No solution of the system of equations y = -2x + 5 and -5y = 10x + 20 ⇒ 2nd answer
Step-by-step explanation:
Let us revise the types of solutions of a system of linear equations
- One solution
- No solution when the coefficients of x and y in the two equations are equal and the numerical terms are different
- Infinitely many solutions when the coefficients of x , y and the numerical terms are equal in the two equations
∵ y = -2x + 5
- Add 2x to both sides
∴ 2x + y = 5 ⇒ (1)
∵ -5y = 10x + 20
- Subtract 10x from both sides
∴ -10x - 5y = 20
- Divide both sides by -5
∴ 2x + y = -4 ⇒ (2)
∵ The coefficient of x in equation (1) is 2
∵ The coefficient of x in equation (2) is 2
∴ The coefficients of x in the two equations are equal
∵ The coefficient of y in equation (1) is 1
∵ The coefficient of y in equation (2) is 1
∴ The coefficients of y in the two equations are equal
∵ The numerical term in equation (1) is 5
∵ The numerical term in equation (2) is -4
∴ The numerical terms are different
From the 2nd rule above
∴ No solution of the system of equations
No solution of the system of equations y = -2x + 5 and -5y = 10x + 20
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Answer:
Step-by-step explanation:
Alright, lets get started.
The two chords are intersection each other at point B.
Both are opposite angles that is 39 degrees.
Angle ABC forms the arc AC which is given 41 degree.
The arc DE will be same length as arc AC because angle ABC and angle DBE are same that is 39 degrees.
So, arc DE = 41
So, the answer is DE = 41 degrees .... Answer : option D
Hope it will help :)
The answer is D). It increases by 13.
If you put the numbers in order from least to greatest.. 26,34,38,49,65,75,81
You will see the 26 is the smallest number and 81 in the highest number. The range between the two numbers is 55. To find the range you take the smallest number and subtract it from the biggest number. But when you add the number 13 to the problem then26 is no longer the smallest Number because 13 replaced it. So then you take 81 and subtract 13 from it and get 68. And then you take 55 and subtract it from 68 and come with 13. Which makes the answer D.
Answer:
Question 11.1
At 7 : 00 pm in Sydney, it will be 10 : 00 pm in Berlin.
Question 11.2
Place | Time
Sydney | 5 : 00 pm
Berlin | 8 : 00 pm
It would be a good time for Mark and Hans to cha,t when it's 5 : 00 pm in Sydney and 8 : 00 pm in Berlin.
hope that helps ...
(b) is the answer.
Step-by-step explanation:
By the Pythagorean Theorem,
A² + B² = C²
Where:
A = Length of side 1
B = Length of side 2
C = Hypotenuse
This rule applies to all right-angled triangles.
The length of the hypotenuse of a right-angled triangle is always the largest value.
Therefore, we can test the answers with the equation above.
(a)
8² + 18² = 20²
64 + 324 = 400
388 ≠ 400
The rule of Pythagorean theorem doesn't work on a, so (a) is not a right-angled triangle.
(b)
12² + 35² = 37²
144 + 1225 = 1369
1369 = 1369
The rule of Pythagorean theorem works here, so (b) is a right-angled triangle.
