The simple/ <span>common sense method:
</span>The typical lay out of a quadratic equation is ax^2+bx+c
'c' represents where the line crosses the 'y' axis.
The equation is only translated in the 'y' (upwards/downwards) direction, therefore only the 'c' component of the equation is going to change.
A translation upwards of 10 units means that the line will cross the 'y' axis 10 places higher.
9+10=19,
therefore <u>c=19</u>.
The new equation is: <u>y=x^2+19 </u>
<span>
<span>The most complicated/thorough method:
</span></span>This is useful for when the graph is translated both along the 'y' axis and 'x' axis.
ax^2+bx+c
a=1, b=0, c=9
Find the vertex (the highest of lowest point) of f(x).
Use the -b/2a formula to find the 'x' coordinate of your vertex..
x= -0/2*1, your x coordinate is therefore 0.
substitute your x coordinate into your equation to find your y coordinate..
y= 0^2+0+9
y=9.
Your coordinates of your vertex f(x) are therefore <u>(0,9) </u>
The translation of upward 10 units means that the y coordinate of the vertex will increase by 10. The coordinates of the vertex g(x) are therefore:
<u>(0, 19) </u>
substitute your vertex's y coordinate into f(x)
19=x^2+c
19=0+c
c=19
therefore <u>g(x)=x^2+19</u>
Answer:
Step-by-step explanation:
You have the polygon MNOPQR which can be expressed as two rectangles pasted one next to each other.
To see the two rectangles in the picture, you can draw a line parallel to segment MR througn point N.
From the original picture you can state the dimensions of both rectangles.
Call S, the point where the line that you drew intercepts the segment RQ.
Then one rectangle is MNSR and the other rectangle is OPQS.
The measures of the sides of the rectangle MNSR are:
- the length of MN = length of SR = base
- the length of MR = the length of NS.= height
So its area is base * height, which you can all A1.
The measured of the rectangle OPQS are:
- segment OP = segment SQ = segment QR - segment SR = base
- segment PQ = segment OS = height
So its area is base * height, which you can call A2.
Then the area of the polygon MNOPQRS is A1 + A2. One of them is 9 u^2 and the other is what the answer is asking for, and that you have calculated above.
With this procedure you can tell the value needed.
Answer:
120 min
or
2 hrs
Step-by-step explanation:
60 min=1 hr
60 min/5=12 min
12(4)=48 min
24 min=1/5 of room
24(5)=120 min
120 min=2 hrs
Answer is:
a) 32
b) 59
Both are arithmetic sequences
