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Ghella [55]
2 years ago
11

Simplify the expression. Quantity cosecant of x to the power of two times secant of x to the power of two divided by quantity se

cant of x to the power of two plus cosecant of x to the power of two.
A. sin^2x
B. cos^2x
C. -1
D. 1
Mathematics
1 answer:
Art [367]2 years ago
3 0

Answer:

D. 1

Step-by-step explanation:

We have the expression, \frac{\csc^{2}x\sec^{2}x}{\sec^{2}x+\csc^{2}x}

We get, eliminating the cosecant function,

\frac{\sec^{2}x}{\frac{\sec^{2}x}{\csc^{2}x}+1}

As, sinx is reciprocal of cosecx and cosx is reciprocal of secx,

i.e. \frac{\sec^{2}x}{\frac{\sin^{2}x}{\cos^{2}x}+1}

i.e. \frac{1}{\cos^{2}x}\times \frac{\cos^{2}x}{\sin^{2}x+\cos^{2}x}

Since, we know that, \sin^{2}x+\cos^{2}x=1

Thus,

\frac{1}{\cos^{2}x}\times \frac{\cos^{2}x}{\sin^{2}x+\cos^{2}x}=1

So, after simplifying, we get that the result is 1.

Hence, option D is correct.

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A line contains the points (-5, 3) and (0, -7). What is the equation of this line in slope-intercept form?
pychu [463]

Answer:

D. y = –2x – 7

Step-by-step explanation:

First, find the <em>rate</em><em> </em><em>of change</em><em> </em>[<em>slope</em>]:

-y₁ + y₂\-x₁ + x₂ = m

- \frac{3 - 7}{5 + 0} = -\frac{10}{5} = -2

In this case, the y-intercept of [0, -7] is ALREADY given to you, so we would not have to go further in this case.

I am joyous to assist you anytime.

8 0
2 years ago
Read 2 more answers
Help plz quick appreciated
Soloha48 [4]
Question 3:
If the diver is being pulled up at 25 feet every minute, in 10 minutes they would have been pulled up 10 times that
10*25=250
The diver is now 200 feet below, but 10 minutes ago they would have been 250 feet deeper so:
200+250=450

450 feet
6 0
3 years ago
1. What is the extraneous solution of √x−3 + x = 9?
Sunny_sXe [5.5K]

Answer:

1. x = 12

2. 3∛4 feet.

Step-by-step explanation:

1. We are given the equation of x as \sqrt{x - 3} + x = 9 and we have to find the extraneous solution of the equation.

Now, \sqrt{x - 3} + x = 9 ............. (1)

⇒ \sqrt{x - 3} = 9 - x

Squaring both sides we get,

⇒ x - 3 = 81 - 18x + x²

⇒ x² - 19x + 84 = 0

⇒ x² - 12x - 7x + 84 = 0

⇒ (x - 12)(x - 7) = 0

⇒ x = 12 or 7.

Now, putting x = 12 in the equation (1) we get,

\sqrt{12 - 3} + 12 \neq   9

Again, putting x = 7 in the equation (1) we get,

\sqrt{7 - 3} + 7 = 9

Therefore, x = 12 is an extraneous solution of this equation. (Answer)

2. The volume of a cube with side lengths a ft. is given to be 108 ft³.

So, a³ = 108

⇒ a = 3∛4 feet.

Therefore, the length of the sides of the cube are each 3∛4 feet. (Answer)

3 0
3 years ago
On a coordinate plane, point B(–6, 1) is translated to B prime(–3, –2). Indira uses these steps to find a rule to describe the t
Lunna [17]

Answer:

The rule of the translation is   (x,y) -----> (x+3,y-3)

The translation is 3 units at right and 3 units down

Step-by-step explanation:

we have that

The translation of point B to point B' is

B(-6,1) -----> B'(-3,-2)

so

(x,y) -----> (x+a,y+b)

B(-6,1) ----> (-6+a,1+b)

Find the value of a

-6+a=-3

solve for a

a=-3+6\\a=3

Find the value of b

1+b=-2

solve for b

b=-2-1\\b=-3

therefore

The rule of the translation is

(x,y) -----> (x+3,y-3)

That means ----> The translation is 3 units at right and 3 units down

3 0
3 years ago
Read 2 more answers
7(-10 + 3x) = -49 Please explain aswell!
bixtya [17]

Answer:

x=1

Step-by-step explanation:

To get the 7 away, we need to multiply it into the parentheses.

7*-10= -70

7*3=21

-70+21x= -49

Now we combine like terms and we move 70 over. Because we're moving it to the other side of the equation, it becomes positive.

21x= -49+70

-49+70 is the same as 70-49

70-49= 21

Now we put it together.

21x=21

To get the x by itself, we need to divide 21 on both sides.

21x/21= 21/21

21/21=1

x=1

6 0
3 years ago
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