Answer:
A. -4
Step-by-step explanation:
Given the function f(x) = x + 3 for x ≤ -1 and 2x - c for x > -1, for the function to be continuous, the right hand limit of the function must be equal to its left hand limit.
For the left hand limit;
The function at the left hand occurs at x<-1
f-(x) = x+3
f-(-1) = -1+3
f-(-1) = 2
For the right hand limit, the function occurs at x>-1
f+(x) = 2x-c
f+(-1) = 2(-1)-c
f+(-1) = -2-c
For the function f(x) to be continuous on the entire real line at x = -1, then
f-(-1) = f+(-1)
On equating both sides:
2 = -2-c
Add 2 to both sides
2+2 = -2-c+2
4 =-c
Multiply both sides by minus.
-(-c) = -4
c = -4
Hence the value of c so that f(x) is continuous on the entire real line is -4
Answer:
Total area = 237.09 cm²
Step-by-step explanation:
Given question is incomplete; here is the complete question.
Field book of an agricultural land is given in the figure. It is divided into 4 plots. Plot I is a right triangle, plot II is an equilateral triangle, plot III is a rectangle and plot IV is a trapezium, Find the area of each plot and the total area of the field. ( use √3 =1.73)
From the figure attached,
Area of the right triangle I = 
Area of ΔADC = 
= 
= 
= 
= 
= 30 cm²
Area of equilateral triangle II = 
Area of equilateral triangle II = 
= 
= 73.0925
≈ 73.09 cm²
Area of rectangle III = Length × width
= CF × CD
= 7 × 5
= 35 cm²
Area of trapezium EFGH = 
Since, GH = GJ + JK + KH
17 = 
12 = 
144 = (81 - x²) + (225 - x²) + 2
144 - 306 = -2x² + 
-81 = -x² + 
(x² - 81)² = (81 - x²)(225 - x²)
x⁴ + 6561 - 162x² = 18225 - 306x² + x⁴
144x² - 11664 = 0
x² = 81
x = 9 cm
Now area of plot IV = 
= 99 cm²
Total Area of the land = 30 + 73.09 + 35 + 99
= 237.09 cm²
So assuming that the total =27
r+b=27
r=-5+3b
r=3b-5
subsitute 3b-5 for r in first equation
3b-5+b=27
4b-5=27
add 5
4b=32
divide by 4
b=8
subsitute
b+r=27
8+r=27
subtracct 8
r=19
red=19
blue=8
Answer:
y = 1/2x + 5
Step-by-step explanation:
Given :
Slope, m = 1/2
(x1, y1) = (6, 8)
y - y1 = m(x - x1)
y - 8 = 1/2(x - 6)
y - 8 = 1/2x - 3
y - 8 + 8 = 1/2x - 3 + 8
y = 1/2x + 5
Stamdard form of equation :
y = mx + c
Hence, equation is :
y = 1/2x + 5
Answer:
about 3 seconds
Step-by-step explanation:
hope this helps