The first two are equivalent to 15 = k + 13
8 = k + 13 - 7 → ( add 7 to both sides )
8 + 7 = k + 13 ⇒ 15 = k + 13 ' is equivalent '
12 = k + 13 - 3 → ( add 3 to both sides )
12 + 3 = k + 13 ' is equivalent '
No because the exponent on 6^3 is 216 and if you use (4•6)^3 then you’ll have to multiply the quotations and then Square it to the third
For starters, create an equation to show David's earnings. We can do this using Danielle's as a basis, which is set up as y=(# of hours)x+(bonus). This gives us y=12x+80. Now, as we need both their ys to be equal, we just set both equations equal to each other, making 15x+50=12x+80. Now, we solve for x, starting with 15x+50=12x+80, subtracting 12x from both sides to get 3x+50=80, subtracting 50 from both sides to get 3x=30, and dividing three from both sides to get x=10. To check, we just plug in our answer to both equations and see if the ys match up. With Danielle's equation, we get y=15(10)+50=150+50=200 and with David's equation, we get y=12(10)+80=120+80=200, proving that our answer is correct.
Answer:
Step-by-step explanation:
We can use the Polynomial Remainder Theorem. It states that if we divide a polynomial P(x) by a <em>binomial</em> in the form (x - a), then our remainder will be P(a).
We are dividing:
So, a polynomial by a binomial factor.
Our factor is (x + k) or (x - (-k)). Using the form (x - a), our a = -k.
We want our remainder to be 3. So, P(a)=P(-k)=3.
Therefore:
Simplify:
Solve for <em>k</em>. Subtract 3 from both sides:
Factor:
Zero Product Property:
Solve:
So, either of the two expressions:
Will yield 3 as the remainder.
3-5y= 2x
-5y= 2x-3
y= (-2/5)x + 3/5
y + 2 = (-2/5)(x + 3)
y + 2 = (-2/5)x - (6/5)
y + 10/5 = (-2/5)x - 6/5
y = (-2/5)x - 16/5 is the answer
