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love history [14]
3 years ago
9

If p-1 is a factor of p^4 +p^2 +p-k, the value of k is what?

Mathematics
1 answer:
Shalnov [3]3 years ago
6 0

Answer:

k = 3

Step-by-step explanation:

Since p - 1 is a factor then p(1) = 0

p(x) = p^{4} + p² + p - k, thus

p(1) = 1^{4} + 1² + 1 - k = 0, that is

1 + 1 + 1 - k = 0

3 - k = 0 ⇒ k = 3

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A plot of land doubles in size by adding x meters to the length and x meters to the width of the land. If the original plot had
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Given:
plot of land doubles in size.
original plot area 200 by 300 meters

Area = 200m * 300m
A = 60,000 m²  original plot area

60,000m
² x 2 = 120,000 m²

(200m + x)(300m + x) = 120,000 m²

60,000m² + 200m*x + 300m * x + x² = 120,000 m²

x² + 500x + 60,000 = 120,000
x² + 500x + 60,000 - 120,000 = 0
x² + 500x - 60,000 = 0

x = -b <u>+</u> (√b² - 4ac)/2a 

a = 1 ; b = 500 ; c = -60,000

x = -500 + (√500² - 4(1)(-60,000)) / 2(1)
x = (-500 + (√250,000 + 240,000)) / 2 
x = (-500 + 700)/ 2
x = 200 / 2
x = 100 meters

(200 + x)(300 + x) = 120,000
(200 + 100)(300 + 100) = 120,000
300 * 400 = 120,000
120,000 = 120,000

8 0
3 years ago
Which of the following is an arithmetic sequence
Ludmilka [50]

Answer:

A sequence that has a contant addition/subtraction to get to the next term

for example:

-3, 0, 3, 6, ...

to get to the next term, we'll need to add 3 each time

Step-by-step explanation:

3 0
3 years ago
Dave runs a 10km race and beats his best time by 5%.
jekas [21]

Answer:

57 minutes

Step-by-step explanation:

Simply what is %5 of 60.

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7 0
3 years ago
I made a fort for my pet porcupine by connecting two boxes. the first box is 10 meters long, 7 meters wide, and 5 meters high. t
Lerok [7]

First, let's find the volume of the two boxes.

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V= \blue{350} \text{ cubic meters}V=350 cubic metersV, equals, start color blue, 350, end color blue, space, c, u, b, i, c, space, m, e, t, e, r, s

V = lwhV=lwhV, equals, l, w, h

V=4\times10\times8V=4×10×8V, equals, 4, times, 10, times, 8

V= \pink{320} \text{ cubic meters}V=320 cubic metersV, equals, start color pink, 320, end color pink, space, c, u, b, i, c, space, m, e, t, e, r, s

Hint #22 / 3

Since my porcupine can play in both boxes, we need to add the volumes of the two boxes.

\blue{350}+\pink{320}=\green{670}350+320=670start color blue, 350, end color blue, plus, start color pink, 320, end color pink, equals, start color green, 670, end color green

Hint #33 / 3

My porcupine has \green{670}670start color green, 670, end color green cubic meters of space to play in his fort.  

670 is your answer i hoped this help please rate me thanks :)

6 0
3 years ago
Read 2 more answers
How do i solve -18-6k=6(1+3k)
olga nikolaevna [1]
-1 is the answer to your question
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3 years ago
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