What expression is equivalent to -3(6x+7)+4(7x+2)
1 answer:
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Answer:
y = 2(x - 2)² + 3 vertex form
y = 2x² - 8x + 11 standard form
Step-by-step explanation:
Vertex form
y = a(x - h)² + k
(h, k) = (2, 3)
y = a(x - 2)² + 3
To find "a" plug in the y-intercept (0, 11)
11 = a(-2)² + 3
11 = 4a + 3
Subtract 3 from both sides
8 = 4a
a = 2
y = 2(x - 2)² + 3
Expand
y = 2(x² - 4x + 4) + 3
y = 2x² - 8x + 11
If we say that side "a" is the shortest (adjacent), side "b" is the second shortest (opposite), and side "c" is the longest (hypotenuse): then angle A would be 30°, angle B would be 60°, and angle C would be 90°
tan B = b/a
or
a tan B = b
they have 4 as the smallest value in all four options, so we know that a=4
4 tan 60° = b
tan 60° = √3
so, 4 tan 60° = 4√3
b=4√3
that leaves two options left, so now we find "c":
c^2 = (a^2) + (b^2)
OR
so a=4, b=4√3, and c=8
Making your answer B
tan B = b/a
or
a tan B = b
they have 4 as the smallest value in all four options, so we know that a=4
4 tan 60° = b
tan 60° = √3
so, 4 tan 60° = 4√3
b=4√3
that leaves two options left, so now we find "c":
c^2 = (a^2) + (b^2)
OR
so a=4, b=4√3, and c=8
Making your answer B