Solve 3|x + 1| –2 < 4.

The time taken for the two trains to pass one another at 324 mi apart is 4 hours.

What is velocity ?

velocity is defined as rate of change of displacement d of the object with respect to rate of change in time t. In mathematics It is written as :

v = d/t

here it is given that :

Robinsport and Titusville trains are 324 mi apart on a railroad line that is distance between then is 324 mi.

also,

Trains leave each of these depots at the same time headed for the other depot and one travels at v₁ = 43 mi/h , the other at v₂ = 38 mi/h in opposite direction that is relative speed will get add-up that is :

Δv = v₁ - v₂

Δv = 43-(-38)

Δv = 81 mi/h

Now, the time taken for the two trains to pass one another is calculated :

Δv = d/t

81 = 324/t

t = 324/81

t = 4 hours

Therefore, the time taken for the two trains to pass one another is 4 hours.

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Answer:

No where

Step-by-step explanation:

The quadratic equation 3x² + 5x - 6 = 0 can be solved by completing the square and applying the square root property. The solutions to the equation are x = -5/6 ± √97/6.

To solve the quadratic equation 3x² + 5x - 6 = 0, we first divide the equation by the leading coefficient 3 to simplify it:

x² + (5/3)x - 2 = 0

Next, we complete the square by adding and subtracting the square of half the coefficient of x:

x² + (5/3)x + (25/36) - (25/36) - 2 = 0

(x + 5/6)² - 49/36 = 0

Now, we can rewrite the equation in the form (x + h)² = k, where h and k are constants:

(x + 5/6)² = 49/36

Taking the square root of both sides, we have:

x + 5/6 = ± √(49/36)

x + 5/6 = ± (7/6)

Now, we can solve for x:

x = -5/6 ± 7/6

x = -5/6 ± √(49/36)

Simplifying the square root, we get:

x = -5/6 ± √97/6

Therefore, the solutions to the quadratic equation are x = -5/6 ± √97/6, which corresponds to option a. - 5/6 ± √97/6.

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The correct answer is C. The Mode.

Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.

This measure of centre is most meaningful when the data is qualitative because it shows the value that appears most frequently in the data set. The mode can be used to identify the most popular item or most commonly occurring outcome. It is the only measure of centre that can be used for qualitative data, as the other measures (mean, median, and range) require numerical data.

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Answer:

for the first answer the second option is correct and 8 will go in the box and for the second question the second option is correct and 40 will go in the box.

Check the picture below.

\(\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =60 \end{cases} \\\\\\ A=\cfrac{8^2}{2}\left( ~~ \cfrac{\pi (60) }{180}-\sin(60^o ) ~~ \right)\implies A=32\left( ~~ \cfrac{\pi }{3}-\sin(60^o ) ~~ \right) \\\\\\ A=32\left( ~~ \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} ~~ \right)\implies A=\cfrac{32\pi }{3}-16\sqrt{3}\implies A\approx 5.8~in^2\)

9514 1404 393

Answer:

  $241.81

Step-by-step explanation:

The interest is given by the formula ...

  I = Prt

Filling in the values and doing the arithmetic, we have ...

  I = $2650×0.0365×2.5

  I = $241.81

The simple interest paid is $241.81.

a18 − a12 = 24 == 24

d == 24

I hope this is correct and helps..

Answer:

103

Step-by-step explanation:

Find the area of the rectangle on the top

A = 7*13 = 91

Now find the area of the rectangle on the bottom

13 - (5+5) = 3

11-7 = 4

The dimensions of the bottom rectangle are 3 by 4

A = 3*4 = 12

The total area is 91+12 = 103

Answer: There is one candle for each night of Hanukkah, and the ninth candle, which sits in the middle, is known as the shamash, which translates to attendant or servant candle. This candle is lit first and is used to light the others.

Step-by-step explanation:

Answer:

first graph

Step-by-step explanation:

To find a function, for every x value there is only one corresponding y value.

If at x=-2, there are two values for y then it is NOT a function.

All the shaded regions of the overlap inequalities represents the located solution region of the system of linear inequalities , the overlap region is called intersection ( option C ).

Graph is attached.

Therefore, the solution region is represented by the shaded region called  (option C) intersection area of the system of linear inequalities.

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Answer:

1. \( \theta = 61.9^\circ \)

2. \( x = 23.7~cm \)

Step-by-step explanation:

Problem 1.

Use the Law of Sines.

This is SSA.

\(\dfrac{a}{\sin A} = \dfrac{c}{\sin C}\)

\( \dfrac{31.2~cm}{\sin 51^\circ} = \dfrac{35.4~cm}{\sin \theta} \)

\( \sin \theta = \dfrac{35.4~cm \times \sin 51^\circ}{31.2~cm} \)

\( \sin \theta = 0.88176 \)

\( \theta = \sin^{-1} 0.88176 \)

\( \theta = 61.9^\circ \)

Problem 2.

m<A + m<B + m<C = 180°

m<A + 67° + 58° = 180°

m<A = 55°

Use the Law of Sines.

\(\dfrac{a}{\sin A} = \dfrac{c}{\sin C}\)

\(\dfrac{x}{\sin 55^\circ} = \dfrac{24.5}{\sin 58^\circ}\)

\(x = \dfrac{\sin 55^\circ \times 24.5}{\sin 58^\circ}\)

\( x = 23.7~cm \)

Answer:

  $0.45 per ounce

Step-by-step explanation:

You want the unit rate of $6.99 for 15.4 ounces.

To find the cost for 1 ounce, divide the cost by the number of ounces:

  $6.99/(15.4 oz) ≈ $0.454 /oz

Rounded to the nearest cent, the cost is $0.45 per ounce.

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Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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b + d ≥ 9 this inequality states that the sum of hours babysitting, b, and hours walking dogs, d, must be greater than or equal to 9 in order for Ryan to meet his weekly work requirement.

What is inequality?

In mathematics, an inequality is a statement that compares two quantities, indicating whether they are equal or not, and in what direction they differ. An inequality is represented by one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to).

The inequality that represents the possible values for the number of hours babysitting, b, and the number of hours walking dogs, d, that Ryan can work in a given week is:

b + d ≥ 9

This inequality states that the sum of hours babysitting, b, and hours walking dogs, d, must be greater than or equal to 9 in order for Ryan to meet his weekly work requirement.

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Answer:

  175°

Step-by-step explanation:

Bearing angles are usually measured clockwise from North. Reverse bearing angles differ from forward bearing angles by 180°. These relations and the usual angle sum relation for a triangle can be used to solve this problem.

Angle PQR will be the difference in the bearings from Q to P and Q to R:

  ∠PQR = 124° -46° = 78°

Triangle PQR is isosceles, so the base angle at P will be ...

  ∠QPR = (180° -78°)/2 = 51°

__

The bearing from P to R will be 51° less than the bearing from P to Q. The bearing from P to Q is 180° more than the bearing from Q to P.

  PR bearing = PQ bearing - ∠QPR

  = PQ bearing - 51°

  = (46° +180°) -51° = 175°

The bearing of R from P is 175°.

Answer:

15 cm

Step-by-step explanation:

Since the square's side length is 8 cm, and one of its sides is the short leg of the triangle, the short leg of the triangle is 8 cm

Using the pythagorean theorem, solve for b (the missing side length x)

a² + b² = c²

8² + b² = 17²

64 + b² = 289

b² = 225

b = 15

So, the missing side length is 15 cm

Answer:

x= 75*2

x= 3/4*200

(The options arent very clear)

Step-by-step explanation:

The equation is

x= 75/100 *200

= 75*2

or 3/4 * 200

Answer:

The answer is B.

Step-by-step explanation:

It  takes for the account to reach $200 is 4 years.

Compound Interest is the interest calculated on the cumulative amount, rather than being calculated on the principal amount only quantity.

Given that aldonia deposits $150 into an account that pays 7.3% annual interest compounded quarterly.

\(A = P(1 +\frac{r}{n})^n^t\)

where:

A = the total account balance after t years

P = the initial deposit $150

r = the annual interest rate =0.073

n = the number of compounding periods per year, which is 4 (quarterly) in this case

t = the number of years the money is in the account

Now let us substitute the values

\(A = 150(1 + \frac{0.073}{4} )^4^t\) is the equation to represent Caldonia's account balance after t years.

Now let us determine the number of  years it will take for the account to reach $200.

\(200 = 150(1 + \frac{0.073}{4} )^4^t\)

200=150(1+0.01825)^4t

\(1.333=1.018^4^t\)

Take log on both sides

log1.333=4tlog(1.018)

0.1248=4t 0.0077

0.1248=0.0309t

Divide both sides by 0.0309

t=4.038

Hence, it takes 4 years to reach account balance of $200

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Step 1

State formula for Power

Hence,

Step 2

Determine the power delivered by the hiker.

Hence the power delivered by the hiker to 3 decimal places is approximately 6.984 J/s or watts

The Walsh basis functions are a set of orthogonal functions commonly used in signal processing and digital communication.

In this case, the first four Walsh basis functions are phi1 = [1, 1, 1, 1], phi2 = [1, 1, -1, -1], phi3 = [1, -1, 1, -1], and phi4 = [1, -1, -1, 1]. Now let's address the questions regarding orthogonality and normality of the Walsh basis functions.

a. The Walsh basis functions are indeed orthogonal to each other. Two functions are said to be orthogonal if their inner product is zero. When we calculate the inner product between any two Walsh basis functions, we find that the result is zero. Hence, the Walsh basis functions satisfy the orthogonality property.

b. However, the Walsh basis functions are not normal. A set of functions is considered normal if their squared norm is equal to 1. In the case of Walsh basis functions, the squared norm of each function is 4. Therefore, they do not meet the condition for being normal.

c. To find the coefficients ck for the vector [2, -3, 4, 7], we need to compute the inner product between the vector and each Walsh basis function. The coefficients ck can be obtained by dividing the inner product by the squared norm of the corresponding basis function. For example, c1 = (1/4) * [2, -3, 4, 7] • [1, 1, 1, 1], where • denotes the dot product. Similarly, we can calculate c2, c3, and c4 using the dot products with phi2, phi3, and phi4, respectively.

d. To find the best three Walsh functions to approximate the vector [2, -3, 4, 7], we can consider the coefficients obtained in part c. The three Walsh functions that correspond to the largest coefficients would be the best approximation. In other words, we select the three basis functions with the highest absolute values of ck.

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(a) The roots of the characteristic equation r = ±2i.

The characteristic equation for the differential equation y'' + 4y = 0 is r^2 + 4 = 0. Solving this quadratic equation, we obtain the roots r = ±2i.

(b) The general solution of the differential equation is given by y(t) = c1 cos(2t) + c2 sin(2t), where c1 and c2 are constants determined by the initial conditions.

(c) To solve the initial value problem y(f/4) = -2 and y'(f/4) = 1, we first need to find the values of c1 and c2 that satisfy the conditions. Using the first initial condition, we have -2 = c1 cos(2f/4) + c2 sin(2f/4), which simplifies to -2 = c1 cos(f) + c2 sin(f).

Differentiating this equation with respect to t and using the second initial condition, we get 1 = -2c1 sin(f) + 2c2 cos(f). Solving these two equations simultaneously, we obtain c1 = -2sin(f)/5 and c2 = (2cos(f)+5)/5. Thus, the solution to the initial value problem is y(t) = -2/5 sin(2t+f) + (2cos(f)+5)/5 cos(2t+f).

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Answer:

6n²+13n-28

Step-by-step explanation:

6n²-8n+21n-28

6n²+13n-28

Hope it helps!

Answer:

A relation is defined as the collection of inputs and outputs which are related to each other in some way. In case, if each input in relation has accurately one output, then the relation is called a function.

Based on the given relation, we found that it is not a function because it has repeating x-values. Remember, for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).

To determine if a relation is a function, you need to check if each input (x-value) corresponds to exactly one output (y-value). You can use the following steps:

1. Identify the given relation as a set of ordered pairs, where each ordered pair represents an input-output pair.

2. Check if there are any repeating x-values in the relation. If there are no repeating x-values, move to the next step. If there are repeating x-values, the relation is not a function.

3. For each unique x-value, check if there is only one corresponding y-value. If there is exactly one y-value for each x-value, then the relation is a function. If there is more than one y-value for any x-value, then the relation is not a function.

Let's consider an example relation: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 1: Identify the relation as a set of ordered pairs: {(1, 2), (2, 3), (3, 4), (2, 5)}.

Step 2: Check for repeating x-values. In our example, we have a repeating x-value of 2. Therefore, the relation is not a function.

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To transform a set of vectors into orthonormal vectors using the Gram-Schmidt process, normalize the first vector, compute the projections onto the previous orthonormal vectors, subtract the projections, and normalize the resulting vectors successively.

To apply the Gram-Schmidt process to transform the set of vectors (1, 2, 1), (1, -1, 0), (0, 1, 0) into orthonormal vectors, follow these steps:

Take the first vector, v1 = (1, 2, 1), and normalize it to obtain the first orthonormal vector, u1:

u1 = v1 / ||v1||, where ||v1|| represents the norm or magnitude of v1.

Compute the projection of the second vector, v2 = (1, -1, 0), onto the first orthonormal vector, u1:

proj(v2, u1) = (v2 · u1) * u1, where · represents the dot product.

Subtract the projection from v2 to obtain a new vector, v2' = v2 - proj(v2, u1).

Normalize v2' to obtain the second orthonormal vector, u2:

u2 = v2' / ||v2'||.

Repeat steps 2-4 for the third vector, v3 = (0, 1, 0), using u1 and u2 as the previous orthonormal vectors.

The resulting vectors u1, u2, and u3 will be the orthonormal vectors obtained through the Gram-Schmidt process.

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Answer:

60%

Step-by-step explanation: