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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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Sara sells fruit juices. She made 400 cups of fruit juice. By the end of the day, 34th of the quantity was sold. How many pints
vredina [299]

To answer the question, we need to convert cups to pints, now here is a way to remember the gallon, quarts, to pints, and to cups

In the Kingdom of Gallons (Write a big G on your paper)

Inside the G write 4 Qs

There were four Queens

Inside the Qs write 2 ps

Each Queen had to princess

In each princess write 2 Cs

And each princess has two Cats

Now we know that there is 2 Cups in each Pints so

since she sold 34 cups of juice in cups then we divide 34 by 2 to get

17 PINTS

7 0
2 years ago
Read 2 more answers
A rectangle has a width that is 50% of its length. The length of the rectangle is 12 inches. What is the area of the rectangle.
Stells [14]

Answer:

72 inches²

Step-by-step explanation:

Let w be equal to the width of the rectangle.

Let l be equal to the length of the rectangle.

\frac{1}{2}l=w

Plug in 12 inches as the length

\frac{1}{2}(12)=w\\6=w

Therefore, the width of the rectangle is 6 inches.

A=lw

Plug in 12 inches as the length and 6 inches as the width.

A=(12)(6)\\A=72

Therefore, the area of the rectangle is 72 inches².

I hope this helps!

7 0
3 years ago
HELP HELP HELP PLEASE
timama [110]
The answer is k=8 (4,6/8,7/12,8)
5 0
3 years ago
Write a function in terms of t that represents the situation.
Nina [5.8K]
S(t) = S0·(1 + rate)t<span>S(t) = salary at year t
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6 0
3 years ago
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Write an equation parallel to y=3x−1 and goes through the point (-2, -13)
solong [7]

Answer:

y=3x-7

Step-by-step explanation:

we use the equation of the line:

y=mx+b

if the line is parallel, then the slope(m) of the line stays the same:

y=3x+b

we then substitute the ordered pair into the equation and solve for b:

-13 = 3(-2)+b

-13 = -6+b

-13+6 = b

-7 = b

now we substitute the b value into the original equation and the answer:

y=3x-7

Hope this helps :)

4 0
3 years ago
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