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3 years ago

Solve the following system of equations . Plot the solution to the system on the provided graph

Mathematics

1 answer:

navik [9.2K]3 years ago

3 0

Answer:

(6, -3)

Step-by-step explanation:

I will solve this system using elimination.

$[tex]\left \{ {{-x+2y=-12} \atop {2x+3y=3}} \right.$ [/tex]

I will multiply $-x+2y=-12$ by 2 so that -x becomes -2x.

2(-x + 2y = -12)

Distribute.

-2x + 4y = -24

Now subtract this from the other equation.

2x + 3y = 3

-2x + 4y = -24

7y = -21

Divide both sides by 7.

y = -3

Now that we have the value of y, plug it into the original equation.

-x + 2(-3) = -12

Simplify.

-x - 6 = -12

Add 6 to both sides.

-x = -6

Divide both sides by -1.

x = 6

(6, -3)

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Right triangle XYZ has right angle Z. If the sin(X)=1213 , what is the cos(X)

AlekseyPX

Given:

Right triangle XYZ has right angle Z.

$\sin(x)=\dfrac{12}{13}$

To find:

The value of $\cos x$ .

Solution:

We know that,

$\sin^2(x)+\cos^2(x)=1$

$\cos^2(x)=1-\sin^2(x)$

$\cos(x)=\pm\sqrt{1-\sin^2x}$

For a triangle, all trigonometric ratios are positive. So,

$\cos(x)=\sqrt{1-\sin^2x}$

It is given that $\sin(x)=\dfrac{12}{13}$ . After substituting this value in the above equation, we get

$\cos(x)=\sqrt{1-(\dfrac{12}{13})^2}$

$\cos(x)=\sqrt{1-\dfrac{144}{169}}$

$\cos(x)=\sqrt{\dfrac{169-144}{169}}$

$\cos(x)=\sqrt{\dfrac{25}{169}}$

On further simplification, we get

$\cos(x)=\dfrac{\sqrt{25}}{\sqrt{169}}$

$\cos(x)=\dfrac{5}{13}$

Therefore, the required value is $\cos(x)=\dfrac{5}{13}$ .

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3 years ago

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laila [671]

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Goshia [24]

Answer:

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natta225 [31]

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3 years ago

The price of an item at the store can be defined by the variable x.

Feliz [49]

Answer:

A) 1.03x ; B) 1.08x ; C) 1.24x

Step-by-step explanation:

Given that :

Price of item = x

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100% of x + percentage added

x + percentage added

No matter the percentage added to x above, the marked up price will be a certain percentage above 100% of x ; that is > 1x

Hence, the Marked up price will always be greater than 1 ;

From the option given, the possible mark up price will be :

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3 0

3 years ago