Find the scale factor applied to figure A to produce figure B
2 answers:
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The hole is 8 feet deep at ground level ⇒ 3rd answer
Step-by-step explanation:
The form of the quadratic function is y = ax² + bx + c, where
- a is the coefficient of x²
- b is the coefficient of x
- c is the y-intercept (at x = 0)
The vertex point of the quadratic is (h , k), where
and k is the value of y when x = h
The table:
→ x : -2 , 0 , 2
→ y : -6 , -8 , -6
∵ x represents distance from hole's center in feet
∵ y represents the depth from level ground
∴ The quadratic function is y = ax² + bx + c
∵ c is the value of y at x = 0 ⇒ y-intercept
- From the table at x = 0 ⇒ y = -8
∴ c = -8
- Substitute its value in the function model
∴ y = ax² + bx - 8
- To find the values of a and b substitute x and y in the model by
the coordinates of the point in the table
∵ x = -2 and y = -6
∴ -6 = a(-2)² + b(-2) - 8
∴ -6 = 4a - 2b - 8
- Add 8 to both sides
∴ 2 = 4a - 2b
- Switch the two sides
∴ 4a - 2b = 2 ⇒ (1)
∵ x = 2 and y = -6
∴ -6 = a(2)² + b(2) - 8
∴ -6 = 4a + 2b - 8
- Add 8 to both sides
∴ 2 = 4a + 2b
- Switch the two sides
∴ 4a + 2b = 2 ⇒ (2)
Now we have a system of equation to solve it
Add equations(1) and (2) to eliminate b
∵ 8a = 4
- Divide both sides by 8
∴ a = 0.5
- Substitute value of a in equation (1) or to to find b
∵ 4(0.5) + 2b = 2
∴ 2 + 2b = 2
- Subtract 2 from both sides
∴ 2b = 0
- Divide both sides by 2
∴ b = 0
Substitute the values of a and b in the function model
∴ y = 0.5x² + (0)x - 8
∴ y = 0.5x² - 8
∵ y represents the depth from level ground
∵ The vertex of the function model is (h , k)
∴ The deep of the hole at ground level is the value of k
∵
∴
∴ h = 0
∵ k is the value of y when x = h
- From the table at x = 0 ⇒ y = -8
∴ k = -8
- Ignore the sign (-) because the k represents the depth of the
hole in feet
∴ The deep of the hole at ground level is 8 feet
The hole is 8 feet deep at ground level
Learn more:
You can learn more about the quadratic function in brainly.com/question/1332667
#LearnwithBrainly
Answer:
a) f(x,y) = ; x = 0, 1 , 2; y = 0, 1 , 2; 0 ≤ x+y ≥ 2
b) =
Step-by-step explanation:
joint probability is a function that characterizes the distribution of a random variable. If X and Y be two random variables then the joint probability will be P(X = x, Y=y)
Given Data,
X = The number of blue Pens
Y = The number of red Pens
a)
possible outcomes(X, Y) are (0, 0), (0, 1), (1, 0), (1, 1), (0, 2), (2,0)
Please refer fig. also
total number ways of selecting any 2 pens = =
=28
f(x,y) = ; x = 0, 1 , 2; y = 0, 1 , 2; 0 ≤ x+y ≥ 2
b)
P(X,Y)∈A = P(X + Y ≤ 1)
= P(0,0) + P(1,0) + P(0,1)
= +
+
=
