X squared - 10x + 13 = 0
Quadratic formula

Answer: Arnav is 1.8m

Step-by-step explanation: I multiplied 1.5 by 0.20 and then added that answer to 1.5 and then I got 1.8

:D

Answer:

1.5 x 2= 3m its really just that easy.... it took me a while to learn this trick but it works for most things.

To find the inverse function of f(x) = 2x - 3, denoted as f⁻¹(x), we need to interchange the roles of x and y and solve for y. The inverse function represents the relationship between the output values of f(x) and the input values of f⁻¹(x).

To find the inverse function, we start by replacing f(x) with y in the given function: y = 2x - 3. Next, we swap the roles of x and y to obtain x = 2y - 3. The goal is to solve this equation for y to find the inverse function.

Rearranging the equation, we get 2y = x + 3. Dividing both sides by 2, we have y = (x + 3)/2. Thus, we have found the inverse function f⁻¹(x) = (x + 3)/2.

To verify that f⁻¹(x) is indeed the inverse of f(x), we can compose the two functions. If we evaluate f⁻¹(f(x)), we should obtain x as the result.

Substituting f(x) = 2x - 3 into f⁻¹(x), we get f⁻¹(f(x)) = [(2x - 3) + 3]/2 = 2x/2 = x. As expected, the composition of f⁻¹(f(x)) yields x, confirming that f⁻¹(x) is indeed the inverse function of f(x) = 2x - 3.

Learn more about inverse here:

https://brainly.com/question/30339780

#SPJ11

The simplified expression is (x + 4) / (3x² + 18x + 15)

We have,

The denominators of both fractions are the same, so we can add the two fractions by combining their numerators over the common denominator:

6 / (3x² + 18x + 15) + (x - 2) / (3x² + 18x + 15)

= (6 + x - 2) / (3x² + 18x + 15)

Simplifying the numerator.

6 + x - 2 = x + 4

Substituting this back into the original expression.

(6 + x - 2) / (3x² + 18x + 15)

= (x + 4) / (3x² + 18x + 15)

Thus,

The simplified expression is (x + 4) / (3x² + 18x + 15)

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Step-by-step explanation:

2/8 = 16/x

2x = 16×8

x = 16*8/2

x = 64.

Hope it helps :)

The cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.

A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value.

From the question , we are given that the laptop costs $350 more than the desktop, therefore,

let x represent the cost of the laptop thus, x-350 will be the cost of the desktop .

The total finance charge of $388 is equal to 8% of the cost of the laptop and 7.5% of the cost of the desktop, we solve as;

388 = 0.08(x) + 0.075(x - 350)

252 = 0.08x + 0.075x - 26.25

278.75 = 0.155x

x = 278.75/0.155

x = 1798

Recall that the cost of desktop = x -350

therefore:

1,798- 350 = 1448

The cost of laptop = $1798

The cost of desktop = $1448

Thus, the cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.

Read more about mathematics operations at:

brainly.com/question/17869111

#SPJ1

2-1. a) The shear stress τ is constant across the flow. b) The velocity is maximum at the center (r = 0) and decreases linearly as the radial distance increases. c)v_max = (P₁ - P₂) / (4μL) * \(R^{2}\) and v_avg = (1 / (π(\(R^{2} -a^{2}\)))) * ∫[a to R] v * 2πr dr 2-2.a) The shear stress is constant for parallel plates. b) The velocity profile shows that the velocity is maximum at the centerline and decreases parabolically .c)v_max = (P₁ - P₂) / (2μh) and v_avg = (1 / (2h)) * ∫[-h to h] v dr.

2-1. Flow in an annular region between concentric cylinders:

(a) Shear stress profile:

In an incompressible fluid flow between concentric cylinders, the shear stress τ varies with radial distance r. The shear stress profile can be obtained using the Navier-Stokes equation:

τ = μ(dv/dr)

where τ is the shear stress, μ is the dynamic viscosity, v is the velocity of the fluid, and r is the radial distance.

Since the flow is at steady state, the velocity profile is independent of time. Therefore, dv/dr = 0, and the shear stress τ is constant across the flow.

(b) Velocity profile:

To determine the velocity profile in the annular region, we can use the Hagen-Poiseuille equation for flow between concentric cylinders:

v = (P₁ - P₂) / (4μL) * (\(R^{2} -r^{2}\))

where v is the velocity of the fluid, P₁ and P₂ are the pressures at the outer and inner cylinders respectively, μ is the dynamic viscosity, L is the length of the cylinders, R is the outer radius, and r is the radial distance.

The velocity profile shows that the velocity is maximum at the center (r = 0) and decreases linearly as the radial distance increases, reaching zero at the outer cylinder (r = R).

(c) Maximum and average velocities:

The maximum velocity occurs at the center (r = 0) and is given by:

v_max = (P₁ - P₂) / (4μL) * \(R^{2}\)

The average velocity can be obtained by integrating the velocity profile and dividing by the cross-sectional area:

v_avg = (1 / (π(\(R^{2} -a^{2}\)))) * ∫[a to R] v * 2πr dr

where a is the inner radius of the annular region.

2-2. The flow between parallel plates:

(a) Shear stress profile:

For flow between very wide or broad parallel plates, the shear stress profile can be obtained using the Navier-Stokes equation as mentioned in problem 2-1. The shear stress τ is constant across the flow.

(b) Velocity profile:

The velocity profile for flow between parallel plates can be obtained using the Hagen-Poiseuille equation, modified for this geometry:

v = (P₁ - P₂) / (2μh) * (1 - (\(r^{2} /h^{2}\)))

where v is the velocity of the fluid, P₁ and P₂ are the pressures at the top and bottom plates respectively, μ is the dynamic viscosity, h is the distance between the plates, and r is the radial distance from the centerline.

The velocity profile shows that the velocity is maximum at the centerline (r = 0) and decreases parabolically as the radial distance increases, reaching zero at the plates (r = ±h).

(c) Maximum and average velocities:

The maximum velocity occurs at the centerline (r = 0) and is given by:

v_max = (P₁ - P₂) / (2μh)

The average velocity can be obtained by integrating the velocity profile and dividing by the distance between the plates:

v_avg = (1 / (2h)) * ∫[-h to h] v dr

These formulas can be used to calculate the shear stress profile, velocity profile, and maximum/average velocities for the given geometries.

Learn more about shear stress;

https://brainly.com/question/30407832

#SPJ4

Answer:

\(\frac{1}{x-1}\)

Step-by-step explanation:

(x - 1) × \(\frac{1}{x-1}\) ( cancel the factor (x - 1) on numerator and denominator

= 1

[ In the same way 2 × \(\frac{1}{2}\) = 1 ]

The required rational expression is \(\frac{1}{x-1}\)

Answer:

True

If the angles are equal A and B are parallel

Step-by-step explanation:

Given :

1- cosA = 1/2

or, CosA = 1 -1/2

Therefore ; CosA = 1/2 = b/h

According to the Pythagoras theorem,

P = root under h^2 - b^2

= root under (2)^2 - (1)^2

= root under 4 -1

= root 3

Again,

SinA = P/h

= root 3 / 2

Why do you want an answer immediately. Just know, don't ever cheat by using 'Brainly'

The difference between F(8) and F(2) is 12

What are Functions?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

Given: Function of Warming Room = F(m) = 2m + 58

To Find: F(8) - F(2)

F(8) = 2*8 + 58 = 16+58 = 74

F(2) = 2*2 + 58 = 4+58 = 62

F(8) - F(2) = 74 - 62 = 12

The difference between F(8) and F(2) is 12

To learn more about Functions from the given link

https://brainly.com/question/22340031

#SPJ1

(h x $6.25) - $20 is a equation to figure how how many hair products she needs to sell to generate a profit of $120.

Profit is just the money left over after costs are paid. A loss is deemed to have occurred if the expenses exceeded the income.

A gain is a positive figure, whereas a loss is a negative one.

To determine whether a contract is lucrative or not, the phrases profit and loss are utilized. These words are frequently used in ordinary conversation. If the selling price exceeds the cost price, the difference between the two amounts is known as the profit.

The equation to determine how many hair products Jackie must sell to make a profit of $120 would be:

$120 (profit) = (h x $6.25) - $20 (cost of online membership)

where h is the number of hair products sold.

To solve for h, we can first add $20 to both sides of the equation:

$120 + $20 = h x $6.25

Next, we can divide both sides of the equation by $6.25 to find the value of h:

h = ( $120 + $20 ) / $6.25

h = 20

So Jackie must sell 20 hair products to make a profit of $120.

To know more about profit  visit:

https://brainly.com/question/29494194

(h x $6.25) - $20 is an equation to figure how many hair products she needs to sell to generate a profit of $120.

Profit is just the money that remains after expenses are covered. A loss is deemed to have occurred if the expenses exceeded the income.

A gain is a positive figure, whereas a loss is a negative one.

The terms profit and loss are used to assess how valuable a transaction is. In everyday discourse, these terms are often employed. The difference between the two sums is referred to as the profit if the selling price is higher than the cost price.

The equation to determine how many hair products Jackie must sell to make a profit of $120 would be:

$120 (profit) = (h x $6.25) - $20 (cost of online membership)

where h is the number of hair products sold.

To solve for h, we can first add $20 to both sides of the equation:

$120 + $20 = h x $6.25

Next, we can divide both sides of the equation by $6.25 to find the value of h:

h = ( $120 + $20 ) / $6.25

h = 20

So Jackie must sell 20 hair products to make a profit of $120.

To know more about profit  visit:

brainly.com/question/29494194

#SPJ1

Answer:

20

Step-by-step explanation:

The population as an exponential function of time t is given by \(n(t) = 2,000,000 * e^(0.022t)\) when the initial value is 2 million.

The population has a yearly per capita growth rate of 2.2% and the initial value is 2 million, we can express the population as an exponential function using the formula:

\(n(t) = a * e^(rt)\)

In this formula, n(t) represents the population as a function of time t, a is the initial value, e is Euler's number (approximately 2.71828), and r is the annual growth rate expressed as a decimal.

The exponential function for the population with an initial value of 2 million and an annual growth rate of 2.2%, we substitute the given values into the formula:

\(n(t) = 2 * e^(0.022t)\)

To simplify the equation, we can multiply both sides by 1,000,000:

\(n(t) = 2,000,000 * e^(0.022t)\)

Therefore, the population as an exponential function of time t is given by \(n(t) = 2,000,000 * e^(0.022t)\) when the initial value is 2 million.

To know more about exponential function

https://brainly.com/question/29287497

#SPJ11

The time taken by the water to reach 49 degree Celsius is 4 minutes.

According to the question, larger amount of sodium chloride is dissolved in the heating water. And the given data states that the water temperature increases 7 degree Celsius every minute.

Initial temperature of water is 21 degree Celsius.

Let us assume, water reaches at 49° C after 'm' minutes.

As per question, every minute temperature increases as 7°C. So, the expression can be written as: (21 + 7m)°C

⇒ 21 + 7m = 49

⇒m = 4 minutes.

Hence, the time taken to reach 49° C is 4 minutes.

What is temperature?

Temperature defines the atmosphere hotness. And it is expressed in different scales as well as in different parameters like Celsius etc. It is measured through the device known as thermometer.

To learn more about the temperature based problems from the given link:

https://brainly.com/question/25677592

#SPJ1

Answer:

let the price of a pen be x

9 pens cost 7.20, so 9x costs 7.20. Therefore,

9x = 7.20

x = 0.8

Each pen is 0.8 dollars (80 cents).

Answer:

D. 64

Step-by-step explanation:

(1/4)^-3 (Given)

= 4^3 (m^-n = (1/m)^n

= 64

These values match the given sequence, so the function that describes the sequence is:

an = 5(2.2 + 0.8182n)ⁿ⁻¹

According to one definition, a function is a relationship between a number of inputs where each input has exactly one output.

To find the function that describes the given geometric sequence, we need to find the common ratio r. We can do this by dividing any term in the sequence by the previous term:

11/5 = 2.2

29/11 = 2.63636...

83/29 = 2.86206...

We can see that the common ratio is increasing, which suggests that the sequence is not a perfect geometric sequence. However, the differences between the ratios are getting smaller, so we can approximate the sequence as a geometric sequence with a changing common ratio.

Let's use the first two terms of the sequence to find an initial approximation for the common ratio:

r ≈ 11/5 = 2.2

Then, we can write the nth term of the sequence as:

an = 5(2.2)ⁿ⁻¹

However, we noticed that the common ratio is increasing, so we need to adjust our formula to account for this. Let's try a formula where the common ratio is a linear function of n:

an = 5(2.2 + 0.8182n)ⁿ⁻¹

Plugging in n = 1, 2, 3, and 4, we get:

a1 = 5(2.2 + 0.8182(1))⁰ = 5

a2 = 5(2.2 + 0.8182(2))¹ ≈ 11

a3 = 5(2.2 + 0.8182(3))² ≈ 29

a4 = 5(2.2 + 0.8182(4))³ ≈ 83

These values match the given sequence, so the function that describes the sequence is:

an = 5(2.2 + 0.8182n)ⁿ⁻¹

where n is the index of the term in the sequence.

To know more about function visit:

https://brainly.com/question/30721594

#SPJ1

Answer:

23

Step-by-step explanation:

Answer: (4,5)

Because I don't know another way I can solve

Step-by-step explanation:

Answer:

x-intercept: (15, 0)

y-intercept: (0, 12)

Step-by-step explanation:

1.) convert the equation to y=mx+b format

4x + 5y= 60

5y = -4x + 60

y = -4/5x + 12

2.) Now we know that "b" in the equation is the y-intercept. 12 is b so the y-intercept is 12.

3.) To find x intercept we will plug in y=0.

0 = -4/5x + 12

-12 = -4/5x

15 = x

Answer:

114.96 pounds at angle 81.76°

Step-by-step explanation:

Let i be the component along x-axis and j be the component along y-axis.

First force that is given is 150 acting at angle 40; \(F1 = 150cos170i + 150sin40j = 114.91i +96.42j\)

The second force 100 is acting at angle 170;

\(F2 = 100cos170i + 100sin170j = -98.48i + 17.36j\)

We now have the resultant force, which is: \(114.91i + 96.42j + (-98.48i + 17.36j) = 16.43i + 113.78j\)

Magnitude of resultant:

\(\sqrt{16.43^{2} + 113.78^{2} }\) = 114.96 pounds

Angle it makes with horizontal; inverse tangent of \(\frac{(113.78)}{(16.43)}\) = 81.76 degrees

Hope this helps; Brainliest appreciated!

Answer:

1. The value of the variable, y is 11

2. (B) QRS is congruent to segment (E) ΔWXY by the hypotenuse leg congruency criteria

Step-by-step explanation:

1. The lengths of the sides of the given triangles ABC are  AB = 14, BC = 27, AC = 19, and ∡A = 32°

The lengths of the sides of the given triangle FGH, FG = 14, GH = 19, FH = 2y + 5, ∡G = 32°

From the given parameters, we have;

Segment AB (AB = 14) is congruent to segment FG (FG = 14)

Segment AC (AC = 19) is congruent to segment GH (GH = 19)

Angle ∡A (∡A = 32°) is congruent to angle ∡G (∡G = 32°)

∴ ΔBAC is congruent to ΔFGH by the Side-Angle-Side rule of congruency

Therefore, segment BC is congruent to segment FH by Congruent Parts of Congruent Triangle are Congruent, CPCTC

Segment BC = Segment FH by definition of congruency

∴ 27 = 2·y + 5

2·y + 5 = 27

2·y = 27 - 5 = 22

y = 22/2 = 11

y = 11

The value of the variable, y = 11

2. For option A. the vertices of triangle ABC are A(-7, 4), B(-4, 1), C(-2, 5)

The length of the sides are;

The length of side AB = √((-4 - (-7))² + (1 - 4)²) = 3·√2

The length of side BC = √((-4 - (-2))² + (1 - 5)²) = √20

The length of side AC = √((-2 - (-7))² + (5 - 4)²) = √26

For option B. the vertices of triangle QRS are Q(3, -4), R(3, -1), S(7, -1)

The length of the sides are;

The length of side QR = √((3 - 3)² + ((-4) - (-1))²) = 3

The length of side RS = √((7 - 3)² + (-1 - (-1))²) = 4

The length of side QS = √((3 - 7)² + ((-4) - (-1))²) = 5

For option C. the vertices of triangle DEF are D(-2, 6), E(1, 3), F(3, 7)

The length of the sides are;

The length of side DE = √(((-2) - 1)² + (6 - 3)²) = 3·√2

The length of side EF = √((3 - 1)² + (7 - 3)²) = √20

The length of side DF = √((3 - (-2))² + (7 - 6)²) = √26

For option D. the vertices of triangle TUV are T(-6, -5), U(-6, 1), V(4, 1)

The length of the sides are;

The length of side TU = √(((-6) - (-6))² + ((-5) - 1)²) = 6

The length of side UV = √(((-6) - 4)² + (1 - 1)²) = 10

The length of side TV = √(((-6) - 4)² + ((-5) - 1)²) = 2·√34

For option E. the vertices of triangle WXY are W(-6, 4), X(-6, 1), Y(-2, 1)

The length of the sides are;

The length of side WX = √(((-6) - (-6))² + (4 - 1)²) = 3

The length of side XY = √(((-6) - (-2))² + (1 - 1)²) = 4

The length of side WY = √(((-6) - (-2))² + (4 - 1)²) = 5

Therefore;

Segment QR of ΔQRS is congruent to segment WX of ΔWXY

Segment RS of ΔQRS is congruent to segment XY of ΔWXY

Segment QS of ΔQRS is congruent to segment WY of ΔWXY

Whereby QS and WY are the hypotenuse side of ΔQRS and ΔWXY respectively, because QS = WY = 5 = √(\(\overline {QR} ^2\) + \(\overline {RS} ^2\)) = (√(3² + 4²)

and also RS = XY, by the definition of congruency, we have;

QRS is congruent to segment ΔWXY by the hypotenuse leg congruency criteria

\(r - 1\)

\(( - r - 5) - ( - 2r - 4) \\ ( - r - 5) + 2r + 4\)

\(( - r - 5) + 2r + 4 \\ - r - 5 + 2r + 4\)

\( - 3 \purple{ - 5} + 2r + \purple{4} \\ - r \purple{ - 1} + 2r\)

\( \purple{ - r } - 1 + \purple{2r} \\ \purple{1r} - 1\)

\(1r - 1 \\ r - 1\)

Hopefully it's help

I copy MissJoy2 answer cuz her/his answer is right

The true statements about the inequality are

n > -24.

The circle is open.

The arrow points right.

To solve for n in the inequality -2/3n < 16, we need to isolate the variable n on one side of the inequality.

First, we can multiply both sides by -3/2 to get rid of the fraction:

(-3/2) * (-2/3n) > (-3/2) * 16

n > -24

Therefore, the solution for n in the inequality -2/3n < 16 is n > -24.

The circle is open means that the inequality sign is either less than or greater than

Having greater that means it points to the right

Learn more about inequality at:

https://brainly.com/question/24372553

#SPJ1

The complete graph with 100 vertices will have \(\( \binom{100}{2} = 4950 \)\)edges. Therefore, the correct option is (a) 4950. A connected graph with 100 vertices must have at least 99 edges.

1. A complete graph with 100 vertices means that there is an edge between every pair of vertices. The number of edges in a complete graph with n vertices is given by the formula \(\( \binom{n}{2} = \frac{n(n-1)}{2} \)\). Substituting n = 100, we get\(\( \frac{100 \cdot 99}{2} = 4950 \)\) edges.

2. In a connected graph with n vertices, the minimum number of edges required to ensure connectivity is n - 1. Therefore, a connected graph with 100 vertices must have at least 99 edges.

3. The given algorithm has a loop that divides the value of k by 2 in each iteration. As long as k is greater than or equal to 1, the loop continues. Since the value of k is halved in each iteration, the loop will run approximately \log ntimes. Therefore, the complexity of the algorithm is \(\( O(\log n) \)\).

4. The Minimum Spanning Tree algorithm is a Greedy method because it makes locally optimal choices at each step to construct the minimum spanning tree.

5. A graph is called connected if there is a path between every pair of vertices. Therefore, if a graph has a path between each two vertices, it is a connected graph.

6. NP-Complete problems are a subset of problems in the NP-class and are also NP-Hard. Therefore, any problem in the NP-Complete class is in both NP-class and NP-Hard class.

7. The algorithm with linear complexity is the Max is in-place Algorithm, which finds the maximum element in an array by comparing each element with the current maximum and updating it if necessary.

8. The worst-case time complexity of Insertion Sort is\(\( O(n^2) \)\) because in the worst case, for each element, it may need to be compared and shifted with every element to its left.

9. Dijkstra's algorithm is an example of the Greedy method for finding the shortest path in a graph.

10. The correct option is not provided for question 10, as none of the given options

Learn more about graph here:

https://brainly.com/question/29140456

#SPJ11

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

Learn more about circle here

brainly.com/question/11878555

#SPJ4

The probability of the event {E} - "picking a 5 and then picking a number less than 7 is P{E} = 0.58.

Probability of an event indicates how likely that event is going to happen. It is in range between 0 and 1.

Given is that You pick a card at random. Without putting the first card back, you pick a second card at random.

We can write the probability of the event {E} - "picking a 5 and then picking a number less than 7" as -

P{E} = 1/4 + 1/3

P{E} = 0.25 + 0.33

P{E} = 0.58

Therefore, the probability of the event {E} - "picking a 5 and then picking a number less than 7 is P{E} = 0.58.

To solve more questions on probability, visit the link below

https://brainly.com/question/29769471

#SPJ1

The distribution for X is a negative binomial distribution, denoted as nb(x;6, 188​), with parameters r = 6 (number of successes), p = 8/18 (probability of success in each trial).

To compute the probabilities:

P(X = 2): nb(2;6, 8/18)

P(X ≤ 2): nb(0;6, 8/18) + nb(1;6, 8/18) + nb(2;6, 8/18)

P(X ≥ 2): 1 - P(X < 2) = 1 - P(X ≤ 1)

To calculate the mean value and standard deviation of X:

Mean (μ) = r * (1 - p) / p

Standard Deviation (σ) = sqrt(r * (1 - p) / (p^2))

learn more about negative binomial distribution

brainly.com/question/32308397

#SPJ11

Amani earns 59 dollars in a week if she sells 18 books.

Amani earns a base amount of $41 per week for working part-time at the bookstore. In addition to that, she earns an extra dollar for each book she sells. The equation A = 41 + b represents her total earnings, where A represents the amount she earns and b represents the number of books she sells.

To find out how much Amani earns in a week if she sells 18 books, we substitute the value of b (18) into the equation:

A = 41 + 18

This simplifies to:

A = 59

Therefore, if Amani sells 18 books in a week, she will earn $59.

For more such questions on sells , Visit:

https://brainly.com/question/24951536

#SPJ11