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3 years ago

Solve for x- 6x^2 + 36x + 54 = 0

Mathematics

1 answer:

lions [1.4K]3 years ago

5 0

Answer:

-3

Step-by-step explanation:

$6x^2+36x+54=0$

First, you can factor out a 6:

$6(x^2+6x+9)=0$

Next, you can factor the quadratic:

$6(x+3)^2=0$

Since the only value of x that could set this equation equal to 0 is -3, that is the answer. Hope this helps!

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Help me with this question of O math

vagabundo [1.1K]

Answer:

domain is { - 1, 0, 1 }

Step-by-step explanation:

The domain are the values of the input x

Substitute the value from the range y into the equation and solve for x

y = 1

2x + 3 = 1 ( subtract 3 from both sides )

2x = - 2 ( divide both sides by 2 )

x = - 1

-------------------------------

y = 3

2x + 3 = 3 ( subtract 3 from both sides )

2x = 0 , then

x = 0

-------------------------------

y = 5

2x + 3 = 5 ( subtract 3 from both sides )

2x = 2 ( divide both sides by 2 )

x = 1

Then the domain is { - 1, 0, 1 }

3 0

3 years ago

Your friend gave you a gift card to a new restaurant. After you spend $36$36 on dinner, there is a balance of $44$44 left on the

JulsSmile [24]

80 dollars was the original balance

4 0

3 years ago

Read 2 more answers

Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE

AVprozaik [17]

Answer:

Step-by-step explanation:

We are given that:

$\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi$

And we want to find the value of tan(2x).

Note that since x is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

$\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}$

Using double angle identities:

$\displaystyle \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}$

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(x) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

$\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}$

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since x is in QII, cosine and tangent will be negative while sine will be positive. Hence:

<h2> $\displaystyle \tan(2x)=\frac{2(2\sqrt{2}/3)(-1/3)}{(-1/3)^2-(2\sqrt{2}/3)^2}$ </h2>

Simplify:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}$

Evaluate:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}$

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

$\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}$

So, our answer is D.

7 0

3 years ago

A prism is dilated by a factor of 1.5. How many times larger is the volume of the resulting prism than the volume of the origina

Margarita [4]

By the term dilated we mean to say that the dimensions of the new polyhedron is increase to a certain size by that times. For the volume, this dilation scale should be cubed in order to determine the number of times the volume of new figure is larger than the original.
r = (1.5)³
= 3.375
Thus, the volume of the new prism is 3.375 times larger than the volume of the original prism.

6 0

3 years ago

Read 2 more answers

3. Is XY Tangent to circle Z? Y 12 X (20 Z 18

Ratling [72]

Answer:

XY is a tangent

Step-by-step explanation:

Given

$XY = 12$