As I've shown on picture that I attached:
∠ADC=∠ADB+∠BDC⇒134=5x+4+7x-2
12x+2=134
12x=132⇒x=132/12
x=11
Angle BDC measure 7x-2=7*11-2⇒∠BDC=75.
Answer:
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a <em>binomial</em> in the form (x - a), then our remainder will be P(a).
We are dividing:
So, a polynomial by a binomial factor.
Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.
We want our remainder to be 3. So, P(a)=P(-k)=3.
Therefore:
Simplify:
Solve for <em>k</em>. Subtract 3 from both sides:
Factor:
Zero Product Property:
Solve:
So, either of the two expressions:
Will yield 3 as the remainder.
Answer:
-40
Step-by-step explanation:
f(a) = a³ - a² + a - 1
f(-3) = (-3)³ - (-3)² + (-3) - 1
f(-3) = (-27) - (9) + (-3) -1
f(-3) = -27 - 9 -3 - 1
f(-3) = -40
Answer:
x = 61
Step-by-step explanation:
Left hand triangle containing 1 angle of 74
Label the other angle opposite the marked side also as 74
Find the third angle. Call it y.
y + 74 + 74 = 180 Combine like terms
y + 148 = 180 Subtract 148 from both sides.
y = 180 - 148
y = 32
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Now work with the triangle on the right.
label the angle making up the right angle = z
32 + z = 90 These two angles are complementary = 90
32 - 32 + z = 90 - 32 Subtract 32 from both sides
z = 58 Use 58 wherever you see z
x + x + z = 180 Substitute
2x + 58 = 180 Subtract 58 from both sides
2x = 122 Divide by 2
x = 61
