Find the y-intercept of the following function:
2 answers:
Answer:
Step-by-step explanation:
2x - 4y = 9
To find the y-intercept, set the x value in the equation to 0.
Rewrite
2(0) - 4y = 9
Simplify
-4y = 9
Multiply both sides of the equation by -1
4y = 9
Divide both sides of the equation by 4
y = -9/4
y = -4.5
Now that we know the y intercept, we can find the coordinate.
(x, y)
Substitute
(0, )
Let me know if you have any questions!
Hi there!
2x - 4y = 9
Begin by isolating the y variable by moving 2x to the right-hand side of the equation. (Subtract 2x from both sides):
2x - 2x - 4y = 9 - 2x
-4y = 9 - 2x
Further isolate by dividing both sides by -4:
-4y / (-4) = (9 - 2x) / (-4)
y = -9/4 - 2x/(-4)
Simplify further:
y = -9/4 + 1/2x
y = 1/2x - 9/4
The "b" value is the y-intercept, therefore:
x = 0 at y = -9/4
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Answer:
The value of n is -6
Step-by-step explanation:
- If the function f(x) is translated k units up, then its image is g(x) = f(x) + k
- If the function f(x) is translated k units down, then its image is g(x) = f(x) - k
- The vertex form of the quadratic function is f(x) = a(x - h)² + k, where a is the coefficient of x² and (h, k) is the vertex
∵ k(x) = x²
→ Its graph is a parabola with vertex (0, 0)
∴ The vertex of the prabola which represents it is (0, 0)
∵ The given graph is the graph of p(x)
∵ Its vertex is (0, -6)
∴ h = 0 and k = -6
∵ a = 1
→ Substitute them in the form above
∴ p(x) = 1(x - 0)² + -6
∴ p(x) = x² - 6
→ Substitute x² by k(x)
∴ p(x) = k(x) - 6
∵ p(x) = k(x) + n
→ By comparing the two right sides
∴ n = -6
∴ The value of n is -6
Look at the attached figure for more understanding
The red parabola represents k(x)
The blue parabola represents p(x)
Answer:
Step-by-step explanation:
The formula of a Surface Area of a rectangular prisms:
<em>l</em><em> - length</em>
<em>w</em><em> - width</em>
<em>h</em><em> - height</em>
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We have:
Substitute: