Slope formula: m = (Knowing that m represents the slope)
Substitute (1,0) for (x1,y1), and (-1,-3) for (x2,y2)
Slope of the line of (1,0) and (-1,-3) is:
m = =
=
(Simplify)
Slope of the line of (1,0) and (-1,-3) is
When u.s. students took the timss, 53 percent of them: a. overestimated their math skills. b. were realistic about their math sk
1 answer:
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Answer:
2 real solutions
Step-by-step explanation:
Remember this messy thing?
The <em>quadratic formula</em>, as it's called, gives us the roots to any quadratic equation in standard form (ax² + bx + c = 0). The information on the <em>type</em> of roots is contained entirely in that bit under the square root symbol (b² - 4ac), called the <em>discriminant</em>. If it's non-negative, we'll have <em>real</em> roots, if it's negative, we'll have <em>complex roots</em>.
For our equation, we have a discrimant of (-3)² - 4(6)(-4) = 9 + 96 = 105, which is non-negative, so we'll have real solutions, and since quadratics are degree 2, we'll have exactly 2 real solutions.
<u>Answer</u>:
The vertices are:
A' = (-3, -3)
B' = (3, -3)
C' = (3, 3)
D' = (-3, 3)
The ratio of area of larger square to smaller square is 9:1
<u>Step-by-step explanation:</u>
Given:
A 2 x 2 square is centered at the origin.
So, the center of the square is (0, 0)
Since it is 2 x 2 square, the side of the square is 2 units.
So, the vertices of the 2 x 2 square are A (-1, -1), B(1, -1), C(1. 1), D(-1, 1)
The above square is dilated by a factor of 3.
Let's name the dilated square A'B'C'D'
To find the coordinates of the vertices of dilated square, we need to multiply each vertices of ABCD by 3.
A(-1, -1) = 3(-1, -1) = A'(-3, -3)
B(1, -1) = 3(1, -1) = B'(3, -3)
C(1, 1) = 3(1, 1) = C'(3, 3)
D(-1, 1) = 3(-1, 1) = D'(-3, 3)
To find the area of the small square
the side of the small square is 2 units
so the are of the small square is = 4 square units
To find the area of the larger square
lets find the side AB of the square using distance formula
=>
=>
=>
=>
=>
=>6
AB =6 units
In a square all the sides will be equal
Now the area of the larger square will be
36 square units
The ratio of larger square to smaller square is
=>36 : 4
=>9 : 1