What are the roots of the polynomial equation x3 - 6x= 3x2 - 8? Use a graphing calculator and a system of equations

The equation has 2 valid solutions; no extraneous solutions

The given equation is:

[tex]\sqrt{x - 1} - 5= x - 8[/tex]

First, we determine the solutions

[tex]\sqrt{x - 1} - 5= x - 8[/tex]

Add 5 to both sides

[tex]\sqrt{x - 1} = x - 8 + 5[/tex]

[tex]\sqrt{x - 1} = x - 3[/tex]

Square both sides

[tex]x - 1 = (x - 3)^2[/tex]

Expand

[tex]x - 1 = x^2- 3x - 3x + 9[/tex]

[tex]x - 1 = x^2- 6x + 9[/tex]

Collect like terms

[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]

[tex]x^2 - 7x + 10 = 0[/tex]

Expand again

[tex]x^2 - 2x-5x + 10 = 0[/tex]

Factorize

[tex]x(x - 2) -5(x -2)= 0[/tex]

Factor out x - 2

[tex](x - 5)(x -2)= 0[/tex]

Split

[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]

[tex]x= 5[/tex] or [tex]x = 2[/tex]

The above values are valid values of x.

Hence, the equation has 2 valid solutions; no extraneous solutions

Read more about equations at:

https://brainly.com/question/2396830

Answer:

That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.

Step-by-step explanation:

for plato users

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

you just have to expand the trig. functions into their corresponding values and then finish them off.

Answer:

12

Step-by-step explanation:

10  8  subtract 2

8 12  add 4

12-10  subtract 2

10 14  add 4

Now we subtract 2

14-2 = 12

Answer:

1.25 dollars- the value of each coffee

0.75 dollars- the value of each doughnut

Step-by-step explanation:

Suppose that value of one coffee is x dollars, when one doughnut costs y dollars. The value o 10 coffee is 10x, when 10 doughnuts cost 10y. The sum is 10x+10y and it is 20.

10x+10y= 20 (we can divide each part by 10)

x+y=2

2coffee cost  2x, 14 doughnuts cost 14y

2x+14y=13 (it can be divided by two)

x+7y=6.5

We have the system of equations x+y=2,  x+7y=6.5

Subtract the first equation from the second one (the left side of the first equation from the left side

x+7y - (x+y)= 6.5-2

6y=4.5

y=4.5/6= 3/4 = 0.75 dollars- the value of each doughnut

x=2-0.75=1.25 dollars- the value of each coffee

Answer:

y = 7/8x - 1

Step-by-step explanation:

graph shown

9514 1404 393

Answer:

  $3277.23

Step-by-step explanation:

The future value of the CD with interest at rate r compounded semiannually for t years will be given by ...

  A = P(1 +r/2)^(2t)

where P is the principal value.

For the given rate and time, this is ...

  A = $2000(1 +0.05/2)^(2·10) = $2000(1.025^20) ≈ $3277.23

The value of the CD at maturity will be $3277.23.

Answer:

D) a = - 5/2

Step-by-step explanation:

2x -5y - 7 = 0

5y = 2x - 7

y = 2/5 x - 7

the slope of this line is therefore 2/5 (factor of x).

the perpendicular slope is then (exchange y and x and flip the sign) -5/2, which is then a and the factor of x.

Answer:

The new price is 66% off the original not 75% off

Step-by-step explanation:

Let x be the original price

First take 60 percent off

x - x*60% = new price

x- .60x = .40x

The new price is .40x

Then take 15 % off

(.40x) - (.40x)*15%

.40x - .40x*.15

.40x - .06x

.34x

100 -.34 =.66

The new price is 66% off the original not 75% off

Answer:

true

Step-by-step explanation:

the incenter of a triangle is the common intersection of the angle bisectors.hence always remains inside the triangle.

Answer:

3 tenths means 3 over ten represented as as 3/10 and 10 has one zero I.e tenth different from hundredths which has 2 zeros so our decimal shld also have one zero which is 0.3...so 0.3 is the answe hope it helps❤

Answer:

Area of yellow portion =54 in

Answer:

(x – 3)^2+ (y – 2)^2 = r^2

Step-by-step explanation:

The co-ordinates of the center=(3,2)

The formula for the equation of a circle is (x – h)^2+ (y – k)^2 = r^2,

(h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

Therefore, (x – h)^2+ (y – k)^2 = r^2

                 =(x – 3)^2+ (y – 2)^2 = r^2

You can find r^2the equation.

Answer:

a) 0.125 = 12.5% probability that it’s not raining and there is heavy traffic and I am not late.

b) 0.2292 = 22.92% probability that I am late.

c) 0.5454 = 54.54% probability that it rained that day.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Question a:

2/3 probability of not raining.

If not raining, 1/4 probability of heavy traffic.

1 - 0.25 = 0.75 = 3/4 probability of not late.

So

[tex]p = \frac{2}{3} \times \frac{1}{4} \times \frac{3}{4} = \frac{2}{16} = 0.125[/tex]

0.125 = 12.5% probability that it’s not raining and there is heavy traffic and I am not late.

b. What is the probability that I am late?

0.5 of (1/3)*(1/2) = 1/6(rainy and heavy traffic).

0.25 of (1/3)*(1/2) = 1/6(rainy and no traffic).

1/8 = 0.125 of (2/3)*(3/4) = 1/2(not rainy and no traffic).

0.25 of (2/3)*(1/4) = 1/6(not rainy and traffic). So

[tex]P(A) = 0.5\frac{1}{6} + 0.25\frac{1}{6} + 0.125\frac{3}{6} + 0.25\frac{1}{6} = \frac{0.5 + 0.25 + 3*0.125 + 0.25}{6} = 0.2292[/tex]

0.2292 = 22.92% probability that I am late.

c. Given that I arrived late at work, what is the probability that it rained that day?

Event A: Late

Event B: Rained

0.2292 = 22.92% probability that I am late.

This means that [tex]P(A) = 0.2292[/tex]

Probability of late and rain:

0.5 of 1/6(rain and heavy traffic).

0.25 of 1/6(rain and no traffic). So

[tex]P(A \cap B) = 0.5\frac{1}{6} + 0.25\frac{1}{6} = \frac{0.5 + 0.25}{6} = \frac{0.75}{6} = 0.125[/tex]

Probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.125}{0.2292} = 0.5454[/tex]

0.5454 = 54.54% probability that it rained that day.

The best option for Kelsie to create a SMART goal is b) "I will get to work before 9 A.M. every day this month."

Option B captures the essence of a smart goal.  A smart goal has the following characteristics: specific, measurable, achievable or attainable, realistic or relevant, and time-bound.

1. Specific: A smart goal like option B is well-defined, clear, and unambiguous.

2. Measurable: A smart goal sets specific criteria that measure Kelsie's progress toward the accomplishment of her goal.  For example, any day that she does not get to work before 9 a.m. she knows that she does not achieve her work arrival goal for that day.

3. Achievable: Kelsie's goal becomes attainable and possible to achieve because there is a set time for her to arrive at her work.

4. Realistic: Kelsie's goal, which she set for this month, is within her reach.  It is realistic, and relevant to her purpose.

5. Time-bound:  Kelsie has set a clearly defined timeline, which creates the needed urgency for her to realize it.  It includes a starting date and a target date, which will encourage her to realize it.

Thus, option B is the correct option that meets the criteria of a SMART goal unlike options A, C, and D, which are ambiguous, unrealistic, and not time-bound.

Learn more about SMART goals from www.brainly.com/question/4939309

Answer:

10

Step-by-step explanation:

ok so you do 12/30 and u get a 0.4 ratio. boom multiply 0.4 by 25 and u get 10. so boom the length is 10

Answer:

XY=10

Step-by-step explanation:

Since they are similar the ratio between each sides should be the same.

Ratio is .4. Found by dividing 12/30.

Multiply .4 by 25= 10

Answer:

48 hours

Step-by-step explanation:

12.5/100 = 6/x

1. cross-multiply

12.5 × x = 12.5x

100 × 6 = 600

2. divide

12.5x/12.5 = x

600/12.5 = 48

3. answer

x = 48

Answer:

[tex]B =102[/tex]

[tex]Y = 32[/tex]

Step-by-step explanation:

Solving (47):

To solve for B, we have:

[tex]B + 50 + 28 = 180[/tex] --- sum of angles in a triangle

This gives

[tex]B + 78 = 180[/tex]

Collect like terms

[tex]B =- 78 + 180[/tex]

[tex]B =102[/tex]

Solving (48):

To solve for Y, we have:

[tex]X + Y+ Z = 180[/tex] --- sum of angles in a triangle

This gives

[tex]Y = 180 - X - Z[/tex]

Where

[tex]W+ X=180[/tex] -- angle on a straight line

Solve for X

[tex]X=180 -W[/tex]

[tex]X=180 -100 = 80[/tex]

So, we have:

[tex]Y = 180 - X - Z[/tex]

[tex]Y = 180 - 80 - 68[/tex]

[tex]Y = 32[/tex]

Answer:

The function with blue line (see attachment) represents the graph of [tex]f(x) = -4\cdot |x|[/tex] after it is translated 3 units down.

Step-by-step explanation:

Mathematically speaking, a translation in the y-direction is defined by the following expression:

[tex]g(x) = f(x) + k[/tex] (1)

Where:

[tex]g(x)[/tex] - Resulting function.

[tex]f(x)[/tex] - Original function.

[tex]k[/tex] - Translation factor ([tex]k > 0[/tex] - Translation in the +y direction/[tex]k< 0[/tex] - Translation in the -y direction).

If we know that original function is translated 3 units down and [tex]f(x) = -4\cdot |x|[/tex], then the resulting function is:

[tex]g(x) = -4\cdot |x|-3[/tex]

Lastly, we graph both original and resulting functions with the help of a graphing tool, whose outcome is presented in the image attached below:

Please notice that the red line represents the original function, whereas the blue line represents the resulting function.

Answer:

b

Step-by-step explanation:

The value of x 85.

The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.

⇒angle= arc/radius

⇒  107°=arc/7

⇒ arc =1o7°*7

⇒arc=107π/180° *7

⇒arc = 85

Learn more about circle here:-brainly.com/question/24375372

#SPJ2

Answer:

Area of the base = (8×6)/2 = 24 yd²

Height of the prism = 8 yd

Perimeter of the base = 8+6+10 = 24 yd

Surface area = 2B + Ph = (2×24)+(24×8) = 48+192 = 240 yd²

Answer:

The answer is "Specific treatment levels".

Step-by-step explanation:

When we experimenting with 'level' which is related to the quantity or magnitude of treatment. For this part of an experiment or study, a group or individual is exposed to a specified set of circumstances. For example: If four categories are exposed to different doses of a given drug, then each dose reflects a level of a treatment factor in the model.

Answer:

pentagons

Step-by-step explanation:

In fact, there are pentagons which do not tessellate the plane. The house pentagon has two right angles. Because those two angles sum to 180° they can fit along a line, and the other three angles sum to 360° (= 540° - 180°) and fit around a vertex.

Answer:

The Regular Pentagon.

Explanation

I got a 100 % on the quiz

Answer:

Step-by-step explanation:

Answer:

stundeez

Step-by-step explanation:

Nicki Minaj hdhsbskdhsnsk

Answer:

3/10

Step-by-step explanation:

2/5*3*4

=6/20

=3/10

Answer:

see below

Step-by-step explanation:

Pi is approximately 3.14

4*3.14 =12.56

So about halfway between 12 and 13

Answer:

This is so hard for me. I can't understand. I am in grade 9 now.

Answer: Passes out in slow

Step-by-step explanation:

Step 1 be Einstein