Answers
For the function f(x) =[tex]\sqrt{8x+10}[/tex] the inverse function [tex]f^{-1}[/tex](x) = [tex]\frac{x^2-10}{8}[/tex] x≥ 0 as can be calculated through the inverse function's formula.
What is an inverse in a function?In mathematics, any kind of inverse is a function that serves to “undo” any other function. That is, if f(x) produces y, then while putting y into the inverse off it produces the output x.
How do you find the inverse of a function?To find the inverse of a function, write the function y as a function of x i.e., y = f(x) and then solve for x as a function of y.
What is inverse example?Inverse operations are seen as opposite operations that provides undo to each other. For example, 5 ✕ 2 = 10 and 10 ÷ 2 = 5 are inverse operations.
What are the properties of inverse function?Every one-to-one function f has an inverse; this inverse is denoted by f−1 and read aloud as 'f inverse'. A function and its inverse 'undo' each other: one function does something, the other undoes it.
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Related Questions
Homework: Section 3.4HomeworkQuestion 6, 3.4.25 >HW Score: 50%, 5 of 10 pointsO Points: 0 of 1SaveFind an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verifythe real zeros and the given function value.n=3;3 and 4 i are zeros;f(2)=40f(x)=(Type an expression using x as the variable. Simplify your answer.)Clear allCheck answerHelp me solve thisView an example Get more help.
Answers
The roots are
[tex]\begin{gathered} x=3 \\ x=4i \\ x=-4i \end{gathered}[/tex]The polynomial can be modellled as ;
[tex]f(x)=a(x-3)(x-4i)(x+4i)[/tex][tex]f(x)=a(x-3)(x^2+16)[/tex]
Let us use f(2) to obtain a value for a
[tex]\begin{gathered} f(2)=a(2-3)(2^2+16) \\ 40=-20a \\ a=-2 \end{gathered}[/tex]The polynomal f(x) is given as
[tex]\begin{gathered} f(x)=-2(x-3)(x^2+16) \\ f(x)=-2x^3+6x^2-32x+96 \end{gathered}[/tex]Imagine you went to the store and bought a video game for $12.98. This item is taxable at 6% tax and the total tax is $0.78. What is the total amount due?
Next, you decide to pay with a $20.00 bill. How much change will you receive after paying for your video game?
Answers
Using simple linear equations we calculate that the change left will be $6.24 .
The equals sign is used to indicate that two expressions on each side of the equal sign are equal in the many mathematical formulas that are utilized to form an equation.
Depending on the language, the definition of the word equation and its cognates may change slightly.The first step in solving a variable equation is to determine the precise values of the unknown variables that lead to the provided equality. The equation's solutions, often referred to as the variables for which the equation must be solved, are the values of the unknowable variables that satisfy the equality.Let the change received be x.
Therefore let us construct an equation for the situation
cost of game + tax + change = 20
or, 12.98 + 0.78 + x = 20
or, 13.76 + x = 20
or, x = 6.24
Therefore he will receive 6.24 after solving the equation.
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The animals at a safari park include crocodiles, deer and penguins.
There are 16 more deer than there are crocodiles. 4 There are 3 times as many penguins as there are crocodiles. There are the same number of deer as there are penguins.
How many crocodiles are there at the safari park?
Answers
Answer:
8
Step-by-step explanation:
8x3 = 24
8+ 16 = 24
10 to the 3d power + 10 to the 2nd power + 10 to the 1st power
Answers
Answer: 1110
Step-by-step explanation:
Answer:
1,110
Step-by-step explanation:
1. Multiply to the powers(?)
10 x 10 x 10 = 1000
10 x 10 = 100
10 = 10
2. Add
1000 + 100 + 10 = 1110
equivalent to 6+12x?
Answers
Answer:
Step-by-step explanation:
6 + 12x
6 ( 1 + 2x )
The blueprint for the moreno’s living room has a scale of 2 inches= 5 feet. The family wants to use a scale of 1 inch= 3 feet. What is the width of the living room on the new blueprint
Answers
The width of the living room on the new blueprint is 15 feet.
How to calculate the width?Based on the information, the scale of the original blueprint will be:
= 2 in / 5 ft
The width of the original blueprint is 6 inches, the actual width of the living room will be:
2/5 = 6/x
where x = width of living room
Cross multiply
x = 5 × 6 / 2
x = 15 feet.
The width is 15 feet.
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Malik had a checking account balance of $92.18. His bank will fund the first debit card purchase that creates a negative balance up to a limit of $100.00, but charges a
$28.00 fee for that overdraft. Malik made a purchase of $36.12 yesterday, and another purchase of $76.50 today. He used a debit card for each purchase. What is Malik's
account balance after the two purchases and any overdraft fees?
negative $140.62
negative $20.44
O negative $112.62
O negative $48.44
Answers
hope this helps!
Helpppp please , fast
Answers
The coordinates of the orthocenter of triangle DEF are given as follows:
(6.67, -2).
How to find the orthocenter of a triangle?The orthocenter of a triangle is the point of intersection of the three altitude lines of the triangle.
Hence, we need to find two of the lines, and them find the intersection point between them, as the third line will necessarily intersect these lines at this point.
The midpoint of segment DE is:
(6, 1).
Which is the mean of the coordinates.
Vertex F is at point (8, -8), hence the slope of the line with these two points is:
m = (-8 - 1)/(8 - 2) = -9/2 = -4.5.
Hence:
y = -4.5x + b.
When x = 6, y = 1, hence we can find b as follows:
1 = -4.5(6) + b
b = 28.
Hence one line is:
y = -4.5x + 28.
The midpoint of segment EF is:
(8, -1.5).
Which is the mean of the coordinates.
Vertex D is at point (4, -3), hence the slope of the line with these two points is:
m = (-1.5 - (-3))/(8 - 4) = 0.375.
Hence:
y = 0.375x + b.
When x = 8, y = -1.5, hence we can find b as follows:
-1.5 = 0.375(8) + b
b = -4.5.
Hence the two lines that we have to find the intersection point is:
y = -4.5x + 28.y = 0.375x - 4.5.Then the x-coordinate of the orthocenter of the triangle is:
-4.5x + 28 = 0.375x - 4.5
4.875x = 32.5
x = 32.5/4.875
x = 6.67.
The y-coordinate of the orthocenter of the triangle is:
y = 0.375(6.67) - 4.5 = -2.
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suppose 9 people arrive at a bank at the same time. in how many ways can they line up to wait for the next available teller? a) 40,320 b) 362,880 c) 9 d) 5,040 e) 81 f) none of the above.
Answers
The number of ways in which they can line up to wait for the next available teller is 362880.
What is termed as the permutation?We occasionally want to understand how many different ways we can order a set of items. A permutation is the number of different ways this may be done.We want to know how many different ways there are to line up 9 people.
We can choose one of the nine people in line to take the first spot. There are just eight people left to select from once we've decided who will fill this position. This means that only eight people can fill this same second position in this line. Now that the first two spots are filled, there are just seven people left to fill the third, and this line of thought can continue until the last spot is filled.= 9×8×7×6×5×4×3×2×1
= 362880
Thus, the number of ways in which they can line up to wait for the next available teller is 362880.
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Calculate the average rate of change of fover the interval -3≤x≤9. Show the calculations that lead to your answer.
Answers
The function has an average rate of change f is 1/2 over the interval
How to determine the average rate of change f?The possible graph that completes the question is added as an attachment
The interval is given as
-3 ≤ x ≤ 9
This can be rewritten as
x = -3 to x = 9
This can also be represented as
(a, b) = [-3, 9]
From the attached graph, we have
f(-3) = -1.5
Also, we have
f(9) = 0.5
The estimate (to one decimal place) of the average rate of change f is calculated as
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(9) - f(-3)]/[9 + 3]
So, we have
Rate = [0.5 + 1.5]/[9 + 3]
Evaluate
Rate = 2/12
Simplify
Rate = 1/6
Hence, the average rate of change f is 1/6
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M= 19.7t² + 310.5t +7539.6
F= 28t² + 368t + 10127.8
modeling with mathematics during a recent period of time, the number (in thousands) of males M and females F that attend degree-granting institutions in the United States can be modeled by M= and F=
where t is time in years. Write a polynomial in standard form to model the total number of people attending degree-granting institutions. The polynomial is P=
Answers
Using addition of polynomials, the function modeling the number of people attending degree-granting institutions is:
P(t) = 48.7t² + 678.5t + 17667.4.
What is the function for the total number of people attending the institutions?The number of males is given by:
M(t) = 19.7t² + 310.5t + 7539.6.
The number of females is given by:
F(t) = 28t² + 368t + 10127.8.
The total number is given by the addition of the number of males and of females, that is:
P(t) = M(t) + F(t).
Which is an addition of polynomials. To add the polynomials, we combine the like terms, that is, adding the terms that have the same variable and exponent. Hence:
P(t) = M(t) + F(t).
P(t) = 19.7t² + 310.5t + 7539.6 + 28t² + 368t + 10127.8.
P(t) = 48.7t² + 678.5t + 17667.4.
Which is the desired function.
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1. (01.01 LC)
Which of the following is a flat surface that extends infinitely, has length and width, but does not have depth?
Angle
O Circle
O Plane
Segment
Answers
Answer:
plane
Step-by-step explanation:
The plane is flat like a wall or the floor. It has infinite length and infinite width but has no thickness (as thick as a line--which has no thickness) basically a line is one-dimensional and a plane is two-dimensional.
See image.
3x = 0Graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation
Answers
we have the equation
3x=0
is the same that
x=0
This is a vertical line (is the equation of the y-axis)
two ordered pairs that lies in this line are
(0,4) and (0,10)
graph the line
plot the points and join them
see the attached figure
Determine if 0.868668666866668666668...0.868668666866668666668... is rational or irrational and give a reason for your answer.
Answers
The numbers given as 0.868668666866668666668... and 0.868668666866668666668... are irrational numbers
How to categorize the numbers?From the question, the numbers are given as
0.868668666866668666668... and 0.868668666866668666668...
As a general rule.
Numbers that end in three dots are irrational numbers
The above is true because
These numbers are non-terminating decimals (i.e. theu do not end)These numbers cannot be represented as a fraction of integersWhen numbers cannot be represented as a fraction of integers, then such numbers are irrational numbers
Hence, the numbers are irrational numbers
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Both the given values 0.868668666866668666668.. and 0.868668666866668666668... are irrational numbers.
What are irrational numbers?An irrational number is a type of real number which cannot be represented as a simple fraction or the values that have face value are irrational numbers. Example: √2, √3, and π are all irrational.
Here,
Both numbers are irrational numbers, because
Thus, Both the given values 0.868668666866668666668.. and 0.868668666866668666668... are irrational numbers.
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resuelve la siguiente ecuación con el metodode suma y resta x + y = 5
2x + y = 4
Answers
La solucion del sistema de ecuaciones es x = 1, y = 4, o (1, 4) en notación standard.
¿Como resolver el sistema de ecuaciones?Aqui tenemos el sistema de ecuaciones:
x + y = 5
2x + y = 4
Si tomamos la segunda ecuación, y a esta le restamos la primera, obtendremos:
(2x + y) - (x + y) = 5 - 4
(2x - x) + (y - y) = 1
x = 1
De esta forma encontramos el valor de x, para encontrar el valor de y, deberemos reemplazar x = 1 en una de las ecuaciones. Yo usare la primear.
x + y = 5
1 + y = 5
y = 5 - 1
y = 4
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after the given information, at least how many more steps are necessary to solve this proof
Answers
The following steps would be:
• TP and TP (for both triangles) are congruent by the reflexive property.
,• The triangles are congruent by the SAS theorem.
,• Angle S and angle O are congruent.
A triangular boat's sail has a total area of 7 square inches.
If the height of the sail is 3 inches less than twice the
length of its base, then find the length of the base and
height.
Answers
Answer: b = 3.5, h = 4
Step-by-step explanation: a = 1/2bh, area of a triangle formula
7 = 1/2((b)(2b-3)) state h in terms of b
7 = 1/2(2b^2-3b) simplify
7 = b^2 - 1.5b simplify
b = 3.5 final answer
Then, solve for h.
h = 7 - 3 substitute
h = 4 final answer
hope this helps!
Step-by-step explanation:
area of a triangle
base × height / 2
in our case
base × height / 2 = 7
base × height = 14
height = 2×base - 3
we can use the last identity in the area equation and get
base × (2×base - 3) = 14
2×base² - 3×base - 14 = 0
the solution to a quadratic equation like
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
base = (3 ± sqrt((-3)² - 4×2×-14))/(2×2) =
= (3 ± sqrt(9 + 112))/4 = (3 ± sqrt(121))/4 =
= (3 ± 11)/4
base1 = (3 + 11)/4 = 14/4 = 7/2 = 3.5 in
base2 = (3 - 11)/4 = -8/4 = -2
negative numbers for sizes of physical objects don't make sense, so, base = 3.5 in is our solution.
height = 2×base - 3 = 2×3.5 - 3 = 7 - 3 = 4 in
base length = 3.5 in
height = 4 in
20$ startup fee and a $5 monthly fee write an equation in slope intercept form that models
Answers
The slope intercept form of equation that models $20 startup fee and $5 monthly fee is y = 5x +20 , y is total fee and x is number of months
What is slope intercept form?The slope intercept form of an equation is y = mx + c
where y is y coordinate, x is x coordinate, m is the slope of the line and c is y intercept.
Let the total fee after x months be y
Then y is sum of startup fee and sum of all month's fee
For x months total monthly fees = 5(x)
Therefore the total fee after x months , y = 5x +20 which is same as slope intercept form y=mx+c
when x= 0 ⇒ y = 20 , startup fee
Thus, the equation in slope intercept form is y = 5x +20 ,where y is total fee and x is number of months.
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Please answer quick i really need help
Answers
Answer:
( - 36, 24 )
Step-by-step explanation:
(- 9, 6)
( - 9×4, 6×4)
( - 36, 24 )
ABCD is a quadrilateral.
Work out angle x.
В.
B
8 cm
A
X
6 cm
D
FIND x (
ABCD IS A QUADRILATERAL)
29%
13 cm
C
Answers
(Use law of sines)
A/Sin a = B/Sin b
10/Sin 29 = 13/Sin x
Sin(x)=(13sin(29))/10
Sin(x)= 0.63
(x=39)
MARKING BRAINLEIST PLS HELP ME OUT HERE
Answers
316 is value of circle's arc BC .
What is an arc in maths?
A circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that might be created by joining the arc's two ends. A semicircular arc is one whose length perfectly divides the circumference of the circle.A circle's circumference forms an arc. An arc length is the length of the arc, whereas an arc measure is the measurement of the angle the arc makes at the center of a circle. This measurement can be expressed in radians or degrees. Using the fact that pi radians = 180 degrees, we can quickly convert between the two.Short arc BC is the difference between 360° and long arc BAC
arc BC = 360 - arc BAC
= 360 - 44
= 316
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Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs \$3.25$3.25dollar sign, 3, point, 25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most \$30$30dollar sign, 30 before tax. The restaurant only sells pancakes in stacks of 444 pancakes for \$5.50$5.50dollar sign, 5, point, 50.
Let SSS represent the number of stacks of pancakes that Benjamin buys.
1) Which inequality describes this scenario?
Choose 1 answer:
Choose 1 answer:
(Choice A, Checked)
A
3.25+S \leq 303.25+S≤303, point, 25, plus, S, is less than or equal to, 30
(Choice B)
B
3.25+S \geq 303.25+S≥303, point, 25, plus, S, is greater than or equal to, 30
(Choice C)
C
3.25+5.50S \leq 303.25+5.50S≤303, point, 25, plus, 5, point, 50, S, is less than or equal to, 30
(Choice D)
D
3.25+5.50S \geq 303.25+5.50S≥303, point, 25, plus, 5, point, 50, S, is greater than or equal to, 30
2) What is the largest number of pancakes that Benjamin can afford?
Answers
The correct option is D that is bill is equal to or greater than $30
3.25 + 5.5s < =30
The first step in building the inequality is modelling Benjamin's spendings.
He buys a chocolate milk that costs $3.25, plus S stacks of pancakes, each at $5.50. Thus, in total, his spendings are of:
3.25 + 5.25s
He wants the bill to be of at most $30, that is, his spending has to be at most $30, thus:
T < 30
3.25 + 5.5s < =30
Thus the correct inequality is option D which is 3.25 + 5.5s < =30
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Two parallel lines are cut by a transversal as shown belc
Suppose m 8 =107 Find m2 1and m2 3
1
2
4
3
5
6
8
7
Answers
The values of the angles m∠1 and m∠3 is equal to 73°.
A transversal may be defined as a line which cuts a pair of parallel lines and forms several angles. When transversal cuts parallel lines the alternate interior angles are equal as well as the corresponding angles are equal. Also, the pair of vertically opposite angles are equal. From the figure attached. ∠4 = ∠8 as they are corresponding angles. So, m∠8 = m∠4 = 107°. Now, we know that ∠1 and ∠4 formed a pair of linear angles and the sum of the measures of the linear angles is 180°. So,
m∠1 + m∠4 = 180°
We know, m∠4 = 107°
m∠1 = 180° - 107°
m∠1 = 73°
Now, ∠1 and ∠3 are vertically opposite angles, so they are equal as the parallel lines are cut by transversal. Therefore, m∠1 = m∠3
=> m∠1 = 73°
=> m∠3 = 73°
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Mohal has a loyalty card good for a discount at his local pharmacy. To find the total he has to pay, before tax, he multiplies the prices by 0.96. What percent discount does the card give?
Answers
The percent discount the card gives can be:
4% or 96%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Royal card for discount.
Multiplying the total price to pay with 0.96 means two cases.
0.96 = 96/100 = 96%
Cases 1:
If the percent discount is 96% we will multiply the total prices to pay by 0.96 and subtract the value from the total price.
Example:
Total price to pay = 100
0.96 x 100 = 96
Total price to pay = 100 - 96 = 4
Cases 2:
If the percent discount is 4% we will multiply the total prices to pay by 0.96 after subtracting 4% from 100%.
Example:
Total price to pay = 100
Discount = 4%
100% - 4% = 96%
96% = 0.96
Total price to pay = 0.96 x 100 = 96
Thus,
The percent discount the card gives can be:
4% or 96%.
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Complete each statement with a number that makes the statement true.
A. __< 7°C.
B. __ <-3°C.
C. -0.8°C <___< -0.1°C
D. __> -2°C
Answers
Answer:
A. 6°C
B. -4°C
C. -0.7°C
D. -1°C
Answer:
A. 6°C < 7°C.
B. -4°C < -3°C.
C. -0.8°C < -0.7°C < -0.1°C
D. -1°C > -2°C
82.8 cm measured to the nearest tenth of a cm.
Answers
Explanation: 80 cm
help pls
1
3
144
432
Answers
The value of the given equation is 12.
What is the value of the equation?In order to solve this question, the BODMAS rule would be used. The BODMAS rule gives the order in which mathematical operations can be solved. The order is:
Bracket OfDivision Multiplication Addition SubtractionIn the numerator:
the addition would be done first: 3² + 1 = 9 + 1 = 10
Then the subtraction would be done next = 14 - 10 = 4
Now determine the square of the term in the bracket : 4²= 16
In the denominator:
The multiplication would be solved first: 3 x 1/4 = 3/4
The next step is to solve the division : 1 ÷ 3/4 = 1 x 4/3 = 4/3
The fraction becomes : 16 ÷ 4/3
16 x 3/4 = 12
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Answer:
The answer is 432
Step-by-step explanation:
I did the k 12 quiz and I got it right! good luck
Yall please help i need to turn this in i have too many demerits
Answers
The answers to all the subparts are:
(A) 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.(B) The new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.(C) The proportional relationship of the table will be x : 5y.(D) According to part (C), the Constant of proportionality will be x : 5y.What is constant proportionality?The ratio of two proportional values at a constant value is known as the constant of proportionality. When either their ratio or product results in a constant, two variables' values are said to be proportionally related. The ratio between the two specified quantities determines the value of the proportionality constant.So, (A) To make the same shade of green:
Cups of blue paint: 2Cups of yellow paint: 10Then, cups of yellow paint when blue paint is just 1 cup:
10/2 = 5/1 = 5
Therefore, 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.
(B) New pair of numbers to make the same green shade:
Old pair:
Cups of blue paint: 2Cups of yellow paint: 10Another pair:
Cups of blue paint: 1Cups of yellow paint: 5The new pair would be:
Cups of blue paint: 2 × 2 = 4Cups of yellow paint: 10 × 2 = 20Therefore, the new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.
(C) Proportional relationship:
Let cups of blue paint be: xCups of yellow paint be: yOld pair:
Cups of blue paint: 2Cups of yellow paint: 10Proportional relationship will be:
2x/10y = x/5y ⇒ x : 5yTherefore, the proportional relationship of the table will be x : 5y.
(D) Constant of proportionality:
According to part (C), the Constant of proportionality will be x : 5y.
Therefore, the answers to all the subparts are:
(A) 5 cups of yellow paint will be needed with 1 cup of blue paint to make the same green shade.(B) The new pair to make the same shade of green will be 4 cups of blue paint and 20 cups of yellow paint.(C) The proportional relationship of the table will be x : 5y.(D) According to part (C), the Constant of proportionality will be x : 5y.Know more about constant proportionality here:
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write four cubed in expanded form and then evaluate
Answers
Answer:
64
Step-by-step explanation:
4^3 = 4 x 4 x 4 which can be written as 2^6 which is equivalent to 64 too
(If this is what you're asking)
A car’s velocity increases from 4.2m/s to 14.8 m/s, E, in 2.5 sec. What is its acceleration?
Answers
The acceleration is 4.24 m^2/s
What is acceleration?
They are accelerations and vector quantities. The direction of an object's acceleration is determined by the direction of the net force acting on it. Acceleration describes the rate at which a speed changes over time.
The velocity is changing over time. The velocity is actually changing at a constant rate of 10 m/s per second. If an object's velocity is changing, it is said to be accelerating; it has acceleration.
According to question,
Acceleration = final velocity- initial velocity/ time
Final velocity = 14.8 and initial velocity = 4.2
Hence, acceleration = 14.8-4.2/2.5
=10.6/2.5
=4.24.
The acceleration is 4.24 m^2/s.
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