Answer:
If gas costs $3.75 per gallon and Berto has $12, then he can purchase 12/3.75 gallons. This is approximately 3.2 gallons. So the coordinate on this line would be (3.2, 12).
Actually... It's from web
<span>______________________________________________________</span>
7y-1=-1+9(y-9)
Add 1 on both sides.
7y=9(y-9)
Distribute.
7y=9y-81
Subtract 7y and add 81 on both sides.
2y=81
y=40.5
______________________________________________________
<span>4c+3=-12+c-1
</span>Subtract 3 on both sides.
4c=-12-1-3+c
Subtract c on both sides.
3c=-16
c=-16/3
______________________________________________________
<span>-(k+1)-10=-5k+3
</span>Add 10 on both sides.
-(k+1)=-5k+13
Distribute.
-k-1=-5k+13
Add 1 and add 5k on both sides.
4k=14
k=4/14
______________________________________________________
-w-10=-9-2(w-8)
Distribute.
-w-10=-9-2w+16
Simplify.
-w-10=-2w+7
Add 2w and 10 on both sides.
w=17
______________________________________________________
-2(n-3)-5=-5n+1
Distribute.
-2n+6-5=-5n+1
Simplify.
-2n+1=-5n+1
Add 5n and subtract 1 on both sides.
3n=0
n=0
______________________________________________________
To make sure you got the right answer, you can check your work by plugging the result back into the question and seeing if both sides become equal. If both sides are equal, then the result is correct.
______________________________________________________
The quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively
<h3>How to determine the quotient and remainder when the first polynomial is divided by the second?</h3>
The polynomials are given as:
-4w^3 + 5w^2 - 8, w - 3
Set the divisor to 0.
So, we have
w - 3 = 0
Add 3 to both sides
w = 3
Substitute w = 3 in -4w^3 + 5w^2 - 8 to determine the remainder
-4(3)^3 + 5(3)^2 - 8
Evaluate the expression
-71
This means that the remainder when -4w^3 + 5w^2 - 8 is divided by w - 3 is -71
The quotient (Q) is calculated as follows:
Q = [-4w^3 + 5w^2 - 8]/[w - 3]
The numerator can be expressed as follows:
Numerator = -4w^3 + 5w^2 - 8
Subtract the remainder.
So, we have:
Numerator = -4w^3 + 5w^2 - 8 + 71
This gives
Numerator = -4w^3 + 5w^2 + 61
So, the quotient becomes
Q = [-4w^3 + 5w^2 + 61]/[w - 3]
Expand
Q = [(w - 3)(-4w^2 - 7w - 21)]/[w - 3]
Evaluate
Q = -4w^2 - 7w - 21
Hence, the quotient and remainder when the first polynomial is divided by the second are -4w^2 - 7w - 21 and -71 respectively
Read more about polynomials at:
brainly.com/question/4142886
#SPJ1
Number of books each of them have:
Jaime: x
Grant: x - 6
Ky: 3 (x - 6)
There are 176 books in total, so we can write it down as:
176 = x + x - 6 + 3 (x - 6)
176 = x + x - 6 + 3 * x + 3 * (-6)
176 = x + x - 6 + 3x - 18
176 = 2x - 6 + 3x - 18
176 = 5x - 24 / + 24 (both sides)
5x = 200 / ÷ 5 (both sides)
x = 40
Doublecheck:
Jamie: 40
Grant: 40 - 6 = 34
Ky: 3 (40 - 6) = 3 * 34 = 102
102 + 34 + 40 = 176, so it's correct :)
Answer:
Column A Column B
1. x² + 6x + 8 x-3,x+2
2. x³ - 7x + 6 x+1, x+2, x+3
3. x³ - 2x² - 5x + 6 x-1, x+2, x-3
Step-by-step explanation:
Column A Column B
1. x² + 6x + 8 x-3,x+2
2. x³ - 7x + 6 x+1, x+2, x+3
3. x³ - 2x² - 5x + 6 x-1, x+2, x-3
Using Factor theorem we put values of x = ±1,±2,±3 in each of the polynomials unless we get a zero.
1. x² + 6x + 8
= 1+6(1) +8= 15
1. x² + 6x + 8
4+ 12+8 = 24
1. x² + 6x + 8
(-1)² + 6(-1)+ 8
= 1-6+8= 3
1. x² + 6x + 8
(-2)² + 6(-2)+ 8
= 4-12+8= 0
1. x² + 6x + 8
(3)²+ 6(3) +8
= 9+18+8 ≠ 0
1. x² + 6x + 8
(-3)²+ 6(-3) +8
= 9-18+8 =-1
For this polynomial we have x+2= 0 or x=-2, x-3= 0 , x=3
2. x³ - 7x + 6
1-7+6= 0
2. x³ - 7x + 6
(-1)³-7(-1) +6
= 13-1≠0
2. x³ - 7x + 6
(2)³-7(2) +6
= 8-14+6= 0
2. x³ - 7x + 6
(-2)³-7(-2) +6
= -8 +14+6
2. x³ - 7x + 6
(-3)³-7(-3) +6
= -27+21+6 = 0
For this polynomial we have x+1= 0 , x+2 = 0 and x+3= 0, or x=-1,-2,-3
3. x³ - 2x² - 5x + 6
(1)³-2(1)²-5(1)+6
= 0
3. x³ - 2x² - 5x + 6
(-1)³-2(-1)²-5(-1)+6
= -1 -2 +5+6
=8
3. x³ - 2x² - 5x + 6
(2)³-2(2)²-5(2)+6
= 8-8-10+6
=-4
3. x³ - 2x² - 5x + 6
(-2)³-2(-2)²-5(-2)+6
= -8-8+10+6
=0
3. x³ - 2x² - 5x + 6
(3)³-2(3)²-5(3)+6
= 27-18-15+6
=0
3. x³ - 2x² - 5x + 6
(-3)³-2(-3)²-5(-3)+6
= -27-18+15+6
=-14
For this polynomial we have x-1= 0 ,x+2=0, x-3= 0or x=1,-2,3