Describe the nature of the roots for this equation.
x² – 2x+1=0
O A. Two complex roots
O B. Two real, irrational roots
O C. Two real, rational roots
O D. One real, double root

Answer:

35/9

Step-by-step explanation:

7y=-3x-1

y=-3/7x-1/7

m=-3/7

Now,

3my=-5x+2

y=-5/3mx+2/3

So

-3/7=-5/3m

-9m=-35

m=35/9

Answer:

35/9

Step-by-step explanation:

What we need to know:

Parallel lines have the same slope

slope intercept form: y = mx + b

m = slope

The first thing we will want to do is put both equations in slope intercept form.

We must do this so we can identify the slope.

First equation:

3x + 7y + 1 = 0

Solve for y

Subtract 1 from both sides

3x + 7y + 1 - 1 = 0 - 1.

3x + 7y = -1

Subtract 3x from both sides

3x - 3x + 7y = -1 - 3x

7y = -3x - 1

Divide both sides by 7

7y/7 = (-3x - 1)/7

y = -3/7x - 1/7

So the equation of the first line is y = -3/7x - 1/7

Second equation:

5x + 3my – 2 = 0

Solve for y

Subtract 5x from both sides

5x - 5x + 3my - 2 = 0 - 5x

3my - 2 = -5x

Add 2 to both sides

3my - 2 + 2 = -5x + 2

3my = -5x + 2

Divide both sides by 3m

3my/3m = (-5x + 2)/3m

y = -5x/3m + 2/3m

So the equation of the second line is y = -5x/3m + 2/3m

So we have the two equations:

y = -3/7x - 1/7 and y = -5x/3m + 2/3m and we want to find the value of m if the two lines are parallel

Lines that are parallel have similar slopes

So the slope of the first equation should be the same as the slope of the second equation

The slope of y = -3/7x - 1/7 is -3/7 as it takes the spot of "m" in y = mx + b.

The slope of y = -5x/3m + 2/3m is -5/3m as it takes the spot of "m"

If the slopes of parallel lines must be similar than -3/7 = -5/3m

(Note that we've just created an equation that we can use to solve for m)

We now solve for m

-3/7 = -5/3m

Cross multiply

3*-3m = -9m

7*-5=-35

we acquire -35 = -9m

Divide both sides by -9

-35/-9 = 35/9

-9m/-9=

We're left with m = 35/9

So we can conclude that the value of m would be 35/9 if the two lines are parallel

Answer: solutions are the same, just written differently, inequality sign is reversed when multiplying by a negative. Yes, both students are correct.Jul 8, 2018

Step-by-step explanation:

A) Use the distance formula to find the length of each side, and then add the lengths.

By solving equations we know that there are 30 giraffes and 40 ostriches in the zoo.

A mathematical statement known as an equation is made up of two expressions joined by the equal sign.

A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the number of the variable x is 7.

So, calculate as follows:

Let g represent giraffes and o represent ostriches.

g + o = 70 ...(1)

4*g + 2*o = 200  ...(2)

g = 70 - o, according to equation 1, therefore we may enter that number in place of g in equation 2 to obtain:

4*g + 2*o = 200

4*(70-o) + 2*o = 200

280 - 4o + 2o = 200

-2o = 200 - 280

2o = 80

o = 80/2

o = 40

Ostriches are 40 then giraffes will be:

70 - 40 = 30

Therefore, by solving equations we know that there are 30 giraffes and 40 ostriches in the zoo.

Know more about equations here:

https://brainly.com/question/28937794

#SPJ4

Answer:

8

Step-by-step explanation:

(Refer to picture)

Plug in the value of A and the value of B into the expression

Answer:

F) The rates are not equivalent.

Step-by-step explanation:

Consider the rates 45 mile in 8 minutes and 4 minutes to travel 25 mile. Select the statement(s) that are true. Multiple select question.

We find the unit rates

a) 45 mile in 8 minutes , we find the unit rate in miles per minute

8 minutes = 45 miles

1 minute = x

8 × x = 45 miles × 1 minute

x = 45 miles/8 minutes

x = 5.625 miles/ minute

b) 4 minutes to travel 25 miles. Find the unit rate is minutes per mile

25 miles = 4 minutes

1 mile = x

25miles × x = 4 minutes × 1

x = 4 minutes/25 miles

x = 0.16 minutes/mile

Hence, the correct option is

F) The rates are not equivalent.

The position function s(t) for a particle with acceleration a(t) = 4t - 1, initial velocity v(0) = -3 cm/s, and initial displacement s(0) = 4 cm is s(t) = t^2 - t + 4t + 4 cm.

To find the position function s(t), we need to integrate the acceleration function a(t) with respect to time twice. Given that a(t) = 4t - 1, we first integrate it once to obtain the velocity function v(t). The integral of 4t - 1 with respect to t is 2t^2 - t + C1, where C1 is a constant of integration. Since the initial velocity is v(0) = -3 cm/s, we can substitute t = 0 and v(0) = -3 into the velocity function to find C1. Solving for C1, we get C1 = -3.

Next, we integrate the velocity function v(t) = 2t^2 - t - 3 with respect to t to find the position function s(t). The integral of 2t^2 - t - 3 with respect to t is (2/3)t^3 - (1/2)t^2 - 3t + C2, where C2 is another constant of integration. Using the initial displacement s(0) = 4 cm, we substitute t = 0 and s(0) = 4 into the position function to find C2. Solving for C2, we get C2 = 4.

Therefore, the position function s(t) for the particle is given by s(t) = (2/3)t^3 - (1/2)t^2 - 3t + 4 cm. This function represents the particle's position at any given time t based on its initial velocity, acceleration, and displacement.

Learn more about displacement here:

https://brainly.com/question/11934397

#SPJ11

In linear equation,   20x + 45y = 440 ,     y = 2x  Where x is the number of small boxes sent and y  is the number of large boxes sent.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let be x the number of small boxes sent and y the number of large boxes sent.

Since each small box can hold 20 books (20x), each large box can hold 45 books (45y)and altogether can hold a total of 440 books, we can write the following equation to represent this

                 20x + 45y = 440

According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation

              y = 2x

Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is

                20x + 45y = 440

                      y = 2x

Learn more about linear equation

brainly.com/question/21835898

#SPJ4    

The number of solutions to x₀ + x₁ + ... + \(x_{k}\) = n with each value of x to be a non-negative integer xₐ is (n +  k).

Solved using the technique of stars and bars, also known as balls and urns.

Imagine you have n identical balls and k+1 distinct urns.

Distribute the balls among the urns such that each urn has at least one ball.

First distribute one ball to each urn, leaving you with n - (k+1) balls to distribute.

Then use k bars to separate the balls into k+1 groups, with the number of balls in each group corresponding to the value of xₐ.

For example, if the first k bars separate x₀ balls from x₁ balls, the second k bars separate x₁ balls from x₂ balls, and so on, with the last k bars separating \(x_{k-1}\) balls from \(x_{k}\) balls.

The number of ways to arrange n balls and k bars is (n + k) choose k, or (n +k) choose n.

This is the number of solutions to x₀ + x₁ + ... + \(x_{k}\) = n, where each xₐ is a non-negative integer.

Therefore, the number of solutions to x₀ + x₁ + ... + \(x_{k}\) = n with non-negative integer xₐ is (n +  k).

Learn more about integers here

brainly.com/question/30886950

#SPJ4

Answer:

\(\mathbb{ ANSWER }\)

NOPE

In this problem, the lower limit of integral is -3 and the upper limit of integration is 3.

We can use the formula for the surface area of a solid of revolution generated by a curve revolving around a given axis. The formula is S = 2π ∫ a b y dx, where a and b are the lower and upper limits of integration, and y is the height of the curve at x. In this problem, the lower limit of integration is -3 and the upper limit of integration is 3. Substituting y = 1/16(e^8x + e^-8x) into the equation gives S = 2π ∫ -3 3 (1/16(e^8x+e^-8x)) dx. Integral this expression gives S = 10512π.

Learn more about integral here

https://brainly.com/question/18125359

#SPJ4

The measure of each exterior angle of a regular hexagon ( six sided regular polygon is 60°.

Option C)60° is the correct answer.

A polygon is simply a two-dimensional a plane shape enclosed by line segments called sides.

The formula for calculating the exterior angles of a polygon is;

E = 360° ÷ number of sides

Given the data in the question;

So we substitute the value for number of sides into the expression above.

E = 360° ÷ number of sides

E = 360° ÷ 6

E = 60°

The measure of each exterior angle of a regular hexagon ( six sided regular polygon is 60°.

Option C)60° is the correct answer.

Learn more about polygons here: brainly.com/question/22408868

#SPJ2

Answer: (C) 60°

Just took it on edge

Given:

\(\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}\)

Express 16 as \(4^{2}\): \(x^2+y^2=16\)

\(x^2+y^2=4^2\\x^2+y^2=4^2 \times 1\)

Trignometry,

\(\cos ^2(t)+\sin ^2(t)=1\)

Now, substitute \(\cos ^2(t)+\sin ^2(t)\) for 1:

\(\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)\)

Law of indicates:
\(\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2\)

Taking positive square roots as follows:

\(x=4 \cos (t), y=4 \sin (t)\)

Recall that, z = xy.

Now, we have:

\(\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}\)

Now, substitute the values:
\(r(t)=x_t i+y_t j+z_t k\)

So, the vector r(t) is: \(r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i\)

Therefore, the vector function r(t) is written as: \(r(t)=x_t i+y_t j+z_t k\)

Know more about vector functions here:

https://brainly.com/question/14895420

#SPJ4

Answer:

0.92 cm

Step-by-step explanation:

Do not pick 0.920 as it is the same as 0.92 but 0.92 is always the preferable option

The accurate measurement for the length of the green box is indeed 0.92 cm.

To measure the length of the green box accurately, we must carefully analyze the given image. By comparing the green box to the provided scale, we can deduce the correct measurement.

Upon examination, the green box appears to span almost the entirety of the "0.1 cm" scale division and extends slightly beyond it. Given that the box reaches around 9 divisions on the scale, it is reasonable to deduce that its length is 0.92 cm. This is because it's covering 9 divisions of 0.1 cm each, and considering the small extension.

Hence, the accurate measurement for the length of the green box is indeed 0.92 cm. This value takes into account its coverage of 0.9 cm (9 divisions) and a slight extension, aligning with the provided options.

To know more about measurement:

https://brainly.com/question/2107310

#SPJ3

Answer:

-25x +  27

Step-by-step explanation:

-7x+9(-2x+3) =  

-7x-18x+27 =

-25x+27 =

Answer:

try resedning the picture it wont open/load

Step-by-step explanation:

the actuarial expression for the account balance after the final deposit is made as:\(FV = $5000 \times [(1.03^{(n-10)}+1)(1.02)^{(204)}-1]/(0.02) + $5000 \times [(1.03^{10}+1)(1.02)^{(104)}-1]/(0.02)\)The account balance after the final deposit is made is \($62,297.36.\)

The account balance after the final deposit is made, the formula for the future value of an annuity due with a growth rate.

Actuarial expression for the account balance after the final deposit is made:

A be the annual deposit amount, n be the number of deposits, i be the nominal annual interest rate, m be the number of compounding periods per year, and g be the annual growth rate of the deposits.

The formula for the future value of an annuity due with a growth rate is:

\(FV = A \times [(1+g)\times (1+i/m)^{((n-1) \times m)+1}] / (i/m)\)

Louis' situation, we have:

\(A = $5000\) for the first 10 years, and then \(A = $5000 \times 1.03^{(n-10)}\) for the remaining 20 years.

n = 30 years

i = 8% nominal annual interest rate, compounded quarterly, so i = 2% per quarter

m = 4 quarters per year

g = 3% annual growth rate for each deposit after the 10th year

The account balance after the final deposit is made:

The above actuarial expression and substituting n=30, we get:

\(FV = $5000 \times [(1.03^{20}+1)(1.02)^{80}-1]/(0.02) + $5000 \times [(1.03^{10}+1)(1.02)^{40}-1]/(0.02)\)

Simplifying this expression gives:

\(FV = $5000 \times (1.03^{20} \times 1.02^{80} + 1.03^{10} \times 1.02^{40})\)

Using a calculator, we get:

\(FV = $5000 \times (10.4619 + 1.7958)\)

\(FV = $62,297.36\)

For similar questions on Account Balance

https://brainly.com/question/13777419

#SPJ11

The smallest number of coins Freddie would need is 4 (one penny, one nickel, one dime, and one quarter).

What is algebra ?

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It includes the study of operations such as addition, subtraction, multiplication, division, and the extraction of roots, as well as the properties of operations such as commutativity, associativity, and distributivity.

In order to be able to pay any amount of money less than a dollar, Freddie would need to have at least one coin of each denomination: pennies, nickels, dimes, and quarters. The smallest number of coins he would need to achieve this is 4. With one penny, one nickel, one dime, and one quarter, he would be able to pay any amount of money less than a dollar by using combinations of these coins.

Therefore , The smallest number of coins Freddie would need is 4 (one penny, one nickel, one dime, and one quarter).

To learn more about algebra visit : brainly.com/question/24875240

#SPJ4

Answer:

26635.2

Step-by-step explanation:

pi18.8^2=~1109.8

1109.8*24=26635.2

The statement that It is sufficient to test an analogy by asking what are its relevant similarities is false.

Analogy refers to the process of comparison of two or more items such that it explains some idea, or classification or familiarity and representativeness. Studying the analogies helps in enhancing, strengthening and reinforcing the skills in areas such as reading comprehension, homophones, deductive reasoning and logic.

Testing an analogy only by relevant similarities will produce partial results which might not be suitable to fully explain the reason. Hence, both relevant similarities and differences are to be considered for more detailed review. Different kind of analogies used to explain the differences or similarities are synonym and antonym, symbol and reference, degree of differences.

Learn more about analogy at:

brainly.com/question/1490242

#SPJ4

Unreasonable Time is the nest option for running the group raffle at an upcoming assembly to give away a prize.

As given that;

Reasonable Time: Algorithms with a polynomial efficiency or lower (constant, linear, square, cube, etc.) are said to run in a reasonable amount of time.

Unreasonable Time: Algorithms with exponential or factorial efficiencies are examples of algorithms that run in an unreasonable amount of time.

Your school is considering running the group raffle at an upcoming assembly to give away a prize.

We have to write a brief explanation of what advice you would give them.

We can use the unreasonable time because  running the group raffle at an upcoming assembly to give away a prize cannot complete their work is the given amount of time.

To learn more about Reasonable and Unreasonable Time link is here

brainly.com/question/30186336

#SPJ4

Answer:

Step-by-step explanation:

2590

Therefore, the parametric equations for the line are x(t) = -5 + 6t, y(t) = 2 + 5t, and z(t) = 5 - 11t, where t is the parameter.

To find the parametric equations for the line through the points (−5, 2, 5) and (1, 7, −6), we need to determine the values of x, y, and z in terms of a parameter t.

We will use the point-slope form of the equation of a line, which is given as follows:

$$ \frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c} $$

where (x1, y1, z1) is a point on the line, and a, b, and c are the direction ratios of the line.

We can obtain these direction ratios by taking the differences between the corresponding coordinates of the two points on the line:

\($$ a = 1 - (-5) = 6 $$ $$ b = 7 - 2 = 5 $$ $$ c = -6 - 5 = -11 $$\)

Therefore, the parametric equations for the line are given by:

\($$ x(t) = -5 + 6t $$ $$ y(t) = 2 + 5t $$ $$ z(t) = 5 - 11t $$\)

To know more about parametric equations, visit:

https://brainly.in/question/8817007

#SPJ11

Answer: $83.35

Step-by-step explanation:

Find 15% of 72.48 = 10.87

10.87 + 72.48 = 83.35

Answer:

1.7, 3.2, 1.6

Step-by-step explanation:

if you add any 2 numbers from the 3 it has to be greater than the last number so

1.7+3.2>1.6

1.6+1.7>3.2

3.2+1.6>1.7

the derivative of the function h(t) = 3cot⁻¹(t) + 3cot⁻¹(1/t) is h'(t) = 0

To find the derivative of the function h(t) = 3cot⁻¹(t) + 3cot⁻¹(1/t), we can apply the chain rule to each term separately.

Let's differentiate each term step by step:

For the first term, 3cot⁻¹(t):

Using the chain rule, we have:

d/dt [cot⁻¹(t)] = -1/(1 + t²)

So, the derivative of the first term is:

d/dt [3cot⁻¹(t)] = 3 * (-1/(1 + t²)) = -3/(1 + t²)

For the second term, 3cot⁻¹(1/t):

Using the chain rule, we have:

d/dt [cot⁻¹(1/t)] = -1/(1 + (1/t)²) * (-1/t²) = 1/(t² + 1)

So, the derivative of the second term is:

d/dt [3cot⁻¹(1/t)] = 3 * (/(t² + 1)) = 3/(t² + 1)

Now, adding the derivatives of both terms, we get the derivative of the function h(t):

h'(t) = d/dt [3cot⁻¹(t)] + d/dt [3cot⁻¹(1/t)]

     = -3/(1 + t²) + 3/(t² + 1)

     = 0

Therefore, the derivative of the function h(t) = 3cot⁻¹(t) + 3cot⁻¹(1/t) is h'(t) = 0

Learn more about derivative here

https://brainly.com/question/25324584

#SPJ4

Complete question is below

Find the derivative of the function. h(t)=3cot⁻¹(t) + 3cot⁻¹(1/t)

Answer:

4a + 25.2.

Step-by-step explanation:

2/3(6a+9)+19.2

= 2/3 * 6a + 2/3 * 9 + 19.2

= 4a + 6 + 19.2

= 4a + 25.2.

1) The freezing point is - 8.62°

2) The boiling point is 102.37°

Freezing point depression refers to the phenomenon in which the freezing point of a solvent is lowered when a non-volatile solute is dissolved in it. It is a colligative property, meaning it depends on the number of solute particles rather than their identity or chemical nature.

1) We have that;

ΔT = K m i

Number of moles of the solute = 25.4 g/62 g/mol

= 0.41 moles

Mass of water = 88.4  g or 0.0884 Kg

ΔT = 1.86 *  0.41 moles /0.0884 Kg * 1

ΔT = 8.62°

Freezing point = 0 - 8.62°

= - 8.62°

2) ΔT = K m i

ΔT = 0.512 * 0.41 moles /0.0884 Kg * 1

= 2.37°

Boiling point = 100 +  2.37°

= 102.37°

Learn more about freezing point:https://brainly.com/question/31357864

#SPJ4

Missing points;

An ethylene glycol solution contains 24.6g of ethylene glycol (C2H6O2) in 88.2mL of water. (Assume a density of 1.00 g/mL for water.)

Determine the freezing point of the solution.

Determine the boiling point of the solution.