Find the value of z in parallelogram BCDE.

Answers

Answer 1

Answer: 3z = z + 22
2z = 22
z = 11

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Prove that given any 17 integers, there exist nine of them whose sum is divisible by 9.(it might help to use the fact that given any five integer you can find three whose sum is divisible by 3)

Answers

Answer:

Step-by-step explanation:

let x,x+1,x+2,x+3,x+4,x+5,x+6,x+7,x+8

be 9 integers

x+x+1+x+2+x+3+x+4+x+5+x+6+x+7+x+8=9x+36=9(x+4)

which is divisible by 9

If one leg of a right triangle measures 3 centimeters and the other leg measures 6 centimeters, what is the length of the hypotenuse in centimeters?

Answers

Pythagorean theorem- a²+b²=c²
so a= 3 b=6 c=hypotenuse
3²+6²=c²
9+36=45
square root of 45 is 6.708203932 so 7.1 (1dp) is the answer

Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Answers

1. The first theorem used is that vertical angles are congruent.
2. The next theorem used is that adjacent angles in a parallelogram are supplementary.
3. The definition of supplementary angles is then used for angle formed by intersecting lines.
4. The theorem on vertical angles is used again.
5. Finally, the definition of the transitivity property is used to prove that alternate exterior angles are congruent.

Using the Corresponding Angles Theorem, Vertical Angles Theorem, and the Transitive Property of Congruence, we can prove that alternate exterior angles (e.g, <4 and <5) are congruent by the alternate exterior angles theorem.

Recall:

Alternate exterior angles are angles that lie outside the two lines that is cut across by a transversal but on opposite sides along the transversal.
Examples of alternate exterior angles are <2 and <7; <4 and <5 as shown in the figure attached below.

If we are given that $m \parallel n$ in the diagram attached below, the following are theorems and definitions we can use to prove that $\angle 4 \cong \angle 5$ (alternate exterior angles).

Statement 1: $\angle 4 \cong \angle 8$

Reason: Corresponding Angles Theorem

The corresponding angles theorem states that when two parallel lines (lines m and n) are intersected by a transversal line (line w), the two corresponding angles formed (e.g. <4 and <8) are congruent.

Statement 2: $\angle 8 \cong \angle 5$

Reason: Vertical Angles Theorem

The Vertical Angles Theorem states that the opposite vertical angles (e.g. <8 and <5) formed when two lines (lines n and w) intersect are congruent to each other.

Statement 3: $\angle 4 \cong \angle 5$

Reason: Transitive Property of Congruence

The Transitive Property of Congruence states that if a = b; and b = c; then a = c.

Therefore, using the Corresponding Angles Theorem, Vertical Angles Theorem, and the Transitive Property of Congruence, we can prove that alternate exterior angles (e.g, <4 and <5) are congruent by the alternate exterior angles theorem.

Learn more here:

brainly.com/question/16182992

Point G is located at (3, −1) and point H is located at (−2, 3). Find y value for the point that is 2 over 3 the distance from point G to point H.

Answers

Answer: The answer is $(5)/(3).$

Step-by-step explanation: Given that the co-ordinates of point G and H are (3, -1) and (-2, 3) respectively.

We are to find the y-value of the point P that is located at two-third distance from point G to point H.

As shown in the attached figure, the ration in which the point P divides the line segment GH is 2 : 1.

Therefore, the co-ordinates of point P will be

$\left((2* (-2)+1* 3)/(2+1),(2* 3+1* (-1))/(2+1)\right)\n\n\n=\left((-4+3)/(3),(6-1)/(3)\right)\n\n=\left((-1)/(3),(5)/(3)\right).$

Thus, the y-value of the point P is $(5)/(3).$

B. 1.67
m : n = 2 : 1
( x, y ) = ( (1*3 + 2*(-2))/(2+1) ; (1 * (-1) + 2 * 3) /(2 + 1) ) =
= ( (3-4)/3 ; (-1+6)/3 ) 1.67

Based on the graph below, what is the total number of solutions to the equation f(x) = g(x)?graph of function f of x equals negative 11 by 3 multiplied by x plus 11 by 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2

One
Two
Three
Four

Answers

Answer:

The total number of solutions is one

Step-by-step explanation:

we have

$f(x)=-(11)/(3)x+ (11)/(3)$

$g(x)=x^(3)+2x^(2)-x-2$

To solve the system of equations equate f(x) and g(x)

$f(x)=g(x)$

The solution of the system of equations is the intersection points both graphs

Using a graphing tool

see the attached figure

The solution of x

$x=1$

There is only one point of intersection both graphs

therefore

The total number of solutions is one

Answer:

the answer is One

Step-by-step explanation:

A solution is where the two lines intersect on the graph, and as you can see, in the picture above, the two lines only intersect once

Can someone help me match these up? i know the given is number one I need help with the rest.1.line RS || segment AB, ∠1=∠2
2.∠B = ∠1
3.∠A = ∠2
4.∠A = ∠B
5.RA = RB

A: If two ∠'s of a triangle are =, sides opposite are =
B: If lines ||, alternate interior ∠'s =
C: Given
D: Substitution
E: If lines ||, corresponding ∠'s are =

Answers

Answer:

1-C, 2-E, 3-B, 4-D, 5-A

Step-by-step explanation:

Firstly, from the figure, it is shown that line RS is parallel to the line segment AB and ∠1=∠2. Therefore, 1 matches with C.

Now, from the definition of parallel lines, the corresponding angles are always equal, therefore ∠B=∠1. Therefore, 2 matches with E.

Since, we are given that the lines are parallel, therefore by property of parallel lines, alternate angles are always equal. Therefore, ∠A=∠2. Hence, 3 matches with B.

Now, we know that ∠B=∠1 and ∠A=∠2, also that ∠1=∠2, therefore from these equations, ∠A=∠B. Hence, 4 matches with D.

If two angles of the triangle are equal that is ∠A=∠B, then the sides opposite to equal angles are always equal, therefore, RA=RB. Hence, 5 matches with A.

$C-1\nE-2\nB-3\nD-4\nA-5$

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