Square <span>polygon is always regular, other have some scenarios which makes them regular but they are not always regular.</span>
The total cost was 116% of the original bill;
Original bill was;
= <span>$22.5</span>
Answer:
The total allowance is $18.5, and the amount spent daily is $3.2
Step-by-step explanation:
let T and x represent the total allowance and the amount spent daily respectively.
It was started that the amount remaining after 2 days is $12.10 , which implies the person has spend an equal amount for 2 days
T - 2x =12.10 (equation 1)
It was started that the amount remaining after 5 days is $2.50 , which also implies the person has spend an equal amount for 5 days
T - 5x =2.5 (equation 2)
subtract equation 2 from 1
T - 2x -( T - 5x ) = 12.10 -2.5
T - 2x -T + 5x = 9.6
3x =9.6
Divide both side by 3
x = 9.6/3 =3.2
from equation 1
T - 2x =12.10
T = 12.10 + 2x = 12.10 + 2*3.2
= 12.10 + 6.4 = 18.5
Let m = slope = -4/5
P(x,y) = P(5,10)
Slope-intercept form for the equation of a line:
y=mx+c
Plug m= -4/5 into the slope-intercept formula
y = -4/5x + c
Plug P(5,10) into point-slope formula
y = -4/5x + c
10 = -4/5(5) + c
10 = -4 + c
substract -4 from both sides,
10 - (-4) = -4 - (-4) + c
14 = c
So, the equation is y = -4/5x + 14
C. â–łADE and â–łEBA
Let's look at the available options and see what will fit SAS.
A. â–łABX and â–łEDX
* It's true that the above 2 triangles are congruent. But let's see if we can somehow make SAS fit. We know that AB and DE are congruent, but demonstrating that either angles ABX and EDX being congruent, or angles BAX and DEX being congruent is rather difficult with the information given. So let's hold off on this option and see if something easier to demonstrate occurs later.
B. â–łACD and â–łADE
* These 2 triangles are not congruent, so let's not even bother.
C. â–łADE and â–łEBA
* These 2 triangles are congruent and we already know that AB and DE are congruent. Also AE is congruent to EA, so let's look at the angles between the 2 pairs of congruent sides which would be DEA and BAE. Those two angles are also congruent since we know that the triangle ACE is an Isosceles triangle since sides CA and CE are congruent. So for triangles â–łADE and â–łEBA, we have AE self congruent to AE, Angles DAE and BEA congruent to each other, and finally, sides AB and DE congruent to each other. And that's exactly what we need to claim that triangles ADE and EBA to be congruent via the SAS postulate.
