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irinina [24]
3 years ago
12

In abc above,what is the length of ad​

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
4 0

Answer:

B

Step-by-step explanation:

First calculate BD using sine ratio in Δ BCD and the exact value

sin60° = \frac{\sqrt{3} }{2}, thus

sin60° = \frac{opposite}{hypotenuse} = \frac{BD}{BC} = \frac{BD}{12} = \frac{\sqrt{3} }{2} ( cross- multiply )

2BD = 12\sqrt{3} ( divide both sides by 2 )

BD = 6\sqrt{3}

-----------------------------------------------------------

Calculate AD using the tangent ratio in Δ ABD and the exact value

tan30° = \frac{1}{\sqrt{3} } , thus

tan30° = \frac{opposite}{adjacent} = \frac{AD}{BD} = \frac{AD}{6\sqrt{3} } = \frac{1}{\sqrt{3} } ( cross- multiply )

\sqrt{3} AD = 6\sqrt{3} ( divide both sides by \sqrt{3} )

AD = 6 → B

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3|1/2x + 5| + 7 = 5
egoroff_w [7]

Answer:

<em>x is -34/3 and -26/3</em>

Step-by-step explanation:

Given the expression

3|1/2x+5| + 7 = 5

Removing the modulus sign

3(1/2x+5) + 7 = 5

Subtract 7 from both sides

3(1/2x+5) + 7 - 7= 5 - 7

3(1/2x+5) = -2

Open the bracket

3/2 x + 15 = -2

Subtract 15 from both sides

3/2 x + 15-15 = -2 - 15

3/2 x = -17

3x = -2*17

3x  = -34

x = -34/3

<em>Hence the value of x is -34/3</em>

<em>For the negative function:</em>

3(1/2x+5) + 7 = 5

Subtract 7 from both sides

3(-(1/2x+5)) + 7 - 7= 5 - 7

3(-1/2x-5) = -2

Open the bracket

-3/2 x - 15 = -2

Add 15 from both sides

3/2 x + 15-15 = -2 + 15

-3/2 x = 13

-3x = 2 * 13

-3x  =26

x = -26/3

<em>Hence the value of x is -26/3</em>

4 0
3 years ago
A web site was hit 300 times over a period of 15 days Show that over some period of 3 consecutive days, it was hit at least 60 t
marshall27 [118]

Answer:

We will divide the 15 days in five periods of 3 consecutive days each.

Now to solve this we will use the pigeonhole principle.

This states that if (N+1) pigeons occupy N holes, then some hole must have at least 2 pigeons.

So, we have n=300 pigeons  and k=5 holes.

[\frac{n}{k} ]=[\frac{300}{5} ]

Hence, there is a period of 3 consecutive days in which the website was hit at least 60 times.

6 0
3 years ago
Mariana solved a linear equation and found that it had an infinite number of solutions. Which could have been the final line of
Fofino [41]

Answer:

0=0

Step-by-step explanation:

Well, the linear equation can be expressed as y=ax+b in the solution of linear equations, there 3 main cases can be concluded as final lines. 1st case - the linear equation has no solution (for example, 0*x=5 has no solutions). 2nd case - the linear equation has one solution (for example 4*x=3 where the only one solution is x=0.75) and the 3rd case - the linear equation has infinite number of solutions (for example 0*x=0). So, in our case (3rd case) the last line can be concluded as 0=0.  

4 0
3 years ago
Find the area of square that can be inscribed in circle of radius 8cm
inysia [295]

Answer:

A≈201.06cm²

Step-by-step explanation:

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2 years ago
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uysha [10]
C=16h
C, the total cost is equal to 16 dollars per hour, h
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