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Marina86
11 days ago
9

Complete the coordinate proof of the theorem. Given: A B C D is a parallelogram. Prove: The diagonals of A B C D bisect each oth

er. Art: A parallelogram is graphed on a coordinate plane. The horizontal x-axis and vertical y-axis are solid. The vertex labeled as A lies on begin ordered pair 0 comma 0 end ordered pair. The vertex labeled as B lies on begin ordered pair a comma 0 end ordered pair. The vertex labeled as D lies on begin ordered pair c comma b end ordered pair. The vertex C is unlabeled. Diagonals A C and B D are drawn by a dotted lines. Enter your answers in the boxes. The coordinates of parallelogram ABCD are A(0, 0) , B(a, 0) , C( , ), and D(c, b) . The coordinates of the midpoint of AC¯¯¯¯¯ are ( , b2 ). The coordinates of the midpoint of BD¯¯¯¯¯ are ( a+c2 , ). The midpoints of the diagonals have the same coordinates. Therefore, AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other.

Mathematics
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leons older brother is 4and 3/4 feet tall. Leon is 1/3 foot shorter than his brother. How tall is leon
zzz [12365]

Answer: 4\frac{5}{12}\ feet

Step-by-step solution:

Leon’s older brother’s height is 4\frac{3}{4} feet

=\frac{16+3}{4}=\frac{19}{4} feet

Because Leon is 1/3 foot shorter than his brother,

Leon’s height = \frac{19}{4}-\frac{1}{3}

Convert to like fractions by multiplying numerator and denominator: multiply 3 for the first fraction and 4 for the second.

So, Leon’s height = \frac{57}{12}-\frac{4}{12}

=\frac{57-4}{12}\\=\frac{53}{12}=4\frac{5}{12} feet

Therefore, Leon’s height is 4\frac{5}{12}\ feet feet.

8 0
3 months ago
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the t
Leona [12618]

B refers to the base of the triangle,
and a signifies the length of the two identical sides.


The measurement labeled as 'a' is larger than 'b' since those equal sides are longer than the base. Given "one of the longer sides measures 6.3 cm," we assign a = 6.3.


Substitute 6.3 for each 'a' in the equation and solve for b:
2a + b = 15.7
2(6.3) + b = 15.7
12.6 + b = 15.7
b = 15.7 - 12.6 (applying subtraction property of equality)
b = 3.1

7 0
3 months ago
The sum of two consecutive integers is one less than three times the smaller integer. Find the two integers
Inessa [12570]

The two integers are 2 and 3n+n+1=3n-1\\\\
2n+1=3n-1\\\\
3n-2n=1+1\\\\
n=2\\
n+1=3

4 0
2 months ago
Read 2 more answers
What is the domain of the function graphed below?
zzz [12365]
The function is applicable within the segments of x:
(-∞, -1) and [-1, 7), meaning it is valid for x < 7.

Importantly,
the function cannot be evaluated at x = -1 in the left part of the linear graph, while it is valid at x = -1 in the right segment of the same line. Additionally, the function is not defined at x = 7 or any value above it.

Conclusion: x < 7.
5 0
2 months ago
Read 2 more answers
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