Answer:
(-18, 2)
Step-by-step explanation:
To rotate a point by 90°:
R₉₀ (x, y) = (-y, x)
R₉₀ (1, 9) = (-9, 1)
To dilate by 2:
D₂ (x, y) = (2x, 2y)
D₂ (-9, 1) = (-18, 2)
Answer:
FG = 39
Step-by-step explanation:
From the question given:
FH = 9x + 15
GH = 5x + 4
FG = ?
From the question given above, we can say that G is the midpoint of FH. This implies that:
FH = FG + GH
With the above idea in mind, we can obtain FG as follow:
FH = 9x + 15
GH = 5x + 4
FG = ?
FH = FG + GH
9x + 15 = FG + 5x + 4
Rearrange
FG = 9x + 15 - 5x - 4
FG = 9x - 5x + 15 - 4
FG = 4x + 11
Next, we shall determine the value of x. This can be obtained as follow:
Since G is the midpoint of FH, it therefore means that FG and GH are equal i.e
FG = GH
With the above idea in mind, we can obtain the value of x as follow:
FG = 4x + 11
GH = 5x + 4
FG = GH
4x + 11 = 5x + 4
Collect like terms
11 - 4 = 5x - 4
7 = x
x = 7
Thus, we can obtain the value of FG as follow:
FG = 4x + 11
x = 7
FG = 4x + 11
FG = 4(7) + 11
FG = 28 + 11
FG = 39
***Check ***
FH = 9x + 15
x = 7
FH = 9(7) + 15 = 63 + 15 = 78
GH = 5x + 4
x = 7
GH = 5(7) + 4 = 35 + 4 = 39
FG = 4x + 11
x = 7
FG = 4(7) + 11 = 28 + 11 = 39
FH = FG + GH
FH = 78
FG = 39
GH = 39
FH = FG + GH
78 = 39 + 39
78 = 78
Answer:
Step-by-step explanation:
x-intercepts are SOLUTIONS to a quadratic whereas when you put those solutions into factor form (in a set of parenthesis), you have the FACTORS of the quadratic. They are the same thing generally, they are just written in different forms. For example, if a solution to a quadratic is x = 3, it has been understood that x = 3 when y = 0. Therefore, if x - 3 = y and y = 0, then x - 3 = 0. Solving that for x, you get x = 3. That factor of x = 3 is (x - 3).
Following that logic, for a:
If the x intercepts are x = 0 and x = 3, it is understood that x + 0 = 0 so x = 0 and the factor is (x + 0) (it could also be x - 0 since adding 0 is the same as subtracting 0); if x = 3 it is understood that x - 3 = 0 and the factor is (x - 3).
For b:
If the x-intercepts are x = -1 and x = 1, then originally the factors were (x + 1) and (x - 1). Again, set each of those equal to 0 and solve for x (THE X-INTERCEPT EXISTS WHERE Y = 0!)
For c:
If the x-intercepts are x = -5 and x = 10, then originally the factors were (x + 5) and (x - 10).
For d:
If the x-intercept is a fraction, do the same thing:
x = 1/2 so
x - 1/2 = 0 Now multiply both the x and the 1/2 by a 2 to get the factor (2x - 1) and the other factor from x = 4 is (x - 4)
Answer:
Step-by-step explanation:
We are given the claim.
Claim: The mean weight of male aerobics instructors in a certain city is more than 182 lbs.
Population mean = 182 lbs
The null hypothesis will state that the sample mean is less than or equal to the population mean 182 lbs.
The alternate hypothesis will state that mean weight of male aerobics instructors in a certain city is more than 182 lbs.
answer I credits: ChiKesselman solved it
V
<span>multiply (2)(5)(3)(2) = number of different levels possible</span>
