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Sonbull [250]
2 years ago
8

Inverse of the function h(x)=\dfrac{3}{2}(x-11)h(x)= 2 3 ​ (x−11)h, left parenthesis, x, right parenthesis, equals, start fracti

on, 3, divided by, 2, end fraction, left parenthesis, x, minus, 11, right parenthesis?
Mathematics
2 answers:
defon2 years ago
6 0

Answer:

h^{-1}(x)=\frac{2}{3}x+11

Step-by-step explanation:

The given function is

h(x)=\dfrac{3}{2}(x-11)

We need to find the inverse of the given function.

Step 1: Substitute h(x)=y.

y=\dfrac{3}{2}(x-11)

Step 2: Interchange x and y.

x=\dfrac{3}{2}(y-11)

Step 3: Isolate y.

\frac{2}{3}x=y-11

\frac{2}{3}x+11=y

Step 4: Interchange sides.

y=\frac{2}{3}x+11

Step 5: Substitute y=h^{-1}(x).

h^{-1}(x)=\frac{2}{3}x+11

Therefore, the inverse of the function is h^{-1}(x)=\frac{2}{3}x+11.

blagie [28]2 years ago
5 0

Answer:

The inverse function of h(x) = 3/2*(X-11)  is:  g(x)= (2/3*X) +11

Step-by-step explanation:

h(x) = Y= 3/2*(X-11)

To find the inverse function, the first step is to exchange the position of the variables with each other. So;

X= 3/2*(Y-11)

Now we need to isolate the variable Y from this equation. The final result will be te inverse function.

X=3/2*(Y-11)

2*X=3*(Y-11)

2/3*X=Y-11

2/3*X +11 = Y

Y= (2/3*X) + 11  (Inverse function)

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Answer:

a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers; b) A series is divergent if it is not convergent. A convergent series is a series for which lim n → ∞ an exists.

Step-by-step explanation:

A sequence is a pattern; it is an ordered list of numbers.  A series, however, is the sum of a sequence.

A convergent series is a series for which the sequence of its partial sums tends to a limit; this means the limit exists.  A divergent series is a series that is not convergent.

7 0
2 years ago
mr. rite wants his roof to be 90degrees at its peak and have a slope of -7/2 on the sunny side of the house. if the height of hi
ruslelena [56]

Answer:

60 feet

Step-by-step explanation:

The slope of the roof is the vertical distance over the horizontal distance. This means for very 7 feet vertical the roof spreads out 2 feet horizontal. So if the roof is 210 feet vertical, then the horizontal will be _____.

This is found by setting up a proportionand solving for the unknown distance.

\frac{7}{2}=\frac{210}{y}

7y = 2*210

7y = 420

y = 60

The horizontal distance will be 60 feet.

3 0
2 years ago
Match the real-world descriptions with the features they represent within the context of Melissa’s garden. Not all tiles will be
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Wheel A has a diameter of 25.4 inches. Wheel B has a diameter of 22.5 inches. About how much farther will Wheel A travel in one
MissTica

Wheel A will travel a distance of approximately 9 in more than wheel B in one rotation.

<u>Explanation:</u>

Given:

Diameter of wheel A, d₁ = 25.4 in

Radius of wheel A, r₁ = 12.7 in

Diameter of wheel B = 22.5 in

Radius of Wheel B, d₂ = 11.25 in

Distance travelled by A = ?

In one rotation, the distance travelled by a wheel is equal to its circumference.

Circumference of a wheel = 2πr

Circumference of wheel A = 2πr₁

                                            = 2 X 3.14 X 12.7 in

                                            = 80 in

Circumference of wheel B = 2πr₂

                                              = 2 X 3.14 X 11.25 in

                                              = 71 in

Therefore, wheel A will travel a distance of approximately 9 (80 - 71 in) in more than wheel B in one rotation.

3 0
2 years ago
Given rectangular prism ABCD. Choose all of the terms that best describe each of the sets of lines or points. Points D, G and J
Yuki888 [10]

Answer:

Two points are collinear when they lie on the same line. Points are collinear but not lines. Rather when two lines lie on the same plane we say they are coplanar.

Hence, line AB and CD are NOT collinear, so they are noncollinear and they are coplanar.

Two or more lines are said to be intersecting, when the lines meet at some point, when lines are not intersecting they are said to be parallel.

Recall that one of the properties of a rectangle is that opposite sides are parallel.

Notice that line AB and CB are the opposite sides of the rectangle ABCD.

Thus, line AB and CD are not intersecting but are parallel.

Therefore, the terms that best describe lines AB and CD are  

parallel  

noncollinear  

coplanar

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
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