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3 years ago

What is the solution √3x +3 - 1 = x

Mathematics

1 answer:

faltersainse [42]3 years ago

3 0

Answer:

Choice A

Step-by-step explanation:

√(3x +3) - 1 = x

Taking square on both sides:

$( \sqrt{3x + 2} ) {}^{2} = (x + 1) {}^{2}$
$3x + 3 = x { }^{2} + 2x + 1$

Subtracting x²+2x + 1 from both sides:

$3x+3−(x {}^{2} +2x+1)=x {}^{2} +2x+1−(x {}^{2} +2x+1)$
$3x + 3 - x {}^{2} - 2x - 1 = 0$
$3x - 2x + 3 - 1 - x {}^{2} = 0$
$x + 2 - x {}^{2} = 0$

Rewrite as,

$-x² + x + 2= 0$

Factoring LHS of the equation:[Middle term factor]

$( - x - 1)(x - 2) = 0$

Now,

$( - x - 1) = 0 \: \: \: \: \: ...(1)$
$x - 2 = 0 \: \: \: \: \: ...(2)$

Equation 1:

$- x - 1 = 0$
$- x = 0 + 1$
$- x = 1$
$x = \boxed{ - 1}$

Equation 2:

$x - 2 = 0$
$x = 0 + 2$
$x = \boxed{2}$

Choice A is accurate.

-1 & 2

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A wheelchair access ramp has an angle of elevation of 31 degrees. If the ramp reaches to the top of a 42 inch high porch, how lo

mixas84 [53]

Answer:

Step-by-step explanation:

sin 31 = 42/x

x sin 31 = 42

x = (sin 31)/42

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3 years ago

A town has a population of 7000 and grows at 4% every year. What will be the population after 13 years, to the nearest whole num

Gennadij [26K]

Answer:

10640

Step-by-step explanation:

In order to see how much the town grows, you would need to do 7000 times .04, which gets 280. Then, multiply what by 13 to get 10640.

8 0

4 years ago

Read 2 more answers

Which figure is the image produced by applying the composition t 0,3 r 0,90 to figure R?

Maksim231197 [3]

Answer:

Option A is correct

The only figure after composition of $t_{0 , 3} (r_{0,90^{\circ}})$ to figure R is Figure H

Step-by-step explanation:

From the given figure in R;

The coordinates in Figure R ;

(1 , -1) , (2, -2) ,(4, -2) ( 0, -4)

Composite function defined as when one function is substituted into another function.

To Apply the composition $t_{0 , 3} (r_{0,90^{\circ}})$ to figure R;

First apply the Reflection $r_{0, 90^{\circ}}$ in Figure R;

The rule of reflection is given by:

$(x,y) \rightarrow (-y,x)$

By applying the rule of reflection in Figure R ,

then, the coordinates becomes;

(1 , -1) $\rightarrow$ (1, 1)

(2 , -2) $\rightarrow$ (2, 2)

(4 , -2) $\rightarrow$ (2, 4)

(0, -4) $\rightarrow$ (4, 0)

Now, apply the translation $t_{0,3}$

Translation : It is a type of transformation that moves each point in a figure the same distance in the same direction.

then,

the rule of translation is:

$(x,y) \rightarrow (x+0,y+3)$

Apply the rule of translation on coordinates (1,1) , (2,2), (2,4) and (4,0)

then

(1 , 1) $\rightarrow$ (1+0 1+3) =(1,4)

(2, 2) $\rightarrow$ (2+0 2+3) =(2, 5)

(2, 4) $\rightarrow$ (2+0 4+3) =(2 ,7) and

(4, 0) $\rightarrow$ (4+0 0+3) =(4 ,3)

Then, the only figure after composition of $t_{0 , 3} (r_{0,90^{\circ}})$ to figure R is Figure H

7 0

4 years ago

Read 2 more answers

How to convert 5/8 to a decimal

Softa [21]

You divide 5 by 8 it’s really easy

5 0

4 years ago

Laura lives 15 miles east of Kevin’s place. Kevin lives 8 miles south of Michelle’s place. How far does Michelle live from Laura

My name is Ann [436]

Answer:

17 miles.

Step-by-step explanation:

Let's define:

North as the positive y-axis

East as the positive x-axis.

We know that Laura lives 15 miles east of Kevin's place.

Kevin lives 8 miles south of Michelle's place.

So, if we define the origin, (0, 0) as Laura's place.

From:

"that Laura lives 15 miles east of Kevin's place."

We have that the location of Kevin's house is 15 miles west from Laura's place, then Kevin's house is at:

(0, 0) + (-15mi, 0) = (-15mi, 0)

From Kevin lives 8 miles south of Michelle's place, we know that Michelle's live 8 miles north of Kevin's place.

Then the location of Michele's house is the location of Kevin's plus (0, 8mi).

Michelle's house is located at:

(-15mi, 0) + (0, 8mi) =(-15mi, 8mi)

Now we want to find the distance between Michelle's house and Laura's house.

Michelle's house is at (-15mi, 8mi)

Laura's house is at (0mi, 0mi)

Remember that the distance between two points (a, b) and (c, d) is given by:

$D = \sqrt{(a - c)^2 + (b - d)^2}$

Then the distance between (-15mi, 8mi) and (0mi, 0mi) is:

$D = \sqrt{(-15mi - 0mi)^2 + (8mi - 0mi)^2} = 17mi$

The correct option is the first one, 17 miles.

6 0

3 years ago