(x^4 + x^3 + x^2 + x) - (x^4 - x^3 + x^2 -x)
x^4 + x^3 + x^2 + x - x^4 + x^3 - x^2 + x
2x^3 + 2x
Answer: (-4, -1)
This means x = -4 and y = -1 pair up together.
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You're on the right track. You'll replace the 'x' with 3y-1, but you made a typo. I think you meant to write the subtraction symbol instead of the equal sign.
Here's what your steps could look like
-2x + 5y = 3
-2(3y-1) + 5y = 3
-6y + 2 + 5y = 3
-y + 2 = 3
-y = 3-2
-y = 1
y = -1
x = 3y-1
x = 3(-1) - 1
x = -3-1
x = -4
Therefore, (x, y) = (-4, -1) is the solution
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As the steps above show, I replaced each copy of x in the second equation with (3y-1). This is due to x = 3y-1. From there, we isolate y. Once you determine that y = -1, it's plugged into the first equation to find x.
If you were to graph x = 3y-1 and -2x+5y = 3 on the same xy coordinate grid, then the two lines would intersect at (-4, -1)
Also, note how plugging x = -4 and y = -1 into the second equation leads to...
-2x+5y = 3
-2(-4)+5(-1) = 3
8 - 5 = 3
3 = 3
We get the same value on both sides, so that verifies the second equation. I'll let you verify the first equation.
Solve for x over the real numbers:
-x^2 - 12 = -87
Add 12 to both sides:
-x^2 = -75
Multiply both sides by -1:
x^2 = 75
Take the square root of both sides:
Answer: x = 5 sqrt(3) or x = -5 sqrt(3) both Answers are correct
C. 1.07p
1.00 is for 100% of the cost and the .07 is for the tax.
Answer:
16. D
17. 5^-1 · 5^-1 and 25^-1
8^0 · 8^3 and 8^3
Step-by-step explanation:
When you multiply two same numbers with exponents, just think of it as adding up exponents.
When you divide two same numbers with exponents, just think of it as subtracting exponents.
If a parenthesis has an exponent outside, then every exponent inside the parenthesis will be multiplied by that outside parenthesis.
(5^-1)^-2 · 5^3 ÷ 5^7
5^2 · 5^3 ÷ 5^7
5^5 ÷ 5^7
5^-2
When exponents are negative, you have to flip them or put them on the other side
5^-2 = 1/5^2 = 1/25
Let's try to find the equivalent pairs
6^7 ÷ 6^-2 = 6^5
6^9 = 6^5 Not equivalent
(6^3)^0 = 6
6^0 = 1 (Any number with a zero exponent is always 1)
1 = 6 Not equivalent
5^-1 · 5^-1 = 25^-1
5^-2 = 25^-1
Flip em
1/5^2 = 1/25
1/25 = 1/25 Equivalent
8^0 · 8^3 = 8^3
8^3 = 8^3 Equivalent
4^-3 ÷ 4^2 = 4^5
4^-5 = 4^5 Not equivalent
