Answer:
x = 27
Step-by-step explanation:
This angle is a right angle, meaning 90 degrees, as whenever it's a right angle, there's a small square on the angle which u can see at the bottom left, so:
x + 8 + 2x = 90
3x + 8 = 90
subtract 8 from both sides
3x = 82
divide by 3
x = 27 1/3
Answer:
Step-by-step explanation:
<u><em>The options of the question are</em></u>
2(x − 1)2 = 4
2(x − 1)2 = −4
2(x − 2)2 = 4
2(x − 2)2 = −4
we have
This is a vertical parabola open upward
The vertex represent the minimum value
The quadratic equation in vertex form is
where
a is a coefficient
(h,k) is the vertex
so
Convert the quadratic equation in vertex form
Factor 2 leading coefficient
Complete the squares
Rewrite as perfect squares
The vertex is the point (1,-4)
Move the constant to the right side
x = quarts of 30% acid solution
y = quarts of 65% solution
x + y = 175
Each quart of the 30% solution contributes 0.30x quarts of acid; similarly, each quart of the 65% solution contributes 0.65y quarts of acid. So
0.3x + 0.65y = 0.55*175 = 96.25
That is, the chemist wants 175 quarts of a new mixture with a 55% concentration of acid, which comes out to 95.25 total quarts of acid. The total amounts of acid from either sides of this equation must balance out.
Now solve for x and y:
x + y = 175 ==> y = 175 - x
0.3x + 0.65y = 96.25 ==> 0.3x + 0.65(175 - x) = 96.25
==> 0.3x + 113.75 - 0.65x = 96.25
==> 17.5 = 0.35x
==> x = 50 ==> y = 125
B,13 students prefered math