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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Right triangle ABC is shown. Which of these is equal to cos(A)?A) cos(B)
B) cos(C)
C) sin(B)
D) sin(C)

Answers

Answer: C

cosA=AC/AB

sinB=AC/AB

hence cosA=sinB

Answer:

C).

Step-by-step explanation:

Since angles A and B are complementary, their cofunctions are equal. So, cos(A) = sin(B).

A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 12 feet more than the length of the shortest side.Find the dimensions if the perimeter is 136 feet

Answers

x - the shortest side

x + 28

The sum of these must be equal to the perimeter of the flower bed, so

x + 2x + x + 28 = 184

4 x + 28 = 184 Combined like terms

4x = 156 Subtracted 28 from both sides

x = 39 Divided both sides by 4.

So the dimensions are 39 feet, 78 feet, and 67 feet

- 5 + 7k = -19
Help pwease

Answers

Answer:

k = -2

Step-by-step explanation:

-5 + 7k = -19

7k = -14

k = -2

A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 V, and the manufacturer wished to test against , using units. Statistical Tables and Charts (a) The critical region is or . Find the value of

Answers

The missing values in the question are shown in bold forms below.

A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation of 0.25 V, and the manufacturer wished to test $\mathbf{ H_o : \mu = 10 V \ against \ H_1 : \mu \neq 10V}$ , using n = 10 units. Statistical Tables and Charts

(a) The critical region is $\mathbf{\overline X < 9.83}$ or $\mathbf{\overline X < 10.17}$ . Find the value of $\mathbf{\alpha }$

Answer:

∝ = 0.032 (to 3 decimal place)

Step-by-step explanation:

From the given information:

$P(\overline X < 9.83 ) + P( X> 10.17) = \bigg (1- P \bigg ( (X - \mu)/((\sigma)/(√(n))) \bigg )< Z< \bigg ( (X - \mu)/((\sigma)/(√(n))) \bigg ) \bigg )$

$P(\overline X < 9.83 ) + P( X> 10.17) = \bigg (1- P \bigg ( (9.83 - 10)/((0.25)/(√(10))) \bigg )< Z< \bigg ( (10.17- 10)/((0.25)/(√(10))) \bigg ) \bigg )$

$P(\overline X < 9.83 ) + P( X> 10.17) = \bigg (1- P \bigg ( (-0.17)/((0.25)/(√(10))) \bigg )< Z< \bigg ( (0.17)/((0.25)/(√(10))) \bigg ) \bigg )$

$P(\overline X < 9.83 ) + P( X> 10.17) = \bigg (1- P \bigg (-2.15 \bigg )< Z< \bigg ( 2.15 \bigg ) \bigg )$

From the z - tables;

$P(\overline X < 9.83 ) + P( X> 10.17) = \bigg (1- (0.9842 -0.0158) \bigg )$

$\alpha = \mathbf{P(\overline X < 9.83 ) + P( X> 10.17) = 0.032}$

Question: What is 32^2?

Answers

Answer: The answer is 1,024.

Explanation: 32^2 is 32 x 32, which is 1,024.

1,024

Explanation: calculator

Please help me understand I am confused

Answers

9514 1404 393

Explanation:

a) The velocity curve is linearly increasing from 0 to 6 m/s over a period of 2 seconds, then linearly decreasing from 6 m/s to 0 over the same period. The acceleration is the rate of change of velocity, so for the first half of the motion the acceleration is a constant (6 m/s)/(2 s) = 3 m/s². Similarly, over the second half of the motion, the acceleration is a constant (-6 m/s)/(2 s) = -3 m/s².

The distance traveled is the integral of the velocity, so the linearly increasing velocity will cause the distance vs. time curve to have a parabolic shape. The shape will likewise be parabolic, but with decreasing slope, as the velocity ramps down to zero. Overall, the distance versus time curve will have an "S" shape.

The motion (position and velocity) will be continuous, but the acceleration will not be. There will be a significant "j.erk" at the 2-second mark where acceleration abruptly changes from increasing the velocity to braking (decreasing the velocity).

b) The attachment shows the (given) velocity curve in meters per second and its integral, the position curve, in meters.

The integral in the attached works nicely for machine evaluation. For hand evaluation, it is perhaps best written piecewise:

$s(t)=\begin{cases}\displaystyle\int_0^t{3x}\,dx\qquad\text{for $x\le2$}\n\n\displaystyle6+\int_2^t{(12-3x)}\,dx\qquad\text{for $2<x\le4$}\end{cases}$

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