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Maslowich
2 years ago
9

The value of k such that (x-5) divides the polynomial p(x)= x^3-6x^2+kx+30 exactly,is

Mathematics
1 answer:
mixas84 [53]2 years ago
3 0

Answer:

k = - 1

Step-by-step explanation:

If (x - 5) is a factor of p(x) then p(5) = 0

p(5) = 5³ - 6(5)² + 5k + 30 = 0 , that is

125 - 150 + 5k + 30 = 0

5 + 5k = 0 ( subtract 5 from both sides )

5k = - 5 ( divide both sides by 5 )

k = - 1

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6 0
3 years ago
The question is:
saul85 [17]
f(x) = \sqrt{x+1} \\ y = \sqrt{x+1} \ or \ y^2 = x+1 \ or \ x = y^2 - 1 \\ Therefore, \ f^{-1}(x)=x^2 - 1

(fof^{-1})(a) = f(f^{-1}(a))=f(a^2-1) \\ =\sqrt{a^2-1+1}=\sqrt{a^2}=a \\  \\ (f^{-1}of)(a)=f^{-1}(f(a))=f^{-1}(\sqrt{a+1})= \\ (\sqrt{a+1})^2-1 = a+1-1 = a

Therefore, (fof^{-1})(a) = (f^{-1}of)(a) = a

8 0
3 years ago
Marcus is traveling from Rome to Capua on the Via Appia (a 132 mile journey). His horse and cart travels at 8 mph. How long will
nalin [4]

Answer: 16.5 hours

Step-by-step explanation:

distance=rate*time

132=8*x

Divide by 8 on both sides

x=16.5

6 0
3 years ago
Find the third side in simplest radical form:
Mkey [24]

Answer: 53

Step-by-step explanation:

They are both right legs. Use a^2+b^2=c^2.

A= 28^2 B=45^2

A= 784 B= 2025. 2025+ 784= 2809 (radical 2809) To simplified is 53

5 0
3 years ago
Find the value of X that will make A||B. Show work please, I need to figure out how to solve it.
Vanyuwa [196]

Answer:

x = 12

Step-by-step explanation:

In order for these lines to be parallel:

5x = 4x + 12

x = 12

Hope this helps

7 0
2 years ago
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