Answer:
The value of x is 16
Step-by-step explanation:
The angle Bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle
In Δ QPR
∵ QS is the angle bisector
∵ PR is the opposite side
→ By using the rule above
∴
= ![\frac{SR}{RQ}](https://tex.z-dn.net/?f=%5Cfrac%7BSR%7D%7BRQ%7D)
∵ PS = x and PQ = 30
∵ PR = 40
∵ RS = PR - PS
∴ RS = 40 - x
∵ RS = 40 - x and RQ = 45
→ Substitute them in the rule above
∴
= ![\frac{40-x}{45}](https://tex.z-dn.net/?f=%5Cfrac%7B40-x%7D%7B45%7D)
→ By using the cross multiplication
∵ x × 45 = 30 × (40 - x)
∴ 45x = 30(40) - 30(x)
∴ 45x = 1200 - 30x
→ Add 30x to both sides
∵ 45x + 30x = 1200 - 30x + 30x
∴ 75x = 1200
→ Divide both sides by 75
∴ x = 16
∴ The value of x is 16
Answer:
(14a+3, 21+4) = 1
Step-by-step explanation:
We are going to use the Euclidean Algorithm to prove that these two integers have a gcd of 1.
gcd (14a + 3, 21a + 4) = gcd (14a+3, 7a + 1) = gcd (1, 7a+1) = 1
Therefore,
(14a + 3, 21a + 4) = 1
Answer:
27Pi units squared
Step-by-step explanation:
step 1
Find the area of complete circle L
The area of circle is given by
![A=\pi r^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E%7B2%7D)
we have
![r=KL=ML=9\ units](https://tex.z-dn.net/?f=r%3DKL%3DML%3D9%5C%20units)
substitute
![A=\pi (9)^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20%289%29%5E%7B2%7D)
![A=81\pi\ units^2](https://tex.z-dn.net/?f=A%3D81%5Cpi%5C%20units%5E2)
step 2
Find the area of the shaded sector
we know that
The area of complete circle subtends a central angle of 360 degrees
so
using proportion
Find out the area of sector by a central angle of 120 degrees
![\frac{81\pi}{360^o}=\frac{x}{120^o}\\\\x=81\pi(120)/360\\\\x=27\pi\ units^2](https://tex.z-dn.net/?f=%5Cfrac%7B81%5Cpi%7D%7B360%5Eo%7D%3D%5Cfrac%7Bx%7D%7B120%5Eo%7D%5C%5C%5C%5Cx%3D81%5Cpi%28120%29%2F360%5C%5C%5C%5Cx%3D27%5Cpi%5C%20units%5E2)
Answer:
Um, no lo sé, lo siento, solo necesito los puntos
Step-by-step explanation:
12 more than the quotient of a number t and 7
is v
12 more than
the quotient of a number t and 7 = v (quotient means to divide)
12 more than t / 7 = v