It is 50. the angles on the side of ABC are the same as on ACD, where they are labelled. When you add the two angles on the other side together, the answer is 50 degrees.
Given three points
P1(-2,8)
P2(0,-4)
P3(4,68)
We need the quadratic equation that passes through all three points.
Solution:
We first assume the final equation to be
f(x)=ax^2+bx+c .............................(0)
Observations:
1. Points are not symmetric, so cannot find vertex visually.
2. Using the point (0,-4) we substitute x=0 into f(x) to get
f(0)=0+0+c=-4, hence c=-4.
3. We will use the two other points (P1 & P3) to set up a system of two equations to find a and b.
f(-2)=a(-2)^2+b(-2)-4=8 => 4a-2b-4=8.................(1)
f(4)=a(4^2)+b(4)-4=68 => 16a+4b-4=68.............(2)
4. Solve system
2(1)+(2) => 24a+0b-12=84 => 24a=96 => a=96/24 => a=4 ......(3)
substitute (3) in (2) => 16(4)+4b-4=68 => b=8/4 => b=2 ..........(4)
5. Put values c=-4, a=4, b=2 into equation (0) to get
f(x)=4x^2+2x-4
Check:
f(-2)=4((-2)^2)+2(-2)-4=16-4-4=8
f(0)=0+0-4 = -4
f(4)=4(4^2)+2(4)-4=64+8-4=68
So all consistent, => solution ok.
Answer:
11 cakes
Step-by-step explanation:
so you know each cup can make 3 cakes so multiply that by 3 then add 2(from the 2/3 cups)
Answer:
3.
Step-by-step explanation:
sin 32 / (1 + tan 45) * 6 / cos 58
= sin 32 / 2 * 6 / cos 58 ( since tan 45 = 1)
= 3 sin 32 / cos 58
Note sine 32 = cos (90 - 32) = cos 58, so we have:
= 3 sin 32 / sin 32
= 3.
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