefore , we get ,
x² -6x +9
= (x + 3)²
A number's square root is a value that, when multiplied by itself, yields the original number. The other way to square an integer is to find its square root. Squares and square roots are hence linked ideas.
Assuming that x is the square root of y, the equation would be written as x=y or as x2 = y. The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number.
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Morgan goes out to lunch. The bill, before tax and tip, was $19.05. A sales tax of 3% was added on. Morgan tipped 23% on the amount after the sales tax was added. How much was the sales tax? Round to the nearest cent.
Answers
The sales tax was $0.57, and the total amount that Morgan paid for the meal, including tax and tip, was $24.13.When calculating the sales tax, we first need to know the rate of the sales tax.
In this case, the rate is 3%. To calculate the amount of the sales tax, we multiply the rate (expressed as a decimal) by the pre-tax amount of the bill. In this case, 3% as a decimal is 0.03, and the pre-tax amount of the bill is $19.05, so:
Sales tax = 0.03 x $19.05 = $0.57
This means that the sales tax on the bill was $0.57.
To find the total amount of the bill, including tax, we add the pre-tax amount and the sales tax. In this case, the pre-tax amount was $19.05, and the sales tax was $0.57, so:
Total bill = $19.05 + $0.57 = $19.62
Now, we need to calculate the tip that Morgan left. Morgan tipped 23% on the amount after the sales tax was added. This means that we need to calculate 23% of the total bill, which includes the sales tax. To do this, we first need to know 23% as a decimal, which is 0.23. Then, we multiply this decimal by the total bill:
Tip = 0.23 x $19.62 = $4.51
So the tip that Morgan left was $4.51.
To find the total amount that Morgan paid for the meal, including tax and tip, we add the pre-tax amount, the sales tax, and the tip. In this case, the pre-tax amount was $19.05, the sales tax was $0.57, and the tip was $4.51, so:
Total amount paid = $19.05 + $0.57 + $4.51 = $24.13
Therefore, the sales tax was $0.57, and the total amount that Morgan paid for the meal, including tax and tip, was $24.13.
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How to estimate the sums and differences
Answers
The graphs are the shame shape but what is the equation of the red line?
Answers
Answer:
A
Step-by-step explanation:
Since the shape and vertex x coordinate of both graphs are the same, the only difference is the vertical displacement. Since the blue graph is 4 above the origin and the red graph is 1 above the origin, its graph is:
\(g(x)=1-x^2\)
Hence, the correct answer is choice A. Hope this helps!
is this one problem ? or several not sure don't understand the plots
Answers
To create a stem-and-leaf plot for the data:
• Use the first two digits to represent the stem.
,• Use the third digit to represent the leaf.
For example, 32 | 5 represents 325
Given the amount earned:
325,326,311,329,325,310,301,319,329,311,304,322,311,301, and 328
Arrange those that have the same first two digits together:
• 301,301,304
,• 310,311,311,311,319
,• 322,325,325,326,328,329,329
The stem-and-leaf plot is attached below:
What is the surface area of the triangular prism???
I really need an answer to this. My math test is tomorrow and I really need to be prepared!
Answers
The surface area of the triangular prism is B. 1,008 \(cm^{2}\)
What is Triangular Prism?Triangular Prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.
How to determine this
The surface area of the triangular prism = Area of the front Triangle + Area of the triangle + Each sides of the triangle by the length of the triangular prism.
Area of the front and back triangle will be the the same given the same base and height
To find the area of the triangle = 1/2 * Base * Height
Where base = 12 cm
Height = 9 cm
Area = 1/2 * 12 cm * 9 cm
Area = 6 * 9 \(cm^{2}\)
Area of the one triangle = 54 \(cm^{2}\)
So, by multiplying each sides of the triangle by the length
= Base * Length
= 12 cm * 25 cm
= 300\(cm^{2}\)
Height * Length
= 9 cm * 25 cm
= 225 \(cm^{2}\)
Then, Hypotenuse * Length
= 15 cm * 25 cm
= 375 \(cm^{2}\)
Surface area = 54\(cm^{2}\) + 54\(cm^{2}\) * 300\(cm^{2}\) + 225\(cm^{2}\) + 375\(cm^{2}\)
Surface Area = 1,008\(cm^{2}\)
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Instructions: Identify the type of sequence and write the explicit rule. write Explicit Rule Sequence: -39, -45, 51, 57,... Type: Arithmetic e Explicit Rule:
Answers
The given sequence does not follow a simple arithmetic or geometric pattern, making it challenging to determine an explicit rule based on the given terms.
To identify the type of sequence and write the explicit rule, we need to examine the pattern of the given sequence: -39, -45, 51, 57, ...
By observing the differences between consecutive terms, we can determine if it follows an arithmetic or geometric pattern.
Arithmetic sequences have a common difference between each term, meaning that by adding (or subtracting) the same value repeatedly, we can generate the sequence. Geometric sequences, on the other hand, have a common ratio between each term, meaning that by multiplying (or dividing) by the same value repeatedly, we can generate the sequence.
Let's calculate the differences between consecutive terms:
-45 - (-39) = -6
51 - (-45) = 96
57 - 51 = 6
From the differences, we can see that the sequence is not arithmetic since the differences are not constant. However, the differences alternate between -6 and 6, indicating a possible geometric pattern.
Let's calculate the ratios between consecutive terms:
-45 / (-39) ≈ 1.1538
51 / (-45) ≈ -1.1333
57 / 51 ≈ 1.1176
The ratios are not constant, indicating that the sequence is neither geometric nor arithmetic.
Therefore, the given sequence does not follow a simple arithmetic or geometric pattern, and it is difficult to determine the explicit rule based on the given terms. It is possible that the sequence follows a more complex pattern or rule that is not apparent from the given terms.
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What is the decimal equivalent of the fraction 8/15?
0.53
_
0.53
Show work!!
Answers
Answer:
its basically what u had put, 8/15= 0.53 lol
~ hope this helped ya out, ig lol~
Step-by-step explanation: