Find all solutions of the equation x^2+3x+5=0 and express them in the form a+ bi

Using linear function you would need to cross the bridge 30 times for the costs of the two toll options to be the same.

To learn more about linear function refer:

brainly.com/question/28441514

#SPJ1

The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

For more such questions on inequality

https://brainly.com/question/30681777

#SPJ8

well, she needs to sell $"x", which oddly enough is the 100%.

now, we also know that 7% of "x" is $12900, which is what Tonya takes home.

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 12900& 7 \end{array} \implies \cfrac{x}{12900}~~=~~\cfrac{100}{7} \\\\\\ 7x=1290000\implies x=\cfrac{1290000}{7}\implies x\approx 184286\)

The length of the original square must be equal to 3 inches.

To find the length of the original square, we have to first assume the unknown length is equal x and then use formula of area of a square to determine it's length.

Since the new length is stretched by 5in, the new length would be.

\(l = (x + 5)in\)

The area of a square is given as

\(A = l^2\)

But the area is equal 64 squared inches; let's use substitute the value of l into the equation above.

\(A = l^2\\l = x + 5\\A = 64\\64 = (x+5)^2\\64 = x^2 + 10x + 25\\x^2 + 10x - 39 = 0\\\)

Solving the quadratic equation above;

\(x^2 + 10x - 39 = 0\\x = 3 or x = -13\)

Taking the positive root only, x = 3.

The side length of the original square is equal to 3 inches.

Learn more on area of square here;

https://brainly.com/question/24487155

#SPJ1

Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.

This common convenience, already-existing variables, or all important elements from the original Diocesan customizable survey that followed a particular event methodology can all be used to achieve the goal. If it does, there will be another chance to get in touch with the entity. If it doesn't, each of the crucial elements of a term proof outcome will surely be lost.

Here,

The quantity of punch produced by the recipe is:

If the punch bowl has an 8-quart capacity and the recipe fills it 3/4 full.

=> 6 pints =  8 * 3/4.

The formula yields 6 quarts of punch as a result.

Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1  

P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q

T T T T T F F F F F T    T

F T T F F T T T T T F    F

P F T F F T T T T T F     F

-P T T F F T T T T T F     F

-Q T T T T F T F F F T     T

-P V -Q T T F F T T T T T F

-P -> Q T T F F T T T T T F

-P -> -Q T T F F T T T T T F

P <-> Q T T T T F T T T T F

Here is a more detailed explanation of how I filled out the table:

P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.

P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.

P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.

-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.

-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.

-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.

-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.

-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.

P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.

for more such questions on truth value

https://brainly.com/question/7483637

#SPJ8

Answer:

7x-1/22 = 3x+1/10

Multiply both sides of the equation by the Lowest common Multiple of the denominators(22 and 10). This is done to clear the fractions.

The LCM of 22 and 10 is 110

So

110 x(7x-1/22) = 110 x (3x+1/10)

110/22 =5

110/10 = 11

So the eqn now becomes

5(7x-1) = 11(3x+1)

Opening the parentheses

35x - 5 = 33x + 11

Collect Like Terms

35x - 33x = 11 + 5

2x = 16

x= 8.

\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}\)

\(\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4\)

Answer:

The answer is D 5

Step-by-step explanation:

because you could multiply by 5 and divide by 5

its proportional

Answer:

Below

Step-by-step explanation:

Gravel is  4 / (4+3+2) = 4/9 ths of the total

    4/9 x 27 m^3 = 12 m^3 gravel

Similarly  sand is 3/9th    3/9 * 27 = 9 m^3

  and the rest is cement   6 m^3

The absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.

What is meant by absolute maximum and absolute minimum values?

A function's absolute maximum point is the point at which it can reach its highest value. A similar absolute minimum point is where the function's least possible value is obtained.

Given: \(f(x)=xe^{\frac{-x2}{32} }\)

Differentiate the function,

\(f'(x)=e^{\frac{-x^{2} }{32} } -\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }\)

\(e^{\frac{-x^{2} }{32} } -\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }=0\)

\(\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }=e^{\frac{-x^{2} }{32} }\)

\(\frac{x^{2} }{16} =1\)

\(x^{2} =16\)

\(x=\) ±\(4\)

The interval is given as: [-2,8]

This means that the value of x = -4, is out of the interval.

So, we have the following critical points:

x = (-2, 4, 8)

⇒ f(x) at x = -2

\(f(-2)=-2\) × \(e^{\frac{-(-2)^{2} }{32} }\)

\(f(-2)=-2\) × \(e^{\frac{-4}{32} }\)

\(f(-2)=-1.765\)

⇒ f(x) at x = 4

\(f(4)=4\) × \(e^{\frac{-(4)^{2} }{32} }\)

\(f(4)=4\) × \(e^{\frac{-16}{32} }\)

\(f(4)=2.426\)

⇒ f(x) at x = 8

\(f(8)=8\) × \(e^{\frac{-(8)^{2} }{32} }\)

\(f(8)=8\) × \(e^{\frac{-64}{32} }\)

\(f(8)=1.083\)

Hence, by comparison, the absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.

To learn more about absolute maximum and absolute minimum values from the given link:

https://brainly.com/question/12752779

#SPJ1

Answer:

Step-by-step explanation:

Answer:   140 days

Step-by-step explanation:

3 times 35 is 105 days

35 plus 105 is 140 days

Answer:

13.27 cm

Step-by-step explanation:

I am using (xy) to mean the length of the side xy

7^2 + (xy)^2 = 15^2

49 + (xy)^2 = 225

(xy)^2 = 225-49

(xy)^2 = 176

Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm

Answer:

Domain:(∞,-∞)

Step-by-step explanation:

Well, I think this is correct because (-3,3) defines the limit. The parabola shows that there are infinite ranges of values within it. It is pretty much straightforward. All values must fit in from (-3,∞) to (-∞,3)
let me know if im wrong im just refreshing my thinking process at this moment.

Answer:

$1913.34

Step-by-step explanation:

$1784 (original amount) * 7.25% (sales tax) = $129.34 Tax paid

129.34 + 1784 = Price after tax

The Sharps purchased a new sectional. The cost was $1784.The total amount paid is $1913.34.

We have given that,

The Sharps purchased a new sectional. The cost was $1,784. They also had to pay 7.25% sales tax.

tax paid=original amount × sales tax

$1784 (original amount) * 7.25% (sales tax) = $129.34 Tax paid

129.34 + 1784 = Price after tax

Therefore, The total amount paid is $1913.34.

To learn more about the amount visit:

https://brainly.com/question/25109150

#SPJ2

Answer:

Proportional relationship:

Use a pair of points (0.14, 0.7) to find the value of k:

The function is:

Fill in the table:

Answer:

5000-5000×0+500+600-1100+10+10-20=5000

Answer:

1) initial investment is A.200

2) interest rate is F. 8%

3) D. 16 years

4) H. 520

tell me if anything is wrong

Step-by-step explanation:

The estimated salary for an employee with 24 years of experience is 83,316.87 .

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.

The regression equation can be represented as
\(Y = f(X_{i} , \beta ) + e_{i}\)  

that is  \(Y = \beta _{0} + \beta _{1} X + e_{i}\)

where , Y = dependent variable

            f = function

           \(X_{i}\) = independent variable

           \(\beta\) = unknown parameters

           \(e_{i}\) = error terms

For the given regression equation ,

29,136.63 + 2257.51 (Years of experience)

Here , \(\beta _{0}\) = 29,136.63
          \(\beta _{1}\) = 2257.51

          X = 24 ( for 24 years experience)

Hence , using the regression equation,

              29,136.63 + 2257.51×24

           = 29136.63 + 54,180.24
           = 83,316.87

So therefore the estimated salary with 24 year experience is 83,316.87.

To know more about regression , go to https://brainly.com/question/14184702

#SPJ4

Answer:

94 more students should be included in the sample.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.99}{2} = 0.005\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).

So it is z with a pvalue of \(1-0.005 = 0.995\), so \(z = 2.575\)

Now, find the margin of error M as such

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

How many students we need to sample to be 99% sure that the sample mean x is within 1 semester hour of the population mean?

We need to survey n students.

n is found when M = 1.

We have that \(\sigma = 4.7\)

So

\(M = z*\frac{\sigma}{\sqrt{n}}\)

\(1 = 2.575*\frac{4.7}{\sqrt{n}}\)

\(\sqrt{n} = 2.575*4.7\)

\((\sqrt{n})^{2} = (2.575*4.7)^{2}\)

\(n = 146.47\)

Rounding up

147 students need to be surveyed.

How many more students should be included...?

53 have already been surveyed

147 - 53 = 94

94 more students should be included in the sample.

Answer:

We can start by using the second equation to eliminate x:

2x + 5y - 2z = 3

2x = -5y + 2z + 3

x = (-5/2)y + z + 3/2

Now we can substitute this expression for x into the first and third equations:

x + y + z = 4

(-5/2)y + z + 3/2 + y + z = 4

(-5/2)y + 2z = 5/2

x + 7y - 7z = 5

(-5/2)y + z + 3/2 + 7y - 7z = 5

(9/2)y - 6z = 7/2

Now we have a system of two equations with two variables, (-5/2)y + 2z = 5/2 and (9/2)y - 6z = 7/2. We can use any method to solve for y and z, such as substitution or elimination. However, we will find that the system is inconsistent, meaning there is no solution that satisfies both equations.

Multiplying the first equation by 9 and the second equation by 5 and adding them, we get:

(-45/2)y + 18z = 45/2

(45/2)y - 30z = 35/2

Adding these two equations, we get:

-12z = 40/2

-12z = 20

z = -5/3

Substituting z = -5/3 into (-5/2)y + 2z = 5/2, we get:

(-5/2)y + 2(-5/3) = 5/2

(-5/2)y - 10/3 = 5/2

(-5/2)y = 25/6

y = -5/12

Substituting y = -5/12 and z = -5/3 into any of the original equations, we get:

x + y + z = 4

x - 5/12 - 5/3 = 4

x = 29/12

Therefore, the solution is (x, y, z) = (29/12, -5/12, -5/3). However, if we substitute these values into any of the original equations, we will find that it does not satisfy the equation. For example:

2x + 5y - 2z = 3

2(29/12) + 5(-5/12) - 2(-5/3) = 3

29/6 - 5/2 + 5/3 ≠ 3

Since there is no solution that satisfies all three equations, the system is inconsistent.

Step-by-step explanation:

Answer:

See below for proof.

Step-by-step explanation:

A system of equations is not consistent when there is no solution or no set of values that satisfies all the equations simultaneously. In other words, the equations are contradictory or incompatible with each other.

Given system of equations:

\(\begin{cases}x+y+z = 4\\2x+5y-2z =3\\x+7y-7z =5\end{cases}\)

Rearrange the first equation to isolate x:

\(x=4-y-z\)

Substitute this into the second equation to eliminate the term in x:

\(\begin{aligned}2x+5y-2z&=3\\2(4-y-z)+5y-2z&=3\\8-2y-2z+5y-2z&=3\\-2y-2z+5y-2z&=-5\\5y-2y-2z-2z&=-5\\3y-4z&=-5\end{aligned}\)

Subtract the first equation from the third equation to eliminate x:

\(\begin{array}{cccrcrcl}&x&+&7y&-&7z&=&5\\\vphantom{\dfrac12}-&(x&+&y&+&z&=&4)\\\cline{2-8}\vphantom{\dfrac12}&&&6y&-&8z&=&1\end{aligned}\)

Now we have two equations in terms of the variables y and z:

\(\begin{cases}3y-4z=-5\\6y-8z=1\end{cases}\)

Multiply the first equation by 2 so that the coefficients of the variables of both equations are the same:

\(\begin{cases}6y-8z=-10\\6y-8z=1\end{cases}\)

Comparing the two equations, we can see that the coefficients of the y and z variables are the same, but the numbers they equate to is different. This means that there is no way to add or subtract the equations to eliminate one of the variables.

For example, if we subtract the second equation from the first equation we get:

\(\begin{array}{crcrcl}&6y&-&8z&=&-10\\\vphantom{\dfrac12}-&(6y&-&8z&=&\:\:\;\;\:1)\\\cline{2-6}\vphantom{\dfrac12}&&&0&=&-11\end{aligned}\)

Zero does not equal negative 11.

Since we cannot eliminate the variable y or z, we cannot find a unique solution that satisfies all three equations simultaneously. Therefore, the system of equations is inconsistent.

Answer:

D

Step-by-step explanation:

A and D are both equidistant from the x- axis, that is

A is 3 units above the x- axis and D is 3 units below the x- axis

then the x- axis is the line of symmetry

Answer:

x = 15

Step-by-step explanation:

3x+1+4x-3 = 103

7x = 105

x = 15