Answer:
(2,-2)
Step-by-step explanation:
The first step is to substitute y in the first equation with the right side of the second equation because they both equal to y.
-3x+4 = 4x-10
-3x-4x+4-4 = 4x-4x-10-4
-7x = -14
-7x/-7 = -14/-7
x = 2
Plugin 2 for x for either equation to solve for y, I'll be using the second equation, but either one is fine.
y = 4(2)-10
y = 8-10
y = -2
Plugin x = 2 and y = -2 into (x,y), and you get (2,-2)
Answer:
- 8) 4 + 2q²/p² - 4r/p + r²/p²
- 9) (3/4, -9/4)
- 10) (3/8, 41/16)
Step-by-step explanation:
8. ============
Given
- α and β are roots of px² + qx + r = 0
The sum of the roots is α + β = -q/p, the product of then roots αβ = r/p
- (2 + α²)(2 + β²) =
- 4 + 2(α² + β²) + (αβ)² =
- 4 + 2((α + β)² -2αβ) + (αβ)² =
- 4 + 2((-q/p)² - 2r/p) + (r/p)² =
- 4 + 2q²/p² - 4r/p + r²/p²
------------------------------
9. ============
<u>Given function</u>
The minimum point is reached at vertex
<u>The vertex is:</u>
- x = -b/2a
- x = -(-3)/2*2 = 3/4
<u>The corresponding y-coordinate is:</u>
- y = 2(3/4)² - 3(3/4) - 1 = 9/8 - 9/4 - 1 = 1/8(9 - 18 - 9) = - 18/8 = - 9/4
<u>So the point is: </u>
---------------
10. ============
<u>Given function</u>
The maximum is reached at vertex
<u>The vertex is:</u>
- x = -b/2a
- x = -(-3)/2(-4) = -3/8
<u>The corresponding y-coordinate is:</u>
- y = 2 - 3(-3/8) -4(-3/8)² = 2 + 9/8 - 9/16 = 1/16(32 + 18 - 9) = 41/16
<u>So the maximum point is:</u>
I'm assuming your question says r² - 94 = 0.
Because this equation is quadratic due to the exponent of 2, we can already say that it has 2 solutions. Those solutions would be √94 , and -√94.
I hope this helps!
First you have to put it into slope intercept form. You have to put it into y = mx + b then m is the slope and b is the y intercept on the graph.
Answer: Rounded to the nearest tenths place, it is 3.7 meters.
Step-by-step explanation:
Using the above formula, let's multiply 2.5 times 2.5 and 4.5 times 4.5.
2.5 times 2.5, or 2.5 squared, equals 6.25
4.5 times 4.5, or 4.5 squared, equals 20.25
Now, let's subtract 20.25 minus 6.25. The difference is 14.00.
What is the square root of 14? It is 3.74165739. Let's round that number to the nearest tenths place.
What is the number in the tenths place? It is 7. And--what is the number that comes after it? Well, it is 4. Therefore, the 7 should stay a seven. If the number next to the tenths place was five or greater, then we should add one.