The correct answer is letter B
Answer:
23 units
Step-by-step explanation:
Use the distance formula: d = 
Plug in the 2 points:
d = 
d = 
d = 23
So, the distance is 23 units
Step-by-step explanation:
4x+10
If x=5
4(5)+10
=20+10
=30
Answer:
Step-by-step explanation:
Area = 192 m²
Perimeter= 56 m
Width = x m
Perimeter = 56
2*(length + width) = 56
Divide the equation by 2
l + x = 56/2
l + x = 28
l = 28 - x
Area = 192 m²
l * w = 192
(28 - x)*x = 192
28x - x*x = 192
0 = 192 - 28x + x²
x² - 28x + 192 = 0
2) Equation is a quadratic equation. The roots of this equation will the dimensions of the rectangular plot.
3) The roots represent the width and length of the rectangle.
x² - 28x +192 = 0
Sum = -28
Product =192
Factors = -16 , -12 {-16 +(-12) = -28 & (-12)*(-16) = 192}
x² - 28x + 192 = 0
x² - 12x - 16x + (-16)*(-12) = 0
x(x -12) - 16(x - 12) = 0
(x - 12)(x -16) =0
x -12 = 0 ; x - 16 = 0
x = 12 ; x = 16
x = 12 ,16
4) Sum of the roots = 12 + 16 = 28
Sum of the roots = half of the perimeter
5) Product of the roots = 12*16 = 192 = area of the rectangle.
Answer:
Step-by-step explanation:
S = (x1,y1) = (0,-5)
T = (x2,y2) = (-8,-7)
<u>Using distance formula to find the length of ST</u>.
![|ST|= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\|ST| = \sqrt{(-8-0)^2+(-7-(-5))^2} \\\\|ST| = \sqrt{(-8)^2+(-7+5)^2} \\\\|ST| = \sqrt{64+(2)^2}\\\\|ST| = \sqrt{64+4} \\\\|ST| = \sqrt{68} \\\\|ST| = 8.2 \ units\\\\\rule[225]{225}{2}](https://tex.z-dn.net/?f=%7CST%7C%3D%20%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D%20%5C%5C%5C%5C%7CST%7C%20%3D%20%5Csqrt%7B%28-8-0%29%5E2%2B%28-7-%28-5%29%29%5E2%7D%20%5C%5C%5C%5C%7CST%7C%20%3D%20%5Csqrt%7B%28-8%29%5E2%2B%28-7%2B5%29%5E2%7D%20%5C%5C%5C%5C%7CST%7C%20%3D%20%5Csqrt%7B64%2B%282%29%5E2%7D%5C%5C%5C%5C%7CST%7C%20%3D%20%5Csqrt%7B64%2B4%7D%20%5C%5C%5C%5C%7CST%7C%20%3D%20%5Csqrt%7B68%7D%20%5C%5C%5C%5C%7CST%7C%20%3D%208.2%20%5C%20units%5C%5C%5C%5C%5Crule%5B225%5D%7B225%7D%7B2%7D)
