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just olya [345]

3 years ago

5

six friends visited a museum to see the new holograms exhibit. the group paid for admission to the museum and $12 for parking. t

he total cost of the visit can be represented by the expression $6x+$12. what was the cost of the visit for one person

1 answer:

Anestetic [448]3 years ago

8 0

It actually depends

One person is $6
Parking is $12
If you want to count the price for one person it is $6
If you want to count the price plus PARKING it would be $18

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Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t

katrin2010 [14]

Answer:

$\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24$

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of $\triangle ACD$ and the hypotenuse of $\triangle ADB$ .

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is $\angle CAD$ . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

$\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}$

Now use this value in the Law of Sines to find AD:

$\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}$

Recall that $\sin 45^{\circ}=\frac{\sqrt{2}}{2}$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ :

$AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}$

Now that we have the length of AD, we can find the length of AB. The right triangle $\triangle ADB$ is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $x$ is the side opposite to the 30 degree angle and $2x$ is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent $2x$ in this ratio and since AB is the side opposite to the 30 degree angle, it must represent $x$ in this ratio (Derive from basic trig for a right triangle and $\sin 30^{\circ}=\frac{1}{2}$ ).

Therefore, AB must be exactly half of AD:

$AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24$

3 0

3 years ago

Read 2 more answers

Find the value of x<br> A. 55 degrees <br> B. 110 degrees <br> C. 220 degrees <br> D. 330 degrees

Olegator [25]

Answer:

B. 110 degrees

Step-by-step explanation:

The measure of an arc equals the measure of its central angle.

5 0

3 years ago

Angle θ is in standard position. If (8, -15) is on the terminal ray of angle θ, find the values of the trigonometric functions.

notsponge [240]

ANSWER

$\sin( \theta) = - \frac{15}{17}$

$\csc( \theta) = - \frac{17}{15}$

$\cos( \theta) = \frac{8}{17}$

$\sec( \theta) = \frac{17}{8}$

$\tan( \theta) = - \frac{15}{8}$

$\cot( \theta) = - \frac{8}{15}$

EXPLANATION

From the Pythagoras Theorem, the hypotenuse can be found.

${h}^{2} = 1 {5}^{2} + {8}^{2}$

${h}^{2} = 289$

$h = \sqrt{289}$

$h = 17$

The sine ratio is negative in the fourth quadrant.

$\sin( \theta) = - \frac{opposite}{hypotenuse}$

$\sin( \theta) = - \frac{15}{17}$

The cosecant ratio is the reciprocal of the sine ratio.

$\csc( \theta) = - \frac{17}{15}$

The cosine ratio is positive in the fourth quadrant.

$\cos( \theta) = \frac{adjacent}{hypotenuse}$

$\cos( \theta) = \frac{8}{17}$

The secant ratio is the reciprocal of the cosine ratio.

$\sec( \theta) = \frac{17}{8}$

The tangent ratio is negative in the fourth quadrant.

$\tan( \theta) = - \frac{opposite}{adjacent}$

$\tan( \theta) = - \frac{15}{8}$

The reciprocal of the tangent ratio is the cotangent ratio

$\cot( \theta) = - \frac{8}{15}$

8 0

3 years ago

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Find the probability. a basket contains 8 apples and four peaches. you randomly selected a piece of fruit and then return it to

Maslowich

<span>Find the probability. a basket contains 8 apples and four peaches. you randomly selected a piece of fruit and then return it to the basket. then you randomly selected another piece of fruit. both pieces of fruit are apples.
</span>
1/12*1/12=1/144

4 0

4 years ago

Find the length of WV

Luba_88 [7]

Answer:

I believe the answer would be 20.

Step-by-step explanation:

28/7 = 4

5*4 = 20

Pls mark brainliest <3

3 0

3 years ago

Read 2 more answers