Short Answer: Tony 40 Cleo 30
Givens
T = Tony
C = Cleo
Equations
1/2 T + 1/3 C = 30 (1)
2/5 T + 1/2 C = 31 (2)
Adjustments
Multiply (1) by 3
Multiply (2) by 2
New Equations
3/2 T + C = 90 (1a)
<u>4/5 T + C = 62</u> (2a) Subtract (2a) from (1a)
(3/2 - 4/5)T = 28 the common multiple of 2 and 5 = 10.
(15/10 - 8/10)T = 28
7/10 T = 28 Multiply by 10
7T = 28*10
7T = 280 Divide by 7
T = 280/7 = 40
Put T = 40 into (1)
1/2 T + 1/3 C = 30
1/2 (40) + 1/3 C = 30
20 + 1/3 C = 30 Subtract 20 from both sides.
1/3 C = 30 - 20
1/3 C = 10 Multiply through by 3
C = 10 * 3
C = 30
Answer:
Cleo has 30 books.
Tony has 40 books.
Check
<em>Use Equation 2</em>
2/5 T + 1/2 C = 31
2/5*40 + 1/2 * 30 = ? 31
16 + 15 =?3`
31 = 31 They are equal.
Answer:
The answer is 
Step-by-step explanation:
Given:
Darcy harvest 8 3/4 acres of corn every 5/6 of an hour.
Now, to find the acres per hour it takes to harvest.
Darcy harvest = 
The time he took to harvest = 
So, to get the acres per hour we put formula:
Therefore, the answer is
First, you should graph the points. For the first number, called the X-Axis, you should to the right or left, and for the second number, called the Y-Axis, you should go up or down.
To find the distance between Point A and Point C, you should simply just count the number of intersections between them (4).
Angle B is a right angle because if the triangle is bisected at B, it will leave a right angle on either side. Therefore, to label it, you should simply just draw a line through Point B all of the way to line (A,C).
The type of triangle you have drawn is an isosceles, because it has 2 equal angles and 2 equal sides.
We know both of the sides that are unknown will be the same because the triangle is bilateral. Then, we can use the bisection we made earlier to solve for the unknown sides using Pythagorean Theorem. Since earlier, we know the entire bottom is 4, we know half of the bottom is 2. We can also see that the height of the triangle is 2. We then plug those numbers into the Pythagorean Theorem (A^2*B^2=C^2) which makes the value of C^2=16. We then take the square root of C^2 and 16 to see that both unknown sides are 4.
Answer:
Area of the shaded region = 23.33 in²
Step-by-step explanation:
Area of a sector = 
Where θ = Central angle subtended by an arc
r = radius of the circle
Area of the sector BCD = 
= 52.36 in²
Area of equilateral triangle BCD = 
= 
= 
in²
= 43.30 in²
Area of the shaded portion in ΔBCD = 52.36 - 43.3
= 9.06 in²
Area of sector CAD = 
= 39.27 in²
Area of right triangle CAD = 
= 
= 
= 25 in²
Area of the shaded part in the ΔACD = 39.27 - 25
= 14.27 in²
Area of the shaded part of the figure = 9.06 + 14.27
= 23.33 in²
Answer:
B
Step-by-step explanation:
