Answer:
the graph of the parabola opens upwards.
Step-by-step explanation:
For any quadratic equation of the form
is true that:
if the main coefficient "a" is negative then the graph of the parabola opens downwards.
If the main coefficient "a" is positive, the parabola opens upwards
In this case the parabola is 
Note that 
and 
therefore the graph of the parabola opens upwards.
Answer:
y= (-3x+8)/4
x = (-4 +8)/3
Step-by-step explanation:
3x + 4y = 8
-3x -3x
4y = -3x +8 divide ALL by 4
y= (-3x+8)/4
3x + 4y = 8
-4y -4y
3x = -4 +8 divide ALL by 3
x = (-4 +8)/3
Answer: P = $ 12000
r = 14%
t = 1 (for first year)
I = (P X r X t)/100
∴ I = (12000 X 14 X 1)/100
= 120 X 14
= $ 1680 <---------- (Interest on loan at the end of first year)
∴ Total amount owing at the end of first year = (P + I)
= (12000 + 1680)
= $ 13680
Repayment = $ 7800
Amount still outstanding (at the start of second year) = 13680 - 7800
= $ 5880
Interest on the outstanding amount at the end of second year,
P (new) = $ 5880
r (same) = 14%
t = 1 (for the current second year)
∴ I = (P X r X t)/100
= (5880 X 14 X 1)/100
= 82320 / 100
= $ 823.2 <-------------------------- (Interest on outstanding amount at the end of second year)
Answer:
Which of the following is the scaling factor a of the function f(x) = 3|x|?
Step-by-step explanation:
To answer this question, we need to recall that: "the diagonals of a rectangle bisect each other"
Thus, if we assign the point of intersection of the two diagonals in the rectangle as point O, we can say that the triangle OQR is an "isosceles triangle". Note that this is because the lengths OR and OQ are equal since we know that: "the diagonals of a rectangle bisect each other". See the below diagram for clarity.
Now, we have to recall that:
- the base angles of any isosceles triangle are equal. This is a fact, and this means that the angles
- also the sum of all the angles in any triangle is 180 degrees
Now, considering the isosceles triangle OQR, we have that:
Now, since the figure already shows that angle 
Now, since we have established that the base angles 
we can now solve the above equation for m<2 as follows:
Therefore, the correct answer is: option D
