Answer:
The values of x and y are x = 25 and y = 18
Step-by-step explanation:
The measure of an arc is equal to the measure of the central angle subtended by it
In circle W
∵ W is the center of the circle
∵ m∠QWS = 90°
∵ ∠QWS is subtended by arc QS
- Use the rule above
∴ m∠QWS = m arc QS
∴ m arc QS = 90°
∵ m arc QS = m arc QR + m arc RS
∵ m arc QR = (x + 11)°
∵ m arc RS = (3y)°
- Add them and equate the answer by 90
∴ (x + 11) + (3y) = 90
- Subtract 11 from both sides
∴ x + 3y = 79 ⇒ (1)
∵ VT passes through W
∴ VT is a diameter in circle W
- Diameter divides the circle into two equal arcs the measure
of its arc is 180° because the measure of the circle is 360°
∴ m arc VQRST is 180°
∵ m arc QRS = 90°
∵ m arc VQRST = m arc VQ + m arc QRS + m arc ST
- Substitute the measures of arc VQRST and QRS
∴ 180 = m arc VQ + 90 + m arc ST
- Subtract 90 from both sides
∴ 90 = m arc VQ + m arc ST
∵ m arc VQ = (y + 7)°
∵ m arc ST = 65°
∴ 90 = (y + 7) + 65
- Add like terms in the right hand side
∴ 90 = y + 72
- Subtract 72 from both sides
∴ 18 = y
Substitute the value of y in equation (1) to find x
∵ x + 3(18) = 79
∴ x + 54 = 79
- Subtract 54 from both sides
∴ x = 25
The values of x and y are x = 25 and y = 18
Answer:
D
Step-by-step explanation:
Using process of elimination we know that it cannot be a,b or c because after you add the 2 new stamps james collected the ratio is 8:12 which cannot be 1:2 because 8 is not half, can't be B because 8 is less than 12, Also cannot be C because 8 is less than 12
Assume x > 0.
To find 100% of the number, when given 20% of the number is x, you would divide x by 0.20 or multiply x by 5. Thus, the entire number is 5x, for x > 0.
In the given question, 20% of a number is represented as x. To find 100% of the number, or the total number itself, we need to set up a simple proportional equation. First, we equate the knowns. Therefore, 20%x is equal to 100% of the unknown number.
So, let's set up the equation: 20%/100% = x/number.
By simplifying this equation, you can calculate the complete number by dividing x by 0.20, or in other words, multiplying x by 5.
If and only if x > 0, the total number is therefore 5x.
#SPJ11
Answer:
they are congruent
Step-by-step explanation:
we can prove triangles congruent by sss
if we know 2 sides are congruent, the third must be congruent to the corresponding side as well (the sides have to match up)