If ΔABC = ΔDEF, angle m∠A = 50, and angle m∠E = 30, what is angle m∠C?

Answers

Answer 1
Answer: 100 degrees
Triangles add up to 180 degrees
30 + 50 = 80
180 - 80 = 100
Answer 2
Answer:

When you indicate triangle congruency, the order of the letters matter. As you see these statements, look at how the side length names correspond to how the letters are written in its order, ΔABC ≅ ΔDEF. (By the way, triangles aren't equal with an = sign. It's a ≅ congruency sign.)

AB is congruent or the same length as DE.

BC is congruent or the same length as EF.

AC is congruent or the same length as DF.

In the same way, all of the angles in the corresponding order are ALSO congruent. By the way, we say that angles are congruent and angle MEASURES (like 30 degrees) are equal.

m∠A = m∠D

m∠B = m∠E

m∠C = m∠F

In the same way, we can try to find m∠C, or measure C!

1. Let's find the missing angle!

So, we know that m∠A is 50 degrees and m∠E is 30 degrees. Since we know that m∠E = m∠B because of the order of the triangles, now we know two of the angles in triangle ABC.

m∠A = 50 degrees

m∠B = 30 degrees

m∠C = 180 degrees - (50 + 30) = 100 degrees

(We minus from 180 degrees because 180 degrees is the sum of the angles in a triangle!)

And that's it! If you have any questions, please feel free to ask questions. I'm not here to judge, and I'm only here to help. Again, ask questions if you need help. It's crucial that you know the basics of geometry!


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Problems1) Paul runs 4 miles in 28 minutes. If he runs each mile at the same pace,
what is his rate in minutes per mile?
1 point
Your answer

Answers

Answer:

7

Step-by-step explanation:

You must divide 28 by 4 which equals 7.

A 40 N force is applied to an object with a mass of 0.1 kg on a frictionless surface. What is the acceleration of the object?

Answers

The acceleration of the object is 400 m/s²

What is the acceleration of the object?

To find the acceleration of an object when a 40 N force is applied to it with a mass of 0.1 kg on a frictionless surface, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

The formula for Newton's second law of motion is:

F = ma

where:

F is the net force,

m is the mass of the object,

a is the acceleration.

In this case, the net force is 40 N and the mass of the object is 0.1 kg.

Substituting these values into the formula, we get:

40 N = (0.1 kg) a

Solving for a, we get:

a = 400 m/s²

Therefore, the acceleration of the object is 400 m/s²

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Answer:

400

Step-by-step explanation:

40 divided by .1

I need help setting up this problem

Answers

R represents regular and F will represent recycled fibers. 
R + F = 27
46.99R + 61.99F = 1433.73 
This is how you would set the problem up to begin. Let me know if you need help from here!

A line with a slope of -2 passes through the point (4, 7). Write an equation for this line in point-slope form.

Answers

Answer:

The equation in point-slope is y-7=-2(x-4).

Step-by-step explanation:

Point-slope is a specific form of linear equations in two variables:

y-b=m(x-a)

When an equation is written in this form, m gives the slope of the line and (a, b) is a point the line passes through.

We want to find the equation of the line that passes through (4, 7) and whose slope is -2. Well, we simply plug m = -2, a = 4, and b = 7 into point-slope form.

y-7=-2(x-4)

\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{7})~\hspace{10em} slope = m\implies -2 \n\n\n \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\n \cline{1-1} \n y-y_1=m(x-x_1) \n\n \cline{1-1} \end{array}\implies y-7=-2(x-4)

David says he has 2/3 of a pipe length​ left, while Don says he has 11/16 of a length left. Which person has the longest section​ left?

Answers

Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.

David says he has 2/3 of a line length left, while Wear says he has 11/16 of a length left.

Convert the fraction numbers 2/3 and 11/16 into the decimal number. Then we have

2/3 = 0.6667

11/16 = 0.6875

The decimal number 0.6875 is greater than 0.6667. Then the fraction number 11/16 is greater than the fraction number 2/3.

Don has the longest section of pipe because the fraction number 11/16 is greater than the fraction number 2/3.

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Answer:

Don

Step-by-step explanation:

1. We make the fractions have common denominators so it is easier to compare them. We can do this buy multiplying 2/3 by a factor of 16, so it becomes 32/48. For 11/16, we multiply by a factor of 3 so it becomes 33/48. It is now apparent that Don has the longer pipe.

If BC = x − 2, CD = 19, and BD = 3x − 11, what is BD? Simplify your answer and write it as a proper fraction, mixed number, or integer. Could you please type the answer in a step by step.

Answers

Answer:

UV = 15

BD= 31

Step-by-step explanation:

Since, U is the midpoint of TV.

Therefore,

TU = UV

x + 10 = 3x

x - 3x = - 10

-2x = - 10

x = - 10/-2

x = 5

UV = 3x = 3*5

UV = 15

BD = BC + CD

3x - 11 = x - 2 + 19

3x - 11 = x + 17

3x - x = 11 + 17

2x = 28

x = 28/2

x = 14

BD = 3x - 11 = 3*14-11 = 42 - 11

BD= 31

Final answer:

We used the relationship that BC + CD = BD and then solved for x, which we found to be 14. We then substituted 14 for x in the equation for BD, which gave us a result of 31.

Explanation:

In the given question, we have a piece of a line divided into different sections: BC, BD, and CD with their respective lengths. BD is represented through a variable equation. We know that BC + CD = BD, this is a fundamental property of geometry that the sum of the lengths of two consecutive sections of a line is equal to the total length. So, substitute the given values:

x − 2 + 19 = 3x − 11

Simplify the equation by combining like terms: x + 17 = 3x - 11. Now, let's solve for x:

First, consolidate x's on one side by subtracting 'x' on both sides. We get 17 = 2x - 11.

Next, add 11 on both sides to solve for x. We get, 28 = 2x.

Finally, divide by 2 on both sides to find x, x = 14.

Now, we can find BD by substituting x into the equation 3x - 11, we get:

BD = 3*14 - 11 = 42 - 11 = 31.

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