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sashaice [31]
3 years ago
14

If x = -8, then which of the following equations makes a true statement?

Mathematics
1 answer:
Sindrei [870]3 years ago
6 0
It would be B. Because if x = -8 2x= -16-2 would be-18
You might be interested in
Find the distance from A(-8,-3,-2) and B(-4,8,0) , find ||AB||
RUDIKE [14]

Answer:

||AB|| = 11.8743

Step-by-step explanation:

Distance between two points:

Suppose that we have two points, (x_1,y_1,z_1) and (x_2,y_2,z_2). The distance between them is given by:

D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}

Distance from A(-8,-3,-2) and B(-4,8,0)

||AB|| = \sqrt{(-4-(-8))^2+(8-(-3))^2+(0-(-2))^2}

||AB|| = \sqrt{4^2 + 11^2 + 2^2}

||AB|| = 11.8743

3 0
2 years ago
For each function, what is the output of the given input?
ki77a [65]

Answer:

1.  d. 10.

2. d. 35t + 2.75; $142.75.

Step-by-step explanation:

1.   f(-2) = -2*-2 + 6

    = 4 + 6

    = 10.

2.  The answer is 35t + 2.75

     and the cost of 4 tickets = 35*4 + 2.75 =  $142.75.

4 0
3 years ago
Question 3 of 10
mestny [16]

Answer:

㋡

Check Answer

♣ Qᴜᴇꜱᴛɪᴏɴ :

If tan θ = \sf{\dfrac{1}{\sqrt{7}}}

7

1

, Show that \sf{\dfrac{cosec ^2 \theta - sec ^2\theta}{cosec^2\theta + sec^2\theta }=\dfrac{3}{4}}

cosec

2

θ+sec

2

θ

cosec

2

θ−sec

2

θ

=

4

3

★═════════════════★

♣ ᴀɴꜱᴡᴇʀ :

We know :

\large\boxed{\sf{tan\theta=\dfrac{Height}{Base}}}

tanθ=

Base

Height

So comparing this formula and value of tan θ from question, we get :

Height = 1

Base = √7

Now we need to Prove the value of : \sf{\dfrac{cosec ^2 \theta - sec ^2\theta}{cosec^2\theta + sec^2\theta }=\dfrac{3}{4}}

cosec

2

θ+sec

2

θ

cosec

2

θ−sec

2

θ

=

4

3

Also :

\large\boxed{\sf{cosec\theta=\dfrac{Hypotenuse}{Height}}}

cosecθ=

Height

Hypotenuse

\large\boxed{\sf{sec\theta=\dfrac{Hypotenuse}{Base}}}

secθ=

Base

Hypotenuse

From this we get :

\large\boxed{\sf{cosec^2\theta=\left(\dfrac{Hypotenuse}{Height}\right)^2}}

cosec

2

θ=(

Height

Hypotenuse

)

2

\large\boxed{\sf{sec^2\theta=\left(\dfrac{Hypotenuse}{Base}\right)^2}}

sec

2

θ=(

Base

Hypotenuse

)

2

But we have Height and Base, we dont have Hypotenuse.

Hypotenuse can be found by using Pythagoras Theorem

Pythagoras Theorem states that :

Hypotenuse² = Side² + Side²

For our question :

Hypotenuse² = Height² + Base²

Hypotenuse² = 1² + √7²

Hypotenuse² = 1 + 7

Hypotenuse² = 8

√Hypotenuse² = √8

Hypotenuse = √8

➢ Let's find value's of cosec²θ and sec²θ

________________________________________

First cosec²θ :

\large\boxed{\sf{cosec^2\theta=\left(\dfrac{Hypotenuse}{Height}\right)^2}}

cosec

2

θ=(

Height

Hypotenuse

)

2

\sf{cosec^2\theta=\left(\dfrac{\sqrt{8}}{1}\right)^2}cosec

2

θ=(

1

8

)

2

\sf{cosec^2\theta=\dfrac{8}{1}}cosec

2

θ=

1

8

cosec²θ = 8

________________________________________

Now sec²θ :

\large\boxed{\sf{sec^2\theta=\left(\dfrac{Hypotenuse}{Base}\right)^2}}

sec

2

θ=(

Base

Hypotenuse

)

2

\sf{sec^2\theta=\left(\dfrac{\sqrt{8}}{\sqrt{7}}\right)^2}sec

2

θ=(

7

8

)

2

\sf{sec^2\theta=\dfrac{8}{7}}sec

2

θ=

7

8

sec²θ = 8/7

________________________________________

Now Proving :

\sf{\dfrac{cosec ^2 \theta - sec ^2\theta}{cosec^2\theta + sec^2\theta }=\dfrac{3}{4}}

cosec

2

θ+sec

2

θ

cosec

2

θ−sec

2

θ

=

4

3

Taking L.H.S :

\sf{\dfrac{cosec ^2 \theta - sec ^2\theta}{cosec^2\theta + sec^2\theta }}

cosec

2

θ+sec

2

θ

cosec

2

θ−sec

2

θ

=\sf{\dfrac{8 - sec ^2\theta}{8 + sec^2\theta }}=

8+sec

2

θ

8−sec

2

θ

=\sf{\dfrac{8 - \dfrac{8}{7}}{8 + \dfrac{8}{7} }}=

8+

7

8

8−

7

8

=\sf{\dfrac{\dfrac{48}{7}}{\dfrac{64}{7} }}=

7

64

7

48

\sf{=\dfrac{48\times \:7}{7\times \:64}}=

7×64

48×7

\sf{=\dfrac{48}{64}}=

64

48

\bf{=\dfrac{3}{4}}=

4

3

= R.H.S

Hence Proved !!!

7 0
3 years ago
Find an equation of variation in which y varies inversely as x and y = 5 and x = 17. then find the value of y when x=10
Brilliant_brown [7]
Y=5 -- x =17
so y= 5*10/17= 50/17 when x = 10
5 0
3 years ago
The ratio of ebooks to novels is 4:5. if there are 32 ebooks how many novels are there?
12345 [234]
<h3>Answer:  40 novels</h3>

================================================

Work Shown:

n = number of novels

(32 ebooks)/(n novels) = 4/5

32/n = 4/5

32*5 = n*4 ............ cross multiply

160 = 4n

4n = 160

n = 160/4 .............. dividing both sides by 4

n = 40

There are 40 novels.

4 0
3 years ago
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