Answer:
a) there is s such that <u>r>s</u> and s is <u>positive</u>
b) For any <u>r>0</u> , <u>there exists s>0</u> such that s<r
Step-by-step explanation:
a) We are given a positive real number r. We need to wite that there is a positive real number that is smaller. Call that number s. Then r>s (this is equivalent to s<r, s is smaller than r) and s is positive (or s>0 if you prefer). We fill in the blanks using the bold words.
b) The last part claims that s<r, that is, s is smaller than r. We know that this must happen for all posirive real numbers r, that is, for any r>0, there is some positive s such that s<r. In other words, there exists s>0 such that s<r.
Answer:
-6x+5y+8
Step-by-step explanation: subtract 9xfrom 3x
Subtract 2 from 10
-6x+5y+10-2
-6x+5y+8
Answer:
Step-by-step explanation:
Solution by substitution method
3x-4y=8
and 18x-5y=10
Suppose,
3x-4y=8→(1)
and 18x-5y=10→(2)
Taking equation (1), we have
3x-4y=8
⇒3x=4y+8
⇒x=(
4y+8)/
3 →(3)
Putting x=
(4y+8
)/3 in equation (2), we get
18x-5y=10
18(
(4y+8)
/3) -5y=10
⇒24y+48-5y=10
⇒19y+48=10
⇒19y=10-48
⇒19y= -38
⇒y=-
38
/19
⇒y= -2→(4)
Now, Putting y=-2 in equation (3), we get
x=4y+8
x=
(4(-2)+8)
/3
⇒x=
(-8+8)/
3
⇒x=
0/
3
⇒x=0
∴x=0 and y= -2
Step-by-step explanation:
Simply use the general equation of a circle to obtain its equation given the center. Because radius is 5 units, this may be referred to the 3-4-5 triangle, meaning the point on circumference is 3 units across in the x-direction and 4 units up in the y-direction.
Y > 2x - 3
3y - x ≤ 6
↓
y = 2x - 3
3y - x = 6
3(2x - 3) - x = 6
3(2x) - 3(3) - x = 6
6x - 9 - x = 6
6x - x - 9 = 6
5x - 9 = 6
<u> + 9 + 9</u>
<u>5x</u> = <u>15</u>
5 5
x = 3
y = 2x - 3
y = 2(3) - 3
y = 6 - 3
y = 3
(x, y) = (3, 3)