Luke takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. If the piece of paper is 16 inches long and 12 inches wide, how long is the dagonal cut that Luke made? Make sure to show your work and explain ypur answer.
Answers
In this question c squared is the diagonal you are trying to figure out.
A squared is any side of the triangle other than c squared, and b squared is the other side of the triangle. So a squared is 16 inches squared, and b squared is 12 inches squared.
To work this out, we square 16 to give 256.
Then 12 is squared - 144.
Then we square root 256 + 144, or the square root of 400.
The square root of 400 is 20, so the diagonal Luke cut was 20 inches long.
Final answer:
The length of the diagonal cut is calculated using the Pythagorean theorem. The sides of the paper form two sides of a right-angled triangle, and by squaring and adding these lengths, then taking the square root of the result, we find that the hypotenuse, or diagonal, is 20 inches long.
Explanation:
In mathematics, particularly in geometry, the Pythagorean theorem is the fundamental principle used to calculate the length of the hypotenuse in a right-angled triangle. In this question, the sheet of paper can be considered a rectangle and when it is cut from one corner to the opposite corner, it forms two right-angled triangles.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c²
Here, the length and width of the paper represent the two sides of the triangle, 16 inches and 12 inches respectively, and the diagonal cut (we'll call it 'd') is the hypotenuse. Thus, the equation becomes:
12² (which equals 144) + 16² (which equals 256) equals d²
Adding 144 and 256 gives 400, so d² = 400. To find 'd', we take the square root of 400, which is 20.
So, the length of the diagonal cut that Luke made is 20 inches.
Learn more about Pythagorean theorem here:
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Related Questions
Just 2 more! Ik we got this! Just please, it’s due at 11pm!
Find the coordinates for the midpoint of the segment with endpoints given. (5, 6) and (8, 2)
And an equation of the line. Write the equation using function notation.Through (-5.-9), parallel to 2x + 5y = 7
What is the best approximation of the solution to the system to the nearest integer values. A.1,3B. 3,2C.2,3D. 3,4
Answers
Answers
x²+2x+1=0
x²+1x+1x+1=0
x(x+1)+1(x+1)
(x+1)(x+1)
x=-1
B. (-3x-6i)(x+2i)
C. (-3x-6i)(x+2i)
D. (-3x-4i)(x-3i)
Answers
Answer:
B. (-3x-6i)(x+2i)
C. (-3x-6i)(x+2i)
Since they are the same answer choice. Should be (-3x-6i)(x-2i) should be the correct answer.
Step-by-step explanation:
The polynomial -3x^2-12 can be factored using GCF into -3(x^2+4).
x^2+4 is a sum of squares and factors into the form (x+ai)(x-ai).
x^2+4 factors into (x+2i)(x-2i).
We put them together and have -3(x+2i)(x-2i) = (-3x-6i)(x-2i)
$3,500 at 9%; $4,300 at 11%
$3,400 at 9%; $3,200 at 11%
$3,100 at 9%; $4,900 at 11%
Answers
Answer:
The answer is $3,100 at 9%; $4,900 at 11%
Step-by-step explanation:
You can solve this problem with a system of equations, that is, a system that can contain 2 or more equations. In this case, arms 2 linear equations with two variables: x and y. So first you define what your variables are:
- x: amount of money invested in the account with 9% interest
- y: amount of money invested in the account with 11% interest
Now you can define the system of equations. On the one hand you know that in the account that has 11% interest Mr. Brownwood deposited $1800 more than in the other account. In an equation and according to the previously defined variables this means: y=x+1800 Equation (A)
On the other hand, you know Mr. Brownwood earned $ 818 in interest. This means that the sum between the interest generated in the account deposited with 9% interest plus the interest generated in the account deposited with 11% interest is $ 818. And to calculate the amount of money generated by interest you multiply the percentage of interest by the amount deposited. Remember that to convert from percentage to decimal you must divide the number by 100. Then 9% is 0.09 and 11% is 0.11. In summary, considering this, you get the equation: 0.09*x+0.11*y=818 Equation (B)
Now you have both equations with the two variables to solve the system. There are several ways to solve the system. One of the most used ways is substitution, which consists in isolating one of the variables from one of the equations and replacing it in the other equation.
In this case you isolate the variable "y" from equation A, and you get: y=1800+x
Now replace it in equation (B): 0.09*x+0.11*(1800+x)=818
First you apply distributive property, which consists of distributing the multiplication by the terms within the parenthesis:
0.09*x+0.11*1800+0.11*x=818
0.09*x+198+0.11*x=818
Now, we leave the variable x on one side of the equality, in this case the left, and the numbers without the variable on the other side, in this case the right. To pass the numbers from one side of the equality to the other, you must keep in mind that you must use the opposite operation, that is, if the number 198 is adding on one side of the equality, the other side is subtracted:
0.09*x+0.11*x=818-198
Now you perform the corresponding operations. Then you isolate the variable and, and as in the previous case, you pass the number that accompanies the variable on the other side of equality with the opposite operation. In this case it is multiplying and its opposite operation is the division:
0.2*x=620
x=3100
Now you replace this value in either of the two equations, A or B, and solve that equation to get the value of y. So: y=4900
Remembering that x was amount of money invested in the account with 9% interest and y was amount of money invested in the account with 11% interest, you can say that $3100 was the amount invested at 9% and $4900 was the amount invested at 11%
Answer:3100 with 9%
Step-by-step explanation:
b. what was the radius of the first ferris wheel?
c. The first ferri wheel took nine minutes to make a complete revolution. how fast was the wheel moving?
Answers
Answer:
a. The radius of the navy pier wheel is 56% of the radius of the first ferris wheel
b. The radius of the first ferris wheel was 179% of the radius of the navy pier ferris wheel
c. The wheel was moving at 0.70
Step-by-step explanation:
Navy pier wheel circumference = Cn
First ferris wheel circumference = Cf
Cn = 0.56*Cf
a.
Circumference Perimeter = 2*π*Radius
Navy pier wheel radius = Rn
First ferris wheel radius = Rf
Cn = 0.56*Cf
2*π*Rn = 0,56*2*π*Rf (equation 1)
dividing both sides by 2π
Rn = 0,56*Rf
b.
From equation 1
2*π*Rn = 0,56*2*π*Rf
dividing both sides by 2π
Rn = 0.56*Rf
dividing both sides by 0.56
Rf = *Rn
Rf = 1.79*Rn
c.
9 minutes / revolution
1 revolution = 2π radians
The wheel makes 2π radians in 9 minutes
Wheel velocity =
Wheel velocity = 0.70
Answers
Answer:
$8,500
Step-by-step explanation:
Let the original gross salary be "X" dollars.
First, it was increased by 8%, which can be calculated as 1.08 times the original salary:
1.08 * X
Then, this new amount was increased by 10%, which can be calculated as 1.10 times the previous amount:
1.10 * (1.08 * X)
The final amount is given as $10,098:
1.10 * 1.08 * X = 10,098
Now, solve for X:
1.188 * X = 10,098
Divide both sides by 1.188 to find X:
X = 10,098 / 1.188
X ≈ 8,500
So, the original gross salary was approximately $8,500.