f(g(x) ) = -2(3x²+5x+14) +10
= -3x²-10x- 28+10
= -3x²-10x -18
Answer:
You will want to compare the width to the length, or 42 mm/ 74mm ...the units cancel, which is what you want for a ratio...and you usually want to simplify your ratio
Hope that helps
Answer: x = 50
Concept:
Here, we need to know the idea of alternative interior angles and the angle sum theorem.
<u>Alternative interior angles</u> are angles that are formed inside the two parallel lines, and the values are equal.
The <u>angle sum theorem</u> implies that the sum of interior angles of a triangle is 180°
If you are still confused, please refer to the attachment below or let me know.
Step-by-step explanation:
<u>Given information:</u>
AC ║ DE
∠ABC = 85°
∠A = 135°
<u>Find the value of ∠BAC</u>
∠A + ∠BAC = 180° (Supplementary angle)
(135°) + ∠BAC = 180°
∠BAC = 45°
<u>Find the value of ∠BCA</u>
∠ABC + ∠BAC + ∠BCA = 180° (Angle sum theorem)
(85°) + (45°) + ∠BCA = 180°
∠BCA = 50°
<u>Find the value of x (∠EBC)</u>
∠EBC ≅ ∠BCA (Alternative interior angles)
Since, ∠BCA = 50°
Therefore, ∠EBC = 50°

Hope this helps!! :)
Please let me know if you have any questions
Given the coordinates of two points, P1 and P2, the distance formula between these two points is deduced.
d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
To find the area of the figure we must first find the area of the rectangle and add the area of the parallelogram.
rectangle area
A = (L) * (w)
L = root ((- 6-2) ^ 2 + (- 1-1) ^ 2) = 8.25
w = root ((- 6 - (- 5)) ^ 2 + (- 1 - (- 5)) ^ 2) = 4.12
A = (8.25) * (4.12) = 33.99
Parallelogram area
A = (b) * (h)
b = root ((3-3) ^ 2 + (3 - (- 3)) ^ 2) = 6
h = root ((3-2) ^ 2 + (3-3) ^ 2) = 1
A = (6) * (1) = 6
The total area is then
Atotal = 33.99 + 6 = 39.99 units ^ 2
Answer
the area of this figure is 39.99 units ^ 2
6922.24 is the balance you have after simple interest and the amount of interest received is 1722.24