To solve this problem you must apply a theorem called: Intersecting secant theorem. The proccedure is shown below:
1) For the figure shown on the left:
(5)(x+5)=(6)(4+6)
5x+25=60
5x=60-25
x=35/5
x=7
2) For the figure shown on the right:
(3)(3+5)=(4)(x+4)
24=4x+16
24-16=4x
8=4x
8/4=x
x=2
The answer is A. a=(-1) b=(7)
Problem 1) The triangles are similar because of the AA (angle angle) Similarity Theorem. The first A is the pair of congruent 39 degree angles. The second pair is unmarked, but look at where the triangles meet. They form a pair of vertical angles which are congruent. So we have two pairs of congruent angles allowing us to use the AA Similarity Theorem.
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Problem 2) We can use the SAS (Side Angle Side) Similarity Theorem to prove that these two triangles are similar. The angles are congruent. They are both 29 degrees. So that checks off the "A" portion of SAS. Then notice how the bottom sides are 32 and 64 for the small and large triangle respectively. They form the ratio 32/64 = 1/2, ie the smaller triangle's side is 1/2 as long as the longer counter part. Similarly, 8/16 = 1/2 as well. The ratio is constant at 1/2. This allows us to use the other "S" portions of SAS.
Answer:
The correct two options are:
The maximum value of the range is 4.
The range of g(x) is {y| –1 < y ≤ 4}.
Step-by-step explanation:
The missing diagram is attached in the image below:
It is pertinent to understand that the domain is the set of all possible mathematical points where a given function is defined. In the diagram attached below, the domain relates to all possible values of x.
The range relates to all possible values of y.
From the graphical diagram;
The domain is (-4 ≤ x ≤ -1 and 0 ≤ x < 3); &
The range is -1 < y ≤ 4.
We could see from the graph as well that, the maximum value of the range extends from -1 to 4 which indicates that the largest possible value is 4.
