Answer:
150
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given: quadrilateral ABCD inscribed in a circle
To Prove:
1. ∠A and ∠C are supplementary.
2. ∠B and ∠D are supplementary.
Construction : Join AC and BD.
Proof: As, angle in same segment of circle are equal.Considering AB, BC, CD and DA as Segments, which are inside the circle,
∠1=∠2-----(1)
∠3=∠4-----(2)
∠5=∠6-------(3)
∠7=∠8------(4)
Also, sum of angles of quadrilateral is 360°.
⇒∠A+∠B+∠C+∠D=360°
→→∠1+∠2+∠3+∠4+∠5+∠6+∠7+∠8=360°→→→using 1,2,3,and 4
→→→2∠1+2∠4+2∠6+2∠8=360°
→→→→2( ∠1 +∠6) +2(∠4+∠8)=360°⇒Dividing both sides by 2,
→→→∠B + ∠D=180°as, ∠1 +∠6=∠B , ∠4+∠8=∠B------(A)
As, ∠A+∠B+∠C+∠D=360°
∠A+∠C+180°=360°
∠A+∠C=360°-180°------Using A
∠A+∠C=180°
Hence proved.
credit: someone else
y = mx , where m is a slope,
m= rise/run
We have y = 15x, so m =15 and rise/run =15, then
rise = 15, run = 1
What are we supposed to do about you losing coins? could you show an image.
Answer:
1). t ≥ -![\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D)
2). k ≥ ![\frac{16}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B3%7D)
3). y < -![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
4). b > ![\frac{250}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B250%7D%7B9%7D)
5). w ≤ 0
Step-by-step explanation:
1). ![14(\frac{1}{2}-t)\leq 28](https://tex.z-dn.net/?f=14%28%5Cfrac%7B1%7D%7B2%7D-t%29%5Cleq%2028)
![\frac{14}{14}(\frac{1}{2}-t)\leq \frac{28}{14}](https://tex.z-dn.net/?f=%5Cfrac%7B14%7D%7B14%7D%28%5Cfrac%7B1%7D%7B2%7D-t%29%5Cleq%20%5Cfrac%7B28%7D%7B14%7D)
![\frac{1}{2}-t\leq 2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D-t%5Cleq%202)
![-t\leq 2-\frac{1}{2}](https://tex.z-dn.net/?f=-t%5Cleq%202-%5Cfrac%7B1%7D%7B2%7D)
![-t\leq \frac{3}{2}](https://tex.z-dn.net/?f=-t%5Cleq%20%5Cfrac%7B3%7D%7B2%7D)
t ≥ -![\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D)
2). 15k + 11 ≤ 18k - 5
15k - 18k ≤ -5 - 11
-3k ≤ - 16
3k ≥ 16
k ≥ ![\frac{16}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B3%7D)
3). 44y > 11 + 88y - 22y
44y > 11 + 66y
44y - 66y > 11
-22y > 11
22y < -11
![\frac{22y}{22}](https://tex.z-dn.net/?f=%5Cfrac%7B22y%7D%7B22%7D%3C-%5Cfrac%7B11%7D%7B22%7D)
y < ![-\frac{1}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7D)
4). ![\frac{7}{9}(b - 27) > \frac{49}{81}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B9%7D%28b%20-%2027%29%20%3E%20%5Cfrac%7B49%7D%7B81%7D)
![\frac{7}{9}(b - 27)\times \frac{9}{7} > \frac{49}{81}\times \frac{9}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B9%7D%28b%20-%2027%29%5Ctimes%20%5Cfrac%7B9%7D%7B7%7D%20%3E%20%5Cfrac%7B49%7D%7B81%7D%5Ctimes%20%5Cfrac%7B9%7D%7B7%7D)
(b - 27) > ![\frac{7}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B9%7D)
b > ![\frac{7}{9}+27](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B9%7D%2B27)
b > ![\frac{250}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B250%7D%7B9%7D)
5). 11w - 8w ≥ 14w
3w - 14w ≥ 0
-11w ≥ 0
w ≤ 0