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Paha777 [63]
3 years ago
15

Write a quadratic function that reflects the x axis, stretches by a factor of 5, and shifts left 6 and up 3

Mathematics
1 answer:
Brums [2.3K]3 years ago
4 0

Answer:

y=(x+6)^5+3

Step-by-step explanation:

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Help me please, this is really hard.
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The points of new triangle is (3,-2), (6,-3) and (2,-5).

<u>Step-by-step explanation:</u>

The given points in the triangle A(-3,7), B(9,3) and C(-7,-5).

The scale factor is \frac{1}{4} and centered at point (5,-5).

The formula to dilate a point that is not centered on a origin is given by,

D(x,y)=(h+t(x-h),k+t(y-t)).

where (h,k) is the center point.

To find A',

D(-3,7)=(5+\frac{1}{4}(-3-5),-5+\frac{1}{4}(7+5)).

D(-3,7)=(5+\frac{1}{4}(-8),-5+\frac{1}{4}(12)).

D(-3,7)=(5-2, -5+3).

D(-3,7)=(3,-2).

To find B',

D(9,3)=(5+\frac{1}{4}(9-5),-5+\frac{1}{4}(3+5)).

D(9,3)=(5+\frac{1}{4}(4),-5+\frac{1}{4}(8)).

D(9,3) = (5+1,-5+2).

D(9.3)=(6,-3).

To find C',

D(-7,-5)=(5+\frac{1}{4}(-7-5),-5+\frac{1}{4}(-5+5)).

D(-7,-5)=(5+\frac{1}{4}(-12),-5+\frac{1}{4}(0)).

D(-7,-5)=(5-3,-5+0).

D(-7,-5)=(2,-5).

∴ The points of new triangle is (3,-2), (6,-3) and (2,-5).

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The table below shows the surface area y, in square feet, of a shrinking lake in x days:
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The scatter graph of the data is shown in the first picture below

The 'line of best fit' shows a negative gradient

Part A: The most likely coefficient is -0.98. 
If the coefficient is -1, then each point would be exactly on the straight line (which they are not as shown on the graph). The graph however still shows a strong negative coefficient. It can be seen from the close distance of each point from the line of best fit. So -0.5 and -0.02 is unlikely as they show weak negative correlation

Part B: Refer to the second picture to see the horizontal and vertical distance between day 15 and day 20

The horizontal distance is 5 units
The vertical distance is read between 61 and 71.5, hence it's 10.5
The slope = Vertical distance ÷ Horizontal Distance = 10.5÷5 = 2.1
The 'downhill' slope shows a negative gradient, hence the value of the slope is -2.1
The value of the slope shows that the surface area of the lake shrinks by 2.1 for every one day

Part C: The data in the table represents the relation between two variables. Since one variable doesn't cause the change in the other variable, the data table represents correlation rather than a causation. 

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