Answer:
1) x = 40° & y = 50°
2) x = 100° & y = 80°
Step-by-step explanation:
1)
ABCD is a cyclic quadrilateral (∵ all the vertices of the quadrilateral are touching on the circle). As it is a cyclic quadrilateral , sum of it's opposite angles will be 180°.
⇒ ∠ADC + ∠ABC = 180°
⇒ 130° + y = 180°
⇒ y = 180 - 130 = 50°
In ΔABC ,
∠ACB = 90° (∵ AB is the diameter of the circle and a diameter subtends an angle of 90° on any point on circle.)
Using angle sum property of triangle ,
∠ABC + ∠ACB + ∠CAB = 180°
⇒ y + 90° + x = 180°
⇒ x + 50° + 90° = 180°
⇒ x + 140° = 180°
⇒ x = 180 - 140 = 40°
2)
ΔABC is an isosceles triangle (∵AB = AC). As it is an isosceles triangle , it's base angles will be equal. So , ∠ABC = ∠ACB = 50°
Using angle sum property of triangle ,
∠ABC + ∠ACB + ∠BAC = 180°
⇒ 50° + 50° + y = 180°
⇒ y + 100° = 180°
⇒ y = 180 - 100 = 80°
ABEC is a cyclic quadrilateral (∵ all the vertices of the quadrilateral are on the circle.). As it is a cyclic quadrilateral , sum of it's opposite angles will be 180°.
⇒ ∠BAC + ∠BEC = 180°
⇒ y + x = 180°
⇒ x + 80° = 180°
⇒ x = 180 - 80 = 100°
The answer is x = 12/7
because you multiply 15 by x to get 15x
15x = 4(2x+3)
next you simplify the right side by using the distributive property by doing 15x = 4(2x) + 4(3)
Then you multiply 2 by 4 to get 8
15x = 8x + 4(3)
and multiply 4 by 3 to get 12
15x = 8x + 12
Now you move terms containing (x) to the left side of the equation.
Since 8x contains the variable to solve for, move it to the left side of the equation by subtracting 8x from both sides.
15x - 8x = 12
subtract 8x from 15x to get 7x
7x = 12
Also , divide each term by 7 and simplify
Divide each term in 7x = 12 by 7
7x/7 = 12/7
Lastly , reduce the expression by cancelling the common factors by
crossing out all 7s 7x/7 and leave 12/7 as it is, and divide x by 1 to get x by
x = 12/7
So the answer is x = 12/7
Answer:
27
Step-by-step explanation:
first we can simplify by dividing by r
the r on the bottom of the fraction will cancel out one of the r's on top, this happens because anything divided by itself is 1, thus r divided by r is 1
finally we can evaluate when r =3,
9r = 9(3) = 27
you need to find how much the output changes for each unit change in the input. (ie from an input change from 5 to 6 the output changes by three units and an input change of 3 (2 - 5 ) units the output changes by 9 units). This will give you the gradient of the equation. then you have to find out the y intercept by finding what the output is when the input is 0. Do this by multiplying the input by the gradient and then subtracting it from that inputs output. This will give you the answer A) 3x
(Sorry, its a bit wordy :) )
Answer:50.18
Step-by-step explanation:
8x+17+9x+11=102
17x+28=102
-28. -28
17x=74
<CAD=9x+11=50.18
x=74/17
