The remainder theorem says that dividing a polynomial <em>f(x)</em> by a 1st-degree polynomial <em>g(x)</em> = <em>x</em> - <em>c</em> leaves a remainder of exactly <em>f(c)</em>.
(a) With <em>f(x)</em> = <em>px</em> ³ + 4<em>x</em> - 10 and <em>d(x)</em> = <em>x</em> + 3, we have a remainder of 5, so
<em>f</em> (-3) = <em>p</em> (-3)³ + 4(-3) - 10 = 5
Solve for <em>p</em> :
-27<em>p</em> - 12 - 10 = 5
-27<em>p</em> = 27
<em>p</em> = -1
(b) With <em>f(x)</em> = <em>x</em> + 3<em>x</em> ² - <em>px</em> + 4 and <em>d(x)</em> = <em>x</em> - 2, we have remainder 8, so
<em>f</em> (2) = 2 + 3(2)² - 2<em>p</em> + 4 = 8
-2<em>p</em> = -10
<em>p</em> = 5
(you should make sure that <em>f(x)</em> was written correctly, it's a bit odd that there are two <em>x</em> terms)
(c) <em>f(x)</em> = 2<em>x</em> ³ - 4<em>x</em> ² + 6<em>x</em> - <em>p</em>, <em>d(x)</em> = <em>x</em> - 2, <em>R</em> = <em>f</em> (2) = 18
<em>f</em> (2) = 2(2)³ - 4(2)² + 6(2) - <em>p</em> = 18
12 - <em>p</em> = 18
<em>p</em> = -6
The others are done in the same fashion. You would find
(d) <em>p</em> = 14
(e) <em>p</em> = -4359
(f) <em>p</em> = 10
(g) <em>p</em> = -13/2 … … assuming you meant <em>f(x)</em> = <em>x</em> ⁴ + <em>x</em> ³ + <em>px</em> ² + <em>x</em> + 20
Step-by-step explanation:
In the picture, That's a correct answer.
Answer:
D
Step-by-step explanation:
8x60=480
480÷3=160
160x4=640
640 is 10 Minutes 40 Seconds
6 Miles is 24 Laps
640x6=3840
3840÷60=64
The Answer Will be 64 Minutes.
<em>Answer-</em> <u>√
26</u>
<em>Explanation:</em>
<u>Use the distance formula:</u>
√
(
y
2
−
y
1
)² + (
x
2
−
x
1
)
²
<u>Plug in your values: </u>
√
(
−
5− (
−
4
) )² + (
2
− (
−
3
)
)²
<u>Simplify: </u>
√
(
−
1
)² + (
5
)²
<u>Simplify:</u>
√
1
+
25
<u>Simplify:</u>
√
26
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<em>Anyways bye!</em>
Answer:
The probability that a randomly selected x-value lies between μ − 2σ and μ is the shaded area under the normal curve shown. P(μ − 2σ ≤ x ≤ μ) = 0.135 + 0.34 = 0.475
Step-by-step explanation:
