Answer:
[tex]h(x) = \frac{1}{4} x[/tex]
Step-by-step explanation:
To find the inverse of a function, the steps are:
Let y= f(x)Make x the subject of formulaReplace x with f⁻¹(x) and y with xIn this case, since h(x) is the inverse function of f(x), we can replace x with h(x) in step 3.
_____
f(x)= 4x
Let y= f(x) [tex]\textcolor{steelblue}{\text{ - step 1}}[/tex]
y= 4x
Divide both sides by 4:
[tex] \frac{1}{4} y = x[/tex]
[tex]x = \frac{1}{4} y \: \: \: \textcolor{steelblue}{\: \text{ - step 2}}[/tex]
Replace x with h(x) and y with x:
[tex]\bf{h(x) = \frac{1}{4} x} \: \: \: \textcolor{steelblue}{\: \text{ - step 3}}[/tex]
Additional:
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https://brainly.com/question/21287415Given the two rectangles below. Find the area of the shaded region. 4 4 9 3
Answer:
60
Step-by-step explanation:
The shaded region's area is the difference between the area of the outer rectangle and the white rectangle.
area = LW - lw
area = (4 + 4)(9 + 3) - (4)(9)
area = (8)(12) - 36
area = 96 - 36
area = 60
Un fabricante de peceras debe indicar el volumen de cada una de ellas. ¿cuál es el volumen de una pecera de forma cilíndrica con un diámetro de 50 cm. Y una altura de 30 cm. ?
El volumen es una cantidad escalar tridimensional. El volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm es 58,904.863 cm³.
¿Qué es el volumen?
Un volumen es un número escalar que expresa la cantidad de espacio tridimensional encerrado por una superficie cerrada.
El volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm será,
Volumen del cilindro = (π/4)×diámetro ²×altura
= (π/4)×(50cm)²×30cm
= 58,904.863cm³
Por lo tanto, el volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm es 58,904.863 cm³.
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Enter the equation of the circle described below.
Center (-3,0), radius = sqrt5
Answer: [tex](x+3)^{2}+y^{2}=5[/tex]
Over What Interval is The Function In This Graph Increasing?
The correct answer is option D.which is -4 ≤ x ≤ 1.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
in the graph, we can see that the value of x is increasing from -4 coordinate of x to the 1 coordinate of x so the interval will be given as -4 ≤ x ≤ 1.
Therefore the correct answer is option D.which is -4 ≤ x ≤ 1.
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Which of the following expressions is equivalent to (x5 y3 z2) (x4 y3 z6) for all real values of x y, and z ?
a. x9y6z8
b. x9y9z8
c. x20y6z8
d. x20y9z12
e. x21y6z12
The product of the expressions (x⁵y³z²) and (x⁴y³z⁶) is equivalent to the expression x⁹y⁶z⁸. Then the correct option is A.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The expression is given below.
(x⁵y³z²) and (x⁴y³z⁶)
Then the product of the expression will be
⇒ (x⁵y³z²) (x⁴y³z⁶)
⇒ x⁵x⁴y³y³z²z⁶
⇒ x⁵⁺⁴y³⁺³z²⁺⁶
⇒ x⁹y⁶z⁸
Then the correct option is A.
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Which is the x-value of the solution of the system of equations? y=3x^2+15 y=5x^2-17
A. x=±1 B. x=±2
C. x=±4 D. x=±16
Answer:
C. x = ±4
Explanation:
Given two equation's:
y = 3x² + 15y = 5x² - 17Solve them simultaneously:
y = y
3x² + 15 = 5x² - 17
5x² - 3x² = 15 + 17
2x² = 32
x² = 16
x = ±√16
x = ±4
If EFG QRS, which statement is not correct
Answer:
hello how are you nice to meet you
X/6=9/20
What is the answer?
Step-by-step explanation:
[tex] \frac{x}{6} = \frac{9}{20} \\ [/tex]
[tex]x \times 20 = 9 \times 6[/tex]
[tex]20x = 54[/tex]
[tex]x = \frac{54}{20} \\ [/tex]
[tex]x = 2.7[/tex]
what's the square root of 2
Answer:
The square root of 2 is 1.41421
Answer:
The square root of 2 is 1.414
Help my semester ends in 17 hours
i'm so confused this is all they put
Apply the Pythagorean Theorem to determine
unknown side lengths in right triangles in real
world and mathematical problems in two and
three dimensions
Please help :) I don’t understand this
Answer:
Step-by-step explanation:
Part A
Neighborhood A :
2, 2, 2, 4, 4, 5, 5, 5, 5
mean = [tex]\frac{2+2+2+4+4+5+5+5+5}{9}[/tex] = [tex]\frac{34}{9}[/tex] ≈ 3.8
median = 4
mode = 5
range = 3
[tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 5 - 2 = 3
===================
Part B.
Neighborhood B :
1, 1, 2, 2, 3, 4, 5, 5, 12
mean = ( 1 + 1 + 2 + 2 + 3 + 4 + 5 + 5 + 12 ) ÷ 9 = [tex]\frac{35}{9}[/tex] ≈ 3.9
median = 3
mode = 1, 2, 5
range = 11
[tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 5 - 1.5 = 3.5
Outlier = 12
1. letica started an online store selling hand made blankets. she sold 92 in her first month. how did she make if each blanket cost $49
Answer:
92 x 49 = 4,508
Step-by-step explanation:
According to the texts, she sold 92 blankets in her first month, bringing her total sales to 92, and each blanket cost $49.
Please Help if you know!
An equation that can be used to determine how much each cookie cost originally is ($13.32 + $7) / 16.
What is the equation that determines the cost of each cookie?
A coupon reduces the price of an item. Thus, the amount paid by Louis would be lower than the original price.
Original price = coupon + price paid
($13.32 + $7)
The cost per cookie, can be determined by dividing the original price by the total number of cookies bought.
($13.32 + $7) / 16
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Answer:
Step-by-step explanation:
Givens
Number of cookies = 16
Deduction = 7
Final Cost = 13.31
Equation
16c - 7 = 13.31
Solution
You are not asked for a solution but I'll put it here anyway.
16c - 7 = 13.32 Add 7 to both sides
16c -7+7 = 13.32+ 7 Combine
16c = 20.32 Divide by 16
16c/16 = 20.32/16
c = 1.27
Part A: Solve for the "h." Show all work
Answer:
2.7 m
Step-by-step explanation:
Corresponding sides of similar triangles are proportional. This figure shows similar triangles ∆ABC ~ ∆ADE.
__
The proportion that can be used to find h = DE is ...
DE/BC = DA/BA
h/(0.9 m) = (12 m+6 m)/(6 m) . . . . . filling in the values given
h = (0.9 m)(18/6) . . . . . multiply by 0.9 m
h = 2.7 m
The value of "h" is 2.7 m.
Please please help me 30 points if you can I need the answer I know how to do it I just suck with the fractions
Answer:
1
Step-by-step explanation:
[tex]\text{Given that,}~ (x_1,y_1) = (-2,4)~ \text{and}~ \text{slope,}~ m = -\dfrac 32\\ \\\text{Equation of line,}~\\\\~~~~~~~y -y_1 = m(x-x_1)\\\\\implies y -4 =-\dfrac 32(x+2)\\\\\implies y-4 =-\dfrac 32x - 3\\\\\implies y = -\dfrac 32x -3 +4\\\\\implies y = -\dfrac 32x +1[/tex]
The current equation of the perpendicular line;
⇒ is the slope-intercept form: [tex]y= mx + b[/tex]
m: is the coefficient in front of the x, which is also the slope's valueb: y-intercept of the functionNow for the point-slope form, we need a point on the line and the slope of the line:
⇒ we have
slope = -3/2point: (-2,4)Since this is the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex]
⇒ where the (x₁,y₁) is the point on the line and m is the slope
[tex]= > Equation: (y-4)=-\frac{3}{2}(x+2)[/tex]
To convert the equation to slope-intercept form:
⇒ must isolate 'y' to one side and everything to the other side
[tex]y= -\frac{3}{2}(x+2)+4\\ y=-\frac{3}{2} x-3+4\\y=-\frac{3}{2}x+1[/tex]
Answer: [tex]y = -\frac{3}{2}x+1[/tex]
Hope that helps!
A timer is started and a few moments later a model airplane is launched from the ground. Its height (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=−(t−12)2+81
. Which of the following statements is true?
The airplane reaches its minimum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
The airplane reaches its minimum height of 81 feet in 12 seconds.
The airplane reaches its maximum height of 12 feet in 81 seconds.
The airplane reaches its maximum height of 81 feet in 12 seconds.
Behavior of curvesIf y = [tex]x^{2}[/tex], it means that the second derivate is 2 which is positive, then there is a minimum turning point.
If y = - [tex]x^{2}[/tex], it means that the second derivative will be -2 which is negative, then there is a maximum turning point.
Analysis:
h(t) = -[tex](t - 12)^{2}[/tex] + 81
By expanding,
h(t) = -([tex]t^{2}[/tex] - 24t + 144) +81
h(t) = -[tex]t^{2}[/tex] + 24t - 144 + 81
h(t) = -[tex]t^{2}[/tex] + 24t - 63
at turning point d/dt(h(t)) = 0
d/dt (h(t)) = -2t +24
-2t +24 = 0
if we differentiate again, second derivative is -2 which is negative, so it is a maximum point.
2t = 24
t = 12 seconds
h(t) at t = 12
h(t) = [tex]-(12)^{2}[/tex] + 24(12) - 63 = 81 feet
In conclusion, the maximum height of the airplane after 12 seconds is 81 feet.
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Hello, can someone help with this problem?
The graph shows the probability distribution of a random variable.
What is the value of P(4≤X≤8)?
0.40
0.45
0.50
0.55
Answer:
P(5 ≤ X ≤ 8) = a rectangle with a width of 3 and height of .15 = 3(.15) = .45
P( 4 ≤ X ≤ 5) = a triangle with a base of 1 and a height of (0.15 -0.05) = .10
So....this area = (1/2)(1)(.10) = .05
And another rectangle with a width of 1 and height of .05 = (1) (.05) = .05
So
Adding these areas
P( 4 ≤ X ≤ 8 ) = .45 + .05 + .05 = .55
Step-by-step explanation:
Hoped this helped!
Which expression equivalent to 9q^ 2 - 2 3 (3q-7)+5q^ 2 ? a 9q ^ 2 - 5/3 * q - 3 b 9q ^ 2 - 2q - 3 14q ^ 2 - 2q + 14/3 d 14q ^ 2 - 5/3 * q - 14/3 d
The equivalent expression of 9q^ 2 - 2/3(3q - 7) + 5q^2 is 14q^ 2 - 2q - 14/3
How to determine the equivalent expression?The expression is given as:
9q^ 2 - 2/3(3q - 7) + 5q^2
Open the bracket
9q^ 2 - 2q - 14/3 + 5q^2
Evaluate the like terms
14q^ 2 - 2q - 14/3
Hence, the equivalent expression of 9q^ 2 - 2/3(3q - 7) + 5q^2 is 14q^ 2 - 2q - 14/3
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Which is the range of the function f(x) = (9)×?
O all real numbers
O all real numbers less than 0
O all real numbers greater than 0
O all real numbers less than or equal to 0
Using it's concept, it is found that the range of the function [tex]f(x) = 9^x[/tex] is given by:
all real numbers greater than 0.
What is the range of a function?It is the set that contains all possible output values for the function.
In this problem, the function is:
[tex]f(x) = 9^x[/tex]
For exponential functions without vertical shifts, as is the case in this problem, the range is given by:
all real numbers greater than 0.
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Megan is one of the cheerleaders in her school. To prepare for the forthcoming Cheer Dance Competition, her coach is teaching them how to control their pom-poms when throwing them up into the air. One exercise is to toss the pom-poms twice as high as the previous toss from the top of their heads. If Megan is able to throw her pom-poms 2 feet above her head during her first toss, how high above her head should her fourth toss be? (problem solving)
Answer:
16 feet
Step-by-step explanation:
her first try is 2 and you multiply by 2 every time so her first would be 2 which we would multiply to get 4 which we would multiply again to get 8 which we would multiply AGAIN to get the final answer of 16
Which equation illustrates the matrix associative property of addition
Answer:
c
cuz it is
first of all 4,3 + 0,0 = 4,3
2,1+0,0 = 2,1
and which is the answer
i need help please thanks
Just give me the new coordinates
Answer: number 1 and number 2 and 4 and 5
Step-by-step explanation:
thank you for this :)
Which of these statements is true for f(x) = 2.3x?
A. The y-intercept is (0, 1).
OB. It is always decreasing.
OC. The domain is x > 0.
OD. The y-intercept is (0, 2).
Answer:D
Step-by-step explanation:when x is 0 we get y=2x3^0=2x1=2
The correct option is D.
What is a function?A function is defined as a relation between a set of inputs having one output each. a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.
Given is a function f(x) = 2·3ˣ, we need to select the correct options regarding the function,
The properties are =
y intercept: y = 2
domain: (-∞, ∞)
decreasing interval: no
Hence the correct option is D.
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Evaluate:
[tex]\bf{\sum^{20}_1\:4(\cfrac{8}{9})^{n-1}[/tex]
(find the sum of the first 20 terms of the geometric series)
Please help A.S.A.P. & show work as well.
Thank you guys!
[tex]\bigstar[/tex]
[tex]\boxed{\sf \sum _{n=1}^{20}\:4\left(\frac{8}{9}\right)^{n-1}}[/tex]
Identify the following:
First Term (a) = 4(8/9)¹⁻¹ = 4Common ratio (r) = 8/9Total Terms (n) = 20Formula Required:
[tex]\rightarrow \quad \sf S_n = \dfrac{a(r^n - 1)}{r-1}[/tex]
Insert values identified:[tex]\rightarrow \sf S_{20} = \dfrac{4(\dfrac{8}{9}^{20} - 1)}{\dfrac{8}{9} -1} \quad\overset{simplify}{\longrightarrow} \quad \dfrac{4\left(9^{20}-8^{20}\right)}{3^{38}} \quad \xrightarrow{\text{In \ Decimals} }\quad 32.58609013[/tex]
Solve the system 2x + 2y = -6 and 3x - 2y = 11 by using graph paper or graphing technology. What is the solution to the system?
Answer:
the solution is (1,-4)
Step-by-step explanation:
A crate is lifting a boat suspended by wire ropes AB and AD. The point C is vertically below A, and BC measures 5.
a) The gradient of AB is 0.8. How high is AC
The boat suspended by wire ropes AB and AD, AC is 4 units high.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The gradient of AB is 0.8, hence:
AC / BC = 0.8
Since BC = 5, therefore:
AC / 5 = 0.8
AC = 4
The boat suspended by wire ropes AB and AD, AC is 4 units high.
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The roots of the quadratic equation x²+bx+c = 0 are a and ß a) Evaluate i) a² + ß², ii) (a − ß)² b) Find the quadratic equation whose roots are (a² +ß²) and (a - 3)²
If ɑ and β are the roots of x² + bx + c = 0, then we can write
x² + bx + c = (x - ɑ) (x - β)
Expanding the right side gives
x² + bx + c = x² - (ɑ + β) x + ɑβ
so that ɑ + β = -b and ɑβ = c.
Recall that for all real numbers m and n,
(m + n)² = m² + 2mn + n²
a) It follows that
(i) ɑ² + β² = (ɑ + β)² - 2ɑβ = (-b)² + c = b² + c
(ii) (ɑ - β)² = ɑ² - 2ɑβ + β² = b² + c - 2c = b² - c
b) I assume you mean to find the quadratic whose roots are ɑ² + β² and (ɑ - β)² (and not (ɑ - 3)²). The simplest quadratic of this form is
(x - (ɑ² + β²)) (x - (ɑ - β)²)
Using the results from part (a), this becomes
(x - (b² + c)) (x - (b² - c))
and expanding, we get
x² - (b² + c + b² - c) x + (b² + c) (b² - c)
= x² - 2b² x + b⁴ - c²
which problem is molded by the equation 4x-5=45?
Answer: B.
Step-by-step explanation:
See attached. We examine the equation and decide which situation, or problem, models it correctly.
The displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d = 0.4 sine (1760 pi t). what is the maximum displacement of the tuning fork?
The maximum displacement of the tuning fork is 0.4 mm
What is a tuning Fork ?A tuning fork is a acoustic resonator , It is used to tune musical Instruments.
It is given in the question that the
displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d = 0.4 sine (1760 pi t).
the maximum displacement of the tuning fork = ?
The equation for a sine function is given by
f(t) = A sin(Bt + C) + D
here A is the maximum Displacement
When this equation is compared with the given equation
d = 0.4 sine (1760 pi t).
A = 0.4
The maximum displacement of the tuning fork is 0.4 mm
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