3/5 * 230 = 138 votes for Nyemi
3/10 * 230 = 69 votes for Luke
1/10 * 230 = 23 votes for Natalie
***************** DOUBLE-CHECK ****************
138 + 69 + 23 = 230 Correct!!
Answer:
∠ B = 126°
Step-by-step explanation:
Since the lines are parallel, then
∠ A = ∠ B ( alternate angles ), thus
8x + 78 = 2x + 114 ( subtract 2x from both sides )
6x + 78 = 114 ( subtract 78 from both sides )
6x = 36 ( divide both sides by 6 )
x = 6
Thus
∠ B = 2x + 114 = 2(6) + 114 = 12 + 114 = 126°
If
<em>f(x)</em> = <em>ax</em> ³ + <em>bx</em> ² - 5<em>x</em> + 9
then
<em>f '(x)</em> = 3<em>ax </em>² + 2<em>bx</em> - 5
Given that <em>f</em> (-1) = 12 and <em>f</em> '(-1) = 3, we get the system of equations
-<em>a</em> + <em>b</em> + 5 + 9 = 12
3<em>a</em> - 2<em>b</em> - 5 = 3
or
-<em>a</em> + <em>b</em> = -2
3<em>a</em> - 2<em>b</em> = 8
Multiply through the first equation by 2 and add it to the second one to eliminate <em>b</em> and solve for <em>a</em> :
2(-<em>a</em> + <em>b</em>) + (3<em>a</em> - 2<em>b</em>) = 2(-2) + 8
-2<em>a</em> + 2<em>b</em> + 3<em>a</em> - 2<em>b</em> = -4 + 8
<em>a</em> = 4
Substitute this into the first equation above to solve for <em>b</em> :
-4 + <em>b</em> = -2
<em>b</em> = 2
Of course it will recive double
