Solomon is 9 years old younger than his brother.His brother is 21.How is brother?
1 answer:
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*see attachment for diagram
Answer:
✔️m<BAC = 72°
✔️m<BCD = 108°
Step-by-step explanation:
Given:
m<ABC = (4x - 16)°
m<ACB = (5x + 7)°
Find the numerical value of m<ABC, m<ACB, m<BAC, and m<BCD.
First we need to determine the value of x.
The ∆ given is an isosceles triangle with two equal sides, therefore, the angles opposite the two equal sides would also be equal.
Therefore:
(4x - 16)° + 2(5x + 7)° = 180° (sum of ∆)
Solve for x
4x - 16 + 10x + 14 = 180
Add like terms
14x - 2 = 180
Add 2 to both sides
14x = 182
Divide both sides by 14
x = 13
Find the measure of each angle by plugging in the value of x where necessary:
✔️m<ABC = (4x - 16)° = 4(13) - 16
m<ABC = 36°
✔️m<ACB = (5x + 7)° = 5(13) + 7
m<ACB = 72°
✔️m<BAC = m<ACB (both are base angles of the isosceles ∆, so they are equal)
Therefore,
m<BAC = 72°
✔️m<BCD = m<ABC + m<ACB (exterior angle theorem of a triangle)
m<BCD = 36 + 72 (Substitution)
m<BCD = 108°
Therefore, the angle measures that are correct are:
✔️m<BAC = 72°
✔️m<BCD = 108°
The statement of Gabriella, “The graph will not have an inverse function.” is incorrect. Option B is correct.
Let us understand about the given graph:
The given graph is a graph of a cube root function.
So, the statement of Noelle, “The graph represents the function ." is correct.
So, option A is not correct.
The inverse of a cube root function is a cubic function.
So, the statement of Gabriella, “The graph will not have an inverse function.” is incorrect.
So, option B is correct.
The domain and range of the cube root function are all real numbers.
So, the statement of Julian, “The domain and range of the function is all real numbers.” is correct.
So, option C is not correct.
From the graph, we can see f(-1) = -1.
So, the statement of Yemen, “The value of f(-1) = -1.” is correct.
So, option D is not correct.
Thus, the statement of Gabriella, “The graph will not have an inverse function.” is incorrect. Option B is correct.
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