Answer:
8 and 9
Step-by-step explanation:
Let the two consecutive integers be x - 1 and x
Smaller = x-1
Largere = x
If the square of the smaller integer is nineteen more than five times the larger integer, then;
(x-1)² = 19 + 5x
Expand
x²-2x+1= 19+5x
x²-2x-5x+1-19 -0
x²-7x-18 =0
Factorize
x²-9x+2x-18 =0
x(x-9)+2(x-9) = 0
(x+2) = 0 and x - 9 = 0
x = -2 and 9
SInce x cannot be negative;
x = 9
Smaller number = 9-1
Smaller number = 8
Hence the two consecutive integers are 8 and 9
Answer:
x = 76 roses
Step-by-step explanation:
Step 1: Define variables
x = # of roses
y = # of tulips
Step 2: Write systems of equations
x = 4y + 8
5x + 2y = 414
Step 3: Use Substitution
5(4y + 8) + 2y = 414
20y + 40 + 2y = 414
22y = 374
y = 17
Step 4: Plug in <em>y</em> to find <em>x</em>
x = 4(17) + 8
x = 68 + 8
x = 76
Answer:
-3/5
Step-by-step explanation:
The slope of a perpendicular line is always the negative reciprocal of the slope of the original line.
1/(5/3) * - 1 = -3/5
Answer:
y = x^2 + 6 given equation
y = m x + b equation of straight line required
dy/dx = 2 x tangent to given curve
dy/dx = slope = 2 * 5 = 10
Thus our line must be of the form
y = 10 x + b
31 = 10 * 5 + b at the point required
b = 31 - 50 = -19
Then our final equation becomes
y = 10 x - 19
