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MrMuchimi
1 year ago
15

Given m//n find the value of x and y (5x+1)° (6x-10)° (y°)

Mathematics
1 answer:
Ilia_Sergeevich [38]1 year ago
4 0

To find the value of x, use the vertical angle theorem.

Vertical angles are congruent.

Thus we have:

6x - 10 = 5x + 1

Solve for x.

6x - 10 = 5x + 1

Add 10 to both sides:

6x - 10 + 10 = 5x + 1 + 10

6x = 5x + 11

Subtract 5x from both sides:

6x - 5x = 5x - 5x + 11

x = 11

To find the value of y, use corresponding angles thoerem.

When two parallel lines are crossed by a transversal, the angles in matching corners are correponding angles.

Corresponding angles are congruent.

Thus, we have:

y = 6x - 10

Substitiute x for 11:

y = 6(11) - 10

y = 66 - 10

y = 56°

ANSWER:

x = 11, y = 56°

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A cable television compan is laying cable in an area with underground utilities. Two subdivisions are located on opposite sides
Schach [20]

Answer:

Step-by-step explanation:

Given:

Point Q = Q is on the north bank 1200 m east of P $40/m to lay cable underground and $80/m way to lay the cable.

Lets denote T be a point on north bank, therefore, point T is t m east and 100m north of P.

Note that 0 < t < 1200

Distance from P to T using Pythagoras theorem:

PT^2 = PQ^2 + QT^2

PT = √(t²+100²) = √(t²+10,000)

Distance from T to Q:

TQ = 1200 - t

From above, Cable from P to T is underwater, and costs $80/m to lay.

Cable from T to Q is underground, and costs $40/m to lay.

Total cost of the cable:

C(t) = 80√(t²+10,000) + 40(1200 - t)

Cost is at its minimum: when dC/dt = C'(t) = 0 and d^2C/dt^2 = C''(t) > 0

dC/dt = C'(t)

= 80 * 1/2 (t² + 10,000)^(-1/2) × 2t + 40 × (-1)

dC/dt = C'(t)

= 80t/√(t² + 10,000) - 40 = 0

80t/√(t² + 10,000) = 40

80t = 40√(t² + 10,000)

2t = √(t² + 10,000)

square both sides:

4t² = t² + 10,000

3t² = 10,000

t² = 10,000/3

t = 100/√3

≈ 57.735

d^2C/dt^2 =

C''(t) = [80√(t² + 10,000) - 80t × t/√(t²+10,000)] /√(t²+10,000)

C''(t) = [(80(t²+10,000) - 80t²) / √(t²+10,000)] /√(t²+10,000)

C''(t) = 800,000 / (t² + 10,000)^(3/2)

C''(t) > 0 for all t

Therefore C(t) is minimized at t = 100/√3

C(100/√3) = 80√(10,000/3 + 10,000) + 40 × (1200 - 100/√3)

= 80 √(40,000/3) + 48,000 - 4000/√3

= 16000/√3 + 48,000 - 4000/√3

= 48,000 + 12,000/√3

= 48,000 + 4,000√3

= 4000 (12 + √3)

≈ 54,928.20

Minimum cost is $54,928.20

This occurs when cable is laid underwater from point P to point T(57.735 m east and 100m north of P) and then underground from point T to point Q (1200 - 57.735)

= 1142.265 m

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3 years ago
A ___ equation is a second-degree equation of the form ax^2+bx+c=0 where a ≠ 0​
klasskru [66]

Answer:

A quadratic equation is second degree equation with the standard form ax^2+bx+c=0 as the highest power is 2.

__________________.

6 0
2 years ago
in a random School sampling of 50 middle school students it was found that 18 students bring their lunch to school everyday if t
dem82 [27]

Answer:

340

Step-by-step explanation:

We can see in the sample that 18/50 people bring lunches to school. If we divide 18 by 50 we get 0.36 now we know that 36% of people bring their lunches in the sample. Now we take that number and multiply it by 942.

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2 years ago
What is -3m + 5m = -14? With work provided
lara [203]

Answer:

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Step-by-step explanation:

-3m+5m=-14

2m=-14

divide both sides by 2

m=-7

5 0
2 years ago
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A hot-air balloon starts 6 feet above the ground and then rises 20 feet each minute.
kari74 [83]

At starting hot-air balloon starts 6 feet.

So, at t = 0 , h = 6 feet.

Now, distance travelled per minute is 20 feet.

So, extra distance travelled in t minutes is 20t feet.

Now,

Total height = Staring height + increase in height w.r.t time.

h = 6 + 20t

Therefore, the height h in feet as a function of time t in minutes is h = 6 + 20t .

Hence, this is the required solution.

8 0
3 years ago
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