Answer:
a vertical shift of 6 units up
Step-by-step explanation:
We have the transformation:
g(x) = f(x) + k
This is what we call a vertical shift, this transformation moves the graph of f(x) k units, and the motion is upwards if k is positive, and downwards if k is negative.
Here we can see that the graph of f(x) intersects the y-axis at y = -2
While the graph of g(x) intersects the y-axis at y = 4.
Then the distance between these two points is:
4 - (-2) = 6
This means that the graph of g(x) is 6 units above the graph of f(x)
Then we have that k must be equal to 6, then the transformation is:
g(x) = f(x) + 6
This is a vertical shift of 6 units up.
Answer:
x = 25, y = 5
The interior angles:
<ABC = 75°
<BCD = 50°
<CDA = 105°
<DAC = 130
Step-by-step explanation:
The question has no attachment. See attachment for complete question.
Polygon ABCD is a cyclic quadrilateral.
For cyclic quadrilaterals, their opposite angles add up to 180°.
Meaning that;
2x + 26y = 180 ---- equation 1
and
3x + 21y = 180 ------ equation 2
These will be solved simultaneously..
Multiply ½ to both sides of equation 1
½(2x + 26y) = ½ * 180
½ * 2x + ½ * 26y = ½ * 180
x + 13y = 90
Make x the subject of formula
x = 90 - 13y
Multiply both sides of equation 2 by ⅓
⅓(3x + 21y) = ⅓ * 180
⅓ * 3x + ⅓ * 21y = ⅓ * 180
x + 7y = 60
Recall that x = 90 - 13y.
So, x + 7y = 60 becomes
90 - 13y + 7y = 60
90 - 6y = 60
Collect like terms
-6y = 60 - 90
-6y = -30
Divide both sides by -6
-6y/-6 = -30/-6
y = 5
Recall that x = 90 - 13y.
So, x = 90 - 13(5)
x = 90 - 65
x = 25
Having calculated x and y, the interior angles can then be calculated.
The interior angles of the polygon are
1. <ABC
2. <BCD
3. <CDA
4. <DAC
Recall that x = 25 and y = 5
<ABC = 3x
<ABC = 3 * 25
<ABC = 75°
<BCD = 2x
<BCD = 2 * 25
<BCD = 50°
<CDA = 21y
<CDA = 21 * 5
<CDA = 105°
<DAC = 26y
<DAC = 26 * 5
<DAC = 130
Hence,
x = 25, y = 5
The interior angles:
<ABC = 75°
<BCD = 50°
<CDA = 105°
<DAC = 130
#10
#11
- Last three i.e Option B,C,D
#13
It started from negative ends at positive hence
#14
#15
#16
Answer:
2.4
Step-by-step explanation:
Add -3.6 and 2 inside the bracket. Then multiply the result by -1.5.
Note: Two negatives make a positive.
Answer:
So to find ratio for questions like these we do x/y
So the ratio for the first one is 5/7
The ratio for the second is 12/7 or 1 5/7
Step-by-step explanation: