Answer: x = 75
Step-by-step explanation: The first thing to note is that what we have here is a quadrilateral. In other words, all the internal angles sum up to 360°. Also take note that the figure is a parallelogram, which means two sides are parallel to each other. Line AD is parallel to BC, and line DC is parallel to AB. That makes angle D equal to angle B (alternate angles), and angle A equals Angle C.
If the sum of the interior angles of a quadrilateral equals 360, then
x + (x + 30) + x + (x + 30) = 360
x + x + 30 + x + x + 30 = 360
Collecting like terms, we have
x + x + x + x + 30 + 30 = 360
4x + 60 = 360
Subtract 60 from both sides of the equation
4x = 300
Divide both sides of the equation by 4
x = 75.
Statement Reason
m∠EGF = 60° & m∠AGF = 90° Given
∠EGF + ∠AGF + ∠AGB = 180° Definition of supplementary angles
60° + 90° + ∠AGB = 180° Substitution
150° + ∠AGB = 180° Add the the similar values
∠AGB = 180° - 150° Subtraction property of equality
∠AGB = 30° Answer
You are free to arrange any of the reasons (and statements) as you wish.
I just want to give you the main idea.
Hope this helps.
Answer:
<h3>
f(x) = 6(x - 2)² + 3</h3>
Step-by-step explanation:
f(x) = a(x - h)² + k - vertex form of the equation of the parabola with vertex (h, k)
"the parabola opens upward" means: a>0
"the parabola has x = 2 as an axis of symmetry" means: h = 2
so f(x) = a(x - 2)² + k
"the parabola contains the point (1, 9)" means:
9 = a(1 - 2)² + k
9 = a(-1)² + k
9 = a + k
k = 9 - a
"the parabola contains the point (4, 27)" means:
27 = a(4 - 2)² + k
so:
27 = a(2)² + 9 - a
27 = 4a + 9 - a
3a = 18
a = 6
and k = 9 - 6 = 3
Therefore the vertex form for this parabola is:
<u> f(x) = 6(x - 2)² + 3</u>
Highest average would be if you got a 100 on the 4th test....add them all up and divide by 4.
330/4 = 82.5 or 83 would be the highest grade