Given:
A number when divided by 780 gives remainder 38.
To find:
The reminder that would be obtained by dividing same number by 26.
Solution:
According to Euclis' division algorithm,
...(i)
Where, q is quotient and 
is the remainder.
It is given that a number when divided by 780 gives remainder 38.
Substituting 
in (i), we get
So, given number is in the form of 
, where q is an integer.
On dividing by 26, we get
Since q is an integer, therefore (30q+1) is also an integer but 
is not an integer. Here 26 is divisor and 12 is remainder.
Therefore, the required remainder is 12.
Answer:
4
Step-by-step explanation:
Given that At the pet owner’s meeting, there are 20 people who own dog, and 35people who own cat and 9 people own goldfish. Some people own both catand dog and some people own both gold fish and cat. No dog owners owngoldfish. There are twice as many people who own both goldfish and catthan people who own both dog and cat.
Total no of people =52
The venn diagram attached gives a clear picture
assuming x to be owners of both dog and cat. Then 2x is for both goldfish and cats.
Totalling all mutually exclusive we get
64-3x=52
x=4
No of owners who own both cat and dog =4
Answer:
b. A = 71.6°; C = 45.40°; b =15.0
Step-by-step explanation:
The missing values can be found with the help of the Law of Cosine and properties of triangles:
Side b (Law of Cosine)
Angle A (Law of Cosine)
Angle C (Sum of internal angles in triangles)
Hence, the right answer is B.
Answer:
We conclude that the rule for the table in terms of x and y is:
Step-by-step explanation:
The table indicates that there is constant change in the x and y values, meaning the table represents the linear function the graph of which would be a straight line.
We know the slope-intercept form of the line equation
y = mx+b
where m is the slope and b is the y-intercept.
Taking two points
Finding the slope between (-2, -4) and (-1, -1)
We know that the y-intercept can be determined by setting x = 0 and finding the corresponding y-value.
Taking another point (0, 2) from the table.
It means at x = 0, y = 2.
Thus, the y-intercept b = 2
Using the slope-intercept form of the linear line function
y = mx+b
substituting m = 3 and b = 2
y = 3x+2
Therefore, we conclude that the rule for the table in terms of x and y is:
Answer:
x = 4
Step-by-step explanation:
1.3x - 10 = 0.8x - 8
Add 10 to both sides.
1.3x = 0.8x + 2
Subtract 0.8x from both sides.
0.5x = 2
Divide by 0.5.
x = 4.
Proof:
1.3x - 10 = 0.8x - 8
1.3(4) - 10 = 0.8(4) - 8
5.2 - 10 = 3.2 - 8
-4.8 = -4.8
