Can someone please solve number 2 ! I would literally love you forever !!!!

Answer:

A quadratic equation is some thing like

(x+2)^2

or

(x+2)(x+5)

In order to solve them, the most basic method is the FOIL method

F-First

O-Outside

I-Inner

L-Last

So for example

(x+2)^2

Which is basically

(x+2)(x+2)

So the first is the 2 Xs

(x+2)(x+2)

x*x=x^2

The outer is the x and the 2,

(x+2)(x+2)

2*x=2x

Now the Inner which is the 2 and the x

(x+2)(x+2)

2*x=2x

And finally the last  which is the 2 and the second 2

(x+2)(x+2)

2*2=4

Now add them all up

X^2+2x+2x+4

Combine like terms

x^2+4x+4

There you have it

Do the same with every other quadratic equation

Answer:

No

Step-by-step explanation:

No

Answer: Get a snack.

2.5(cos 5π/6  + i sin 5π/6) is the polar form  of the complex number

Complex numbers are numbers that are expressed in the form of a+ib, where a and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1)

Given: the complex number (5√3)/4 - 5/4 i

In polar form:

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

θ  = tan⁻¹( (-5/4) / (5√3 /4) )

θ = -30°

θ = -30+180 = 150°

θ = 5π/6

r = √( (5√3)/4)² +(- 5/4)²) = 2.5

Thus,

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

r(cosθ + isinθ) = 2.5(cos 5π/6  + i sin 5π/6 )

Therefore, the polar form  of the complex number is 2.5(cos 5π/6  + i sin 5π/6)

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The low temperatures for the past 6 days were ​-5, 4​, 9​, -9 ​, 1​, and 6, then the average low temperature for the past 6 days is -4.

What is the average?

A mean in maths is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers. For example, with the data set: 8, 9, 5, 6, 7, the mean is 7, as 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7.

To find the average of these 6 temperatures, we need to add them up and then divide by 6, since there are 6 temperatures:

Average = ( -5 + 4 + 9 - 9 + 1 + 6 ) / 6

Adding up the temperatures, we get:

= -4

Therefore, the average low temperature for the past 6 days is -4.

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The optimal solution for the given all-integer linear program is x1 = 2 and x2 = 4, with a maximum objective value of 46.

To solve the given all-integer linear program, we'll use the branch and bound algorithm. Here's the step-by-step process:

Start with the initial feasible solution by setting x1 = x2 = 0.

Calculate the objective function value for the initial solution:

f(x1, x2) = 5x1 + 8x2 = 5(0) + 8(0) = 0.

Check the feasibility of the initial solution by evaluating the constraints:

For the first constraint: 5x1 + 6x2 ≤ 32,

5(0) + 6(0) = 0 ≤ 32, which is satisfied.

For the second constraint: 10x1 + 5x2 ≤ 46,

10(0) + 5(0) = 0 ≤ 46, which is satisfied.

For the third constraint: x1 + 2x2 ≤ 10,

0 + 2(0) = 0 ≤ 10, which is satisfied.

All constraints are satisfied, so the initial solution is feasible.

Initialize the best objective value as the objective function value of the initial solution: best_obj = 0.

Create a priority queue to store the subproblems.

Branching:

Choose a non-integer variable to branch. Let's choose x1 in this case.

Create two subproblems by adding the branching constraints:

Subproblem 1: x1 ≤ 0 (Round down constraint)

Subproblem 2: x1 ≥ 1 (Round up constraint)

Solve each subproblem:

Subproblem 1:

Update the constraint bounds based on the branching constraint: x1 ≤ 0.

Solve the modified linear program:

Maximize: 5x1 + 8x2

Subject to: 5x1 + 6x2 ≤ 32, 10x1 + 5x2 ≤ 46, x1 + 2x2 ≤ 10, x1 ≤ 0, x1, x2 ≥ 0

Determine the feasibility and calculate the objective value:

If feasible, calculate the objective value and update the best_obj if necessary.

If infeasible, discard the subproblem.

Subproblem 2:

Update the constraint bounds based on the branching constraint: x1 ≥ 1.

Solve the modified linear program:

Maximize: 5x1 + 8x2

Subject to: 5x1 + 6x2 ≤ 32, 10x1 + 5x2 ≤ 46, x1 + 2x2 ≤ 10, x1 ≥ 1, x1, x2 ≥ 0

Determine the feasibility and calculate the objective value:

If feasible, calculate the objective value and update the best_obj if necessary.

If infeasible, discard the subproblem.

Repeat steps 6 and 7 for each active subproblem, considering branching on the non-integer variables until no subproblems are left.

The best_obj value obtained during the branching process is the optimal solution of the linear program.

In this case, the branch and bound algorithm would explore different combinations of x1 and x2 to find the optimal integer solution that maximizes the objective function while satisfying all the constraints.

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Answer:

x

y        x

y

0

−

2

2

0

0

−

2

2

0

Step-by-step explanation:

Show all the calculation if it is a numerical question.

To find the volume of the solid with equilateral triangular cross-sections, we need to integrate the area of each equilateral triangle over the interval [0,π]. The area of an equilateral triangle with side length s is given by (s^2√3)/4. Since the triangles have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x. Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2√3/4 dx

Simplifying, we get:

V = √3∫[0,π] sin x dx

Using the substitution u = cos x, we get:

V = √3∫[-1,1] √(1 - u^2) du

Using the formula for the integral of the half-circle, we get:

V = (√3/2)π

Therefore, the volume of the solid is (√3/2)π.

To find the volume of the solid with square cross-sections, we need to integrate the area of each square over the interval [0,π]. Since the squares have bases running from the x-axis to the curve y=2√sin x, their side lengths will be 2√sin x.

Therefore, the volume is given by the integral:

V = ∫[0,π] (2√sin x)^2 dx

Simplifying, we get:

V = 4∫[0,π] sin x dx

Using the identity ∫sin x dx = -cos x + C, we get:

V = -4cos x ∣[0,π]

Since cos π = -1 and cos 0 = 1, we get:

V = -4(-1 - 1) = 8

Therefore, the volume of the solid is 8.

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Answer: What is the value of the expression 30 - 9 + 3 - (12dividedby4?

18 20 21 24

Step-by-step explanation:

IT"S APPLE!!!

Answer:

13.5-14

Step-by-step explanation:

it is 13.8

Using the substitution U = (2x + 1) is correct, and the statement is True.

We can set U = (2x + 1) by applying the substitution rule. We obtain dU = 2dx by dividing both sides with regard to x. When we solve for dx, we get dx = (1/2)dU.

Now, we substitute these values in the integral:

∫4(2x + 1)² dx = ∫4U² (1/2)dU

Simplifying the expression, we have:

(1/2)∫4U² dU

Now we can integrate with respect to U:

(1/2) * (4/3)U³ + C

(2/3)U³ + C

Finally, substituting back U = (2x + 1), we get:

(2/3)(2x + 1)³ + C

Therefore, using the substitution U = (2x + 1) is correct, and the statement is True.

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Answer: 2(8-c)

Step-by-step explanation:

First take our given numbers

16-2c

Now we must factor out the constants

We do that by dividing by 2

2(8-c)

The solution to the equation \(\frac{1}{h-5} +\frac{2}{h+5} =\frac{16}{h^2-25}\) is h = 7.

In Mathematics and Geometry, a system of equations has only one solution when both equations produce lines that intersect and have a common point and as such, it is consistent independent.

Based on the information provided above, we can logically deduce the following equation;

\(\frac{1}{h-5} +\frac{2}{h+5} =\frac{16}{h^2-25}\)

By multiplying both sides of the equation by the lowest common multiple (LCM) of (h + 5)(h - 5), we have the following:

\((\frac{1}{h-5}) \times (h + 5)(h - 5) +(\frac{2}{h+5}) \times (h + 5)(h - 5) =(\frac{16}{h^2-25}) \times (h + 5)(h - 5)\)

(h + 5) + 2(h - 5) = 16

h + 5 + 2h - 10 = 16

3h = 16 + 10 - 5

h = 21/3

h = 7.

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Complete Question:

What is the solution to the equation \(\frac{1}{h-5} +\frac{2}{h+5} =\frac{16}{h^2-25}\)?

Answer: C

Step-by-step explanation:

(fog)(3) is the same as finding f(g(3)). To solve, we first need to solve g(3). then, we solve for f(g(3)).

g(3)=5(3)                  [multiply]

g(3)=15

Now, we plug in 15 into f(x).

f(g(3))=-2(15)+8       [multiply]

f(g(3))=-30+8           [add]

f(g(3))=-22

Now, we know that C is the correct answer.

Answer:

B

Step-by-step explanation:

ABD (half of the rectangle) is a right-angled triangle.

so, Pythagoras applies.

c² = a² + b²

c is the Hypotenuse (the baseline opposite of the 90 degree angle) and in our case the line BD.

a and b are the 2 sides enclosing the 90 degree angle. in our case here the lines AD and AB.

so,

BD² = AD² + AB² = (6-1)² + (5-2)² = 5² + 3² = 25 + 9 = 34

BD = sqrt(34)

The factored form of 3y - 18 using the G.C.F. is 3 * (y - 6).

What is the factor?

Factor is a mathematical expression or a number that divides another expression or number evenly. The factor of an expression is a number that divides the expression evenly, leaving no remainder.

The expression 3y - 18 can be factored using the greatest common factor (G.C.F.) of 3.

The G.C.F. of 3 and 3y is 3.

So, 3y - 18 can be factored as:

3 * (y - 6)

Hence, The factored form of 3y - 18 using the G.C.F. is 3 * (y - 6).

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Answer:

120

Step-by-step explanation:

Add angle ABC and angle CBD together.

The dilated triangle ABC by scale factor 1/2 to produce triangle A'B'C' will have the value of B'C' = 8 and m∠A' = 14°. Option C is correct.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

The dilation of the triangle ABC by 1/2 implies each corresponding sides of triangle ABC is multiplied by 1/2 to produce triangle A'B'C'

B'C' = BC × 1/2

B'C' = 16 × 1/2

B'C' = 8

m∠A' = m∠A × 1/2

m∠A' = 28° × 1/2

m∠A' = 14°

Therefore, the dilated triangle ABC by scale factor 1/2 to produce triangle A'B'C' will have the value of B'C' = 8 and m∠A' = 14°

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According to the Triangle Inequality Theorem, the sum of the lengths of two sides of a triangle is greater than the length of the third side of the triangle.

In this case, you know the lengths of two sides of the triangle, and you also know that "x" represents the length of the third side. Then, you can set up the following:

Solving the inequality, you get:

You can rewrite it as:

Hence, the answer is:

The exact value of tan(2arcsin(x)) is 2x / √(1 - x²), where |x| ≤ 1.

To find the exact value of tan(2arcsin(x)), we start by considering the definition of arcsin. Let θ = arcsin(x), where |x| ≤ 1. From the definition, we have sin(θ) = x.

Using the double angle identity for tangent, we have tan(2θ) = 2tan(θ) / (1 - tan²(θ)). Substituting θ = arcsin(x), we obtain tan(2arcsin(x)) = 2tan(arcsin(x)) / (1 - tan²(arcsin(x))).

Since sin(θ) = x, we can use the Pythagorean identity sin²(θ) + cos²(θ) = 1 to find cos(θ). Taking the square root of both sides, we have cos(θ) = √(1 - sin²(θ)) = √(1 - x²).

Now, we can determine the value of tan(arcsin(x)) using the definition of tangent. We know that tan(θ) = sin(θ) / cos(θ). Substituting sin(θ) = x and cos(θ) = √(1 - x²), we get tan(arcsin(x)) = x / √(1 - x²).

Finally, substituting this value into the expression for tan(2arcsin(x)), we obtain tan(2arcsin(x)) = 2x / (1 - x²).

Therefore, the exact value of tan(2arcsin(x)) is 2x / √(1 - x²), where |x| ≤ 1.

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Answer:

see explanation

Step-by-step explanation:

(a)

calculate the lengths using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )

JK = \(\sqrt{(3-(-3))^2+(-8-(-7))^2}\)

    = \(\sqrt{(3+3)^2+(-8+7)^2}\)

    = \(\sqrt{6^2+(-1)^2}\)

    = \(\sqrt{36+1}\)

    = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )

MN = \(\sqrt{(7-8)^2+(-3-3)^2}\)

      = \(\sqrt{(-1)^2+(-6)^2}\)

     = \(\sqrt{1+36}\)

     = \(\sqrt{37}\)

repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )

PQ = \(\sqrt{-2-(-8))^2+(2-1)^2}\)

      = \(\sqrt{(-2+8)^2+1^2}\)

      = \(\sqrt{6^2+1}\)

      = \(\sqrt{36+1}\)

      = \(\sqrt{37}\)

(b)

JK ≅ MN ← true

JK ≅ PQ ← true

MN ≅ PQ ← true

Answer:

m(<M) > m(<N)

Step-by-step explanation:

Answer:

m<M < m<N is right one.hope it helps

When the measurement scale provides information regarding greater than or less than, but not how much greater or less, it is in the form of ordinal data.

Ordinal data is a type of categorical data, which is a type of data that fits into discrete categories, such as gender, or levels of education. Ordinal data does not provide numerical values for comparison, only information on the order of the categories.

For example, a survey may ask respondents to rate their opinion of a product on a scale of one to five. The scale provides information on the order of the categories (one being least favorable and five being most favorable), but it does not provide numerical values that can be used to calculate the average opinion of the product.

Mathematically, ordinal data is usually represented using an ordered set of numbers, with each number representing the order of the categories. For example, the survey mentioned above would be represented this way: 1, 2, 3, 4, 5. This set of numbers can then be used to calculate the median, mode, and range of the data. For example, the median value of the example survey would be 3, the mode would be 5, and the range would be 4 (5 - 1 = 4).

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The best illustration of a probability distribution as it relates to next year's economy is "40 percent chance of recession, 60 percent chance of a normal economy". Option B is correct.

This choice accurately represents a probability distribution by assigning probabilities to different outcomes (recession and a normal economy) based on their likelihoods. The 40 percent chance of a recession and 60 percent chance of a normal economy provide a clear indication of the potential outcomes and their corresponding probabilities.

This distribution allows for a more realistic assessment of the future state of the economy, acknowledging the possibility of both positive and negative scenarios. By presenting these probabilities, decision-makers can better understand the potential risks and make informed choices based on the likelihood of different economic outcomes.

This probability distribution offers a balanced perspective, highlighting the uncertainty and potential variations that may occur in the next year's economy.

Option B holds true.

This question should be provided as:

Which one of these best illustrates a probability distribution at it relates to next year's economy? Multiple choice question:

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Answer: What you must do for this case is to graph each of the ordered pairs that you have in the table to obtain the dispersion chart. Note that in your table you have eight ordered pairs, therefore, your scatter chart must have eight pairs.

Step-by-step explanation:

The values of x that provide meaningful predictions for the output value y are given as follows:

c. Prediction values are meaningful only for X-values in (or close to the range of the original data.

Regression equations are built from a sample of a data-set, and are used to model the entire data.

Depending on the behavior of the data, the regression equation can be linear, quadratic, logistic, exponential, and so on...

These regression equations are not valid for all values of the input x, some conditions are given as follows:

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FG = 8.5

GH = 11.4

FH = 17.5

JK = 11.4

KL = 17.5

JL = 8.5

The triangles are congruent by SSS

To determine how long each section should be, use the distance formula. For instance, the segment FG's length equals the distance between points F and G.

F= (x1,y1)=(-5,10)

G = (x2,y2) = (-2,2) d distance from F to G = d = segment length FG

d = √ [(x2 - x1)² + (y2 - y1)²]

d = √ (-5 + 2)² + (2 - 10)²

d = √ 9 + 64

d = √73

d = 8.5

Segment FG has a length of around 8.5 units. The similar approach is used for the other side lengths. The Pythagorean Theorem can be used as an alternative.

Observe that we have the following three pairs of comparable congruent sides once you have calculated all six lengths:

GH = JK = 11.4

FH = KL = 17.5

FG = JL = 8.5

We may use the SSS (side side side) congruence theorem to demonstrate that the triangles are congruent since we have three pairs of equal sides. Therefore, we have two triangles that are exactly the same. One triangle is a mirror image of the other that has been rotated.

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