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Korvikt [17]
1 year ago
11

Triangles A C B and M Q R are shown. Sides A B and M R are congruent. Angles C A B and M R Q are 42 degrees. Angle C B A is 53 d

egrees. Angle M Q R is 85 degrees.
Are the triangles congruent? Why or why not?

Yes, all the angles of each of the triangles are acute.
Yes, they are congruent by either ASA or AAS.
No, AngleB is not congruent to AngleQ.
No, the congruent sides do not correspond.
2 triangles are connected at one side. The triangles have 2 congruent sides and 1 congruent angle. The first triangle is rotated and then translated down to form the second triangle.
Mathematics
1 answer:
miss Akunina [59]1 year ago
4 0

By ASA postulate it can be say that the triangle ABC and triangle MRQ are congruent

<h3>What is Angle Sum Property?</h3>

The sum of all three angles(interior) of a triangle is 180 degrees, and the exterior angle of a triangle measures the same as the sum of its two opposite interior angles.

Using Angle Sum Property, in ΔMRQ

<M + <R + <Q= 180

<M + 42 + 85 = 180

<M = 180 -42

<M= 53°

Now, In ΔMRQ and ΔABC  

<A= <R ,

<B = <M

AB = MR

Hence, By ASA criteria ΔMRQ ≅ ΔABC  

Learn more about this concept here:

brainly.com/question/3486366

#SPJ1

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Pete corporation produces bags of peanuts. It's fixed cost is $18,900. Each bag sells for $2.17 with a unit cost of $1.27. What
pentagon [3]

Answer:

in units: 18,900

in dollars: $ 41,013

Step-by-step explanation:

The break even point is the sales dollar amount or sales in unit at whichthe operating income of the firm equals to zero:\frac{Fixed\:Cost}{Contribution \:Margin} = Break\: Even\: Point_{units }

Where:

\frac{Contribution \: Margin}{Sales \: Revenue} = Contribution \: Margin \: Ratio

<em><u>Contribution margin:</u></em>

2.17 - 1.27 = 1 dollar per unit

Break even:

$18,900 fixed cost /  $1 per unit = 18,900 units

Then, in sales:

18,900 x $2.17 each = 41.013‬

break even point:

3 0
3 years ago
Read 2 more answers
Help with math please example 1
hram777 [196]

Answer:

I'm not very sure about this one what icing in probably not going to be right but what I think is that they're not the same because look at the size difference imagine putting an adult's next to a baby that's kind of what it's like the bigger quadrilateral is also the adults while the little one is the baby what do you think about that I probably think that they're not saying

Step-by-step explanation:

sorry I gave it to you in my answer

3 0
3 years ago
In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.
konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

BC^2=BD\cdot AB.

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.

Take positive value x. You get

AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.

2. According to the previous theorem,

AC^2=AD\cdot AB.

Then

AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

Answer: AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0
3 years ago
Read 2 more answers
Aisha wants to paint the four walls of her living room.
sergiy2304 [10]

The total amount Aisha would pay to paint her room is $54.

<h3>What is the cost of painting the rooms?</h3>

The first step is to determine the area of the walls. The walls have the shape of a rectangle. Thus, the formula for the area of a rectangle would be used to determine the area of the wall.

Area of the three walls without a door : 3 x (length x width)

3 x (2.4 x 5.2) = 37.44 m²

Area of the fourth wall with a door : area of the wall - area of the door

(2.4 x 5.2) - (2 x 0.8) = 10.88m²

Total area of the walls : area of the three walls + area of the wall with the door

10.88m² + 37.44 m² = 48.32 m²

The next step is to determine the number of tins that would be needed:

48.32 /12 = 4.03

5 tins would needed

Cost of the 5 tins: (4 x 12) + (0.5 x 12) = $54

To learn more about how to calculate the area of a rectangle, please check: brainly.com/question/16595449

#SPJ1

3 0
2 years ago
Solve the inequality for x -5x - 49 &gt; 113
Anika [276]
X < -40.5

To find this, here are the steps:

Combine like terms like so:

-4x - 49 > 113

Then, begin to isolate the variable x by adding 49 to both sides leaving you with:

-4x > 162

Then divide by negative four. Don’t forget, dividing by negatives switches the way the sign points so your final product will be:

x < -40.5

Hope this helps!
3 0
3 years ago
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