y=Ax^2 + Bx + C is the solution of the DEQ: By' = 2x + 7. Determine A,B. Separate variables, & integrate.

the answer is lines 3 and 5

After solving the equation the linear equation is x = 27/5 , y = 7/5.

What do you mean by linear equation?

Equations with the highest degree of 1 are called linear equations. This means that the exponent of the variable in the linear equation is greater than 1. The graph of a linear equation is always a straight line.

A linear equation is an algebraic equation in which each term has exponent 1, and the graph of this equation is always a straight line. For this reason, it is called a "linear equation".

Given system of equation:

7x - 7y = 28 ..........(1)

2x - 7y = 1 .............(2)

Solve this system of linear equation. Find the value of 7y from equation (1) and substitute in equation(2)

7x - 7y = 28

7x - 28 =7y .............(3)

Substitute this value in equation (2)

2x - (7x - 28) = 1

2x - 7x + 28 = 1

-5x + 28 = 1

5x = 28 - 1

5x = 27

x = 27/5

Substitute this value in equation (3)

7y = 7(27/5) - 28

7y = 189/5 - 28

7y = 49/5

y = 7/5

Therefore, x = 27/5 , y = 7/5

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Answer:The probability would be 5 out of 12.

The straight-line distance from the wilderness area to the Morrisons' campsite is approximately 5 miles.

To find the straight-line distance from the wilderness area to the Morrisons' campsite, we can use the Pythagorean theorem.

Let's consider the campsite as the origin (0, 0) on a coordinate plane. The wilderness area is located 3 miles due north and 4 miles due east from the campsite. Therefore, its coordinates are (4, 3).

Using the Pythagorean theorem, the straight-line distance d is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the coordinates of the campsite (0, 0) and the wilderness area (4, 3) into the formula, we get:

d = √((4 - 0)² + (3 - 0)²)

= √(4² + 3²)

= √(16 + 9)

= √25

= 5

Therefore, the straight-line distance from the wilderness area to the Morrisons' campsite is approximately 5 miles.

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Answer:

AC ≅ AC

Step-by-step explanation:

A S A ---> Angle Side  Angle

∠DAC ≅∠ BCA          {Alternate interior angle}

AC ≅ AC                      {Reflexive property}

∠DCA ≅∠BAC           {Alternate interior angle}

Answer: x and x+5

Step-by-step explanation:

\(x^{2} +5x\)

common factor of that expression is x, so you can factor it out into

x(x+5)

Answer:

then KD would be equal?

Step-by-step explanation:

not sure, but try that

(a) -2.5A has an x-component of 13.225 m and a y-component of -10.857 m. (b) For A + B, the magnitude is approximately 18.098 m, and the direction is approximately 14.198° counterclockwise from the +x-axis. (c) For A - B and B - A, both have a magnitude of approximately 28.506 m, and the direction is approximately -8.080° counterclockwise from the +x-axis.

Given Magnitude of vector A: |A| = 7.5 m

Angle from the positive x-axis: θ = 145° (counterclockwise)

(a) X-component of vector A:

Ax = |A| * cos(θ)

  = 7.5 * cos(145°)

  ≈ -5.290 m

(b) Y-component of vector A:

Ay = |A| * sin(θ)

  = 7.5 * sin(145°)

  ≈ 4.343 m

Now, let's calculate the components of vector -2.5A.

(a) X-component of -2.5A:

(-2.5A)x = -2.5 * Ax

        = -2.5 * (-5.290 m)

        ≈ 13.225 m

(b) Y-component of -2.5A:

(-2.5A)y = -2.5 * Ay

        = -2.5 * (4.343 m)

        ≈ -10.857 m

Next, let's consider vector B, which has triple the magnitude of vector A and points in the +x direction.

Given:

Magnitude of vector B: |B| = 3 * |A| = 3 * 7.5 m = 22.5 m

Direction: Since vector B points in the +x direction, the angle from the positive x-axis is 0°.

Now, we can calculate the desired quantities using vector addition and subtraction.

(a) A + B: Magnitude: |A + B| = :\(\sqrt{((Ax + Bx)^2 + (Ay + By)^2)}\)

                  = \(\sqrt{((-5.290 m + 22.5 m)^2 + (4.343 m + 0)^2)}\)

                  = \(\sqrt{((17.21 m)^2 + (4.343 m)^2)\)

                  ≈ 18.098 m

Direction: Angle from the positive x-axis = atan((Ay + By) / (Ax + Bx))

                                        = atan((4.343 m + 0) / (-5.290 m + 22.5 m))

                                        = atan(4.343 m / 17.21 m)

                                        ≈ 14.198° (counterclockwise from the +x-axis)

(b) A - B: Magnitude: |A - B| = \(\sqrt{((Ax - Bx)^2 + (Ay - By)^2)}\)

                  = \(\sqrt{((-5.290 m - 22.5 m)^2 + (4.343 m - 0)^2)}\)

                  = \(\sqrt{((-27.79 m)^2 + (4.343 m)^2)}\)

                  ≈ 28.506 m

Direction: Angle from the positive x-axis = atan((Ay - By) / (Ax - Bx))

                                        = atan((4.343 m - 0) / (-5.290 m - 22.5 m))

                                        = atan(4.343 m / -27.79 m)

                                        ≈ -8.080° (counterclockwise from the +x-axis)

(c) B - A:Magnitude: |B - A| = \(\sqrt{((Bx - Ax)^2 + (By - Ay)^2)}\)

                  = \(\sqrt{((22.5 m - (-5.290 m))^2 + (0 - 4.343 m)^2)}\)

                  = \(\sqrt{((27.79 m)^2 + (-4.343 m)^2)}\)

                  ≈ 28.506 m

Direction: Angle from the positive x-axis = atan((By - Ay) / (Bx - Ax))

                                        = atan((0 - 4.343 m) / (22.5 m - (-5.290 m)))

                                        = atan((-4.343 m) / (27.79 m))

                                        ≈ -8.080° (counterclockwise from the +x-axis)

So, the complete step-by-step calculations provide the values for magnitude and direction for each vector addition and subtraction.

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The complete question is:

The magnitude of vector  A  is 7.5 m. It points in a direction which makes an angle of 145  ∘  measured counterclockwise from the positive x-axis. (a) What is the x component of the vector −2.5  A  ? m (b) What is the y component of the vector −2.5  A  ? m (c) What is the magnitude of the vector −2.5  A  ? m following vectors? Give the directions of each as an angle measured counterclockwise from the +x-direction. If a vector A has a magnitude 9 unitsand points in the -y-directionwhile vector b has triple the magnitude of A AND points in the +x direction what are te direction and magnitude of the following.

(a)  A  +  B  magnitude unit(s) direction ∘ (counterclockwise from the +x-axis) (b)  A  −  B  magnitude unit(s) direction ∘ (counterclockwise from the +x-axis) (c)  B  −  A  magnitude unit(s) direction - (counterclockwise from the +x-axis)

Answer:

-1.5

Step-by-step explanation:

y=-1.5x-5

(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

70 * 10 = 700

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As per the 95% confidence interval, the true average age of all students in the university is approximately 23 to 24.

Confidence interval

Confidence interval means the interval calculation, obtained from the observed data that holds the actual value of the unknown parameter.

Given,

A random sample of 64 students at a university showed an average age of 23 years and a sample standard deviation of 3 years.

And we need to find the 95% confidence interval for the true average age of all students in the university.

While we looking through the given question we have identified the following,

Number of samples = 64

Average age = 23

Standard deviation = 3

Confidence interval = 95%

Based on this confidence interval, the z score is 1.96

According to the formula,

u = 23 ± 1.96 x 3/√64

u = 23  ± 1.96 x (3/8)

u = 23  ± 1.96 x 0.375

u = 23  ± 0.735

u = 23.735, 22.635

Therefore, the average age of the student is approximately 23 to 24.

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Answer:

The total money Jo has after 18 months is $4871.25

Step-by-step explanation:

Answer:

10c3 =(10)!/(3!*7!) = (10*9*8)/(3*2*1) = 10*3*4 =120

Let us call the number of children "c" and the number of adults "a." Based on the facts provided, we can then construct two equations: c + a = 259 (equation 1) (equation 1).  

1.5c + 4a = 676 (2nd equation)

In equation 1, we may solve for one variable in terms of the other:

c = 259 - a

So, in equation 2, substitute this expression for "c":

1.5(259 - a) + 4a = 676

Distribute the 1.5:1:1:1:1:1:1:1:

388.5 - 1.5a + 4a = 676

Merge similar terms:

2.5a = 287.5

Multiply by 2.5:

a = 115

This translates to 115 adults being accepted. We can plug this number back into equation 1 to find "c":

c + 115 = 259

c = 144

As a result, 144 youngsters were hospitalised.

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There is No statisti-cally signi-ficant evidence against the teacher's-claim that Charlie is just guessing because the probability is very low.

The total number of True-false questions are = n = 201.

The probability of getting a correct answer by guessing is = p = 0.5,

Charlie answered 53.7% = 0.537 of the questions correctly,

So, P(p' ≥ 0.537)

⇒ P(z ≥ (0.537 - 0.5)/√(0.5×0.5)/201,

⇒ P(z ≥ 1.05) = 1 - P(z < 1.05)

⇒ 0.1469

Since, the probability is very low,

Therefore, there is not any significant evidence against the teachers claim.

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Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

interval in mathematics stands for a set of real numbers,

denoted by [a,b] where a and b are the starting and ending real numbers both inclusive respectively.

thus, interval [a,b] is the set of real numbers starting from a to b both are real numbers and are included.

Answer:

45 degrees, x,5, 7

Step-by-step explanation:

you just gotta do the math

Answer:

radius: 8.4   Area: 221.5

Step-by-step explanation:

16.8 divided by 2 = 8.4

The Formula for finding the area of circle= R₂ (radius squared: radius times itself) Multiplied by pi. pi = 3.14

8.4₂ multiplied by 3.14

The slope of the line is 1/2

Answer:

-33

Step-by-step explanation:

trust me, I did all the math in my notebook

Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.

A translation occurs whenever an object is transported from one place to another without altering its dimension, form, or orientation. We can draw the translation in the coordinate plane if we know which way and how far to move the figure.

The triangle can be translated in the following ways:

Step 1: Find the coordinates of each of the triangle's vertices in step one.

Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.

Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.

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An increase in T and r both have a positive effect on Y, resulting in higher national income.

(a) The degrees of freedom of a system of equations can be determined by subtracting the number of equations from the number of variables. In this case, we have four variables (Y, C, /, T) and three equations (i, ii, iii). Therefore, the degrees of freedom of this system of equations are 4 - 3 = 1.

(b) To express Y in terms of T and r, we can substitute the equations (ii) and (iii) into equation (i) and solve for Y:

Y = C + / + 1200

Y = (0.5(Y - T) - 3r) + (351 - 5r) + 1200

Simplifying the equation, we have:

Y = 0.5Y - 0.5T - 3r + 351 - 5r + 1200

0.5Y - Y = -0.5T - 8r + 1551

-0.5Y = -0.5T - 8r + 1551

Y = T + 16r - 3102

Therefore, the expression for Y in terms of T and r is Y = T + 16r - 3102.

(c) An increase in T will directly increase the value of Y, as evident from the expression Y = T + 16r - 3102. This is because an increase in T represents an increase in tax revenue, which in turn leads to higher national income (Y).

(d) An increase in r will also increase the value of Y, as seen in the expression Y = T + 16r - 3102. This indicates that an increase in the interest rate leads to higher investment (/) and subsequently boosts national income (Y).

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Answer:

first day: 650, second day: 325

Step-by-step explanation:

Let x be the number of miles travelled on the second day and  2x the number of miles travelled on the first day. They add up to 975.

2x+x=975

3x=975

x=325

x represents the number of miles travelled on the second day so they travelled 650 miles on the first day and 325 miles on the second day.

Answer:

650 miles the first day, 325 miles the second day

Step-by-step explanation:

We can call the distance they traveled on the first day as 2x and the distance they traveled on the second day as x. The former is 2x because they traveled twice as far the first day compared to the second day. Since the total distance traveled is 975 miles, we can write the following equation to solve for x:

\(2x + x = 975\)

\(3x = 975\) (Simplify LHS; 2x + x = 3x)

\(\frac{3x}{3}=\frac{975}{3}\) (Divide both sides of the equation by 3 to get rid of the coefficient on x)

\(x = 325\) (Simplify)

Therefore, \(2x = 2 * x = 2 * 325 = 650\) so the final answer is they traveled 650 miles the first day and 325 miles the second day. Hope this helps!

Answer:

Function

Step-by-step explanation:

We can tell if the graph is function or not by doing line test.

First, we draw a vertical line.

Second, if the graph intercepts the line more than two points then it won't be a function.

If the graph only intercepts the line only once (one point) then It is a function.

From the graph, It is a function.

Answer:

Step-by-step explanation:

You want the domain, range, intercepts, asymptotes, and holes of the rational function f(x) = (2x³ +10x² +8x)/(x³ +7x² +12).

The given function can be simplified by cancelling common factors from numerator and denominator. These cancelled factors show where the holes are in the graph.

  \(f(x)=\dfrac{2x^3+10x^2+8x}{x^3+7x^2+12}=\dfrac{2x(x+4)(x+1)}{(x(x+4)(x+3)}=2\left(\dfrac{x+1}{x+3}\right)\quad x\notin\{-4,-3,0\}\)

The function is defined for all real numbers except those where the denominator is zero: {-4, -3, 0}.

The function can produce every output value except the value of the horizontal asymptote: y = 2. The range is all real numbers except 2.

The x-intercept is found where the numerator of the simplified function is zero: x = -1

The y-intercept is the function value at x=0. The function is undefined there, so the y-intercept does not exist. (The limit as x approaches zero is y = 2/3.)

The function has a horizontal asymptote at the y-value corresponding to the ratio of the highest-degree terms of the numerator and denominator: y = 2.

The vertical asymptote is at the uncanceled denominator zero, x = -3.

The holes are where a numerator and denominator factor cancel. The y-value at the hole is the limit of the function value as x approaches the hole location. This is the value of the simplified function.

The holes are (-4, 6) and (0, 2/3).

Answer:

5 5/6

Step-by-step explanation:

Convert to improper numbers

2 1/3 = 7/3

2 1/2 = 5/2

7/3 * 5/2 = 35/6

35/6 as a mixed fraction is 5 5/6

Answer:

5 \(\frac{5}{6}\)

Step-by-step explanation:

2 1/3 * 2 1/2 = 7/3 * 5/2 (converting into improper fraction)

= 7*5 / 3*2

= 35 / 6

= 5 \(\frac{5}{6}\)      (35/6 as mixed fraction)

Answer:

Step-by-step explanation:

Intersecting secants theorem: