For a better understanding of the solution given here please find the attached file which has the relevant diagram.
To answer this question we will have to make use of <u>the Isosceles Triangle Theorem</u> which states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. Thus, as a corollary we know that is EF is the angle bisector of the vertex angle ∠E, then, EF is the perpendicular bisector of the of the base DK.
Please follow the diagram of a complete understanding of the logic and the solution.
As EF is the angle bisector as given in the question, thus we will have:
.
Also, from the Theorem we know that KF will be half of DK and thus, KF will be:
centimeters.
Likewise, from the same theorem we have: ![m\angle EFD=90^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20EFD%3D90%5E%7B%5Ccirc%7D)
If they won 55 of the games, that means they lost the rest of the 75. So,
75 - 55 = 20 games lost. To find the percentage of 20 out of 75, you set up a proportion:
![\frac{20}{75}=\frac{x}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7B75%7D%3D%5Cfrac%7Bx%7D%7B100%7D)
where x = the percentage of games lost. Cross multiply and divide to isolate the x:
![\frac{20}{75}=\frac{x}{100}\\75x=2000\\75x/75=2000/75\\x=26.6666667](https://tex.z-dn.net/?f=%5Cfrac%7B20%7D%7B75%7D%3D%5Cfrac%7Bx%7D%7B100%7D%5C%5C75x%3D2000%5C%5C75x%2F75%3D2000%2F75%5C%5Cx%3D26.6666667)
Rounded to the nearest hundredth, the Royals lost 26.667 % of their games.
Answer:
x<u><</u>5 (x=# of shirts) or 8x <u><</u> 70-30
Step-by-step explanation:
she has $40 left for shirts, 40/8 = 5. 5 is the maximum shirts she can buy.
Answer:
- The rate of change of function 1 = 0
- The rate of change of the function 2 = 3
Therefore, the rate of change of function 2 is 3 more than the rate of change of function 1.
Hence, option C is true.
Step-by-step explanation:
Function 1
A horizontal straight line is drawn joining the ordered pairs (0, 3) and (4, 3).
Given the points
It means
at x = 0, y = 3
at x = 4, y = 3
Since the y-values are same, it means the points lie on a horizontal.
The rate of change or slope of a horizontal line is zero because it does not rise vertically ( i.e. y₁ - y₂ = 0).
Therefore, the rate of change of function 1 = 0
Function 2
y = 3x+1
comparing with the slope-intercept form
y = mx+b
here m is the rate of change or slope and b is the y-intercept
so the rate of change of the function 2 = m = 3
Conclusion:
- The rate of change of function 1 = 0
- The rate of change of the function 2 = 3
Therefore, the rate of change of function 2 is 3 more than the rate of change of function 1.
Hence, option C is true.