The given triangle is isosceles, so the two remaining angles in the triangle both have measure <em>xº</em>. The interior angles of any triangle sum to 180º, so that
58º + <em>xº</em> + <em>xº</em> = 180º
58 + 2<em>x</em> = 180
2<em>x</em> = 122
<em>x</em> = 61
Angles <em>y</em> and <em>z</em> are supplementary to angle <em>x</em>, so that
<em>xº</em> + <em>yº</em> = 180º
and
<em>xº</em> + <em>zº</em> = 180º
and consequently, <em>y</em> = <em>z</em>. In particular, we get
<em>y</em> = 180 - 61
<em>y</em> = 119
and so
<em>z</em> = 119
Answer:
A, or 8
Step-by-step explanation:
the total angle is 102, so we can subtract 54 from 102 to get 6x, then divide by 6.
102 -54 = 48/6 =8
The answer is <span>5, 4, 2
</span>
Among all choices we have 5, so
x = 5
x - 5 = 0
Let's divide the expression by (x - 5) using the long division:
x³ - 11x² + 38x - 40
(x - 5) * x² = x³ - 5x² Subtract
____________________________
-6x² + 38x - 40
(x - 5) * (-6x) = -6x² + 30x Subtract
____________________________
8x - 40
(x - 5) * 8 = 8x - 40 Sutract
____________________________
0
Thus: x³ - 11x² + 38x - 40 = (x - 5)(x² - 6x + 8)
Now, let's simplify x² - 6x + 8.
x² - 6x + 8 = x² - 2x - 4x + 8 =
= x² - 2*x - (4*x - 4*2) =
= x(x - 2) - 4(x - 2) =
= (x - 4)(x - 2)
Hence:
x³ - 11x² + 38x - 40 = (x - 5)(x - 4)(x - 2)
To calculate zero:
x³ - 11x² + 38x - 40 = 0
(x - 5)(x - 4)(x - 2) = 0
x - 5 = 0 or x - 4 = 0 or x - 2 = 0
x = 5 or x = 4 or x = 2
Answer:
0.375 pages per minute.
Step-by-step explanation:
