Three copies of a triangle were rotated and positioned as shown.
1 answer:
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Answer:
Step-by-step explanation:
Given: The snow started melting at a rate of 0.75 inches per hour and it is known that 4 hours after the storm ended, after the storm ended, the depth of snow was down to 9 inches.
Snow melted in 4 hours =
Initial depth of snow = 9 + 3 inches = 12 inches.
Now, depth of snow on Tristan's lawn = Initial depth -0.75(Number of hours)
Let S(t) be the depth of snow on Tristan's lawn, in inches, t hours after the snow stopped falling.
Then,
Starting off with the polynomial in standard form would be extremely difficult, but we can construct one fairly easily with the zeroes we've been given.
We know from the given zeroes that our function has the value 0 when x = 1, x = -2, and x = 2. Manipulating each equation, we can rewrite them as x - 1 = 0, x + 2 = 0, and x - 2 = 0. To construct our polynomial, we simply use all three of the expressions on the left side of the equation as factors and multiply them together, obtaining:
Notice that we can easily obtain each our three zeroes by dividing both sides by the two other factors. From here, we just need to expand the left-hand side of the equation. I'll show the work required here:
=0\\ (x^2-x+2x-2)(x-2)=0\\ (x^2+x-2)(x-2)=0\\ (x^2+x-2)x-(x^2+x-2)2=0\\ x^3+x^2-2x-(2x^2+2x-4)=0\\ x^3+x^2-2x-2x^2-2x+4=0\\ x^3+(x^2-2x^2)+(-2x-2x)+4=0\\ x^3-x^2-4x+4=0\\](https://tex.z-dn.net/?f=%28x-1%29%28x%2B2%29%28x-2%29%3D0%5C%5C%0A%5Cbig%5B%28x-1%29x%2B%28x-1%292%5Cbig%5D%28x-2%29%3D0%5C%5C%0A%28x%5E2-x%2B2x-2%29%28x-2%29%3D0%5C%5C%0A%28x%5E2%2Bx-2%29%28x-2%29%3D0%5C%5C%0A%28x%5E2%2Bx-2%29x-%28x%5E2%2Bx-2%292%3D0%5C%5C%0Ax%5E3%2Bx%5E2-2x-%282x%5E2%2B2x-4%29%3D0%5C%5C%0Ax%5E3%2Bx%5E2-2x-2x%5E2-2x%2B4%3D0%5C%5C%0Ax%5E3%2B%28x%5E2-2x%5E2%29%2B%28-2x-2x%29%2B4%3D0%5C%5C%0Ax%5E3-x%5E2-4x%2B4%3D0%5C%5C)
So, in standard form, our cubic polynomial would be
We know from the given zeroes that our function has the value 0 when x = 1, x = -2, and x = 2. Manipulating each equation, we can rewrite them as x - 1 = 0, x + 2 = 0, and x - 2 = 0. To construct our polynomial, we simply use all three of the expressions on the left side of the equation as factors and multiply them together, obtaining:
Notice that we can easily obtain each our three zeroes by dividing both sides by the two other factors. From here, we just need to expand the left-hand side of the equation. I'll show the work required here:
So, in standard form, our cubic polynomial would be
Answer:
(6y + 2)² = 4x²
Step-by-step explanation:
Given: x - 1 = 3y
Dividing by 3,
⇒ y =
Now, to determine 6y, multiply the equation throughout by 6y.
⇒ 6y =
⇒ 6y = 2(x - 1)
⇒ 6y = 2x - 2
Now, for 6y + 2, add 2 on both sides.
⇒ 6y + 2 = 2x - 2 + 2
⇒ 6y + 2 = 2x
Finally, Squaring both sides, will give us (6y + 2)².
⇒ (6y + 2)² = (2x)²
= 4x² which is the required answer.