Answer:
B. 12
Step-by-step explanation:
✔️Find the value of x
The side lengths of two similar triangles are always proportional.
Given that ∆ABC ~ ∆LMN, therefore:
AB = 5
LM = 10
AC = x + 5
LN = 3x + 3
Plug in the values
Cross multiply
(distributive property)
Collect like terms
Divide both sides by 5
x = 7
✔️Find AC
AC = x + 5
Plug in the value of x
AC = 7 + 5
AC = 12
Answer:
g(x) = - x² - 4 ⇒ A
Step-by-step explanation:
Let us revise the reflection and translation of a function
- If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k
f(x) = x² is the blue curve
g(x) is its image is the red curve
∵ g(x) is the image of f(x)
∵ f(x) is opened upward
∵ g(x) is opened downward
→ That means the sign of y-coordinates of all points on the blue
graph are opposite
∴ f(x) is reflected about the x-axis
∴ Its image is - f(x)
∵ The vertex of f(x) is (0, 0)
∵ The vertex of g(x) = (0, -4)
→ That means the function translated 4 units down
∴ - f(x) is translated 4 units down
∴ Its image is - f(x) - 4
∴ g(x) = - f(x) - 4
∵ f(x) = x²
∴ g(x) = - x² - 4
Answer:
Step-by-step explanation:
Using the slope formula:
9514 1404 393
Answer:
- 4 3-point baskets
- 7 2-point baskets
Step-by-step explanation:
Let x represent the number of 2-point baskets Nicoli made. Then (x -3) is the number of 3-point baskets. The total number of points is ...
2x +3(x -3) = 5x -9 = 26
5x = 35 . . . . . . add 9
x = 7 . . . . . . . divide by 5
(x -3) = 4 . . . find the number of 3-point baskets
Jokic made 7 2-point baskets and 4 3-point baskets.
To do this problem, you will need to know the side lengths of the triangle. If you have those, just plug them in for a, b, and c and evaluate the square root.
Here is an example. If the sides are 3, 4, 5.
It would be:
The 6 is in the formula because it is the semi-perimeter (half).
