Answer:
x = 11º
Step-by-step explanation:
1. Notice Parallel Lines
2. Understand Angle Relationships When Parallel Lines Are Present (e.g., alternate interior/exterior)
3. ∠CAB ≅ ∠DCA ∴ m∠CAB = 33º
4. Use exterior angle theorem: the sum of non-adjacent angles of the same triangle which the exterior angle is drawn is equal to the measure of that angle.
5. Therefore write and solve the equation 2x + 33º (sum of non-adjacent interior angles) = 5x (exterior angle).
- 2x + 33 = 5x (C.L.T or <u>C</u>ombine <u>L</u>ike <u>T</u>erms)
- 3x = 33 (inverse operations; divide by 3)
- x = 11º (remember to apply units)
Answer:
Step-by-step explanation:consecutive integers are represented by x, x+1 , so for this problem the greater one is represented by x + 1.
Now you need to translate the problem. the greater is seven less than 1/3 the smaller
---> x + 1 = (1/3)*x - 7 ---> now solve for x (the smaller) and x+1 (the greater)
***hint: to get rid of fractions in an equation you can always multiply EVERYTHING by the denominator , 3 in this case
Answer:
The bag costs 1500, while the umbrella cost 500
Step-by-step explanation:
Let the cost of the bag be b and the cost of the umbrella be u
Total cost is;
b + u = 2,000 •••••(i)
From the second part of the question;
b = 5u-1000 ••••••(ii)
Substitute ii into i
5u-1000 + u = 2000
6u = 2000 + 1000
6u = 3000
u = 3000/6
u = 500
To get b, substitute the value of u into equation ii
b = 5(500)-1000
b = 2500-1000
b = 1500
