Answer:
Step-by-step explanation:
Given equation is,
x² + (p + 1)x = 5 - 2p
x² + (p + 1)x - (5 - 2p) = 0
x² + (p + 1)x + (2p - 5) = 0
Properties for the roots of a quadratic equation,
1). Quadratic equation will have two real roots, discriminant will be greater than zero. [(b² - 4ac) > 0]
2). If the equation has exactly one root, discriminant will be zero [(b² - 4ac) = 0]
3). If equation has imaginary roots, discriminant will be less than zero [(b² - 4ac) < 0].
Discriminant of the given equation = 
For real roots,

p² + 2p + 1 - 8p + 20 > 0
p² - 6p + 21 > 0
For all real values of 'p', given equation will be greater than zero.
Q is located at (0,6)
The translation rule is
which says to add 7 to the x coordinate and subtract 5 from the y coordinate. Doing that to (0,6) moves it to (7,1) which is where point Q' is located.
In other words, if you shift point Q(0,6) seven units to the right and five units down, then it arrives at Q ' (7,1)
<h3>Answer: (7, 1)</h3>
Okay so here's the definition of quantitative just in case you ever need it :) Categorical. Categorical variables take on values that are names or labels. The color of a ball (e.g., red, green, blue) or the breed of a dog (e.g., collie, shepherd, terrier) would be examples of categorical variables. And the answer would be A the color of your car because it talks about in the definition of the color of a ball so A would be the correct answer! Please mark brainliest :)
Answer:
3/4
Step-by-step explanation:
Since we have two points, we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 5 - -1)/( 4 - -4)
= ( 5+1)/(4+4)
= 6/8
= 3/4