Which of the following statements must be true about the diagram

Step-by-step explanation:

To prove that two lines are perpendicular, when all we have are those two lines, we can use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.

Our diagonals intersect at point O, so we'd need to show the two linear angles formed at that intersection point are equal, and we can do that with triangle congruency.

A rhombus is a parallelogram, so we will use what we already know about parallelograms - that the diagonals bisect each other.

It is then easy to show that the triangles  ΔAOD and  ΔAOB are congruent using the Side-Side-Side postulate, and from that that ∠AOD ≅ ∠AOB.

And now, since ∠AOD and ∠AOB are a linear pair, we use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.

PROOF

(1) ABCD is a rhombus //Given

(2) AB=AD                     //definition of rhombus

(3) AO=AO                    //Common side, reflexive property of equality

(4) BO=OD // A rhombus is a parallelogram, a parallelogram's diagonals bisect each other

(5) △AOD≅△AOB   //Side-Side-Side postulate.    

(6) ∠AOD ≅ ∠AOB     //Corresponding angles in congruent triangles (CPCTC)

(7) AC⊥DB     //Linear Pair Perpendicular Theorem

The converse of this is also true: if a parallelogram's diagonals are perpendicular, it is a rhombus.

Answer:

I think that is correct because I got the same answer

Answer:

The answer is 4.7

Step-by-step explanation:

[tex]y = \frac{l1y1 + l2y2}{l1 + l2} \\ y = \frac{ \frac{2}{3} \times 7 + \frac{1}{3} \times 0 }{ \frac{2}{3} + \frac{1}{3} } \\ y = \frac{14}{3} = 4.7[/tex]

Answer:

1. 100000

2. 16777216

3. x7

4.64

5.1/64  (Decimal: 0.015625)

Step-by-step explanation:

Answer:

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9514 1404 393

Answer:

  450 L

Step-by-step explanation:

Let x represent the number of liters of 70% solution needed. Then the amount of 15% solution needed is (550-x), and the total amount of acid in the mixture is ...

  0.70x + 0.15(550-x) = 0.60(550)

  0.55x + 82.5 = 330 . . . . simplify

  0.55x = 247.5 . . . . . . . . . subtract 82.5

  x = 450 . . . . . . . . . . . divide by 0.55

450 liters of 70% acid solution must be used.

Answer:

-11x = -55

x = 5

Step-by-step explanation:

Hope that helps!

Answer:

s cm+s cm+s cm+s cm

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer: 15

Step-by-step explanation: 2:3.       10 baskets

10 -:- 2 = 5 so write 5 THREE times

5,5,5     Now  Add.

5+5+5= 15 :) pls thanks this ty bye ❤️‍

Answer:

10x - 5

Step-by-step explanation:

Perimeter is found by adding up all the side lengths.

(2x-4) + (5x+6) + (3x-7) = 10x - 5

Answer:

28

Step-by-step explanation:

let x be the number,

(3/4)x+5=26

(3/4)x=21

x=21*(4/3)

x=28

Answer:

<2, <3, <4

Step-by-step explanation:

You have parallel lines cut by a transversal, so alternate interior angles are congruent. Also, alternate exterior angles are congruent. Corresponding angles are congruent.

Vertical angles are always congruent.

I'll write each congruent angle and the reason.

<2, vertical

<3, corresponding

<4, alternate exterior angle

Answer:

nice flex

Step-by-step explanation:

Answer:

7 white and 8 dark bars

Step-by-step explanation:

x white bars

15-x dark bars

cost of white bars is 2 * x

cost of dark bars is 2,5 * (15-x)

Write an equation

2x + 2,5 * (15-x) = 34

2x + 37,5 - 2,5x = 34

-0,5 x = - 3,5

x = 7

So we have x = 7 white bars

and 15 - x = 15 - 7 = 8 dark bars

Answer:

Should be 24%

Step-by-step explanation:

12/50= .24

Answer:

x = -4, x = 4

Step-by-step explanation:

A denominator cannot equal zero since division by zero is undefined.

Set the denominator equal to zero and solve for x. That will give you the values of x that would cause the denominator to be equal to zero and must be excluded from the domain.

x^2 - 16 = 0

(x + 4)(x - 4) = 0

x + 4 = 0  or  x - 4 = 0

x = -4  or  x = 4

Answer: x = -4, x = 4

Answer:

50

Step-by-step explanation:

Direct labour rate variance is $3,000

Direct labour efficiency variance is $5,000

Actual direct labour costs is $100,000

Therefore the standard direct labour production during the month of January can be calculated as follows

= 100,000/5,000-3,000

= 100,000/2,000

= 50

Answer:

photomath, assistant in mathematics, will decompose everything and give the correct answer.

Answer:

$67

Step-by-step explanation:

So 5x12+7=C

PEDMAS so:

5x12 = 60

60+7 = 67

67 = C

Answer:

I guess its the 3rd one not sure

Answer:

16. 53 = 14.50 + p  The answer is 38.50. 17a. Your final bowling score is 105-14, which is equal to 91.

Step-by-step explanation:

53 = 14.50 + p

53-14.50=p

38.50=p

For b... I don't know what a "10nth frame" is. Or a spare. Sorry...

Answer:

38

Step-by-step explanation:

96/16  

+(25)(2)−15−3

=6+(25)(2)−15−3

=6+50−15−3

=56−15−3

=41−3

=38

Answer:

289.877 ft

Step-by-step explanation:

You can draw the eagle and mouse by using a right triangle. You know that the height of the triangle will be 280 feet and the distance between eagle and mouse should be the hypotenuse. Since we know the angle and one side of the triangle, we can use trignometry (cosine(angle)=adjacent/hypotenuse). Plug in your values and solve for the hypotenuse.

Answer:

a is how many times bella went 2 yard depot

b is how many gardening gloves she bought

c is how many gardening hats she bought