the roots of x+1/x=3 are: (x not equal to 0)​

Answers

Answer 1

Answer:

x^2-2x-3

Step-by-step explanation:

(x+1)(x-3)

x(x-3)+1(x-3)

Answer 2
Multiply both sides by x
x^2 + 1 = 3x
x^2 - 3x + 1 = 0
Completing the square
x^2 - 3x + (1.5)^2 - 1.25 = 0
(x - 1.5)^2 = 1.25
x - 1.5 = +- sr(1.25)
x = 1.5 +- sr(1.25)
x = 2.61803… or 0.381966…

You could use the quadratic formula x = (-b +- sr(b^2 - 4ac)) / 2a where ax^2 + bx + c = 0

Related Questions

Suppose a deposit of $ 2 , 000 in a savings account that paid an annual interest rate r (compounded yearly) is worth $ 2 , 209 after 2 years. using the formula a = p ( 1 + r ) t , we have 2 , 209 = 2 , 000 ( 1 + r ) 2 solve for r to find the annual interest rate (to the nearest tenth).

Answers

Answer:

5.1% (nearest tenth)

Step-by-step explanation:

Annual Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]

where:

A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)

Given:

A = $2,209P = $2,000t = 2 years

Substitute the given values into the formula and solve for r:

[tex]\implies \sf 2209=2000\left(1+r\right)^{2}[/tex]

[tex]\implies \sf \dfrac{2209}{2000}=(1+r)^2[/tex]

[tex]\implies \sf 1.1045=(1+r)^2[/tex]

[tex]\implies \sf \sqrt{1.1045}=1+r[/tex]

[tex]\implies \sf r = \sqrt{1.1045}-1[/tex]

[tex]\implies \sf r = 0.05095194942...[/tex]

[tex]\implies \sf r = 5.095194942...\%[/tex]

Therefore, the annual interest rate is 5.1% (nearest tenth)

Now write 40,630 in scientific notation

Answers

Answer:

40630=4.063× 10 power 4

For a 70-year-old investor, selling a weak stock at a loss may be (5 points)
O
a smart move to avoid potential additional future losses

® a poor decision, as the stock will most likely come back

an opportunity to buy as many as possible of the same stock

a red flag for the government to penalize that company

Answers

When you acquire stock in a firm, you are acquiring a little portion of that company known as a share. The correct option is A.

What are stocks?

When you acquire stock in a firm, you are acquiring a little portion of that company known as a share. Investors buy stocks in firms they believe will increase in value. If this occurs, the value of the company's shares rises as well.

For a 70-year-old investor, selling a weak stock at a loss may be a smart move to avoid potential additional future losses.

Hence, the correct option is A.

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Divide.

6√3 cis(7π/6) ÷ 3√5 cis(π/3)

Answers

[tex]\dfrac{6\sqrt 3~ \text{cis} \left( \dfrac{7 \pi} 6 \right)}{3 \sqrt 5 ~\text{cis} \left( \dfrac{\pi}{3}\right)}\\\\\\=\dfrac{2\sqrt 3 \cdot e^{i\tfrac{7\pi}{6}}}{\sqrt 5\cdot e^{i \tfrac{\pi}{3}}}\\\\\\=\dfrac{2 \sqrt 3}{\sqrt 5} \cdot \left(e^i \right)^{\tfrac{7\pi}{6} - \tfrac{\pi }{3}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\text{cis}~ \theta = e^{i \theta}\right]\\\\\\=\dfrac{2 \sqrt{3}}{\sqrt 5} \cdot \left(e^i\right)^{\tfrac{5\pi}6}\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\cdot e^{i\tfrac{5 \pi}6}\\\\\\[/tex]

[tex]=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ \cos \left(\dfrac{5\pi}{6}\right) + i \sin \left(\dfrac{5\pi}{6}\right) \right]~~~~~~~~~~~~~~~~~~;\left[e^{i\theta} = \cos \theta + i \sin \theta} \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\left[ \cos \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) + i\sin \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ -\cos \left(\dfrac{\pi}{6}\right) + i \sin \left(\dfrac{\pi}{6}\right) \right]\\\\\\[/tex]

[tex]=\dfrac{2\sqrt{3}}{\sqrt 5}\left( -\dfrac {\sqrt{3}}{2} + i \cdot \dfrac 12 \right)\\\\\\=-\dfrac{3}{\sqrt 5} + i \dfrac{\sqrt 3}{\sqrt 5}[/tex]

Answer:

Step-by-step explanation:

Just took the test:

6sqrt3 cis (7pie/6)/ 3sqrt5 cis (pie/3)=

2sqrt15/5 cis (5pie/6)

URGENT!!! PLEASE HELP!!! Find x and y.

Answers

Answer:

x is 48 and y is 100

Step-by-step explanation:

Angle y = 100 degree

Angle x = 48 degree

The lowest point in the United States is the Death Valley in California. Its altitude is 282 feet below sea level. Identify the integer representing the lowest point (Death Valley).

Answers

Answer:

-282

Step-by-step explanation:

Any altitude below sea level would have a negative sign in front of it.

A solid right pyramid has a regular hexagonal base with an area of 7.4 units2. The pyramid has a height of 6 units.

Answers

It should be noted that the volume of the pyramid will be 14.8 unit³.

From the information given, the solid right pyramid has a regular hexagonal base with an area of 7.4 units².

The height of the pyramid is also 6 units.

Therefore, the volume of the pyramid will be

What is the formula for the area of the pyramid?

= 1/3 × Area of the base × height

= 1/3 × 7.4 × 6

= 14.8 units³

In conclusion, the volume of the pyramid is 14.8 unit³.

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Given the image below, find the maximum value for z.

-3.5 < z < ___

I am so confused on how it's even possible to solve this

Answers

Answer:

-2.5 < x < 71

Step-by-step explanation:

I don't see a 'z' here, so I'll use x from the picture.

You would line up your values as such:

0 < 2x+5 < 71

You have a zero at the beginning because even without having an x value, your outcome would still be 5.

Subtract 5 from all sides.

-5 < 2x < 66

You now divide by two on both sides.

-2.5 < x < 33.

Which is your final answer.

You cannot go over 33, since 71 is your largest angle, and having something like say, 34, would give you 73.

-2.5 is your lowest value since if you went lower, you would have a negative angle, which isn't possible.

20 poinnttsss !! help please

Janie writes a polynomial expression using only one variable, x, with degree 3. Max writes a polynomial expression using only one variable, x, with degree 7.
What can you determine about the degree of the sum of Janie’s and Max’s polynomials?
What can you determine about the degree of the difference of Janie’s and Max’s polynomials?

Answers

Answer:

The sum of the polynomials is a 7th degree polynomial.

The difference of the polynomials is a 7th degree polynomial.

Step-by-step explanation:

Janie's polynomial is a 3rd degree with only x terms. Maybe she wrote:

f(x) = x^3

or maybe she was fancy and wrote:

f(x) =

x^3 + 2x^2 - 7x + 4

could be anything really, but the biggest exponent is 3.

Then Max does like:

g(x) = x^7

or

g(x) = x^7-x^4-3x+2

Whatever he made up, but the biggest exponent is 7.

So if they add or subtract their two polynomials, there's no x^7 in Janie's to add with the x^7 in Max's. MAYBE Max put some x^3 or x^2 or x or constants that might combine with the terms in Janie's.

Either way, anything that Max put in his polynomial that is a bigger power than 3 (4th, 5th, 6th, or 7th power) is just going to end up in the sum or difference.

Which graph represents the following system of inequalities? x < - 2x + 4; y < x + 3; x < 3

Answers

Graph C represents the following system of inequalities. For clarification refer to the attachment.

What is the definition of inequality?

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

Given relations;

x < - 2x + 4

y < x + 3

x < 3

Hence graph C represents the following system of inequalities.

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A grocery store had 38 employees but then they hired 4 more people. What is the percent change in their staff?

Answers

Answer:

+ 10.53 % change

Step-by-step explanation:

Percent change is   4 more people added to 38

   4 / 38  * 100% = 10.53 %

38+4=42
38=100%
42=42/38 X 100% =110 10/19%
110 10/19% - 100% = 10 10/19%

Find the slope of every line that is parallel to the line on the graph.​

Answers

Answer:

-1/5

Step-by-step explanation:

What are parallel lines?

Lines that are parallel never touch. They can extend infinitely and they will still never touch. In order for this to happen the slope of the two lines must be the same. So if we want to find the slope of every line that is parallel to the line on the graph, we simply find the slope of the line of the graph.

Finding the slope

We can find the slope using the following formula:

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where the x and y values are derived from any given points on the line (x1,y1) and (x2,y2)

Here the given points are (-5,-1) and (0,-2)

So we have (x1,y1) = (-5,-1) meaning x1 = -5 and y1 = -1

We also have (x2,y2) = (0,-2) meaning x2 = 0 and y2 = -2

Now we plug these values into the formula

Recall formula : [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

==> Plug in x1 = -5 , y1 = -1 , x2 = 0 and y2 = -2

[tex]Slope=\frac{-2-(-1)}{0-5}[/tex]

==> simplify numerator and denominator

[tex]slope = \frac{1}{-5}[/tex]

So the slope of the line is -1/5

This means the slope of any parallel line to that line would also have a slope of -1/5

Can you please help me

Answers

Answer:

1/3

Step-by-step explanation:

DE/AB = EF/BC = FD/CA

15/45 = 9/27 = 8/24 = 1/3

hope this will help u

expand and simplify (2x+5)(3x+1`)

Answers

Answer:

6x^2 + 17x + 5

Step-by-step explanation:

(2x + 5)(3x + 1)

= 6x^2 + 2x + 15x + 5

= 6x^2 + 17x + 5

The expression (2x+5)(3x+1) is a product of two binomials. To expand this product, we multiply each term in the first binomial by each term in the second binomial, using the distributive property of multiplication.

When we multiply 2x by 3x, we get 6x^2.

Then we multiply 2x by 1, which gives us 2x.

Next, we multiply 5 by 3x, which gives us 15x.

Finally, we multiply 5 by 1, which gives us 5.

Putting these terms together gives us the expanded form of the expression:

(2x+5)(3x+1) = 6x^2 + 2x + 15x + 5

Simplifying, we can add the 2x and 15x terms to get 17x, giving us the final simplified expression:

(2x+5)(3x+1) = 6x^2 + 17x + 5.

What type of polynomial is P(x)=x^3-1?

Answers

That is binomial because it has 2 terms

According to no. of terms it's binomial since it has two terms , according to the power it's cubic function since the power of X is 3

PLEASE GIVE BRAINLIEST

Please help!!!!!!!! Asap, i need to finish

Answers

The solution to the given quadratic expression is x = -1 and x = 5

Factoring quadratic equation

Given the quadratic equation below

f(x) = x^2 - 4x - 5

Factorize

f(x) = x^2 - 5x + x - 5 = 0
f(x) = x(x - 5) + 1(x - 5) = 0
(x+1)(x-5) = 0
x = -1 and x = 5

Hence the solution to the given quadratic expression is x = -1 and x = 5

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Answer:

x = -1; x = 5

Step-by-step explanation:

Standard Form of a Quadratic Function: f(x) = ax² + bx + c, where a ≠ 0

Given function: f(x) = x² - 4x - 5

⇒ a = 1, b = -4, c = -5

We are asked to solve the following function by factoring. In order to do so, let's rewrite the middle term by finding the factors that give a product of the first and last terms (a • c = -5) and give us the sum of the middle term (b = -4).

Factors that give a product of a • c: 1 • -5 = -5

Factors that give a sum of b: 1 + (-5) = -4

Step 1: Substitute f(x) = 0.

⇒ 0 = x² - 4x - 5

Step 2: Rewrite the equation with the factors.

⇒ 0 = x² + x - 5x - 5

Step 3: Factor out x and -5.

⇒ 0 = (x² + x) + (-5x - 5)

⇒ 0 x(x + 1) - 5(x + 1) [ Factor out the common factor. ]

⇒ 0 = (x - 5)(x + 1)

Step 4: Apply the Zero-Product Property (if m•n = 0, then m = 0 or n = 0)

a) 0 = x - 5 ⇒ 0 + 5 = x - 5 + 5 ⇒ 5 = x

b) 0 = x + 1 ⇒ 0 - 1 = x + 1 - 1 ⇒ -1 = x

Therefore, the missing solution for this quadratic function is x = 5.

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URGENT PLEASE HELP

If a+b= -5, find |a+b|+5 / |-a-b|


Answers

Answer:

2

Step-by-step explanation:

[tex]a+b=-5[/tex]

[tex]-(a+b)=-a-b=5[/tex]

[tex]\frac{|-5| + 5}{|5|}[/tex]

[tex]\frac{5+5}{5}[/tex]

[tex]2[/tex]

Answer:

2

Step-by-step explanation:

Given:

a + b = -5

To find -a - b  

Factor out the common term -1:

⇒ -a - b = -(a + b)

Substitute a + b = -5:

⇒ -a - b = -(-5)

Apply rule -(-x) = x:

⇒ -a - b = 5

Therefore:

[tex]\begin{aligned}\implies \sf \dfrac{|a+b|+5}{|-a-b|} & = \sf \dfrac{|-5|+5}{|5|}\\\\& = \sf \dfrac{5+5}{5}\\\\& = \sf \dfrac{10}{5}\\\\& = \sf 2\end{aligned}[/tex]

Note:  |-x| = x

16-2t=3/2t+9 solve for t

Answers

answer: t=2

steps:

16-2t = 3/2t+9

7 = 3/2t + 2t

2 is 4/2

7 = 3/2t + 4/2t

7 = 7/2t

7/2t = 7

(2/7)7/2t=7(2/7)

t=7(2/7)

t=2

Which of the following segments is tangent to the circle? 1 overline HI 2 ) overline DE 3) overline FG 4 ) overline AC

Answers

Answer:

DE

Step-by-step explanation:

a tangent is a straight line that only touches the circle at one point.

If lines / and mare parallel, and D6 = 1150, which is D4? ​

Answers

Answer:

D. 115

Step-by-step explanation:

because if Angle 6 is 115 then so is Angle is 4 due to AIA (alternate Interior Angles)

i need these missing blanks please..

Answers

What number can divide
42, 42x and -35x^2

How to rationalise 1000/3

Answers

Answer:

Step-by-step explanation:

there is no root in denominator so I think it is rationalised

The coordinate grid shows points A through K. Which points are solutions to the
system of inequalities listed below? (2 points)
2x + y < 10
2x - 4y > 8

EFGHJ

EFG

ACDM

AEF

Answers

Answer:

E is the solution of the inequality

Coordinates of points A = (-5,4)B = (4,7)C= (-2,7)D= (-7,1)E= (4, -2)F = (1 , -6)G= (-3, -10)H= (-4 , -4)I= (9, 3)J= (7 , -4)K= (2 ,3)

putting the values of coordinates in equation to check for the solution.

For A

2x + y < 10

2(-5) + 4 < 10.

-10 - 4 < 10

-14 < 10 ( true)

2x - 4y > 8

2(-5) - 4(4) > 8

-10 - 16 > 8

-26 > 8

false..

it is not the solution of the equation.

similarly we can find for other coordinates.

E is the solution

The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 9.7% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that 9.7% of his customers buy a magazine is correct, what is the probability that exactly 5 out of the first 10 customers buy a magazine?

Answers

The probability that exactly 5 out of the first 10 customers buy a magazine is 0.00126.

Given suspicion of 9.7% that buy a magazine is correct.

We have to find the probability that exactly 5 out of the first 10 customers buy a magazine. Probability is the chance of happening an event among all the events possible.

The binomial distribution is the probability of exactly x successes on n repeated trials and X can only have two outcomes.

[tex]P(X=x)=C_{n,x}p^{x} (1-p)^{n-x}[/tex]

In which [tex]C_{n,x}=n!/x!(n-x)![/tex]

And P is the probability of happening of X.

In the question 9.7% of his customers buy a magazine.

So the value of P=0.097

This can be calculated by :

P(X=5) when n=13

[tex]P(X=x)=C_{n,x} p^{x} (1-p)^{n-x}[/tex]

[tex]P(X=5)=C_{10,5} (0.097)^{5} (1-0.097)^{10-5}[/tex]

=[tex]P(X=5)=C_{10,5} (0.097)^{5} (0.903)^{5}[/tex]

[tex]=10!/5!5!*0.0000085*0.600397[/tex]

=252*0.00000510

=0.001286

Hence the probability that exactly 5 out of the first 10 customers buy a magazine is 0.001286.

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The difference between two positive integers is two if the smaller is added to the square of the larger the sum is 70

Answers

Step-by-step explanation:

ATTACHED IS THE SOLUTION.Tell me if you have any questions.

Find the slope of the line

Answers

Answer:

-3

Step-by-step explanation:

The points (3,-4) and (1,2) lie on the line.

m = (-4-2)/(3-1) = -3

What number were both the numerator and denominator multiplied by to arrive at the equivalent fraction? What number were both the numerator and denominator multiplied by to arrive at the equivalent fraction ?​

Answers

Answer:

Both the numerator and denominator should be multiplied by the same number to arrive at the equivalent fraction.

Step-by-step explanation:

Equivalent fractions =  two or more than two fractions are said to be equal if both results the same fraction after simplification.

For example, consider the fraction 1/3

Multiplying numerator and denominator with 2, we get 1/3 × 2/2 = 2/6

Multiplying numerator and denominator with 3, we get 1/3 × 3/3 = 3/9

Multiplying numerator and denominator with 4, we get 1/3 × 4/4 = 4/12

Therefore, we can conclude that,

1/3 = 2/6 = 3/9 = 4/12 these are equivalent fractions.

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Answer: 2 and 6/8

Step-by-step explanation:

The ratio of boys to girls in a classroom is 2 : 3. If there are
20 children in total, how many boys are there?

Answers

Answer:

8

Step-by-step explanation:

let the ratio constant be 'x'

=> 2x:3x

sum = 2x + 3x = 5x

Total number of boys

=>(2x/5x)20 = 8

Question -:

The ratio of boys and girls in a classroom is 2 : 3 respectively. If the total number of children is 20. How many boys are there in the class ?

Explanation -:

In this question we are provided with the ratio of boys isto girls that is 2 : 3 it is also given that total number of children are 20. We are asked to calculate number of boys.

[tex] \green{ \small \pmb{\tt{ First \: we \: will \: form \: an \: equation }}}[/tex]

Let us assume the number of girls as 3x and number of boys as 2x.

Total number of children = 20

3x + 2x = 20

[tex] \orange{\small \pmb{\tt{ Now \: we \: will \: solve \: this \: equation }}}[/tex]

[tex] \small\frak{ 3x + 2x = 20}[/tex]

[tex] \small\frak{ 5x = 20}[/tex]

[tex] \small\frak{ x = \dfrac{20}{5} = 4}[/tex]

[tex] \small \underline{ \boxed{\pmb{x = 4} }} \large \: \star[/tex]

Boys = 2 × 4 = 8

Girls = 3 × 4 = 12

Hence 8 boys and 12 girls are there in the classroom.

[tex] \tiny \tt{spbankingandsscseries}[/tex]

1 more NEXT WILL BE ANOTHER 25 POINTS

Answers

Answer:

B.

Step-by-step explanation:

if x is 3 then you just substitue every instance of x as 3. 2(x-4) + 3x - x^2 =

2(3 - 4) + 3(3) - 3^2 =

6-8 + 9 - 9 =

-2

You have two exponential functions. One function has the formula g(x) = 5x. The other function has the formula h(x) = 5-x. Which option below gives formula for k(x) = (g - h)(x)? k( x) = 10 x k( x) = 5 x - 5 -x k( x) = 2(5 x) k( x) = 5 x + 5 -x

Answers

The correct option is k(x) = 5x - (5-x)

What is Function?

The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, the given functions are;

g(x) = 5x                  h(x) = 5 - x

Now,

        k(x) = (g - h)(x)

        k(x) = g(x) - h(x)

        k(x) = 5x - (5 - x)

Thus, the correct option is k(x) = 5x - (5-x).

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