Answer:
Step-by-step explanation:
<h3><u>Given that:</u></h3>
Exterior angle of L = 5x + 12
M = 3x - 2
N = 50
<h3><u>Statement:</u></h3>
- Exterior angle is equal to the sum of non-adjacent interior angles.
So, the exterior angle that is adjacent to L is equal to the sum of non-adjacent sides (M and N) of the triangle.
Here,
Exterior angle of L = M + N
5x + 12 = 3x - 2 + 50
5x + 12 = 3x + 48
Subtract 12 to both sides
5x = 3x + 48 - 12
5x - 3x = 36
2x = 36
Divide 2 to both sides
x = 18
So,
<h3><u>Measure of angle M:</u></h3>
= 3x - 2
= 3 (18) - 2
= 54 - 2
= 52°
Now,
<h3><u>Measure of angle L:</u></h3>
<u>We know that,</u>
- Sum of all the interior angles of triangle is 180 degrees.
L + M + N = 180°
L + 52 + 50 = 180
L + 102 = 180
Subtract 102 to both sides
L = 180 - 102
L = 78°
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Answer:
D
Step-by-step explanation:
Given
6x² - 2x + 36 = 5x² + 10x ( subtract 5x² + 10x from both sides )
x² - 12x + 36 = 0 ← in standard form
(x - 6)² = 0 ← in factored form, thus
x - 6 = 0 ⇒ x = 6 → D
Answer: Ann = 67 Josh = 60 Claire = 30
Step-by-step explanation: You get the equation 5x+7 = 157. You get the equation because for example, Claire = x then josh = 2x and Ann = 2x + 7. You do all the math and boom! You get the answer :)
Exercise 1:
exponential decay:
The function is given by:
y = A (b) ^ ((1/3) * t)
Where,
A = 600
We look for b:
(480/600) * (100) = 80%
b = 0.8
Substituting:
y = 600 * (0.8) ^ ((1/3) * t)
We check for t = 6
y = 600 * (0.8) ^ ((1/3) * 6)
y = 384
Answer:
exponential decay:
y = 600 * (0.8) ^ ((1/3) * t)
Exercise 2:
linear:
The function is given by:
y = ax + b
Where,
a = -60 / 2 = -30
b = 400
Substituting we have:
y = -30 * x + 400
We check for x = 4
y = -30 * 4 + 400
y = 280
Answer:
linear:
y = -30 * x + 400
Exercise 3:
exponential growth:
The function is given by:
y = A (b) ^ ((1/3) * t)
Where,
A = 512
We look for b:
(768/512) * (100) = 150%
b = 1.5
Substituting:
y = 512 * (1.5) ^ ((1/2) * t)
We check for t = 4
y = 512 * (1.5) ^ ((1/2) * 4)
y = 1152
Answer:
exponential growth:
y = 512 * (1.5) ^ ((1/2) * t)
In which place? Of the value one tens hunderd thousnd
