1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anna11 [10]
3 years ago
14

Solve (x + 3)2 + (x + 3) – 2 = 0. Let u = Rewrite the equation in terms of u. (u2 + 3) + u – 2 = 0 u2 + u – 2 = 0 (u2 + 9) + u –

2 = 0 u2 + u + 1 = 0 Factor the equation. What are the solutions of the original equation?
Mathematics
2 answers:
Artyom0805 [142]3 years ago
6 0

Answer:

Part 1 is x + 3

Part 2 is B u2 + u - 2 + 0

Part 3 is (u + 2)(u - 1) = 0

Part 4 is x = -5 or x = -2

Step-by-step explanation:

on edg... Good Luck!!!

Verdich [7]3 years ago
4 0

Answer:

The solutions of the original equation are x=-5 and x=-2

Step-by-step explanation:

we have

(x+3)^2+(x+3)-2=0

Let

u=(x+3)

Rewrite the equation

(u)^2+(u)-2=0

Complete  the square

u^2+u=2

u^2+u+1/4=2+1/4

u^2+u+1/4=9/4

rewrite as perfect squares

(u+1/2)^2=9/4

square root both sides

(u+1/2)=\pm\frac{3}{2}

u=(-1/2)\pm\frac{3}{2}

u=(-1/2)+\frac{3}{2}=1

u=(-1/2)-\frac{3}{2}=-2

the solutions are

u=-2,u=1

<em>Alternative Method</em>

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

(u)^2+(u)-2=0

so

a=1\\b=1\\c=-2

substitute in the formula

u=\frac{-1\pm\sqrt{1^{2}-4(1)(-2)}} {2(1)}

u=\frac{-1\pm\sqrt{9}} {2}

u=\frac{-1\pm3} {2}

u=\frac{-1+3} {2}=1

u=\frac{-1-3} {2}=-2

the solutions are

u=-2,u=1

<em>Find the solutions of  the original equation</em>

For u=-2

-2=(x+3) ----> x=-2-3=-5

For u=1

1=(x+3) ----> x=1-3=-2

therefore

The solutions of the original equation are

x=-5 and x=-2

You might be interested in
1.Graph the equation y = 6x -18:
RSB [31]

Answer:

1. Given the equation: y =6x-18                        ......[1]

The intercepts of a line are the points where the line intercepts or crosses the horizontal and vertical axes.

(A)

Horizontal intercept(x) states that the point where the line crosses the x-axis and at this point y=0

Put y=0 in equation [1]

0=6x-18 or

6x=18

<h3>⇒x=3</h3>

Ordered pair of horizontal intercept(x) = (3,0)

(B)

Vertical intercept(y) states that the point where the line crosses the y-axis and at this point x=0.

Put x=0 in equation [1]

y=6\cdot 0-18 or

y=-18

<h3>⇒y=-18</h3>

Ordered pair of vertical intercept(y) = (0,-18)

You can also see the graph  of the function y =6x-18 as shown in Figure-1.

2.

Graph the equation y+2x =4

to find the horizontal intercept and vertical intercept we follow the same process as done in 1

(A)

Horizontal intercept (x) = 2

Ordered pair = (2,0)

(B)

Vertical intercept (y) = 4

Ordered pair = (0,4)

Also, you can see these in the graph as shown in the Figure-2

3.

Given: The slope(m) of a line is \frac{3}{4}

Two lines are parallel if their slopes are equal and they have different y - intercepts.

(A).

The slope of a line parallel to it is, \frac{3}{4}

(B)

The slope of the original line is  \frac{3}{4}.

A line perpendicular to another line  has a slope that is the negative reciprocal of the slope of the other line.

Therefore, slope of a line perpendicular to it is; -\frac{1}{m} = -\frac{4}{3}

4.

The graph of the equation y =4x+5 as shown in figure 3

The x-intercept of this line is \frac{-5}{4} = -1.25

And the y-intercept of this line is y =5.

5.

Graph of the equation y = -3 represents the line as shown in figure 4.

6.

Solve the equation:

6y-18x = -18

6y = 18x-18

Divide by 6 to both sides of an equation ; we get

y = 3x-3 or

y = 3(x-1)


8 0
3 years ago
X + 5 &lt; –4<br><br> Solve for x.<br> Answer must be simplified.
Monica [59]

Answer:

x < -9

Step-by-step explanation:

Hi there,

To isolate the variable x, you do the same steps like solving a regular equation.

x + 5 < -4      ← subtract 5 from both sides to make x by itself

x < -9            ← final answer (already in simplest form)

Hope this explanation helps. Cheers.

3 0
3 years ago
Read 2 more answers
Can you help me with this its easy
Darina [25.2K]

Answer:

C. 1/8

Step-by-step explanation:

You gotta find the LCD and combine

4 0
3 years ago
Read 2 more answers
The statistical difference between a process operating at a 5 sigma level and a process operating at a 6 sigma level is markedly
Svet_ta [14]

Answer:

True

Step-by-step explanation:

A six sigma level has a lower and upper specification limits between \\ (\mu - 6\sigma) and \\ (\mu + 6\sigma). It means that the probability of finding no defects in a process is, considering 12 significant figures, for values symmetrically covered for standard deviations from the mean of a normal distribution:

\\ p = F(\mu + 6\sigma) - F(\mu - 6\sigma) = 0.999999998027

For those with defects <em>operating at a 6 sigma level, </em>the probability is:

\\ 1 - p = 1 - 0.999999998027 = 0.000000001973

Similarly, for finding <em>no defects</em> in a 5 sigma level, we have:

\\ p = F(\mu + 5\sigma) - F(\mu - 5\sigma) = 0.999999426697.

The probability of defects is:

\\ 1 - p = 1 - 0.999999426697 = 0.000000573303

Well, the defects present in a six sigma level and a five sigma level are, respectively:

\\ {6\sigma} = 0.000000001973 = 1.973 * 10^{-9} \approx \frac{2}{10^9} \approx \frac{2}{1000000000}

\\ {5\sigma} = 0.000000573303 = 5.73303 * 10^{-7} \approx \frac{6}{10^7} \approx \frac{6}{10000000}  

Then, comparing both fractions, we can confirm that a <em>6 sigma level is markedly different when it comes to the number of defects present:</em>

\\ {6\sigma} \approx \frac{2}{10^9} [1]

\\ {5\sigma} \approx \frac{6}{10^7} = \frac{6}{10^7}*\frac{10^2}{10^2}=\frac{600}{10^9} [2]

Comparing [1] and [2], a six sigma process has <em>2 defects per billion</em> opportunities, whereas a five sigma process has <em>600 defects per billion</em> opportunities.

8 0
3 years ago
Write 0.0002839 in scientific notation.
Anika [276]

Answer:2.84 x 10-4

There you go!

8 0
3 years ago
Read 2 more answers
Other questions:
  • the regular price of pants is $38.00 the pants are discounted 35% how much do the pants cost after the discount is applied
    8·2 answers
  • The length of a rectangle is twice the width. If the perimeter of the rectangle is 60 units, find the area of the rectangle.
    7·1 answer
  • A particular species of salmon has an average weight of 57 lb, with a standard deviation of 6.3 lbs. Researchers studying salmon
    12·1 answer
  • Levi would like to use a credit card to make a $3000 purchase. He is considering two credit options. The first requires
    14·1 answer
  • What’s the answer?(SOMEONE PLEASE HELP ME)
    9·1 answer
  • What is x + 5?? need help
    14·1 answer
  • Which multiplication equation can be used to explain the solution to 15: ?
    12·1 answer
  • Can someone pls help me
    6·2 answers
  • Si sen A = 7/25 donde "A" pertenece al segundo cuadrante y el cos B = -4/5 donde "B" pertenece al segundo cuadrante Calcular cos
    13·1 answer
  • Langston estimated the temperature to be 45°F . The thermometer showed the actual temperature to be 50°F. Complete the steps bel
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!