Answer:
a. 74°
Step-by-step explanation:
Angle BCD and angle ACB are supplementary because they form a straight line. This means they add up to 180. We can write an equation to model the situation:
m<BCD + m<ACB = 180
106 + m<ACB = 180
m<ACB = 74
Since we are given two sides of the triangle are congruent, the triangle is isosceles. The base angles of an isosceles triangle are congruent, so we can say:
m<ACB = m<A
This means m<A is equal to 74°
It would only take 1 second to reach maximum height.
<span><span>h<span>(1)</span></span>=<span><span>−<span>16<span>(<span>1^2</span>)</span></span></span>+<span><span>(570)</span><span>(1) after simplification, h would be 554.
If you kept increasing t, h would get smaller.
</span></span></span></span>
X = plan A and y = plan B
7x + 9y = 720
5x + 3y = 360.....multiply by -3
---------------
7x + 9y = 720
-15x - 9y = -1080 (result of multiplying by -3)
---------------add
-8x = - 360
x = -360/-8
x = 45 minutes <== plan A
5x + 3y = 360
5(45) + 3y = 360
225 + 3y = 360
3y = 360 - 225
3y = 135
y = 135/3
y = 45 minutes <== plan B
so both plans last 45 minutes <==
Answer:
Step-by-step explanation:
By adjacent interior angles theorem,
If a transversal line 'r' intersects two parallel lines 'm' and 'n' then the consecutive interior angles are supplementary.
a° + (3x - 18)° = 180°
a° = 180° - (3x - 18)°
By vertical angles theorem,
If two straight lines intersect each other at a point, opposite angles formed are equal in measure.
180° - (3x - 18)° = (5x - 10)°
(5x - 10) + (3x - 18) = 180
(5x + 3x) - (10 + 18) = 180
8x - 28 = 180
8x = 180 + 28
8x = 208
x = 26
Answer:
0
Step-by-step explanation:
This equation is in "vertex form," meaning that you can identify the vertex and other features of the graph from the equation.
y = a(x -h)² +k . . . . . the vertex is (h, k); the vertical scale factor is "a"
Comparing to your equation, you see ...
a = -1/2, h = 3, k = -1
The vertex is (h, k) = (3, -1). The vertical scale factor is negative.
__
This tells you the graph opens downward (the scale factor is negative), and the vertex (maximum point) is below the x-axis. (It has a negative y-coordinate.)
Because it start below the x-axis and goes down from there, the graph does not intersect the x-axis. There are zero (0) x-intercepts.