Answer:
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f(x) = x^2+3x-10
f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5
f(x+5) = (x^2+10x+25)+3(x+5)-10
f(x+5) = x^2+10x+25+3x+15-10
f(x+5) = x^2+13x+30
Compare this with x^2+kx+30 and we see that k = 13
Factor and solve the equation below
x^2+13x+30 = 0
(x+10)(x+3) = 0
x+10 = 0 or x+3 = 0
x = -10 or x = -3
The smallest zero is x = -10 as its the left-most value on a number line.
Answer:
h= -144
Step-by-step explanation:
Answer:
z = 8.544[cos(20.6) + isin(20.6)}
Step-by-step explanation:
Given
8 + 3i
Required
Rewrite in trigonometric form.
The trigonometric form of a complex equation is
z = r[cosθ + isinθ]
Let a = 3 and b = 8
Where
r is calculated by
r² = b² + a²
And
θ is calculated by
θ = arctan(a/b)
Substituting 3 for a and 8 for b
r² = a² + b² becomes
r² = 3² + 8²
r² = 9 + 64
r² = 73
√r² = √73
r = √73
r = 8.544
Calculating θ
θ = arctan(a/b) becomes
θ = arctan(3/8)
θ = arctan(0.375)
θ = 20.556°
θ = 20.6 --- Approximated
Hence, z = r[cosθ + isinθ] becomes
z = 8.544[cos(20.6) + isin(20.6)}
Answer:
AB = 5
Step-by-step explanation:
Since this is an isosceles triangle, you can conclude that there will be two sides of equal length and two angles of equal measurement.
The circular marks on Angle C and Angle A represent congruence between the two angles (The are the same measurement.). From this, you can also conclude that their opposite sides are congruent as well.
From this information you can set up your equation:
AB = BC
Substitute in the corresponding values to solve for x:
3x - 4 = 5x - 10
-2x = -6
x = 3
Substitute x into 3x - 4 to find the length of AB:
AB = 3(3) - 4
AB = 9 - 4
AB = 5
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