There were 14 hens and 18 pigs in the backyard
Step-by-step explanation:
Katie was visiting her grandpas farm
- She saw only hens and pigs
- Katie counted 32 heads and 100 feet in the backyard
We need to find how many hens and pigs in the backyard
Assume that there are x hens and y pigs in the backyard
∵ There are x hens and y pigs in the backyard
∵ There are 32 heads
∴ x + y = 32 ⇒ (1)
∵ Each hen has 2 feet
∵ Each pig has 4 feet
∵ There are 100 feet
∴ 2x + 4y = 100 ⇒ (2)
Let us solve the system of equations to find how many hens and pigs
Multiply equation (1) by -2 to eliminate x
∴ -2x - 2y = -64 ⇒ (3)
- Add equations (2) and (3)
∴ 2y = 36
- Divide both side by 2
∴ y = 18
Substitute the value of y in equation (1) to find the value of x
∵ x + 18 = 32
- Subtract 18 from both sides
∴ x = 14
There were 14 hens and 18 pigs in the backyard
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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Answer:Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
Step-by-step explanation:
Given:
Terri plans to charge a base fee of $10 plus $7 per hour for babysitting.
To find:
The function that could be used to represent her total charge for the babysitting service, y, as a function of the number of hours she babysits, x.
Solution:
Let y be the total charge for the babysitting service for x hours.
Base fee = $10
Additional fee for one hour = $7
Additional fee for x hour = $7x
Total fee = Base fee + Additional fee for x hours
![y=10+7x](https://tex.z-dn.net/?f=y%3D10%2B7x)
Therefore, the equation of required function is
.
The dimensions of screen are height 20cm and width 30cm
• In Mathematics, rectangle is a four sided polygon, having all the internal angles equal to 90.The opposite sides of the rectangle are equal in length which makes rectangle different from square.
• Area of rectangle is the product of length and breadth of rectangle. Perimeter of rectangle is twice the sum of its length and breadth.
• Area = l*b
Perimeter = 2(l+b)
The width of the laptop screen is 10 cm more than the height and the area of the screen is 600cm2.
Let the height of the screen be x cm
Width of the screen will be = x+10 cm
Area of screen = width * height
Area given = 600 cm²
x(x+10) = 600
x²+ 10x = 600
Solving Quadratic Equation
x²+10x -600=0
x² +30x-20x-600=0
x(x+30) – 20(x+30) = 0
(x-20)(x+30)= 0
x = 20 and x = -30
As the value of the height of the screen cant be negative. So x = 20
Height = 20cm
Width = 20+10 = 30cm
Therefore, the dimensions of screen are height 20cm and width 30cm .
Learn more about height and width
brainly.com/question/25292087
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To answer this, you need to make a systems of equations.
25x + 35y = 1450
x + y = 50 ----> y = 50 - x
25x + 35(50-x) = 1450
25x + 1750 - 35x = 1450
25x - 35x + 1750 = 1450
-10x + 1750 = 1450
- 1750 -1750
-10x = -300
x = 30
He played tennis for 30min