Answer:
(-7, 7)
Step-by-step explanation:
The formula for calculating the coordinate point is expressed as;
M(X, Y) = (ax1+bx2/a+b, ay1+by2/a+b)
X = ax1+bx2/a+b
X = 2(-10)+3(-5)/2+3
X = -20-15/5
X = -35/5
X = -7
Y = ay1+by2/a+b
Y = 2(10)+3(5)/2+3
Y = 20+15/5
Y = 35/5
Y = 7
hence the required coordinate is (-7, 7)
Let s be the measure of the measure of the sides of the square such that its area is s². From the conditions above, the length of the rectangle is s + 5 and its width is 0.5s. The area of the rectangle is (s+5)(0.5s)
s² = (s + 5)(0.5s)
The value of s is 5. Thus the dimension of the rectangle in w x h is 2.5 x 10.
Answer:

Step-by-step explanation:
Let's find a particular solution. We need a function of the form
such that
and


then, 3a= 8, 2b+6a =0 and c+2b = 0. With the first equation we obtain
a = 8/3 and replacing in the second equation 2b+6(8/3) = 2b + 16 = 0. Then, b = -8. Finally, c = -2(-8) = 16.
So, our particular solution is
.
Now, let's find the solution
of the homogeneus equation
with the method of constants coefficients. Let 


then 



and
.
So,
and the solution is
.
Mr. Zelman gave 400 books to his nephew
<em><u>Solution:</u></em>
Given that, Mr. Zelman wants to give 50% of his comic book collection to his nephew Alex
Mr. Zelman has 800 comic books
Number of books with Zelman = 800
Mr. Zelman wants to give 50% of books to Alex
Number of books given to nephew = 50 % of books of Zelman
Therefore, we have to find 50 % of 800


Thus he gave 400 books to his nephew
1190 pairs of shoes are defective
<em><u>Solution:</u></em>
Given that shoe company found that 4.25% of the production is defective
The company made 28,000 pairs of shoes
To find: Number of pairs of defective shoes
From given information, 4.25% of the production is defective which means 4.25% of 28,000 pairs of shoes
Defective shoes = 4.25% of 28,000
Defective shoes 
Defective shoes 
Thus 1190 pairs of shoes were defective