All categories

3 years ago

Camilla has three times as many points as Lynn. Lynn has five

Mathematics

1 answer:

REY [17]3 years ago

5 0

Step-by-step explanation:

l x 3 = c

k + 5 = l

(c + l + k) x 2 = 25

c = 33

l = 11

k = 6

You might be interested in

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

If f(3) = 3(x+5+2, what is f(a+ 2)?

Mamont248 [21]

Solution:

f(3) = 3(x + 5 + 2)

f(3) = 3(3 + 5 + 2)

f(3) = 3(10)

f(3) = 30

Substitute 30 for a:

f(30 + 2)

f(32)

Best of Luck!

8 0

4 years ago

Anyone know this answer?

s344n2d4d5 [400]

The average salary is $18,725

To find the answer add up each job's salary then divide by the number of jobs.

28,700 + 18,600 + 14,66 + 13,00 = 74,900

Then divide 74,900 by 4 ( added 4 numbers )

6 0

3 years ago

If Cindy works 18 hours a week at 5.15 an hour how much did she make for the whole year?

kipiarov [429]

Find how many weeks are in a year and times by 5.15

3 0

3 years ago

Read 2 more answers

Triangle PQR is transformed to triangle P′Q′R′. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P′Q′R′ has v

pav-90 [236]

lo siento de antemano! Necesito los puntos para hacer una publicación sobre mi amigo desaparecido. Ella desapareció y no puedo encontrarla. Ella se ha ido desde Halloween gracias por su comprensión. 8 9 028 los números son para covienes que estoy cosiendo el quistoion. Lo siento, nuevamente.

3 0

3 years ago