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elena-s [515]
2 years ago
11

Given that the expression x³_ ax² + bx+c leaves the same remainder when divided by x + 1 or x-2, find 'a' in terms of 'b'.​

Mathematics
1 answer:
goblinko [34]2 years ago
5 0

Answer:

Hi,

a=b+3

Step-by-step explanation:

\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&c-a-b-1\\\end{array}

\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=2&&2&4-2a&2b+8-4a\\---&---&---&---&---\\&1&2-a&b+4-2a&c+2b+8-4a\\\end{array}

Thus:

c+2b+8-4a=c-a-b-1

3b-3a=-9

<u>a=b+3</u>

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For this Q:

mean=31
st.dev.=0.8
x=32

Calculate z-score:
z=(x-m)/s = (32-31)/0.8=1.25

This z-score value corresponding to the probability of 0.8944

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6 0
3 years ago
Apr 23, 8:46:54 AM<br> What is the missing term?
kipiarov [429]
Answer: -10x
Explanation: Multiply -2 by 5x
7 0
3 years ago
Which of the following ordered pairs
ozzi

The ordered pairs  that make this equation true is (4, 10)

A linear equation is given by:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

Given the linear equation: y = 10x - 30:

At (1, -12): y = 10(1) - 30 = -20 ≠ -12

At (8, 1): y = 10(8) - 30 = 50 ≠ 1

At (4, 10): y = 10(4) - 30 = 10

At (6, 20): y = 10(6) - 30 = 30 ≠ 20

The ordered pairs  that make this equation true is (4, 10)

Find out more at: brainly.com/question/13911928

5 0
3 years ago
PLS HELP! URGENT!!!! A circular flower bed is 20 m in diameter and has a circular sidewalk around it that is 3 m wide. Find the
krok68 [10]

Answer: Area of sidewalk is 217m²

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle

π is a constant whose value is 3.14

A circular flower bed is 20 meters in diameter.

radius = diameter/2 = 20/2 = 10 meters

Area of the flower bed = 3.14 × 10²

= 314m²

The circular flower bed has a circular sidewalk around it that is 3 meters wide. This means that the total diameter would be

3 + 20 + 3 = 26m

Radius = 26!2 = 13m

Total area = 3.14 × 13² = 530.66m²

Therefore, area of the sidewalk is

530.66 - 314 = 216.66

The area of sidewalk is 217m² to the nearest whole number

6 0
3 years ago
Can you help with this please?​
insens350 [35]

Answer:

A

Step-by-step explanation:

the answer is A. if you notice the y-intercept, it its at -5

A is the only answer choice that gives -5 as the y-intercept

another way to make sure that A is the right answer is to calculate the slope

when you increase 3 units UP (y), you increase 5 units to the RIGHT (x)

since slope is y/x, it should be 3/5 which is also in A

another way to check A is to plug in points

hope this helps!

6 0
3 years ago
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