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kondor19780726 [428]
2 years ago
7

How many solutions does this system of equations have y=2x y=x^2+2

Mathematics
1 answer:
finlep [7]2 years ago
5 0

The resulting equation has a leading degree of 2, hence the system of equation will have 2 solutions

<h3>Quadratic equations</h3>

Quadratic equations are equations that has a leading degree of 2. Given the following system of equations

y=2x

y=x^2+2

Equate to have:

2x = x^2+ 2

Equate to zero

x^2 - 2x +2 = 0

Since the resulting equation has a leading degree of 2, hence the system of equation will have 2 solutions

Learn more on system of equations here: brainly.com/question/14323743

#SPJ1

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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
2 years ago
Chetan makes a necklace for his sister. Twelve beads take up 5 inches of string. How many beas fit on 1 foot of string
Setler [38]
Find the amount of beads per inch:
12/5 = 2.4 (this doesn't make sense, but it will)
Now find the total beads on one foot, or 12 inches
2.4 x 12 = 28.8 
Since 29 wont fit, 28 will be the largest whole number of beads that can fit on the string

7 0
2 years ago
A trampoline has a rectangular jumping surface that is 10.3 feet long and 9.2 feet wide. What is the area of the jumping surface
Maslowich
The area of the trampoline is 94.76 because if you multiply 10.3 and 9.2 you will get the answer
4 0
3 years ago
Find the perimeter of the figure. I’ll mark brainliest if correct
koban [17]

Answer:

66 ft.

Step-by-step explanation:

Add 9+9+9+9+30 and that equals 66.

4 0
2 years ago
Read 2 more answers
A baker is making bread dough. He uses 3 cups of flour for every 8 ounces of water. How many cups of flour will he use if he use
Alekssandra [29.7K]

Answer:

36

Step-by-step explanation:

This is the fraction we use to solve this problem \frac{Ounces}{Flour}

Fractions are \frac{8}{3} and \frac{96}{x}

We now ask ourselves

8 * x = 96\\x = 12

Since whatever we do to the numerator we have to to the same to the denominator, we multiply 3 and 12

3 * 12 = x\\x = 36

Hope this helps!

PLZZZ give brainliest

4 0
3 years ago
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