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PolarNik [594]
3 years ago
12

The proof that ΔMNS ≅ ΔQNS is shown. Given: ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. Prove: ΔMNS ≅

ΔQNS
We know that ΔMNQ is isosceles with base MQ. So, MN ≅ QN by the definition of isosceles triangle. The base angles of the isosceles triangle, ∠NMS and ∠NQS, are congruent by the isosceles triangle theorem. It is also given that NR and MQ bisect each other at S. Segments_____are therefore congruent by the definition of bisector. Thus, ΔMNS ≅ ΔQNS by SAS.

NS and NS
NS and RS
MS and RS
MS and QS

Mathematics
2 answers:
klio [65]3 years ago
8 0
The answer is "MS and QS". Trust me I just took the test and made a 90
natali 33 [55]3 years ago
5 0

Answer:

The correct option is MS and QS

Step-by-step explanation:

Given ΔMNQ is isosceles with base MQ, and NR and MQ bisect each other at S. we have to prove that ΔMNS ≅ ΔQNS.

As NR and MQ bisect each other at S

⇒ segments MS and SQ are therefore congruent by the definition of bisector i.e   MS=SQ

In ΔMNS and ΔQNS

MN=QN       (∵ MNQ is isosceles triangle)

∠NMS=∠NQS     (∵ MNQ is isosceles triangle)

MS=SQ         (Given)

By SAS rule, ΔMNS ≅ ΔQNS.

Hence, segments MS and SQ are therefore congruent by the definition of bisector.

The correct option is MS and QS

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A train is traveling at a speed of 80 km/h when the conductor applies the brakes. The train slows with a constant acceleration o
hodyreva [135]

Answer:

The train will travel 493.817 meters until it stops completely.

Step-by-step explanation:

In this case, we know that train applies the brakes and decelerates at constant rate until rest is reached after travelling an unknown distance. Travelled distance (\Delta s), measured in meters, can be found by using this kinematic formula:

v^{2} = v_{o}^{2}+2\cdot a \cdot \Delta s (Eq. 1)

Where:

v_{o} - Initial speed, measured in meters per second.

v - Final speed, measured in meters per second.

a - Acceleration, measured in meters per square second.

Now travelled distance is cleared within the formula:

\Delta s = \frac{v^{2}-v_{o}^{2}}{2\cdot a}

If we know that v_{o} = 22.222\,\frac{m}{s}, v = 0\,\frac{m}{s} and a = -0.5\,\frac{m}{s^{2}}, then the distance travelled by the train is:

\Delta s = \frac{\left(0\,\frac{m}{s} \right)^{2}-\left(22.222\,\frac{m}{s} \right)^{2}}{2\cdot \left(-0.5\,\frac{m}{s^{2}}\right) }

\Delta s = 493.817\,m

The train will travel 493.817 meters until it stops completely.

3 0
3 years ago
the sum of two numbers is -14. If you subtract the smaller number from. the larger number the total is 12. what are the two numb
lara31 [8.8K]
------------------------------------------------------------
Define the two numbers
------------------------------------------------------------
Let one number be x and the other be y

------------------------------------------------------------
Form equations and solve
------------------------------------------------------------
x + y = -14 --------------- (1)
y - x = 12 ------------------(2)

------------------------------------------------------------
(1) + (2)
------------------------------------------------------------
2y = -2
y = -1

------------------------------------------------------------
Substitute y = -1 into (2)
------------------------------------------------------------
y - x = 12
-1 - x = 12
x = -1 -12
x = -13

------------------------------------------------------------
Answer: x = -13, y = -1
------------------------------------------------------------


6 0
3 years ago
Which temperature is 15°F colder than 45°F?<br><br> A) −15°F <br> B) 25°F <br> C) 30°F <br> D) 55°F
Natalija [7]

Answer: (C) 30°F

Step-by-step explanation: Simply add -15 to 45, which gives you 30. -15 + 45 = 30

Its like subtracting 45-15, which equals 30.

4 0
3 years ago
Read 2 more answers
URGENT! Describe step by step how to find the following equations.
yuradex [85]

Answer:

1. x = 45°

2. x = 330°

3. x = 105°

4. x = 30°

5. x = 60°

6. x = 30° or x = -45° (315°) or x = 45°

Step-by-step explanation:

1. For

cos x = sin x

∴ sin x/(cos x) = 1 = tan x

Hence, x = tan⁻¹1 = 45°

2. For

csc(x) + 3 = 1

∴ csc(x) = 1 - 3 = -2

Which gives sin x = -1/2

∴ x = sin⁻¹(-1/2) = -30° = 360 +(-30) = 330 °

3. For

cot(3x) = -1

∵ cot(3x) = 1/(tan(3x))

Hence, 1/(tan(3x)) = -1

∴ tan(3x) = -1

3·x = tan⁻¹(-1) = -45° = 360 + (-45) = 315°

Which gives, x = -45/3 = -15° or x = 105°

4. For

2·sin²(x) + 3·sin(x) = 2

We put sin(x) = y to get

2·y² + 3·y = 2 or 2·y² + 3·y - 2 =0

Factorizing gives

(2·y -1)(y+2) =0

∴ y = 1/2 or y = -2

That is, sin(x) = 1/2 or sin(x) = -2

Hence, x = sin⁻¹(1/2) = 30° or x = sin⁻¹(-2) = (-π/2 + 1.3·i)

∴ x = 30°

5. For

4cos²(x) = 3 we have;

cos²(x) = 3/4

cos(x) = √(3/4) = (√3)/2

∴ x = cos⁻¹((√3)/2) = 60°

6. For

4·sin³(x) + 1 = 2·sin²(x) + 2·sin(x)

We put sin(x) = y to get;

4·y³ + 1 = 2·y² + 2·y which gives;

4·y³ + 1 - (2·y² + 2·y) = 0 or 4·y³ -2·y² - 2·y + 1 = 0

Factorizing gives;

\frac{(2x-1)(2x+\sqrt{2}) )(2x-\sqrt{2})}{2} =0

Therefore, x = 1/2 or x = -(√2)/2 or (√2)/2

Therefore, sin(x) = 1/2 or -(√2)/2 or (√2)/2

That is x = sin⁻¹(1/2) = 30 or sin⁻¹(-(√2)/2) = -45 or sin⁻¹((√2)/2) = 45.

8 0
3 years ago
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ololo11 [35]

Answer:

it 18

Step-by-step explanation:

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7 0
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