Algebra For questions 1-5, find the value of the variable.

1.
x =

(1 point)

2.
y =

(1 point)

3.
x =

(1 point)

4.
x =

(1 point)

5. (1 point)
x = , y = , b = 90
x = , y = 3, b = 95
x = , y = 2, b = 90
x = , y = , b = 130
In Exercises 6-8, decide whether the statement is true or false. If true, explain why. If false, show a counterexample.
6. A quadrilateral with congruent diagonals is an isosceles trapezoid or rectangle. (1 point)
True; diagonals are congruent in the following example:


False; diagonals are equal in the following example:

False; diagonals are equal in the following example:

7. The diagonals of a kite separate the quadrilateral into four congruent triangles. (1 point)
False; no triangles are congruent.
False; only two triangles at a time are congruent.

True; four triangles are congruent.
8. Each diagonal of a kite bisects two angles of the kite. (1 point)
True;


False;
True;
False;
Give the coordinates for point A without using any new variables.
9. (1 point)
(m, n)
(m, 0)
(n, m)
(0, n)
10. (1 point)
(k, p)
(-k, p)
(k, 0)
(0, p)

1)51

2)32
3)2
4)3
5)A
6)C
7)B
8)B
9)C
10)C

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Is this true or false (-5)sqeure roof of two

To find the value of the variable in algebraic equations, you need to isolate the variable on one side of the equation.

For example, in question 1, you need to find the value of x. If the equation given is something like "3x = 12," you would divide both sides of the equation by 3 to isolate x:

3x/3 = 12/3

x = 4

In question 2, if the equation is "2y - 5 = 11," you would add 5 to both sides of the equation to isolate y:

2y - 5 + 5 = 11 + 5

2y = 16

y = 8

Similarly, follow these steps for questions 3 and 4 to find the values of x:

For question 3, isolate x by performing the necessary operations or inverse operations on both sides of the equation.

For question 4, follow the same process as in the previous questions to isolate x.

For question 5, there seem to be multiple variables given (x, y, and b) and their corresponding values. Simply choose the set of values that satisfy the given conditions (in this case, one set is x = 90, y = 2, and b = 90).

Moving on to questions 6-8, you need to determine whether the statement is true or false and provide an explanation or counterexample.

For question 6, the statement says that a quadrilateral with congruent diagonals is an isosceles trapezoid or rectangle. To determine if this is true, you can provide a valid example where the diagonals are congruent (like the first option) or show a counterexample where the diagonals are not congruent (like the second and third options).

For question 7, you need to decide if the statement about the diagonals of a kite separating the quadrilateral into four congruent triangles is true or false. Based on your knowledge of kites, you can determine whether the statement is correct or provide a counterexample to show it is false.

Similarly, for question 8, you need to decide if each diagonal of a kite bisects two angles of the kite. Again, you can use your understanding of kite properties to determine if the statement is true or false and provide a valid explanation or counterexample.

For the final two questions, you are asked to give the coordinates for point A without using any new variables. Look at the given options and choose the one that represents the coordinates of point A.

I hope this explanation helps you understand how to approach these algebraic problems.