Let f(x)=-2x+7 and g(x)=-6x+3. Find f•g and state it’s domain

The solutions to the equation 2cos^2x-1=0 is x = π/4, -π/4 (in radians),      x = 45 degrees, -45 degrees (in degrees).

To solve the equation 2cos^2(x) - 1 = 0, we can follow these steps:

Step 1: Add 1 to both sides of the equation to isolate the cosine term:

2cos^2(x) = 1

Step 2: Divide both sides of the equation by 2 to solve for cos^2(x):

cos^2(x) = 1/2

Step 3: Take the square root of both sides of the equation:

cos(x) = ±√(1/2)

Step 4: Find the solutions for x by taking the inverse cosine (cos⁻¹) of both sides:

x = cos⁻¹(±√(1/2))

Now, let's evaluate the inverse cosine of ±√(1/2) to find the solutions for x:

For cos⁻¹(√(1/2)):

x = cos⁻¹(√(1/2))

x = π/4 or 45 degrees

For cos⁻¹(-√(1/2)):

x = cos⁻¹(-√(1/2))

x = -π/4 or -45 degrees

Therefore, the solutions to the equation 2cos^2(x) - 1 = 0 are:

x = π/4, -π/4 (in radians)

x = 45 degrees, -45 degrees (in degrees)

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Answer:  Which shows Angle P O Q?  Option (A)

(A)    Q   Line segments Q O and O P combine to form an angle.

         P

         R

         P

Step-by-step explanation:

Answer:

its a

Step-by-step explanation:

Answer:

I Also need the answer plese helep ussss

Step-by-step explanation:

Answer:

-25

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The true statement is Quadrilateral WXYZ can be mapped onto quadrilateral MATH using a sequence of rigid motions.

The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Given:

MATH is congruent to quadrilateral WXYZ.

Then congruent sides are

MA= WX

AT = XY

TH = YZ

and, congruent angles are

<M = <W

<A = <X

<T= <Y

<H = <Z

So, if the quadrilateral is congruent then they equal in measure.

Hence, the true statement is  Quadrilateral WXYZ can be mapped onto quadrilateral MATH using a sequence of rigid motions.

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After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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Answer:

D. 132.3 miles

Step-by-step explanation:

Create a proportion where x is the actual distance between the two cities.

\(\frac{1.1}{15}\) = \(\frac{9.7}{x}\)

Cross multiply and solve for x:

1.1x = 145.5

x = 132.3

So, the two cities are 132.3 miles apart.

The correct answer is D. 132.3 miles

If f(2) = 1 and the tangent line at x has slope (x − 1)ex2 − 2x. f(x) = ((x^2 - 2x + 1)/2)e^(x^2 - 2x).

To find f(x), we'll first integrate the given slope function to obtain the original function. The slope of the tangent line is given as (x - 1)e^(x^2 - 2x).

Let F'(x) = (x - 1)e^(x^2 - 2x). To find f(x), we need to integrate F'(x) with respect to x:

∫(x - 1)e^(x^2 - 2x) dx

Now, we can use substitution. Let u = x^2 - 2x, then du = (2x - 2) dx. Therefore, the integral becomes:

∫((u + 1)/2)e^u du

Now, we can integrate by parts. Let v = e^u, then dv = e^u du. Let w = (u + 1)/2, then dw = 1/2 du. Using integration by parts formula:

∫w dv = wv - ∫v dw

∫(u + 1)/2 * e^u du = ((u + 1)/2)e^u - ∫(1/2)e^u du

Now integrate the remaining part:

∫(1/2)e^u du = (1/2)e^u + C

Substituting back:

f(x) = ((x^2 - 2x + 1)/2)e^(x^2 - 2x) + C

Now, use the given condition f(2) = 1:

1 = ((2^2 - 2*2 + 1)/2)e^(2^2 - 2*2) + C

1 = (1)e^0 + C

C = 0

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Answer:

24x1.35=32.4

He should have recieved $32.40 in change.

The image of the triangle is missing, so i have attached it.

Also, the options are;

A) The apothem can be found using the Pythagorean theorem.

B) The apothem can be found using the tangent ratio.

C) The perimeter of the equilateral triangle is 15 cm.

D) The length of the apothem is approximately 2.5 cm.

E) The area of the equilateral triangle is approximately 65 cm².

Answer:

Options A, B & D are true

Step-by-step explanation:

A) We are told that the triangle is an equilateral triangle.

Thus, the 3 sides equal 8.7 cm.

Now from the image, b is half of one of the sides.

Thus, b = 8.7/2 = 4.35 cm

Now, we want to find the apothem "a".

Using Pythagoras theorem, we have;

a² + 4.35² = 5²

a² = 25 - 18.9225

a² = 6.0775

a = √6.0775

a ≈ 2.5 cm.

Thus, option A is true as Pythagoras theorem was able to calculate the apothem "a"

B) since the main triangle is equilateral, it means each angle is 60°.

Now, the radius line from one corner point to the center will divide the 60° angle into 2 equal parts.

Thus, the angle made by the radius line with the base of the triangle is 60/2 = 30°

Now, from tangent ratios, we know that;

Opposite/Adjacent = tan θ

In the small triangle, opposite is apothem "a" while adjacent is b = 4.35 cm

Thus;

a/4.35 = tan 30

a = 4.35 tan 30

a ≈ 2.5 cm.

Thus, option B is correct as Tangent ratio can be used to find the apothem

C) The perimeter of equilateral triangle = 3x

Where x is length of one side.

One side is 8.7 cm

Thus, perimeter = 3 × 8.7 = 26.1 cm

Thus option C is not correct.

D) From calculations above, we saw that in both options A & B, the apothem is approximately 2.5 cm.

Thus, option D is true.

E) Area of triangle is;

A = ½ × base × height

Base = 8.7 cm

To get height, we will use trigonometric ratio. Thus;

h/8.7 = sin 60°

h = 8.7 sin 60°

Thus;

A = ½ × 8.7 × 8.7 sin 60°

A = 32.77 cm²

Thus is not equal to 65 cm². Thus, option E is not correct.

The statements that are true for the considered equilateral triangle are:

For a regular polygon, the apothem is the line segment from the center of the polygon to the mid of one of the sides of the considered polygon.

For this case, referring to the figure attached below, we have:

Since the triangle is equilateral, there can be 6 congruent triangles like BOD.

Thus, Area of triangle ABC = 6 × Area of triangle BOD

Area of BOD = \(\dfrac{1}{2} \times x \times 4.35 = 2.175x \: \rm cm^2\)

Area of ABC = \(6 \times 2.175x = 13.05x \: \rm cm^2\)

The length of the apothem is x cm, and can be obtained by using Pythagoras theorem.

We can also use the tangent ratio as the line segment BO is bisecting the internal angle B (each internal angle is of 60 degrees in an equilateral triangle), so angle OBD is of 60/2 = 30 degrees. So using angle and the fact that tangent ratio is ratio of side opposite to angle and the remaining adjacent side(not hypotenuse).

\(tan(30^\circ) = x/4.35 \implies x = 4.35 \times \tan(30^\circ) \approx 2.5 \: \rm cm\)

Using Pythagoras theorem too, we can get the value of x as:

\(5^2 = 4.35^2 + x^2\\x = \sqrt{25 - 18.9225} \approx 2.465 \: \rm cm \approx 2.5 cm\)

Thus, area of the equilateral triangle ≈ \(13.05 \times x \approx 13.05 \times 2.5 = 32.575 \: \rm cm^2\)

This isn't 65 sq. cm.

Thus, the statements that are true for the considered equilateral triangle are:

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Answer:

Step-by-step explanation:

Death Valley is 282 ft below sea level, so it can be seen as -282

Riverside is 827 ft above sea level, so it is 827

827-(-282)

827+282 = 1109ft

Answer: 7

Step-by-step explanation:

First, do 221 divided by 13 to get how many dollars per hour which is 17 and then do 119 divided by 17 to get the amount of hours.

We are given two numbers and we want to find the smaller one, we can use a comparison operator to determine which number is larger and which is smaller. the two numbers are 7 and 18  .

Let's say the two numbers are x and y, where x is greater than y.

According to the statement, we have:

x+y = (x-y) + 2y

Simplifying this equation, we get:

x+y = x-y

This is true, since we started with x and y as the two numbers.

So, the statement is always true for any two numbers x and y, where x is greater than y.

Since the maximum value of the product occurs at x=18, which represents the larger number, the smaller number can be found by subtracting it from the sum of the two numbers:

Smaller value = Sum - Larger value

Smaller value = 25 -18

Smaller value  = 7

Therefore, the two numbers are   7 and 18  .

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it is a relatively easy way to draw a sample while ensuring randomness is the answer.

Systematic sampling is a probabilistic sampling method in which a researcher selects members of a population at regular intervals. For example, select every 15 people from the list of populations. If the population is in random order, this can mimic the benefits of a simple random sample.

These are generally preferred by researchers because they are easy to implement and understand. The important assumption that the results represent the majority of the normal population ensures that the entire population is sampled equally. The process also provides a higher level of control for systematic sampling compared to other sampling methods. systematic sampling also has a lower risk factor because the data is unlikely to be contaminated.

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a) To find the extreme points and determine if they are minimum or maximum, we need to take the derivative of the function and set it equal to zero.

a) f(x) = x^2 + x - 6

Taking the derivative:

f'(x) = 2x + 1

Setting it equal to zero and solving for x:

2x + 1 = 0

2x = -1

x = -1/2

To determine if it is a minimum or maximum, we can examine the concavity of the function. Since the coefficient of x^2 is positive (1), the function opens upward and the critical point at x = -1/2 is a minimum.

b) f(x) = x^3 + x^2

Taking the derivative:

f'(x) = 3x^2 + 2x

Setting it equal to zero and solving for x:

3x^2 + 2x = 0

x(3x + 2) = 0

This gives two critical points:

x = 0 and x = -2/3

To determine if they are minimum or maximum, we need to examine the concavity of the function. Since the coefficient of x^3 is positive (1), the function opens upward. The critical point at x = 0 is a minimum, while the critical point at x = -2/3 is a maximum.

b) Graphical method:

To solve the problem graphically, we will draw a graph representing the constraints and find the feasible area. Then we will identify the corner point feasible solutions (CPFS) and determine if there is an optimal solution.

a) Maximize subject to:

x1 + x2

2x1 + 5x2 <= 5

x1 + x2 <= 5

3x1 + x2 <= 15

x1, x2 >= 0

b) Minimize subject to:

x1 + x2

-x1 + x2 <= 5

x2 <= 3

3x1 + x2 >= 7

x1, x2 >= 0

Unfortunately, the given optimization problems are incomplete as there are no objective functions specified. Without an objective function, it is not possible to determine an optimal solution or solve the problem graphically.

Please provide the objective function for the optimization problems so that we can proceed with the graphical solution and find the optimal solution, if any.

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a) The extreme point for the function f(x) = x² + x - 6 is a minimum point.

b) The extreme point for the function f(x) = x³ + x² is neither a minimum nor a maximum point.

Step 1: For the function f(x) = x² + x - 6, to find the extreme points, we can take the derivative of the function and set it equal to zero. By solving for x, we can identify the x-coordinate of the extreme point. Taking the second derivative can help determine if it is a minimum or maximum point. In this case, the extreme point is a minimum because the second derivative is positive.

Step 2: For the function f(x) = x³ + x², finding the extreme points follows the same process. However, after taking the derivative and solving for x, we find that there are no critical points. Without any critical points, there are no extreme points, meaning there are no minimum or maximum points for this function.

In summary, for the function f(x) = x² + x - 6, the extreme point is a minimum, while for the function f(x) = x³ + x², there are no extreme points.

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Answer:

y = 2/3x

Step-by-step explanation:

Answer:

30.07%

Step-by-step explanation:

I'm built different

The measure of <5 is 47

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

m<4=5x-42

and m<5=-x+82

as, <4 and <5 are in co- interior angle

<4 + <5 = 180

5x - 42 + (-x + 82) = 180

5x -42 - x + 82= 180

4x +40 = 180

4x = 140

x= 140/4

x= 35

Hence, the measure of <5 = -x+ 82 = -35 + 82 = 47

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Answer:

c = 0

Step-by-step explanation:

Step 1: Write equation

15 - 5(4c - 7) = 50

Step 2: Solve for c

Step 3: Check

Plug in c to verify it's a solution.

15 - 5(4(0) - 7) = 50

15 - 5(-7) = 50

15 + 35 = 50

50 = 50

The sentence "64% of women in the sample are the principal investor in their household" serves as an example of descriptive statistics.

This sentence provides a summary of the survey's data and a descriptive statistic (percentage) that characterizes the sample's characteristics.

According to the survey's findings, "there is a correlation between American women and being the principal investor in their household." The sample data are used to draw this conclusion about the population. Despite the fact that the sample is not representative of all American women, the findings indicate that a sizable number of the women in the sample are the principal investors in their households.

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Answer:

-7/3

Step-by-step explanation:

The first step is to combine like numbers. Although there are several different ways to go about doing this, I started by adding 2y to both sides which left me with -8-6y=6. I then added 8 to both sides and got 6y=14. Now divide 6 on both sides to get "y" by itself which left me with y = -14/6. When you simplify the answer you get -7/3.

Answer: I'm pretty bad at math, but I made it more simple for you :)

Step-by-step explanation:

The answer is y = 4 + 5x/4

I hope it helped a bit sorryy

Answer:

1024

Step-by-step explanation:

4x4= 16

8x8= 64

sqrt4 x sqrt8

The square root of 4 is 2.

The square root of 8 is 2.83.

2x2.83=5.66

hope it helps!

Answer:

-1

Step-by-step explanation:

To solve the problem, it is suggested to use a number line.

~Please look at image attached

We know the following:

Statement: 5 units to the right of -6.

Therefore, we know the following:

Ending point: -6 + 5 = -1

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4y = x + 6 is the equation of the line using the slope value.

The steepness of a line segment is explained by the slope of the line. It is a ratio of the vertical x-axis coordinates and the y-axis coordinates. The classification of whether two lines are parallel or perpendicular depends on the slope value.

The parameters for the line segment are as follows, in accordance with the question:

The coordinate points (6, 3) and the slope of a line (1/4) are as follows: (x = 6; y = 3)

Using the line segment's standard equation now: y = mx + c

If (x, y) are coordinates, "m" is the slope, "c" is the y-intercept,

The following results are obtained by replacing the slope and y-intercept values in the formula:

y = mx + c

⇒ 3 = (1/4)(6) + c

⇒ c = 3 - 3/2 = 3/2

Consequently, c = (3/2) is the y-value. intercept's

by changing the slope value and y-intercept value in the line's equation:

y = (1/4)x + (3/2) = 4y = x +6

Consequently, 4y = x + 6 is the equation of the line using the slope value.

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Balloon's altitude = 43.7ft as

change in altitude/500 = tan 5°  

change in altitude = .0875*500

                              =43.7ft