Answer:
(-1,-1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
(1+-3)/2 = -2/2 = -1
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
(-6+4)/2 = -2/2 = -1
(-1,-1)
9/10. make the bottom numbers the same to add fractions. you can do that by multiplying 7/10 by 10/10.
70/100 + 20/100 = 90/100
90/100 = 9/10
you can also reduce 20/100 to 2/10.
7/10 + 2/10 = 9/10
Answer:
1) x- y = 8
x + y = 12
eliminate one variable by adding the equations
2x = 20
divided by 2 on both sides
x = 10
substitute the value of x in the equation 1
10 - y = 8
-y = 8- 10
y =2
[x , y]
[10 , 2]
2) 2x - y = 4
3x + y = 6
eliminate one variable by adding the equations
5x = 10
x = 2
substitute the value of x in the equation
2(2) - y = 4
4 - y = 4
y = 0
[x ; y]
[2; 0]
3) x + 2y = 10
x + 4y = 14
multiply equation 1 by - 1
-x -2y = -10
x + 4y = 14
eliminate one variable by adding the equations
2 y = 4
y = 2
substitute the value of y in the equation 1
x + 2(2) = 10
x + 4 = 10
x = 6
[x ; y]
[6 ; 2]
4 ) 3x + y = 9
y = 3x + 6
simplify the expression
3x + y = 9
- 3x + y = 6
eliminate one variable by adding the equations
2y = 15
y = 15/2
substitute the value of y in equation 1
3x + 15/ 2 = 9
3x = 3/2
x = 1/2
[x ; y]
[1/2 ; 15/ 2]
5) 4x + 5y = 15
6x - 5y = 18
eliminate one variable by adding the equations
10 x = 33
× = 33/10
substitute the value of x in equation I
4 (33/10) + 5y = 15
66/5 + 5y =15
5y = 9/5
y = 9/25
[x ; y]
[33/10 ; 9/25]
6) 5x = 7y
x + 7y = 21
in equation I move the variable to the left
5x - 7y = 0
x + 7 y = 21
eliminate one variable by adding the equations
6x = 21
x = 7/2
substitute the value of x in the equation
5(7/2) = 7y
35/2 = 7y
5/2 = y
[x ; y ]
[7/2 ; 5/2 ]
Answer:
The rectangle's area is 48 square meters
Step-by-step explanation:
Recall that the perimeter of a rectangle of base b and height h is given by the formula:
Perimeter = 2 b + 2 h
we know that the perimeter is 28 meters, then we can create our first equation;
2 b + 2 h = 28
which means:
2 (b + h) = 28
b + h = 28/2
b + h = 14
the tell us that the diagonal is 10 meters, so we use the Pythagorean theorem to write a second equation using the rectangle's base, height, and diagonal (which form in between the three a right angle triangle where the hypotenuse is the rectangle's diagonal:
So, we can use the equation : b + h = 14 to write one variable in terms of the other one and use it as substitution in the second (quadratic) equation:
h = 14 - b
then:
which we have reduced at the end by dividing both sides by 2.
we can use factoring to solve these equation;
Se we find two possible solutions: b = 6 m or b = 8 m
If we call b = 8 m, then the height becomes h = 14 - (8) = 6 m
and viceversa.
So a rectangle with such dimensions will render an area that equals :
Area = b x h = 8 x 6 = 48 square meters.
