All categories

3 years ago

Can you please help thanks

Mathematics

1 answer:

katrin2010 [14]3 years ago

6 0

Answer:5/2a + 10/3b

Step-by-step explanation:

(1/6)(15a+20b)

=(1/6)(15a)+(1/6)(20b)

You might be interested in

What is the d value of the following arithmetic sequence? 5, 2, -1, -4, -7,…

Andrew [12]

The d value is going to be -3 because you have to compute the differences of all the adjacent terms. 2-5=-3 -1-2=-3 -4-(-1)=-3 -7-(-4)=-3 The difference between all the adjacent terms is the same and equal to -3

6 0

3 years ago

Read 2 more answers

What is the least common multiple (LCM) of 15 and 45? A. 15 B. 675 C. 45 D. 90

harkovskaia [24]

Answer:

C - 45 is the LCM of 15 & 45

Step-by-step explanation:

Find the multiples:

15, 30, 45, 60

45, 90

They both have 45 in common

3 0

3 years ago

A game has 3 possible outcomes, with probabilities p1, p2, and p3. The amount of money that you will win or lose for each outcom

3241004551 [841]

That expression is the expected value of your winnings, or "the average amount you will win (or lose) per game in the long run".

4 0

3 years ago

Read 2 more answers

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 $\sin 30^{\circ}=\frac{1}{2}$ ).