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3 years ago

What value of x will satisfy the equation:cos( x) = sin( 2x+ 57 )

Mathematics

1 answer:

netineya [11]3 years ago

7 0

Step-by-step explanation:

$cos \: x = sin \: (2x + 57) \\ \\ \therefore \: sin(90 \degree - \: x) = sin \: (2x + 57) \\ \\ \therefore \:90 - \: x = 2x + 57 \\ \\ 90 + 57 \: = 2x + 3 \\ \\ \therefore \:3x = 147 \\ \\ \therefore \: x = \frac{147}{3} \\ \\ \huge \orange{ \boxed{\therefore \: x = 49 \degree}}$

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How to find missing angle of a right triangle given 2 sides

tekilochka [14]

Answer:

As a rule of thumb, if you know only the two shorter side, their ratio is the tangent of the angle opposed to the side you use as a numerator.

If you know one side and the hypotenuse, the ratio side/hypotenuse is either the sine of the opposite angle, or the cosine of the adjacent angle.

8 0

2 years ago

Factor the perfect square trinomial y2 + 20y + 100.

klemol [59]

Step-by-step explanation:

First find the factors of 100 then

y2 + 20y +100

y2 +10y + 10y +100

y ( y + 10) + 10(y + 10)

So the factor is ( y + 10)

Option C is the correct answer

3 0

2 years ago

use the distance formula to find the distance between the two points. (0, -2) and (9, 10) give the exact length (leave in radica

kkurt [141]

Answer:

15 units

Step-by-step explanation:

Calculate the distance d using the distance formula

d = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (9, 10)

d = $\sqrt{(9-0)^2+(10+2)^2}$

= $\sqrt{9^2+12^2}$

= $\sqrt{81+144}$

= $\sqrt{225}$

= 15

6 0

2 years ago

Prove each statement that is true and ﬁnd a counterexample for each statement that is false. Assume all sets are subsets of a un

tekilochka [14]

Answer with Step-by-step explanation:

We are given that A, B and C are subsets of universal set U.

We have to prove that

$A\cap (B-C)=(A\cap B)-(A\cap C)$

Proof:

Let x $\in A\cap (B-C)$

Then $x\in A$ and $x\in(B-C)$

When $x\in ( B-C)$ then $x\in B$ but $x\notin C$

Therefore, $x\in( A\cap B)$ but $x\notin (A\cap C)$

Hence, it is true.

Conversely , Let $x\in(A\cap B)$ but $x\notin(A\cap C)$

Then $x\in A$ and $x\in B$

When $x\notin ( A\cap C)$ then $x\notin C$

Therefor, $x\in A\cap (B-C)$

Hence, the statement is true.

5 0

2 years ago

Ursula bought 9 dozen rolls of first aid tape for the health office. The rolls were divide equally into 4 boxes. How many rolls

vredina [299]

We know that 12 equals one dozen. It is not asking for a dozen, but for 9 dozen. So, we need to multiply 9 by 12. 9*12 = 108.

It says the rolls of first aid tape were divided equally into 4 boxes. We need to divide these 108 rolls into 4 equal groups, since that is what took place in the problem. So, we divide 108 by 4.
108/4 = 27. There are 27 rolls in each box.

4 0

2 years ago