This pattern of question is always coming up. Since we can't easily guess, then let us set up simultaneous equation for the statements.
let the two numbers be x and y.
Multiply to 44. x*y = 44 ..........(a)
Add up to 12. x + y = 12 .........(b)
From (b)
y = 12 - x .......(c)
Substitute (c) into (a)
x*y = 44
x*(12 - x) = 44
12x - x² = 44
-x² + 12x = 44
-x² + 12x - 44 = 0.
Multiply both sides by -1
-1(-x² + 12x - 44) = -1*0
x² - 12x + 44 = 0.
This does not look factorizable, so let us just use quadratic formula
comparing to ax² + bx + c = 0, x² - 12x + 44 = 0, a = 1, b = -12, c = 44
x = (-b + √(b² - 4ac)) /2a or (-b - √(b² - 4ac)) /2a
x = (-(-12) + √((-12)² - 4*1*44) )/ (2*1)
x = (12 + √(144 - 176) )/ 2
x = (12 + √-32 )/ 2
√-32 = √(-1 *32) = √-1 * √32 = i * √(16 *2) = i*√16 *√2 = i*4*√2 = 4i√2
Where i is a complex number. Note the equation has two values. We shall include the second, that has negative sign before the square root.
x = (12 + √-32 )/ 2 or (12 - √-32 )/ 2
x = (12 + 4i√2 )/ 2 (12 - 4i√2 )/ 2
x = 12/2 + (4i√2)/2 12/2 - (4i√2)/2
x = 6 + 2i√2 or 6 - 2i√2
Recall equation (c):
y = 12 - x, When x = 6 + 2i√2, y = 12 - (6 + 2i√2) = 12 - 6 - 2i√2 = 6 - 2i√2
When x = 6 - 2i√2, y = 12 - (6 - 2i√2) = 12 - 6 + 2i√2 = 6 + 2i√2
x = 6 + 2i√2, y = 6 - 2i√2
x = 6 - 2i√2, y = 6 + 2i√2
Therefore the two numbers that multiply to 44 and add up to 12 are:
6 + 2i√2 and 6 - 2i√2
Answer:
95.5
Step-by-step explanation:
you can using toa
tan = opp/adj
tan 37° = 72/x
x = 72/ tan 37°
x = 95.547 feet
x = 95.5
Answer:
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line -3x-4y-9 = 0 and calculate its properties. Graph of a Straight Line : Calculate the Y-Intercept : Notice that when x = 0 the value of y is 9/-4 so this line "cuts" the y axis at y=-2.25000. y-intercept = 9/-4 = -2.25000.
Step-by-step explanation:
Find the X and Y Intercepts 3x-4y=9. 3x − 4y = 9 3 x - 4 y = 9. Find the x-intercepts. Tap for more steps... To find the x-intercept (s), substitute in 0 0 for y y and solve for x x. 3 x − 4 ⋅ 0 = 9 3 x - 4 ⋅ 0 = 9. Solve the equation. Tap for more steps... Simplify 3 x − 4 ⋅ 0 3 x - 4 ⋅ 0.
Use your keyboard and if that doesn’t work on the right top comet there’s a pen that should work :))
Answer:
-0.5
Step-by-step explanation:
- slope=rise/run or y/x in other words(y2-y1/x2-x1)
- (y2-y1) is 3-2 so y2-y1=1
- (x2-x1) is 3-5 so x2-x1= -2
- -1/2 or -0.5 would be the slope.
