Which steps will verify that a parallelogram is a rectangle? Check all that apply.Calculate the lengths of the diagonals, and show that they are equal.
Calculate the lengths of all sides, and show that both pairs of opposite sides are congruent.
Calculate the slope of each diagonal, and show that the lines are perpendicular.
Calculate the midpoints of each diagonal, and show the diagonals bisect each other.
Calculate the slopes of every side, and show that adjacent sides are perpendicular.
Answers
The steps that will verify that a parallelogram is a rectangle are options A and E.
What is a parallelogram?
That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle.
A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
Therefore, the steps that will verify that a parallelogram is a rectangle are options A and E.
A. Calculate the lengths of the diagonals, and show that they are equal.
E. Calculate the slopes of every side, and show that adjacent sides are perpendicular.
Learn more about parallelogram;
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A & E
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Related Questions
Which of the following statements are true regarding functions? *Check all that applyA. The horizontal line test may be used to determine whether a function is one-to-one.B. A function is a relation in which each value of the input variable is paired with exactly one value of the output variable.C. The vertical line test may be used to determine whether a function is one-to-one.D. A sequence is a function whose domain is the set of real numbers.
What method would you choose to solve the equation 2x2 – 7 = 9? Explain why you chose this method.
Give the first four terms of a geometric sequence having a1=18 and r = 2.
the student council is organizing a trip to a rock concert. all proceeds from ticket sales will be donated to a charity. tickets to the concert cost $31.25 per person if a minimum of 104 people attend. for every 8 extra people that attend, the price will decrease by $1.25 per person.a). how many tickets need to be sold to maximize the donation to charity?b). what is the price of each ticket that maximizes the donation?c). what is the maximum donation?
Answers
-3y + 7 = y - 6(¹/₂y) - 6(2)
-3y + 7 = y - 3y - 12
-3y + 7 = -2y - 12
+ 3y + 3y
7 = y - 12
+ 12 + 12
19 = y
Answers
5.9 years.
Explanation:
Let x be the number of years. For the checking account, our expression would be 10000-1200x, since he withdraws $1200 from his account each year, and he begins with $10,000.
The formula for simple interest is:
I=prt
where:
p is the principal, r is the rate and t is the time
using our information, we have
p=2000,
r=8%=8/100=0.08, and
t=x.
This gives us 2000(0.08)(x).
However, we must add the $2000 to this (interest is added on to the principal); this gives us:
2000+2000(0.08)(x).
Setting these two equal, we have:
10000-1200x = 2000+2000(0.08)(x).
Simplifying the right hand side, we have:
10000-1200x=2000+160x.
Add 1200x to both sides:
10000-1200x+1200x=2000+160x+2000x;
10000=2000+1360x.
Subtract 2000 from both sides:
10000-2000=2000+1360x-2000;
8000=1360x.
Divide both sides by 1360:
5.9=x.
Let x be the number of needed years.
1. He deposits $10,000 into his checking account and he will withdraw $1,200 from his checking account each year. Then after x years he will have $10,000-$1,200x in his checking account.
2. He deposits $2,000 into his savings account and his savings account earns 8% interest each year, then after x years he will have
3. Equate these amounts of money:
4. Solve this equation:
- divide the equation by 400:
- plot graphs of the function
and
(see attached diagram);
- find the common point of these two graphs: (6.663,5.01).
Conclusion: he needs nearly 6.663 years.
always
sometimes
never
inconclusive
Answers
A square is always a rectangle. Then the correct option is A.
What is a rectangle?
A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
If all the sides of the rectangle become equal. Then the rectangle is known as a square.
A square is always a rectangle.
Thus, the correct option is A.
More about the rectangle link is given below.
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Answers
Answer: -1/2x - 2.
Step-by-step explanation:
To find the quadratic function y = a(x-h) that passes through the points (6, -1) and (4, 0), we can substitute the given points into the equation and solve for a and h. Let's go through the steps:
1. Substitute the coordinates of the first point (6, -1) into the equation:
-1 = a(6 - h)
2. Substitute the coordinates of the second point (4, 0) into the equation:
0 = a(4 - h)
3. Now we have a system of two equations with two unknowns. We can solve this system to find the values of a and h.
From the equation -1 = a(6 - h), we can rewrite it as:
-a(6 - h) = 1
From the equation 0 = a(4 - h), we can rewrite it as:
-a(4 - h) = 0
4. Simplifying the equations, we get:
-6a + ah = 1 (equation 1)
-4a + ah = 0 (equation 2)
5. Subtracting equation 2 from equation 1 eliminates the ah term:
-6a + ah - (-4a + ah) = 1 - 0
-6a + ah + 4a - ah = 1
-2a = 1
6. Solving for a, we divide both sides by -2:
a = -1/2
7. Substitute the value of a back into either equation (let's use equation 2) to solve for h:
-4(-1/2) + h(-1/2) = 0
2 + h/2 = 0
h/2 = -2
h = -4
8. Now we have the values of a = -1/2 and h = -4. We can substitute these values back into the original equation y = a(x-h) to find the quadratic function:
y = -1/2(x - (-4))
y = -1/2(x + 4)
y = -1/2x - 2
Therefore, the quadratic function that passes through the points (6, -1) and (4, 0) is
AI-generated answer
To find the quadratic function y = a(x-h) that passes through the points (6, -1) and (4, 0), we can substitute the given points into the equation and solve for a and h. Let's go through the steps:
1. Substitute the coordinates of the first point (6, -1) into the equation:
-1 = a(6 - h)
2. Substitute the coordinates of the second point (4, 0) into the equation:
0 = a(4 - h)
3. Now we have a system of two equations with two unknowns. We can solve this system to find the values of a and h.
From the equation -1 = a(6 - h), we can rewrite it as:
-a(6 - h) = 1
From the equation 0 = a(4 - h), we can rewrite it as:
-a(4 - h) = 0
4. Simplifying the equations, we get:
-6a + ah = 1 (equation 1)
-4a + ah = 0 (equation 2)
5. Subtracting equation 2 from equation 1 eliminates the ah term:
-6a + ah - (-4a + ah) = 1 - 0
-6a + ah + 4a - ah = 1
-2a = 1
6. Solving for a, we divide both sides by -2:
a = -1/2
7. Substitute the value of a back into either equation (let's use equation 2) to solve for h:
-4(-1/2) + h(-1/2) = 0
2 + h/2 = 0
h/2 = -2
h = -4
8. Now we have the values of a = -1/2 and h = -4. We can substitute these values back into the original equation y = a(x-h) to find the quadratic function:
y = -1/2(x - (-4))
y = -1/2(x + 4)
y = -1/2x - 2
Therefore, the quadratic function that passes through the points (6, -1) and (4, 0) is y = -1/2x - 2.
:48
Answers
Answer:
84:48
Step-by-step explanation:
7:4 = x:48
7*48 = 4x
7*48/4 = x
x = 7*12 = 84
So, the equivalent ratio is 84:48