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lora16 [44]
3 years ago
14

1. In ABC, C is a right angle and BC = 11. If B = 30°, find AC. (1 point)

Mathematics
2 answers:
faltersainse [42]3 years ago
7 0

Answer:

AC=\frac{11\sqrt{3}}{3}

Step-by-step explanation:

Given that triangle ABC is a right angle triangle. Where angle C is a right angle. Also we have been given that BC = 11, B = 30°. Now we need to find the value of AC.

Apply formula:

\tan\left(\theta\right)=\frac{opposite}{adjacent}

\tan\left(B\right)=\frac{AC}{BC}

\tan\left(30^o\right)=\frac{AC}{11}

\frac{1}{\sqrt{3}}=\frac{AC}{11}

\frac{11}{\sqrt{3}}=AC

AC=\frac{11}{\sqrt{3}}

or

AC=\frac{11}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}

or

AC=\frac{11\sqrt{3}}{3}

Hence final answer is AC=\frac{11\sqrt{3}}{3}.

Mademuasel [1]3 years ago
7 0
The answer is the first one (A)
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A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s
yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2}  = \frac{1 \pm 9 }{-0.4}

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

3 0
2 years ago
Write the denominator of the fractiona 7/20 as the product of prime factors
gtnhenbr [62]

Answer:

Step-by-step explanation:

prime factors of 20 = 2 * 2 * 5

\frac{7}{20}=\frac{7}{2*2*5}

5 0
3 years ago
Answer qn in attachment​
leva [86]

Answer:

\implies \dfrac{ -4x+7}{2(x-2) }

Step-by-step explanation:

The given expression to us is ,

\implies \dfrac{\frac{ 3}{x-1} -4 }{ 2 -\frac{2}{x-1}}

Now take the LCM as ( x - 1 ) and Simplify , we have ,

\implies \dfrac{\frac{ 3 -4(x-1) }{x-1} }{ \frac{2-2(2x-1)}{x-1}}

Simplifying further , we get ,

\implies \dfrac{ -4x+7}{2(x-2) }

Hence the second option is correct .

4 0
3 years ago
On a coordinate plane, lockers is 5 units to the left and 3.5 units up. Water fountain is 2.5 units to the left and 3 units up.
VLD [36.1K]

Answer:

it's d water fountain

Step-by-step explanation:

hope this helps edge 2021 Jan 08

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Gwar [14]

Answer:

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