Answer:
A = 30 unit^2
Step-by-step explanation:
To find the area of the triangle
A = 1/2 b*h where b is the length of the base and h is the height
b = 12 and h =5
A = 1/2 (12*5)
A = 1/2 *60
A = 30 unit^2
The solutions to the given system of equations is (0, -6) and (1, -5)
<h3>Simultaneous equations</h3>
From the question, we are to determine the solutions to the given system of equations
The equations are
x − y = 6 --------- (1)
y = x² −6 ---------- (2)
From equation (1)
x - y = 6
∴ x = 6 + y ------- (3)
Substitute into equation (2)
y = x² −6
y = (6+y)² −6
y = (6+y)(6+y) -6
y = 36 + 6y + 6y +y² -6
y = 36 + 12y + y² - 6
Simplifying
y² + 12y - y + 30 = 0
y² + 11y + 30 = 0
Solve quadratically
y² + 11y + 30 = 0
y² + 6y + 5y + 30 = 0
y(y +6) +5 (y +6) = 0
(y + 5)(y + 6) = 0
y + 5 = 0 OR y + 6 = 0
y = -5 OR y = -6
Substitute the values of y into equation (3)
x = 6 + y
When y = -5
x = 6 + (-5)
x = 6 -5
x = 1
When y = -6
x = 6 + (-6)
x = 6 -6
x = 0
∴ When x = 0, y = -6 and when x = 1, y = -5
Hence, the solutions to the given system of equations is (0, -6) and (1, -5)
Learn more on Solving simultaneous equations here: brainly.com/question/16863577
#SPJ!
Answer:
The scale factor is
Step-by-step explanation:
Line segmentAB has vertices A(−3, 4) and B(1, −2) .
A dilation, centered at the origin, is applied to AB. The image has vertices
A'(-1,4/3) and B′(1/3, −2/3) .
We know the rule for dilation by scale factor of k, is
This means that;
But we know, A' has coordinates (-1,4/3)
This means that
We could also compare:
4k=4/3
Which gives
k=⅓
We know the rule of change: a b/c= (ac+b):c
So we have 2 7/8= (2x8+7):8= 23/8
and the second: 2 1/4 = (2x4+1):4= 9/4
We do the division: 23/8: 9/4= 23/8 x 4/9= (23x4):(8x9)= 23/18= 1 5/18
Hello,
<span>List all possible rational roots of the polynomial equation x3 – x2 – x – 3 = 0
Answer -1,1,-3,3
but none is a root.
</span>
