Answer:
1. 474
2. 397
Step-by-step explanation:
1. If the three-digit number is xyz, then y = z + 3.
When rounded to the nearest ten and reduced by 320, the result is 150. 150 + 320 = 470, so x = 4. y = 6 if z ≥ 5, and y = 7 if z < 5.
So the number is either 463 or 474. 463 doesn't round to 470, so the answer is 474.
2. If the three-digit number is xyz, then z = x + 4. y is the largest of the three digits; since all the digits are odd, y is either 5, 7, or 9. So z is either 5 or 7, and x is either 1 or 3.
When rounded to the nearest hundred and reduced by 100, the result is 300. 100 + 300 = 400, and y > 5, so xyz is rounded up to 400, which means x = 3. So z = 7 and y = 9.
The answer is 397.
Answer:
y > 4x + 1
Step-by-step explanation:
Equation of the dotted line:
Slope = (-3-1)/(0-1) = 4
Y intercept is +1
y = 4x + 1
Shaded region:
y > 4x + 1
Answer:
a) The coordinates of the missing vertex = (7, 8)
b) Area = 18 square units
Perimeter = 18 units
Step-by-step explanation:
a) We know three of the four vertices:
A: (4, 2) C ______ D(?)
B: (7, 2) | |
C: (4, 8) A |______| B
To find the coordinates of the missing vertex we need to calculate the distance in the x-direction from point A to point B:
Hence, the distance of point D from point C in the x-direction is:
Now, to find the coordinate in "y" we need to calculate the distance in the y-direction between point C and point A:
Then, the distance of point D from point B in the y-direction is:

Therefore, the coordinates of the missing vertex (point D) are:
b) The area of the rectangle is:

The perimeter is given by:

I hope it helps you!
Here it is given that the width is x ft and total length of the fence is 2400 ft .
Let the length be y ft
So we have

Let A represents area, and area is the product of length and width .
So we get

Substituting the value of y, we will get

Second part
The area is maximum at the vertex, and vertex is

And

And that's the required dimensions .
Answer:
Final answer is 
Step-by-step explanation:
We need to find the equation of the line that is parallel to x=6y-5 and that passes through (5,-3).
So first we need to find the slope of given line.
rewirite x=6y-5 in y=mx+b form
x+5=6y

Compare given equation with y=mx+b
we get: m=1/6
We know that parallel equations has equal slope.
Then slope of required line m=1/6
Now plug the given point (5,-3) and slope m=1/6 into point slope formula:





Now we need to rewrite that equation in standard form. Ax+By=C.
6y=x-23
x-23=6y
x-6y=23
Hence final answer is 