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Natali5045456 [20]
3 years ago
12

If (x+2) is a factor of x^3-6x^2+kx+10, k=

Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
5 0
If a polynomial is divisible by x-a, then a is a root of this polynomial.
Here (x-a) is equal to x+2:

x-a=x+2 \\
-a=2 \\
a=-2

So -2 is a root of the polynomial. That means <span>x³-6x²+kx+10</span>=0 for x=-2. Now substitute -2 for x in the equation and solve for k:

(-2)^3-6 \times (-2)^2+ k \times (-2)+10=0 \\&#10;-8-6 \times 4-2k+10=0 \\&#10;-8-24-2k+10=0 \\&#10;-2k-22=0 \\&#10;-2k=22 \\&#10;\boxed{k=-11}
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Nick made his histogram showing the number of sport caps each of his friends own.
pickupchik [31]

Answer:

A. 7

Step-by-step explanation:

2 or 3 caps = 13

6 or 7 caps = 6

13 - 6 = 7

- hope this helps! -

3 0
2 years ago
A toy baseball and bat cost $1.50 together. The bat costs $1.00 more than the baseball. How much does the baseball cost?
Nataly [62]
$0.50 is the answer. If the bat is $1.00 more than the baseball, you would subtract that from the total cost which is $1.50 so the answer would be $0.50.
4 0
3 years ago
Read 2 more answers
Can I get some help..please?​
krek1111 [17]

Answer:

-2 and 21/50

Step-by-step explanation:

PEMDAS says that paranthases go first, so we solve 2 and 1/5 minus 33/12. 2 and 1/5 simplifies to the improper fraction, 11/5. Then we find a common denominater between 11/5 and 33/12 to get 60. 11/5=132/60, and 33/12=165/60. (132/60)-(165/60)=-33/60. Then we multipl that by 4 and 2/5, which can simplify to the improper fraction, 22/5. (22/5)*(-33/60) is -726/300, and simplifies to -2 and 21/50. Hope this helps!

7 0
3 years ago
6x + 4y=10 12x + y= -29
Olin [163]

Answer: x=-3    y=7.

Step-by-step explanation:

\displaystyle\\\left \{ {{6x+4y=10\ \ \ \ \ (1)} \atop {12x+y=-29\ \ \ \ (2)}} \right.\\  We\  multiply\  both\  sides\  of\  equation\  (1)\  by\  -2:\\\left \{ {{(-2)*6x+(-2)*4y=(-2)*10} \atop {12x+y=-29}} \right. \\\\\left \{ {{-12x-8y=-20} \atop {12x+y=-29}} \right. \\We\  summarize\  equations\  (1)\  and\  (2):\\-7y=-49\\-7*y=-7*7\\Divide\  both\  sides\  of\  the\  equation\  by\  -7:\\y=7.\\We\  substitute\  the\  value\  of\  y\  into \ equation\  (1):\\6x+4*7=10\\6x+28=10\\6x+28-28=10-28\\6x=-18\\6*x=6*(-3)\\Divide\  both\  sides\  of\  the\  equation\  by\  6:\\x=-3.

3 0
2 years ago
Find the number of triangles with c =7, b=11, and B=21 degrees
muminat
<h3>Answer:</h3>

1

<h3>Step-by-step explanation:</h3>

The given angle is opposite the longest given side, so there will be exactly one solution.

_____

The number of solutions may be 0, 1, or 2 when the given angle is opposite the shortest given side.

6 0
3 years ago
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