The inverse of the function f(x) = x + 10 is shown.
==
h(x) = 2x-0
What is the missing value?
01
05
O 10
O 20
Answers
Answer:
So, the answer is 20
Step-by-step explanation:
[tex]f(x) = \frac{1}{2} x + 10 = = = > \\ f(x) - 10 = \frac{1}{2} x = = = > \\ 2f(x) - 20 = x = = = > \\ {f}^{ - 1} (y) = 2y - 20 = = = > {f}^{ - 1} (x) = 2x - 20[/tex]
The missing value of the inverse function is 20.
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the inverse of a function, we usually replace f(x) with y, then solve for x in terms of y, and finally replace y with the inverse function notation h(x).
So let's do that with the given function:
f(x) = (1/2)x + 10
y = (1/2)x + 10
2y = x + 20 (multiply both sides by 2 to isolate x)
x = 2y - 20 (subtract 20 from both sides)
Now we can replace x with h(x) and y with x to get the inverse function:
h(x) = 2x - 20
Thus,
The missing value is 20.
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Related Questions
Alaric wants to determine if he can get a better grade in math by studying for longer periods of time.
He plans to experiment for 4 weeks.
Which statement is true of this experiment?
a.) The duration of Alaric's experiment is the explanatory variable.
b.) Alaric's math grade is the explanatory variable.
c.) The amount of time Alaric spends studying is the response variable.
d.) Alaric's math grade is the response variable.
Answers
The statement (d) Alaric's maths grade is the response variable is correct because maths grade is a dependent variable.
What is an explanatory variable?It is defined as the variable which is independent. They show the expected results and the result is known as the response variable which is dependent on the explanatory variable.
We have given:
Alaric wants to determine if he can get a better grade in maths by studying for longer periods of time.
The duration of the experiment is 4 weeks which is known or constant.
But the number of hours she studied is a variable, and it is independent.
The maths grade is the dependent variable which is on the number of hours Alaric study variable.
Thus, the statement (d) Alaric's maths grade is the response variable is correct because maths grade is a dependent variable.
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A bag contains 3 blue, 7 green and 1 purple counter. One counter is picked
at random. What is the probability that the counter is green or purple? Give
your answer as a fraction.
Answers
A bag contains 3 blue, 7 green and 1 purple counter. One counter is picked at random, the probability of selecting a green or purple counter is 8/11.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.
There are a total of 11 counters in the bag, 3 of which are blue, 7 are green, and 1 is purple.
The probability of selecting a green or purple counter is the sum of the probabilities of selecting a green counter and a purple counter, since the events are mutually exclusive (a counter cannot be both green and purple at the same time).
So the probability of selecting a green or purple counter is:
Probability = (Number of green counters + Number of purple counters) / Total number of counters
Probability = (7 + 1) / 11
Probability = 8/11
Therefore, the probability of selecting a green or purple counter is 8/11.
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fy= 2x² + 2x + 1
y = 2x + 3
What is the solution to this system of equations?
o (-1, 3) and (0,4)
o (0, 1) and (1,5)
○ (0, 1) only
o (-1, 1) and (1, 5)
Answers
The answer is (-1,1) and (1,5)
The table shows ordered pairs of the function y=8-2x. What is the value of y when x = 8?
X
-3
-1
1
4
8
10
y
14
10
6
0
?
-12
Answers
Answer: -8
Step-by-step explanation:
[tex]y=8-2(8)=\boxed{-8}[/tex]
What is the present value of a cash inflow of 1250 four years from now if the required rate of
return is 8% (Rounded to 2 decimal places)?
Answers
Using simple interest, it is found that the present value of the cash inflow is of 947.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
A(t) = A(0)(1 + rt)
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.In this problem, the parameters are given as follows:
r = 0.08, t = 4, A(t) = 1250.
We have to solve for A(0) to find the present value, hence:
A(t) = A(0)(1 + rt)
1250 = A(0)(1 + 0.08 x 4)
A(0) = 1250/1.32
A(0) = 947.
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Please help whilst I try to solve this as well.
Answers
Answer:
420
Step-by-step explanation:
Answer:
V = 340 cm3
Step-by-step explanation:
Calculate the volume of the prism without the gap, then subtract the volume of the gap.
[tex]V=(5)(10)(8)-(3)(2)(10)=400-60=340cm^{3}[/tex]
Hope this helps
HELP DUE SOON A farmer has decided to divide his land area in half in order to plant soy and corn. Calculate the area of the entire area so he knows how much soil is needed.
A parallelogram with a height of 6 yards and side length 9 yards. The height forms a triangle with the slanted side of the rhombus with a base of 2.5 yards. Rhombus is split into a soy half and a corn half.
Each bag of soil covers 20 square yards. How many bags should the farmer purchase?
Answers
The farmer should purchase 2 bags of soil for his farm.
What is Area of parallelogram?A parallelogram is a two-dimensional figure with four sides. It is a special case of the quadrilateral, where opposite sides are equal and parallel. The area of a parallelogram is the space enclosed within its four sides. Area is equal to the product of length and height of the parallelogram.
The shape of the farm, according to the picture is a parallelogram. Therefore, the total area can be calculated as follows:
Area = base X height
where
b = base
h = height
base = 6.5 + 2.5 = 9.0 yards
height = 6 yards
Area = 6 × 9 = 54 square yards.
40 square yards requires 1 bag of soil .
54 square yards will require ?
Bags required = 54 / 40 = 1.35 bag
Thus, the farmer will require 2 bags of soil for his farm.
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Question 15 (06.01 LC)
Classify the expression: 5x³ - 4x²
Quadratic expression
Linear expression
Cubic expression
Constant expression
Answers
Answer:
Cubic expression
Step-by-step explanation:
Polynomials with a degree of 3 are known as cubics.
Answer:
cubic expression
Step-by-step explanation:
it is cubic when raised to the power of 3
On a certain day, the high temperature in city A was 93° F. On the same day, the high temperature in city B was -6° F. What was the difference in temperature between city A and city B?
Answers
Answer:
99°F
Step-by-step explanation:
The high temperature in city A was 93° F. On the same day, the high temperature in city B was -6° F.
The difference in temperature will be:
= 93 - (-6)
= 93 + 6
= 99
Convert the following angle from degrees to radians. Express your answer in simplest
form.
495°
Answers
Answer:
11/4 Pi
Step-by-step explanation:
because 1.= 70/180. (180.=Pi)
so 495 x 70/180
=11/4 Pi
What are the zeros of the quadratic function f(x) equals 6X squared +12 X -7
Answers
The zeroes of the function will be [tex]\rm -1 \pm \dfrac{\sqrt{78}}{6}}[/tex]
What is a Quadratic Function ?A quadratic function is given by ax² +bx+c = f(x)
The given quadratic function is
f(x) = 6x² +12x - 7
The zeroes of the function will be given by
f(0) = 0
6x² +12x - 7 = 0
The zeroes are given by
[tex]\rm \dfrac {-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]
here
a = 6
b = 12
c = -7
Therefore the zeroes of the function will be
[tex]\rm \dfrac {-12 \pm \sqrt{12^2 -4*6*(-7)}}{2 *6}[/tex]
[tex]\rm \dfrac {-12 \pm \sqrt{312}}{12}[/tex]
[tex]\rm -1 \pm \dfrac{\sqrt{78}}{6}}[/tex]
Therefore these are the two zeroes of the function.
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If y varies directly as the square of x and Y--54 when x-9, then -- when x-6.
True or false
Answers
Answer:
24.012
Step-by-step explanation:
y=kx^2
54=81k
k=54/81
k=0.667
y=kx^2
y=0.667×36
y=24.012
its false ik this because im one of the boyzz
A rectangular prism and a cylinder both have a height of 8m, and their cross-sectional areas are equal at every level parallel to their respective bases.
Complete the steps to find the prism.
Answers
1) [tex]V=lwh=5(x)(8)=\boxed{40x}[/tex]
2) [tex]V=\pi r^{2}h=(\pi)(3^{2})(8)=\boxed{72}\pi[/tex]
3) [tex]40x=72\pi\\\\x=\frac{72\pi}{40} \approx \boxed{5.7}[/tex]
Hello what is the next number in the sequence 7, 11, 2, 18, -7, ?
Answers
The next number in the sequence 7, 11, 2, 18, -7, would be -11.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.
Given sequence;
7, 11, 2, 18, -7,
We can see that the fifth term is similar to the first term, except for the negative.
So, we can conclude that the integers start from the fifth term and leads to the next term as a negative of the second one.
Therefore, The next number in the sequence 7, 11, 2, 18, -7, would be -11.
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Solve x2 + 4x + 12 = 0 by completing the square.
x = –2 + 2i, x = –2 –2i
x = –2 + i, x = –2 – i
x = –2 + 2i, x = –2 – 2i
x = 0, –4
Answers
Answer:
See below
Step-by-step explanation:
x2 + 4x + 12 = 0 Complete the square ( take 1/2 of the 'x' coefficient, then square it and add it to both sides of the equation
x^2 + 4x + 2^2 + 12 = 2^2 Subtract 12 from both sides
x^2 + 4x + 4 = -8
(x+2)^2 = - 8 sqrt both sides
(x+2) =± sqrt (-8) simplify just a bit
x+2 = ±(2i sqrt2) subtract 2 from both sides
x = -2 ± 2i sqrt 2 <===== I do not see that answer listed
10 times the sum of certain numbers x and y
Answers
This can be represented by [tex]\boxed{10(x+y)}[/tex]
The USD appreciates 2% versus the JPY. The USD appreciates 4% versus the MXN. What is the approximate appreciation or depreciation we might see in the JPY/MXN cross exchange rate? Fill in the blanks: The JPY/MXN cross rate should ______________ about ______________ percent
Answers
The approximate appreciation or depreciation we might see in the MXN/JPY cross exchange rate is 3%.
What is Depriciation?
The term depreciation refers to an accounting method used to allocate the cost of a tangible or physical asset over its useful life. Depreciation represents how much of an asset's value has been used.
The approximate appreciation or depreciation we might see in the MXN/JPY cross exchange rate can be stated using the following 3 steps.
Step 1. State the initial exchange rates of the currency pairs.
Let first assume the initial exchange rates are as follows:
USD1 = JPY1
USD1 = MXN1
Therefore, we have the initial cross rate as follows:
MXN1 = USD1 = JPY1
MXN1 = JPY1
Step 2. Determine the new exchange rates
The new exchange rates can be determined as follows:
When the USD depreciates 2% versus the JPY, this implies that
USD1 X (100% + 2%) = USD1.02
has to be exchanged for JPY1.
Therefore, we now have:
USD1.02 = JPY1, or
USD1 = JPY1/1.02
USD1 = JPY0.98
Also, when The USD appreciates 1% versus the MXN, this implies that USD1 X (100% - 1%) = USD0.99
has to be exchanged for MXN1.
Therefore, we now have:
USD0.99 = MXN1, or
USD1 = MXN1/0.99
USD1 = MXN1.01
Therefore, we have the new cross rate as follows:
MXN1.01 = USD1 = JPY0.98
MXN1.01 = JPY0.98
MXN1.01 / 1.01 = JPY0.98/1.01
MXN1 = JPY0.97, or
MXN1/0.97 = JPY0.97/0.97
MXN1.03 = JPY1
Therefore, the new exchange rates are as follows:
USD1.02 = JPY1
USD0.99 = MXN1
MXN1.03 = JPY1
c. Determination of appreciation or depreciation we might see in the MXN/JPY
Percentage of depreciation of MXN against JPY = ((Initial MXN/JPY - New MXN/JPY) / Initial MXN/YPY) X 100 = ((1.03 - 1) / 1) * 100 = 3%
Since the percentage of depreciation of MXN against JPY is 3%, this also implies that the percentage of appreciation of JPY against MXN is 3%.
Thus, the approximate appreciation or depreciation we might see in the MXN/JPY cross exchange rate is 3%.
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Tim go to school.His age is a cube number.His age is double 1 square number and half a different square number.How old is Tim?
Answers
find the volume of the rectangular prism WILL MARK BRAINLEST
Answers
Step-by-step explanation:
volume= l×w×h
1.1/3×1/2×2/3
=1/9
2. 3/4×1/8×13/16
=39/512
3. 1/12×7/8×1/4
=7/384
4. 3/2×1/7×7/8
=3/16
5. 1/5×9/10×2/3
=3/25
6.6/7×7/8×1/2
=3/8
Volume = w * h * l
1) V = 1/9 ft^3
Height (h) = 1/2 ft
Length (l) = 2/3 ft
Width (w) = 1/3 ft
Therefore,
= w * h * l
= 1/3 * 1/2 * 2/3
= 1/6 * 2/3
= 2/18
=> 1/9
Volume = 1/9 ft^3
2) V = 39/512 in^3
Height (h) = 13/16 in
Length (l) = 3/4 in
Width (w) = 1/8 in
Therefore,
= w * h * l
= 1/8 * 13/16 * 3/4
= 13/128 * 3/4
=> 39/512
Volume = 39/512 in^3
3) V = 7/384 cm^3
Height (h) = 1/12 cm
Length (l) = 7/8 cm
Width (w) = 1/4 cm
Therefore,
= w * h * l
= 1/4 * 1/12 * 7/8
= 1/48 * 7/8
=> 7/384
Volume = 7/384 cm^3
4) V = 1/12 cm^3
Height (h) = 2/3 cm
Length (l) = 7/8 cm
Width (w) = 1/7 cm
Therefore,
= w * h * l
= 1/7 * 2/3 * 7/8
= 2/21 * 7/8
= 14/168
= 1/12
Volume = 1/12 cm^3
5) V = 3/25 m^3
Height (h) = 1/5 m
Length (l) = 2/3 m
Width (w) = 9/10 m
Therefore,
= w * h * l
= 9/10 * 1/5 * 2/3
= 9/50 * 2/3
= 18/150
= 6/50
=> 3/25
Volume = 3/25 m^3
6) V = 3/8 yd^3
Height (h) = 1/2 yd
Length (l) = 6/7 yd
Width (w) = 7/8 yd
Therefore,
= w * h * l
= 7/8 * 1/2 * 6/7
= 7/16 * 6/7
= 42/112
=> 3/8
Volume = 3/8 yd^3
The function y = f(a) is graphed below. What is the average rate of change of the
function f(a) on the interval -8 < < 8?
Answers
Answer: -35/16
Step-by-step explanation:
[tex]f(8)=-5\\\\f(-8)=30\\\\\frac{f(8)-f(-8)}{8-(-8)}=\frac{-5-30}{16}=\boxed{-\frac{35}{16}}[/tex]
true or false
The slope of the least-squares regression line is the average change in the predicted
values when the explanatory variable increases by 1 unit. [Select]
Answers
Answer:
false fake false false false.............
Step-by-step explanation:
.....,........................
Find dy/dx if y =x^3+5x+2/x²-1
How would I go about finding this? I would appreciate if you could be as detailed as possible!
Answers
Differentiate using the Quotient Rule –
[tex]\qquad[/tex][tex]\pink{\twoheadrightarrow \sf \dfrac{d}{dx} \bigg[\dfrac{f(x)}{g(x)} \bigg]= \dfrac{ g(x)\:\dfrac{d}{dx}\bigg[f(x)\bigg] -f(x)\dfrac{d}{dx}\:\bigg[g(x)\bigg]}{g(x)^2}}\\[/tex]
According to the given question, we have –
f(x) = x^3+5x+2 g(x) = x^2-1Let's solve it!
[tex]\qquad[/tex][tex]\green{\twoheadrightarrow \bf \dfrac{d}{dx}\bigg[ \dfrac{x^3+5x+2 }{x^2-1}\bigg]} \\[/tex]
[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{(x^2-1) \dfrac{d}{dx}(x^3+5x+2) - ( x^3+5x+2) \dfrac{d}{dx}(x^2-1)}{(x^2-1)^2 }\\[/tex]
[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{(x^2-1)(3x^2+5) - ( x^3+5x+2) 2x}{(x^2-1)^2 }\\[/tex]
[tex]\qquad[/tex][tex] \pink{\sf \because \dfrac{d}{dx} x^n = nx^{n-1} }\\[/tex]
[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{3x^4+5x^2-3x^2-5-(2x^4+10x^2+4x)}{(x^2-1)^2 }\\[/tex]
[tex]\qquad[/tex][tex]\twoheadrightarrow \sf \dfrac{3x^4+5x^2-3x^2-5-2x^4-10x^2-4x}{(x^2-1)^2 }\\[/tex]
[tex]\qquad[/tex][tex]\green{\twoheadrightarrow \bf \dfrac{x^4-8x^2-4x-5}{(x^2-1)^2 }}\\[/tex]
[tex]\qquad[/tex][tex]\pink{\therefore \bf{\green{\underline{\underline{\dfrac{d}{dx} \dfrac{x^3+5x+2 }{x^2-1}} = \dfrac{x^4-8x^2-4x-5}{(x^2-1)^2 }}}}}\\\\[/tex]
A triangle has two sides of lengths 4 and 15. What value could the length of
the third side be? Check all that apply.
A. 19
B. 11
C. 4
OD. 15
OE. 12
F. 13
Answers
The value could the length of the third side will be 11,12,13,15. Options B, D, E, and F are the correct answers.
What is the triangle?A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.
According to the triangle Inequality theorem, any two triangle sides must add up to more than the third side's length.
You may get the potential length of a triangle by multiplying the sum of two sides by the difference between two sides.
Therefore,
Let x is the possible length of the third side of a triangle.
14-4<x<15+4
10<x<19
The values of the third side is lies between the 10 and 19.The value could the length of the third side will be 11,12,13,15
Hence, options B, D, E, and F are the correct answers.
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4(n+3)=24 solve for n
Answers
In the fall, you charge people $8 for going to their house to rake leaves, then
$5 for every hour you rake. If you make $38 one day, how many hours did you
spend raking?
Answers
Reason
Using formula Y=mx + b
Y is your total $
M is your y/x rate
B is your y intercept, the starting point
38 = 5/1 x + 8
Solve
38 = 5x + 8 subtract 8 from both sides to isolate x
30 = 5x
now divide both sides by 5 to solve for x
X=6
Now check your work
38 = (5)(6) + 8
38 = 38
So it equals !
How much vinegar would be in each container if the total amount in all cups were redistributed equally between the 8 containers?
Answers
Answer:
Step-by-step explanation:
1/8
find the area dimensions are in centimeters.
Answers
Answer:
[tex]9600cm^{2}[/tex]
Step-by-step explanation:
Get the area of the triangle and the rectangle, then subtract the triangle's area for the rectangle's
pls help me solve for x in this equation! + brainest
Answers
Answer:
x = -3
Explanation:
[tex]\rightarrow \sf \sqrt[3]{\sf 3x + 1} = -2[/tex]
[tex]\rightarrow \sf \sf 3x + 1 = (-2)^3[/tex]
[tex]\rightarrow \sf \sf 3x + 1 = -8[/tex]
[tex]\rightarrow \sf \sf 3x = -8-1[/tex]
[tex]\rightarrow \sf \sf 3x = -9[/tex]
[tex]\rightarrow \sf \sf x = -3[/tex]
Answer:
[tex]\sqrt[3]{3x+1} =-2\\(\sqrt[3]{3x+1})^{3} =(-2)^{3} \\3x+1=-8\\3x=-9\\x=-3[/tex]
Hope it helps!
3x+6-2 = 6x-(7/2*9/0)
Answers
[tex]3x+6-2 = 6x-( \frac{7}{2} \times \frac{9}{0} ) \\ \\ 3x + 4 = 6x - \frac{63}{0} \\ \\ 3x + 4 = 6x - 0 \\ \\ 4 + 0 = 6x - 3x \\ \\ 3x = 4 \\ \\ x = \frac{4}{3} .[/tex]
The value of x is 4/3 .
Answer: No Solution
Why?
Any number divided by 0 is not defined, but we are given 9/0 in the question. Hence we cannot solve the equation for the value of ‘x’.
Answer this! Thanks so much in advance (:
Answers
Answer:
ai) m = 17, applicable past x = 23/17; aii) m = 4; applicable past 3 dad jokes
Step-by-step explanation:
to calculate slope you use the (y2 - y1) / (x2 - x1) equation
so for the first one
(62 - 11) / (5 - 2)
51 / 3 = 17
the equation for this is y = 17x + b
plug in values to find b
11 = 34 + b
b is -23
y = 17x - 23
because distance cannot be negative we must find when x is exactly 0 to find where it is applicable
17x = 23
x = 23/17
for the second one we can subtract again
(10 - 2) / (5 - 3)
8 / 2
4 is the slope
like before we must find b and then find where y is 0
y = 4x + b
2 = 12 + b
b = -10
y = 4x - 10
4x = 10
x = 5/2
since you cannot have 1/2 a dad joke we round up from 2 1/2 to 3