Which graph type would be best suited for showing the median population for the state capitals in the United States?
1 answer:
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Answer:
<u>Given function</u>
- h(x) = 2x - 1
#15 Find the inverse of h(x)
<u>Substitute x with y and h(x) with x and solve for y:</u>
- x = 2y - 1
- 2y = x + 1
- y = 1/2x + 1/2
<u>The inverse is:</u>
- h⁻¹(x) = 1/2x + 1/2
#16 The graph with both lines is attached.
The x- and y-intercepts of both functions have reversed values.
#17 Table of the inverse function will contain same numbers with swapped domain and range.
<u>Initial look is like this:</u>
- <u>x | -3 | -2 | -1 | 0 | 1 | 2 | 3</u>
- h⁻¹(x) | -1 | | 0 | | 1 | | 2
<u>The rest of the table is filled in by finding the values:</u>
- <u>x | -3 | -2 | -1 | 0 | 1 | 2 | 3</u>
- h⁻¹(x) | -1 | -0.5 | 0 | 0.5 | 1 | 1.5 | 2
Answer: ∠A=48°,∠B=48°,∠C=84°.
Step by-step explanation:
Given: AD and BE are the angle bisectors of ∠A and ∠B
i.e ∠6=∠7 ( ∵ Angles formed after AD bisected ∠A)
∠4=∠5 ( ∵ Angles formed after BE bisected ∠B)
Also, DE║AB
⇒ ∠2=∠7 (∵ Alternate interior angles)
∠3=∠6 (∵ Alternate interior angles)
And ∠ADE : ∠ADB =∠2:∠3= 2:9 =2x : 9x ..(1)
To Find: ∠A,∠B,∠C.
Solution: ∠2=∠7 (∵ Given) ...(2)
∠2=∠4 (∵ angles on the same segment) ...(3)
∠4=∠5 =∠B/2 (∵ Given) ...(4)
∴ In Δ ABD
∠3+∠4+∠5+∠7 = 180 (∵ Sum of interior angles of a triangle)
From equation 2,3,4,5, Put values
9x+2x+2x+2x =180°
⇒15x = 180°
⇒x=12°
Putting values in equation (4) ⇒ ∠ B =2*(2*12) = 48°
Also, <u>∠B=∠A=48°</u>
Now,in Δ ABC
∠C+∠B+∠A= 180°
⇒48°+48°+∠C= 180°
<u><em>⇒∠C=84°</em></u>
