Find f−1(x) for f(x)=15+12x.
Answer:
[tex]\text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]
Step-by-step explanation:
[tex]\text{f}^{-1}(x)[/tex] is the notation for the inverse of a function.
The inverse of a function is a reflection in the line y = x.
Given function:
[tex]\text{f}(x)=15+12x[/tex]
To find the inverse of the given function:
Step 1
Replace f(x) with y to get an equation for y in terms of x:
[tex]\implies y=15+12x[/tex]
Step 2
Rearrange the equation to make x the subject:
[tex]\implies y-15=15+12x-15[/tex]
[tex]\implies y-15=12x[/tex]
[tex]\implies \dfrac{y-15}{12}=\dfrac{12x}{12}[/tex]
[tex]\implies x=\dfrac{y-15}{12}[/tex]
Step 3
Replace x with [tex]\text{f}^{-1}(x)[/tex] and y with x → this is the inverse function:
[tex]\implies \text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]
Step 4 (if necessary)
The domain of the function is the range of the inverse function.
The range of the function is the domain of the inverse function.
Therefore, as the domain and range of the given function are unrestricted, so too are the domain and the range of the inverse function:
Domain: (-∞, ∞) → all real numbersRange: (-∞, ∞) → all real numbersLearn more about inverse functions here:
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[tex]\\ \rm\leadsto y=15+12x[/tex]
Interchange x and y
[tex]\\ \rm\leadsto x=15+12y[/tex]
Solve for y
[tex]\\ \rm\leadsto 12y=x-15[/tex]
[tex]\\ \rm\leadsto y=\dfrac{x-15}{12}[/tex]
That's the inverse
4. In the figure above ABCD is a parallelogram with
mLB = 60°, BC = XC = AZ = 4, XZ BC. What
is the perimeter of parallelogram ABCD?
Answer:
G. 24
Step-by-step explanation:
The perimeter of the figure is the sum of its side lengths. The given dimensions tell us all of the side lengths.
AnalysisTriangle BCX is given as an isosceles triangle with a base angle of 60° and side lengths of 4. Such a triangle is equilateral, so all side lengths will have a measure of 4.
The given information tells us all sides that appear parallel are parallel, so the figure consists of 4 equilateral triangles. Every short line segment has length 4.
PerimeterThe perimeter is the length of 6 short line segments, so is ...
P = 6×4 = 24
The perimeter of parallelogram ABCD is 24 units.
use long division to convert 3/10 into decimals.
Answer:
3/10 as a decimal is expressed as 0.3.
11) Find the mode of the data set.
O a.) 9
Ob.) 8
Oc.) 7
O d.) 6
Data:
5, 8, 12, 6, 7, 10, 14, 6, 13
4
Answer:
6
Step-by-step explanation:
The mode is the number that is repeated the most in the data set. 6 is the only number that is repeated twice, so it is the mode.
Brainliest, please :)
if f x is a linear function, f(-1)=3, and f(1)=5, find an equation for f(x)
The equation of f(x) is f(x) = x + 4
How to determine the equation?The given parameters are
f(-1) = 3 and f(1) = 5
Start by calculating the slope (m) using:
[tex]m = \frac{f(1) - f(-1)}{1 - -1}[/tex]
This gives
[tex]m = \frac{5 - 3}{1 + 1}[/tex]
Evaluate
m = 1
The equation is then calculated as;
f(x) = m(x - x1) + f(-1)
This gives
f(x) = 1(x + 1) + 3
Expand
f(x) = x + 4
Hence, the equation of f(x) is f(x) = x + 4
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In a stock of 12 blouses, 90 are sleeveless. How many percent of the stock are sleeveless?
75 percent of the stock are sleeveless
How to determine the percentage?The given parameters are:
Blouse = 120
Sleeveless = 90
The percentage is calculated as:
Percentage = Sleeveless/Blouse * 100%
So, we have:
Percentage = 90/120* 100%
Evaluate the expression
Percentage = 75%
Hence, 75 percent of the stock are sleeveless
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What is the value of pi (i need to unlock the safe because is an inhibitor there) DYING LIGHT 2
The number π (pi) is a mathematical constant which is equal to the ratio of a circle's circumference to its diameter. It has a value of π = 22/7
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The number π (pi) is a mathematical constant which is equal to the ratio of a circle's circumference to its diameter. It is given by:
π = 22/7
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What are the solutions to 4x^3 + 16x^2 + 28x = 0
Step-by-step explanation:
the third option is the answer.
If m4 = 108°, what is the measure of 26?
Answer:
108
Step-by-step explanation:
When the lines cut through by a transversal are parallel, alternate interior angles are congruent. angle 4 = angle 6 = 108
Which of the following statements is TRUE about rectangle ABDC.
The statement that is TRUE of the rectangle is AB + BD > AD. Option A
Facts about the rectangleWE have that a diagonal divides the rectangle into two equal triangles
line AD is the length of the diagonal
With the diagonal drawn, we have
AD = hypotenuse
AB and BD are the two other sides
From the Pythagorean theorem, we have that the square root of the square sum of the other two sides fives the hypotenuse. This mean that their sum is greater than the hypotenuse
Thus, the statement that is TRUE is AB + BD > AD. Option A
The complete question is;
Which of the following statements is TRUE about rectangle ABDC.
a. AB + BD > AD
b. AB + BD < AD
c. AB + BD = AD
d. (AB) (BD) = AD
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For the piecewise function, find the values g(-1), g(2), and g(5). g(x)= x+4, for x≤2 9-x, for x>2
Answer:
g(-1) = 3, g(2) = 6, g(5) = 4
Step-by-step explanation:
Please refer to attached photo. (Apologies for the terrible handwriting.)
From here we can see,
g(x) = x + 4 applies for values x less than or equal to 2.
g(x) = 9 - x applies for values x more than 2 (which does not include 2.)
g(-1):
Since -1 < 2,
g(-1) = -1 + 4 = 3
g(2) = 2 + 4 = 6
g(5):
Since 5 > 2,
g(5) = 9 - 5 = 4
231 ( 40 + 15 ) = 231 x 40 + ------------ x -----------
which property is this
Answer:
12705
Step-by-step explanation:
The problem could be solved in two different methods:
1:
231×(55)=12705
2.
231×40+231×15=9240+3465=12705
Can u guys please give me the correct answer
Angles on straight line = 180
180 - 115 = 65
So, angle above 4 in the top corner is 65.
Co-interior angles add up to 180.
(180-65=115)
Thus, the value of 4 is 115 degrees.
Hope this helps!
Solve the following:
3 x 10³ - 7000
(8 × (−5)) + (4² +2²)
Give your answer in simplest form.
Enter can you help me solve this I was doing very good up to now
Answer:
3x(10x10x10): 3x(1000): 3000-7000: -4000. (8x(-5)): -40. (4x4) +(2x2): (16 +4): 20
You are training to compete in a 10-kilometer race, and you know the circular running trail at your park is one mile long. How many times will you need to run this trail in order to run 10 kilometers?
Answer:
6.2 rounds
Step-by-step explanation:
since 1 kilometer is 0.62 miles
10 kilometers is 6.2 miles
so about 6 and 1/5 rounds
Diego Company manufactures one product that is sold for $70 per unit in two geographic regions—the East and West regions. The following information pertains to the company’s first year of operations in which it produced 53,000 units and sold 48,000 units.
Variable costs per unit:
Manufacturing:
Direct materials $ 21
Direct labor $ 10
Variable manufacturing overhead $ 2
Variable selling and administrative $ 4
Fixed costs per year:
Fixed manufacturing overhead $ 1,060,000
Fixed selling and administrative expense $ 557,000
The company sold 36,000 units in the East region and 12,000 units in the West region. It determined that $270,000 of its fixed selling and administrative expense is traceable to the West region, $220,000 is traceable to the East region, and the remaining $67,000 is a common fixed expense. The company will continue to incur the total amount of its fixed manufacturing overhead costs as long as it continues to produce any amount of its only product.
15. Assume the West region invests $43,000 in a new advertising campaign in Year 2 that increases its unit sales by 20%. If all else remains constant, what would be the profit impact of pursuing the advertising campaign?
The 53,000 units produced and the increase in sales of 50,400 - 48,000 = 2,400 units, give an impact (increase) in profit of $168,000
How can the impact in profit be found?Price per unit = $70
Number of units produced = 53,000
Number of units sold = 48,000
Material cost per unit = $21
Labour cost per unit = $10
Manufacturing overhead = $2
Selling and administrative overhead = $4
Fixed cost = $1,060,000
Administrative expenses = $557,000
Advertising cost = $43,000
Percentage increase in sales = 20%
Number of units sold in Year 2 = 1.2 × 12,000 = 14,400
Total cost = 53000×(21+10+2+4) + 1,060,000 + 557,00 = 3,578,000
Total revenue in Year 1 = 70 × 48,000 = 3,360,000
Profit = Revenue - CostProfit in Year 1 = 3,360,000 - 3,578,000 = -218,000
Total revenue in Year 2 = 70 × (36,000+14,400) = 3,528,000
Profit in Year 2 = 3,528,000 - 3,578,000 = -50,000
The impact on the profit is therefore;
-50,000 - (-218,000) = 168,000
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W
If 15 cans of food are needed for 7 campers for 2 days,
the number of cans needed for 4 campers for 7 days
is? (round up to nearest whole number)
Answer:
30 cans
Step-by-step explanation:
cross multiply
14x = 28 * 15
14x = 420
x = 420/14
x = 30 cans
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180
The true options regarding the triangle diagram are;
m∠5 + m∠6 = 180°
m∠2+ m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
How to prove congruent angles?We see the attached image showing ΔABC with Exterior angles as;
∠ 1 , ∠ 4 ,and ∠ 6
Now, the exterior angle property of triangles states that; An exterior angle of a triangle is equal to the sum of the opposite interior angles.
For Exterior ∠1 we have;
∠1 = ∠5 + ∠3 (Exterior angle Property of Triangle)
Similarly,
For Exterior ∠ 4 we have;
∠4 = ∠5 + ∠2 (Exterior angle Property of Triangle)
For Exterior ∠6 we have;
∠6 = ∠2 + ∠3 (Exterior angle Property of Triangle)
From Triangle Sum Property, we know that the sum of the measures of angles in a triangle is equal to 180°. Thus;
m∠2 + m∠3 + m∠5 = 180° (Triangle Sum Property)
Linear Pair of angles states that the measure of a straight angle is 180° and as such a linear pair of angles must add up to 180°. Thus;
m∠5 + m∠6 = 180° (Linear Pair)
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You are building a ramp for your grandparent's house. The ramp will replace the steps that go
to their front door which is 3 feet off the ground. You want the ramp to start 10 ft from the
front door. How long will the ramp need to be?
Using right triangle, the length of the ramp is 10.44 ft.
How to find the length of the ramp using right triangle?The situation forms a right angle triangle.
The length of the ramp is the hypotenuse side of the right triangle.
Therefore, using Pythagoras theorem,
c² = a² + b²
where
a and b are the other legsc is the hypotenuse sideTherefore,
c² = 10² + 3²
c² = 100 + 9
c = √109
c = 10.4403065089
c = 10.44 ft
Therefore, the length of the ramp is 10.44 ft.
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What is the value of a?
O 5 units
05/
units
6 units
O 7 units
From the Δ YWZ we get c = 5 then the value of [tex]$a= 5 \frac{1}{3}[/tex].
How to estimate the value of a?In the given Δ YWZ
WZ² = YW² + YZ²
c² = 4² + 3² = 16 + 9 = 25
c = 5
In the Δ XYW
b² = 4² + a²-----(1)
In the right-angle Δ WXZ
(a + 3)² = b² + c²
a² + 9 + 6a = b²+ c²
By putting the value of b² from (1)
a² + 9 + 6a = 16 + a² + 25
Simplifying the above equation, we get
6a + 9 = 41
6a = 41 - 9
6a = 32
[tex]$a = \frac{32}{6} = \frac{16}{3}[/tex]
[tex]$a= 5 \frac{1}{3}[/tex]
Therefore, the value of [tex]$a= 5 \frac{1}{3}[/tex].
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Mary’s rectangular garden is 27 units long and 49 units wide. What is the perimeter?
Answer:
152 units
Step-by-step explanation:
Two sides of the rectangle are 27 units long and the other two sides are 49 units wide. You just add all the numbers up (27+27+49+49). When you do that, you get 152. I hope this helps!
Carter and Isabella run a carwash business. They split the revenue 50/50. They are deciding on if they should join forces with Carla's carwash. If they join with Carla, the combined carwash will make $2400 more per month, but they'll have to split revenue equally (33.3/33.3/33.3). On an average month, Carter and Isabella's carwash makes $6000. How much more or less would Carter or Isabella individually make if they merged with Carla's carwash?
we can see that when they join with Carla, Carter and Isabella will get $200 less (individually).
How much more or less would Carter or Isabella individually make if they merged with Carla's carwash?
When Carter and Isabella work together, they have a revenue of $6000, which is split in 50/50, so each one gets:
$6000/2 = $3000
Carter wins $3000 and Isabella wins $3000.
If they join with Carla, the revenue increases by $2400, so now the total revenue is:
$6000 + $2400 = $8400
And now they split it between 3, so each one gets:
$8400/3 = $2800
The difference of Carter's (Or Isabella's) part is:
$3000 - $2800 = $200
Then we can see that when they join with Carla, Carter and Isabella will get $200 less (individually).
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A rectangular waterbed is 8 ft long, 7 ft wide, and 1.5 ft tall. How many gallons of water are needed to fill the waterbed? Assume 1 gallon is 0.13 cu ft. Round to the nearest whole gallon.
646 gallons of water are needed to fill the waterbed
How to determine the gallons of water?The dimensions are given as:
8 ft long, 7 ft wide, and 1.5 ft tall
The volume is calculated as:
Volume = Length * Width * Height
So, we have
V = 8 * 7 * 1.5 cubic feet
Evaluate
V = 84 cubic feet
1 gallon = 0.13 cubic feet
So, we have:
V = 84/0.13 gallon
Evaluate
V = 646 gallons
Hence, 646 gallons of water are needed to fill the waterbed
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spent a total of $5.58 for carrots, priced at $0.90 per pound. How many pounds of
carrots did Trina buy?
Answer:
6.2 pounds
Step-by-step explanation:
$5.58 / $.9 = 6.2 pounds of carrots bought
8⁄9 ÷ 1⁄3 what is the answer please
Answer:
8/3
Step-by-step explanation:
8/9
Solve for x.
BC = 2
CD =2x-6
BD X+2
Answer:
6
Step-by-step explanation:
Assuming C lies on segment BD, we know that by the segment addition postulate,
[tex]BC+CD=BD \\ \\ 2+2x-6=x+2 \\ \\ 2x-4=x+2 \\ \\ x=6[/tex]
The values of BC = 2, CD = 2x - 6 and BD = x + 2 then the value of x = 6.
How to find the value of x?The algebraic expression should be any one of the conditions such as addition, subtraction, multiplication, and division.
In mathematics, an algebraic expression exists as an expression built up from integer constants, variables, and algebraic operations. For example, 3x² − 2xy + c exists as an algebraic expression.
To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
Given: BC = 2, CD = 2x - 6 and BD = x + 2 then
BC+CD= BD
2+2x-6=x+2
Simplifying,
2x-4=x+2
Thus,
x=6
Therefore, the value of x = 6.
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Decide whether the conditions create a unique triangle, multiple triangles, or no triangle m∠A=65∘ m∠B=75∘ m∠C=40∘
Answer:
multiple triangles
Step-by-step explanation:
add the numbers up it adds to 180 which is the sum of a triangle and could create other triangles
A perimeter of a movie screen is 56 meters. the area is 171 square meters what are the dimensions of the screen
Using the formula for the perimeter and area of rectangle, the dimensions are: Length = 19 m; width = 9 m.
What is the Perimeter and Area of a Rectangular Shape?Perimeter = 2(length + width)
Area = (length)(width).
Let x represent the length and y the width, therefore:
2(x + y) = 56 --> eqn. 1
xy = 171 --> eqn. 2
Rewrote eqn. 1
x + y = 56/2
x = 28 - y
Substitute x = (28 - y) into eqn. 2
171 = (28 - y)y
171 = 28y - y²
171 - 28y + y² = 0
y² - 28y + 171 = 0
Factorize
(y - 9)(y - 19)
y = 9 and y = 19
Therefore, the dimensions are: Length = 19 m; width = 9 m.
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Name the type of angle relationship. Set up the equation and solve for x.
Equation:
Solve: x :
Answer:
Same side interior angles
x=10
Step-by-step explanation:
The angles are same side interior angles
The add to 180 degrees
6x+10 + 110 = 180
Combine like terms
6x+120 =180
Subtract 120 from each side
6x = 180-120
6x= 60
Divide by 6
6x/6 = 60/6
x = 10
Answer:
Same-Side Interior Angles
Equation: 6x + 10 + 110 = 180
x = 10
Step-by-step explanation:
Hello!
The sum of the two given angles is 180°, as they are same-side interior angles.
Equation: 6x + 10 + 110 = 180
Solve for x6x + 10 + 110 = 1806x + 120 = 1806x = 60x = 10The value of x is 10°.
what two equal numbers add to the number 40
Answer:
3+37
11+29
17+23
20+20
Step-by-step explanation:
It's 20
(20+20 = 40)
Hope this helps!