15 min is 1/4 of an hour so it can run 44x 1/4 or 44/4 =11miles in 15 min
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:
x = 15
y = 63
Step-by-step explanation:
9x - 7 + 4x - 8 = 180
13x = 195
x = 15
9x - 7 = 2y + 2
126 = 2y
y = 63
Answer:
g = 6
Step-by-step explanation:
<em>To find the slope you do:</em>
m = change in y ÷ change in x or (y2 - y1) ÷ (x2 - x1)
- x1 = 4, y1 = -7
- x2 = g, y2 = -3
- m (the slope) = 2
<em>Sub in the values:</em>
2 = (-3 - -7) ÷ (g - 4) - we can simplify this
2 = (4) ÷ (g - 4)
4 divided by what gives us 2? 2. This means that g - 4 = 2, g = 2 + 4 which is 6:
g = 6
Hope this helps!
