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adoni [48]
4 years ago
13

 Find k if x^3+6x^2+kx+12 is divisible by (x+4)

Mathematics
1 answer:
konstantin123 [22]4 years ago
8 0
If a polynomial p(x) is divisible by q(x), the roots of q(x) are roots of p(x), too.

In this question, p(x)=x³+6x²+kx+12 and q(x)=x+4. Clearly, the root of q(x) is -4. By what was written initially, -4 is a root of p(x). So:
p(-4)=0\\\\
(-4)^3+6(-4)^2+k(-4)+12=0\\\\
-64+6\cdot16-4k+12=0\\\\
-64+96-4k+12=0\\\\
4k=44\\\\
k=\dfrac{44}{4}\\\\
\boxed{k=11}
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If L is parallel to M, find the values of x, y, and all 3 angles.
lesya [120]

Answer:

8x - 14 = 5x + 34 (alternate exterior angles)

8x - 5x = 34 + 14

3x = 48

x = 48/3

x = 16

5y + 16 + 8x - 14 = 180 (linear pair)

5y + 16 + 8(16) - 14 = 180

5y + 16 + 128 - 14 = 180

5y + 130 = 180

5y = 180 - 130

5y = 50

y = 50/5

y = 10

∠ (8x - 14) = 114   [(8 × 16 -14)=114]

∠ (5x + 34) = 114  [(5 × 16 +34)=114]

∠ (5y + 16) = 66   [(5 × 10 +16)=66]

hope this helps you!

4 0
3 years ago
The ratio of passenger cars to cargo cars in
gayaneshka [121]

Answer:

126

Step-by-step explanation:

the number of cargo cars is represented by the 35 part of the ratio , then

105 ÷ 35 = 3 ← value of 1 part of the ratio , then

passenger cars = 7 × 3 = 21

total cars = 105 + 21 = 126

4 0
2 years ago
What is the slope of the line shown?? Please help i been stuck on this all day yesterday and now today..
Talja [164]
I hope this helps.if you have any questions regarding what I did you can ask

4 0
4 years ago
Veterinary researchers at a major university veterinary hospital calculated a 99% confidence interval for the average age of hor
mestny [16]

Answer:

c. we are 99% confident that the true mean age of horses with laminitis is between 6.3 and 7.4 years old.

Step-by-step explanation:

Given that veterinary researchers at a major university veterinary hospital calculated a 99% confidence interval for the average age of horses admitted for laminitis, a foot disease that leaves the horse severely lame, as 6.3 to 7.4 years.

i.e. if X is the age of horses admitted for laminitis then the sample mean i.e. x bar follows a distribution with 99% confidence interval as

(6.3,7.4)

The interpretation of 99% confidence interval is the for sample of large size drawn at random from population we can be 99% confident that the sample mean will fall within this interval.

So the correct option is

c. we are 99% confident that the true mean age of horses with laminitis is between 6.3 and 7.4 years old.

8 0
3 years ago
This is worth 20 points. If you do both questions you get brainlest!
Ugo [173]
5.78♡︎♡︎ and 2.4♡︎♡︎ it’s possible i may be wrong but i’m pretty sure i’m right!✨ ♡︎Brainliest please!♡︎ Good luck with your test or homework hope this helped♡︎♡︎
6 0
3 years ago
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