Answer:
C
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (- 8, - 42 ) and (x₂, y₂ ) = (- 3, - 17 ) ← 2 ordered pairs from the table
m =
=
=
= 5
The line crosses the y- intercept at (0, - 2 ) , then
y = 5x - 2 → C
Answer:
A diagonal of this rectangle has length 10.
Step-by-step explanation:
The vertices (-4, 4) and (-4, -4) have the same x-coordinate (-4) and different y-coordinates (4 and -4). These two points are the endpoints of a vertical side of the rectangle which has length 4 - (-4) = 8.
Similarly, the vertices (2, -4) and (-4, -4) have the same y-coordinate (-4) but different x-coordinates (2 and -4). To find the horizontal dimension of the rectangle, we calculate 2 - (-4), which comes out to 6.
Thus, the width of the rectangle is 6 and the length is 8.
Using the Pythagorean Theorem, we find the length of a diagonal as follows:
d = √(6^2 + 8^2) = √(36 + 64) = √100 = 10.
A diagonal of this rectangle has length 10.
Answer:
C
Step-by-step explanation:
idk it just sounds like a conditional probability to me.
Answer:
(- 1, 8 ) and (5, 2 )
Step-by-step explanation:
Given the 2 equations
y = - x + 7 → (1)
y = 0.5(x - 3)² → (2)
Substitute y = 0.5(x - 3)² into (1)
0.5(x - 3 )² = - x + 7 ← expand and simplify left side
0.5(x² - 6x + 9) = - x + 7 ( multiply both sides by 2 )
x² - 6x + 9 = - 2x + 14 ( subtract - 2x + 14 from both sides )
x² - 4x - 5 = 0 ← in standard form
(x - 5)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
Substitute these values into (1) for corresponding values of y
x = 5 : y = - 5 + 7 = 2 ⇒ (5, 2 )
x = - 1 : y = 1 + 7 = 8 ⇒ (- 1, 8 )