Answer:
![\displaystyle \frac{7\frac{3}{4}}{\frac{1}{4}}=31](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B7%5Cfrac%7B3%7D%7B4%7D%7D%7B%5Cfrac%7B1%7D%7B4%7D%7D%3D31)
Step-by-step explanation:
<u>Fractions</u>
We are given the expression:
![\displaystyle \frac{7\frac{3}{4}}{\frac{1}{4}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B7%5Cfrac%7B3%7D%7B4%7D%7D%7B%5Cfrac%7B1%7D%7B4%7D%7D)
We'll find an equivalent expression that results when simplifying the given fraction.
The numerator is a mixed fraction, which we'll convert into an improper fraction as follows:
![7\frac{3}{4}=7+\frac{3}{4}=\frac{4*7+3}{4}=\frac{31}{4}](https://tex.z-dn.net/?f=7%5Cfrac%7B3%7D%7B4%7D%3D7%2B%5Cfrac%7B3%7D%7B4%7D%3D%5Cfrac%7B4%2A7%2B3%7D%7B4%7D%3D%5Cfrac%7B31%7D%7B4%7D)
Now it follows:
![\displaystyle \frac{7\frac{3}{4}}{\frac{1}{4}}=\frac{\frac{31}{4}}{\frac{1}{4}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B7%5Cfrac%7B3%7D%7B4%7D%7D%7B%5Cfrac%7B1%7D%7B4%7D%7D%3D%5Cfrac%7B%5Cfrac%7B31%7D%7B4%7D%7D%7B%5Cfrac%7B1%7D%7B4%7D%7D)
Instead of dividing fraction, we multiply by the reciprocal of the denominator:
![\displaystyle \frac{7\frac{3}{4}}{\frac{1}{4}}=\frac{31}{4}\cdot \frac{4}{1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B7%5Cfrac%7B3%7D%7B4%7D%7D%7B%5Cfrac%7B1%7D%7B4%7D%7D%3D%5Cfrac%7B31%7D%7B4%7D%5Ccdot%20%5Cfrac%7B4%7D%7B1%7D)
Simplifying:
![\mathbf{\displaystyle \frac{7\frac{3}{4}}{\frac{1}{4}}=31}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdisplaystyle%20%5Cfrac%7B7%5Cfrac%7B3%7D%7B4%7D%7D%7B%5Cfrac%7B1%7D%7B4%7D%7D%3D31%7D)
Make it into slope intercept form
-3y = -12x + 3
Y = 4x - 1
Perpendicular = opposite sign and reciprocal
Parallel: same slope
Perpendicular: y = -1/4x
Parallel: y = 4x
A ) This is a quadratic function:
y = a x² + b x + c
If the starting point is ( 0, 0 ) then c = 0
b ) The function is:
y = - 0.2 x² + 3.6 x
( with coefficients to the nearest tenth )
The graph is in the attachment.
c ) The roots:
x 1 = 0,
0.2 x = 3.6
x = 3.6 : 0.2
x 2 = 18d ) This is near the target ( 17 m ) . So the pumpkin
will hit near the target.
if an ordered pair is a solution, it should satisfy the equation.
see the first option
, if you put $x=4$ and $y=12$
you'll get $12=12$ which is true.
now the last option, $y=8-x$ put $x=4$ and $y=12$
$12=8-4\implies 12\ne4$ thus it is not a solution.
So option 4 is correct
Answer:
Step-by-step explanation:
2x + 23 + 9x - 5 = 95
11x + 18 = 95
11x = 77
x = 7
2(7) + 23 = 14 + 23 = 37 = m<ABD
9(7) - 5 = 63 -5 = 58 = m<DBC