ABCD is a rectangle. Find the length of each diagonal.ac=2(5a+1) bd=2(a+1).
Answers
The length of the diagonal of the rectangle is d = 2
What is the diagonal of a rectangle?
The diagonal of a rectangle is calculated by the formula
From the Pythagoras Theorem , The hypotenuse² = base² + height² , and
Diagonal of a Rectangle = √ ( Length )² + ( Width )²
Given data ,
Let the rectangle be represented as ABCD
Now , the diagonal of the rectangle is AC and BD
The measure of AC = 2 ( 5a + 1 )
And , the measure of BD = 2 ( a + 1 )
For a diagonal of a rectangle ,
The two diagonals of the rectangle will be same
So , the measure of AC = measure of BD
Substituting the values in the equation , we get
2 ( 5a + 1 ) = 2 ( a + 1 )
On simplifying the equation , we get
Divide by 2 on both sides of the equation , we get
5a + 1 = a + 1
Subtracting a on both sides of the equation , we get
4a + 1 = 1
Subtracting 1 on both sides of the equation , we get
4a = 0
a = 0
Now , substitute the value of a in measure of AC , we get
The measure of diagonal AC = 2 ( 5 ( 0 ) + 1 )
The measure of diagonal AC = 2
Hence , the measure of diagonals of the rectangle = 2
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Rectangle diagonals are equal.
2(5a+1) = 2(a+1)
10a + 2 = 2a + 2
10a -2a = 2 - 2
8a = 0
⇒ a = 0
AC = 2(5a+1) = 2(5 × 0 +1)= 2(0 + 1) = 2 × 1 = 2
BD = 2(a+1) = 2(0 + 1) = 2 × 1 = 2
Ansver: AC = BD = 2
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Since 1.3 is greater than 1.05; This mens;
the small has will be;
1.3 ounces of raw
y=4.9x-1.64
The approximate solution to the system is (____,____).
Answers
When solving the problem graphically we must take into account the following:
1) The solution of the system of equations is given by the intersection of both functions.
2) The solution is an ordered pair of the form (x, y)
For this case we observe that the solution is given by:
Note: see attached image.
Answer:
The approximate solution to the system is (1.23, 4.39)
The approximatesolution to the system is (1.23,4.39).
what is Graphical method?
Graphical method, or Geometric method, allows solving simple linear programmingproblems intuitively and visually. This method is limited to two or three problems decision variables since it is not possible to graphically illustrate more than 3D.
For this case we have the following system of equations:
y=-0.25x+4.7
y=4.9x-1.64
The above linear system equation can be solved using graph, using
1) The solution of given system of equations can be determined by the intersecting point of equation.
2) Then the solution will be an ordered pair, form (x, y).
Now considering the above two points, the graph is attached below:
look at the intersecting point here, the x- coordinate is 1.23 and the ycoordinate is approx. 4.40.
Hence, the approximate solution to the system is (1.23,4.39)
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5:50
6:10
6:50
Answers
5:50 + 20 minutes = 5:70
60 minutes in 1 hour
therefore
70 - 60 = 10
6:10 (plus one hour that you take away from 70)