Can anyone help me out with this question please

Given the following triangle, if c = square root of 7 and a = 1, find the measure of B.

Darya [45]

Answer:

68°

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relation between the angle's adjacent side and the hypotenuse is ...

Cos = Adjacent/Hypotenuse

This means ...

cos(B) = a/c

B = arccos(1/√7) ≈ 68°

5 0

3 years ago

Three times the second of three consecutive even integers is twelve less than twice the sum of the first and third integers.Find

Tresset [83]

Answer:

The largest even integer is 14.

Step-by-step explanation:

Given:

Three times the second of three consecutive even integers is twelve less than twice the sum of the first and third integers.

Now, to find the largest even integers.

As, 2 is an even number.

Let an even integer be $2x.$

So, the three consecutive even integers are:

$2x,\ 2x+2,\ and\ 2x+4.$

Now, we have to add two to get next even number.

Thus, 3 times the second one of these is:

$3(2x + 2) \\= 6x + 6$

Now, the sum of the first and third ones are:

$2x + 2x + 4 \\= 4x + 4$

So, the twice the sum of the first and third integers is less than twelve:

$2(4x+4)-12\\=8x+8-12\\=8x-4$

Now, 3 times the second is 12 less than twice the sum of the other two:

$6x+6=8x-4$

Getting the variables on one side and the number on other:

$6+4=8x-6x$

$10=2x$

Dividing both sides by 2 we get:

$5=x$

$x=5.$

Now, the even numbers we get are:

$2x=2\times 5=10\\2x+2=2\times 5+2=10+2=12\\2x+4=2\times 5+4=10+4=14.$

Thus, the third number is the largest number which is 14.

Therefore, the largest even integer is 14.

8 0

3 years ago

You want to put $8,000 in a simple interest account. It has a 2% annual interest rate. How long must you invest that money to ea

balandron [24]

Dear Sadaadams73, to solve this problem, we use the formula I=Prt. The equation will look like 400=8000 x 0.02 x t. Multiply 8000 by 0.2 to get 1600t=400. Then divide both sides by 400 to get 4 years.

6 0

3 years ago

Two computers working together can finish a search in 30 seconds. One of these computers can finish in 50 seconds. How long woul

vivado [14]

It would take the second computer 75 seconds because:

$\frac{1}{30} - \frac{1}{50} = \frac{1}{75}$

6 0

3 years ago

Stardust the unicorn, covered a distance of 50 miles on his first trip to the forest. On a later trip he travelled 300 miles whi

timama [110]

For this case, the first thing we must take into account is the following definition:
d = v * t
Where,
d: distance
v: speed
t: time
Substituting values we have:
Trip 1:
50 = v * t1
We cleared t1:
t2 = (50) * (1 / v)
Trip 2:
300 = (3 * v) * t2
We cleared t2:
t2 = (300/3) * (1 / v)
t2 = (100) * (1 / v)
Rewriting:
t2 = 2 (50) * (1 / v)
t2 = 2 * t1
Answer:
His new time compared with the old time was:
Twice the old time.
t2 = 2 * t1.

4 0

3 years ago