Answer:
<em>The length of AB is 40</em>
Step-by-step explanation:
<u>The Midpoint of a Segment</u>
If A and B are the endpoints of a segment, and C is the midpoint of AB, then the distance from A to C is equal to the distance from B to C.
We are given the lengths BC=3x-7 and AC=9x-61:
9x - 61 = 3x - 7
Subtracting 3x:
6x - 61 = - 7
Adding 61:
6x = 54
Dividing by 6:
x = 9
The total length AB is
BC+AC=3x - 7 + 9x - 61 = 12x - 68
Substituting x=9:
AB = 12*9 - 68 = 40
The length of AB is 40
F(x) = 2ln(x) + c [integral of 1/x is ln x]
f(e^(1/2)) = 2ln(e^(1/2)) + c = 5
2(1/2) + c = 5 [ln(e^a) = a]
1 + c = 5
c = 4
So:
f(e) = 2ln(e) + 4 = 2 + 4 = 6
<span>Answer is 6.
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Answer:
The midpoint is ( 1.5, -1.5)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
( -2+5)/2 = 3/2 =1.5
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
( 3-6)/2 = -3/2 =-1.5
The midpoint is ( 1.5, -1.5)
Answer:
86.28 ft²
Step-by-step explanation:
The figure given consists of a rectangle and a semicircle. The area of the figure = area of rectangle + area of semicircle
Area of rectangle =
Where,
l = 10 ft
w = 8 ft
Area of semicircle:
Area of semicircle = ½ of area of a circle = ½(πr²)
Where,
π = 3.14
r = ½ of 8 = 4 ft
Area of semi-circle = ½(3.14*4) = 6.28 ft²
Area of the figure = area of rectangle + area of semi-circle = 80 + 6.28 = 86.28 ft² (nearest hundredth)
<span>Let's call these friends by their first initial:
K = Kiana, G = Gary, M = Monty, W = Willa
Now we can convert the question to a system of linear equations:
Gary has 3 cards more than Kiana, so G = K + 3
Monty has 7 cards more than Kiana, so M = K + 7
Willa has twice as many cards as Monty, so W = 2M = 2(K + 7) = 2K + 14
74 cards given out = all the friends combined, so
74
= K + G + M + W
= K + (K + 3) + (K + 7) + (2K + 14)
= 5K + 3 + 7 + 14
= 5K + 24
50 = 5K
10 = K, so Kiana had 10 cards
G = K + 3 = 13, so Gary had 13 cards
M = K + 7 = 17, so Monty had 17 cards
W = 2M = 34, so Willa had 34 cards
Checking our work, 10 + 13 + 17 + 34 = 74 cards total.</span>