Do the segments connecting points A, B, and C form a right triangle? Show work that leads to your answer. Round to the nearest tenths place if necessary.
A= -2,2
B=6,2
C=0,6

There 2 terms in the algebraic expression x + 8 + 3x.

An expression that contains variables, constants, and algebraic operations is defined as just an algebraic expression in mathematics (addition, subtraction, etc.). Terms comprise expressions. A mathematical statement with variables, constants, coefficients, and algebraic operations is known as an algebraic expression.  

Terms comprise expressions, Algebraic equations are declarations of the equality of two expressions created by performing the algebraic operations of adding, subtracting, multiplying, dividing, raising to a power, and root extraction to a collection of variables.

There 2 algebraic expression in x + 8 + 3x, as x + 3x = 4x, these are: 8 and 3x.

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Step-by-step explanation:

the area of a triangle is

baseline × height / 2

so, we only have to sum all 6 triangles and the base area :

6 × 6×8/2 + 93.5 = 36×4 + 93.5 = 144 + 93.5 =

= 237.5 in²

The constant terms of f(x) and h(x), it can be determined that 9(0) = 7.

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Graphing the equations x - y = 4 and -2x + 2y = -8, we get two lines that are parallel and do not intersect, which confirms that the system does not have a unique solution.

To solve the system of equations by substitution, we can use one of the equations to solve for one variable in terms of the other, and then substitute that expression into the other equation to get an equation with only one variable. We can then solve for that variable, and use the solution to find the value of the other variable.

Let's use the first equation, x - y = 4, to solve for x in terms of y:

x - y = 4

x = y + 4

Now we can substitute this expression for x into the second equation:

-8 = -2x + 2y

-8 = -2(y + 4) + 2y

Simplifying and solving for y:

-8 = -2y - 8 + 2y

-8 = 0y - 8

0 = 0

We end up with 0 = 0, which means that the second equation is an identity and does not provide any useful information about the values of x and y. This suggests that the system of equations does not have a unique solution and may have an infinite number of solutions, or no solutions at all.

To confirm this, we can graph the two equations and see if they intersect at a single point (indicating a unique solution), multiple points (indicating an infinite number of solutions), or no points (indicating no solutions).

Graphing the equations x - y = 4 and -2x + 2y = -8, we get two lines that are parallel and do not intersect, which confirms that the system does not have a unique solution.

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The inequality equation is x < 3.1 and the number of biking outfits is 3

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the total amount with Evan be = $ 580

The cost of bicycle = $ 396.95

The cost of each reflectors = $ 7.40

The cost of 4 reflectors = 4 x 7.40 = $ 29.60

The cost of pair of bike gloves = $ 22.94

So , the total cost = $ 396.95 + $ 29.60 + $ 22.94

On simplifying the equation , we get

The total cost = $ 449.49

So , the remaining amount with Evan = total amount with Evan - total cost

The remaining amount with Evan = $ 580 - $ 449.49

The remaining amount with Evan = $ 130.51

Now , the cost of biking outfits = $ 42.10

The cost of x biking outfits = 42.10x

So , the number of outfits Evan can purchase while staying within his budget is given by

42.10x < 130.51

Divide by 42.10 on both sides of the equation , we get

x < 3.1

Therefore , the number of biking outfits is 3

Hence , the inequality equation is 42.10x < 130.51

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Answer: this is the true answer

Step-by-step explanation:

inequality is 42.1x+44.49≤580

answer x ≤ 3.1

Rate of consumption refers to the rate at which a particular resource or material is being used up. It is usually expressed as the amount consumed per unit of time, such as kilograms per hour, gallons per day, etc. The rate of consumption can be used to measure the efficiency of a process, as well as to predict future needs for the resource or material. It is also important to consider the environmental impacts of consumption, as the rate of consumption can have a significant effect on the environment if it is too high.

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Answer:

Step-by-step explanation:

i don't know convert

Therefore , the solution of the given problem of compound sentence's comes out to be { x|–2< x < 5}

Indicated by the conjunction "or," the compound sentence is true as long as either of the two statements is true. In other words, it is the union or combination of the solution sets for each unique assertion. The term "conjunction" refers to a compound inequality that contains the word "and". The words "and" and "or," which are considered to be variables of speech, have a different meaning in mathematics than they do in grammar.

Here,

Given :

=> On the number line

=> -5 to -2

and 5 to infinity .

So,

Both x| x > -2 and x < 5

The following is another method to state this solution set:

{ x|–2< x < 5}

It is assumed that the word "and" will always be used in compound inequality expressions when neither "and" nor "or" is explicitly used. You say, "x is more than  -2 and (reading to the right) x is less than 4," reading from the "x" position as "x|-2" "x," "x," and "x," respectively. This is the solution set's graph.

The Complete Question.

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The the length of each side of the triangle are: 5 units, 8.7 units and 10 units respective

A triangle is a polygon with three sides, three angles, three vertices and sum of angles equal to 180 degrees

From the triangle, Using the trigonometric ratio of sine

Sin C = opposite/Hypothenuse

Sin30 = 5/H

Making h the subject of the relation we have

h= 5/sin30

h=5/0.5

Therefore the value of h=10 units

To find the third side use Pythagoras theorem

10² = 5²+p²

100-25 = p²

75 = p²

Taking the square of both sides

p=√75

p=8.7 units

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The interval on which the function f(x) is both increasing and concave up is given as follows:

x > 26.923.

The function is increasing and concave up as follows:

The function for this problem is given as follows:

f(x) = x³ - 42x² - 87x.

The first derivative is given as follows:

f'(x) = 3x² - 84x - 87.

Hence the positive intervals are:

x < 1.077 or x > 26.923.

The second derivative is given as follows:

f''(x) = 6x - 84.

Hence it is positive when:

6x - 84 > 0.

6x > 84

x > 84/6

x > 14.

Hence the interval for which the function is both increasing and concave up is given as follows:

x > 26.923.

(intersection of x < 1.077 or x > 26.923 and x > 14).

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twelve is two percent of six hundred

The statement "Participation in the FDIC is mandatory and required for all U.S. Banks" is false.

The Federal Deposit Insurance Corporation is one of two agencies that supply deposit insurance to depositors in American depository institutions, the other being the National Credit Union Administration, which regulates and insures credit unions.

Given is the statement as -

"Participation in the FDIC is mandatory and required for all U.S. Banks."

The given statement is false. It is not mandatory for all U.S. Banks to participate in FDIC

Therefore, the statement "Participation in the FDIC is mandatory and required for all U.S. Banks" is false.

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Answer and Step-by-step explanation:

To solve this equation, we will assume the given that is x will be assumed equal to twelve.

We will replace the place value of x with 12 everywhere in the given equation.

3(x - 2) =30+x-2-x+2

3 (12 - 2) = 30 + 12 - 2 - 12 + 2

3 (10) = 44 - 14

30 = 30

We can see that the left-hand side is the same as the right-hand side i.e. LHS = RHS.

This means that the value of the equation is stable after we put (x=12) in the above-given equation.

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Answer:

x >5 and x <-2

Step-by-step explanation:

x >5 and x <-2

To find the area of the regular 12-gon inscribed in a unit circle, first calculate the area of a regular octagon. The area of a regular octagon is equal to two times the length of one side squared, multiplied by the constant π/2. Since all the sides of a regular octagon inscribed in a unit circle have length 1, we can calculate the area of the octagon as 21^2(π/2) = π.

Next, divide the octagon into four red regions, each with an area of 12. To calculate the area of the blue region, subtract the total area of the four red regions (12*4 = 48) from the area of the octagon (π). This gives us an area of π - 48 = 8 for the blue region.

To find the distance from O to PQ in the isosceles triangle OPQ, use the Pythagorean theorem. Since the base of the triangle has length 2, and the legs of the triangle have length OP=OQ, we can calculate the distance from O to PQ as the square root of 2^2 - (OP)^2, which is equal to √2.

To find the area of the smaller hexagon, subtract the area of triangle ACE from the area of triangle BDF. The area of an equilateral triangle with side length 2 is √3/4, so the area of triangle ACE is (√3/4)2 = √3/2. Similarly, the area of triangle BDF is (√3/4)2 = √3/2. Subtracting these two values gives us an area of 0.5 for the smaller hexagon.

Lastly, to find the measure of [ABCDE], use the fact that the sum of the interior angles of a regular polygon is equal to (n-2)180°, where n is the number of sides of the polygon. In this case, n = 5, so the measure of [ABCDE] is (5-2)180° = 120°.

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The required interest rate would be approximately 6%.

The Compound Annual Growth Rate (CAGR) is a measure of the average rate of return of an investment over a specified time period, assuming the investment is compounded at regular intervals. It gives the average growth rate that would have transformed the initial investment value into the final investment value over the specified time period.

To calculate the required interest rate, we need to find the CAGR using the following formula:

[tex]\text{CAGR} = (\frac{V_\text{final}}{V_\text{begin}} )^{(1/n) }- 1[/tex] where,

Substituting the given values, we get:

CAGR = ($20,886.24 / $5,000)^(1/15) - 1

= (4.17248)^(1/15) - 1

= 1.06 - 1

= 0.06 or 6%

So, the required interest rate to have $20,886.24 at the end of 15 years, assuming compounded interest, would be 6%.

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Answer(s):

[tex]\displaystyle y = 3cos\:(\frac{1}{4}x - \frac{\pi}{2}) - 1 \\ y = -3sin\:(\frac{1}{4}x \pm \pi) - 1 \\ y = 3sin\:\frac{1}{4}x - 1[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{\frac{\pi}{2}}{\frac{1}{4}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{8\pi} \hookrightarrow \frac{2}{\frac{1}{4}}\pi \\ Amplitude \hookrightarrow 3[/tex]

OR

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow -1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{8\pi} \hookrightarrow \frac{2}{\frac{1}{4}}\pi \\ Amplitude \hookrightarrow 3[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the sine graph, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 3cos\:\frac{1}{4}x - 1,[/tex] in which you need to replase “sine” with “cosine”, then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [photograph on the right] is shifted [tex]\displaystyle 2\pi\:units[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle 2\pi\:units,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{2\pi} = \frac{\frac{\pi}{2}}{\frac{1}{4}}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3cos\:(\frac{1}{4}x - \frac{\pi}{2}) - 1.[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-10\pi, -4],[/tex]from there to [tex]\displaystyle [-2\pi, -4],[/tex]they are obviously [tex]\displaystyle 8\pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle 8\pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = -1,[/tex]in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

yes because see below

Step-by-step explanation:

300²+400²=500²

so it has to be right angle

Answer:

Step-by-step explanation:

yes, the parcel of land will have a right angle.

300x300=90,000

400x400=160,000

500x500=250,000

90,000+160,000 = 250,000

The triangles' corresponding angles are identical.The pre-image was reduced to create the picture.The triangle's form is unaffected by either dilation or rotation.

Reason: For forms to resemble one another:

1. The sides should be proportionate to one another.

Angles in the first and second shapes should be same.

With a scale factor of 0.2, the sides of the picture are now 0.2 of the original shape's length. Angles, however, are not modifications.

Let's examine the options:

1. The triangles' corresponding sides are congruent:

Due to the fact that dilation alters the side lengths, this choice is wrong.

2- The triangles' corresponding angles are identical:

This is the best choice because neither rotation nor dilation change the angles' measurements.

3. The image's matching sides are five times longer than the pre- image's:

The sides of the picture are only 0.2 times as long as those of the pre-image, therefore this choice is erroneous.

4. The picture is a condensed version of the original:

This choice is appropriate since the sides of the picture are 0.2 times those of the pre-image, reducing the form.

5- The triangle's shape is unaffected by either dilation or rotation: This choice is valid because dilation and rotation are rigid transformations that do not modify the triangle's shape (a triangle stays a triangle).

The complete question is

A triangle is dilated by a scale factor of 1/5 and then rotated 90 degree clockwise about the origin. Why is the image similar to the pre-image? Check all that apply.

A) The corresponding sides of the triangles are congruent.

B) The corresponding angles of the triangles are congruent.

C) The corresponding sides of the image are 5 times as long as those of the pre-image.

D) The image is a reduction of the pre-image.

E) Neither the dilation nor the rotation change the shape of the triangle.

F) The rotation reduces the size of the triangle.

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The  average rate of change between the intervals x = -2 and x = 4 of the function f(x) = 4x³ - 15x + 3 is; 33

The average rate of change is defined as a measure of how much the function changed per unit, on average, over a given interval.

We are given the function;

f(x) = 4x³ - 15x + 3

Between the intervals x = -2 and x =4, the average rate of change can be gotten from;

[f(4) - f(-2)]/(4 - (-2)

f(4) = 4(4)³ - 15(4) + 3

f(4) = 199

f(-2) = 4(-2)³ - 15(-2) + 3

f(-2) = -32 + 30 + 3

f(-2) = 1

Thus;

Average rate of change = (199 - 1)/(4 - (-2)

= 198/6

= 33

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Altogether 50 adult tickets were sold and 175 student tickets were sold.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Let, The number of adult tickets be 'x' and the number of students

ticket be  'y'.

Therefore, From the given information x + y = 225...(i) and 4x + 2y = 650...(ii)

Multiplying equation (i) by 2, we have 2z = 2y = 550 and subtracting it from

equation (ii) we have,

2x = 100.

x = 50 and y = 175.

So, 50 adult tickets were sold and 175 student tickets were sold.

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The algebraic expression can be written as follows:

9 + x/2

We will use x as our unknown value (or also called the variable).

The expression that we want to write is:

"nine add to half of a number"

So we need to write the sum between 9 and half of our variable, this can be written as:

9 + x/2

That is the expression that represents the mathematical statement above.

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Answer:

C

Step-by-step explanation:

A proportion is a statement that compares two or more quantities and shows their relationship.

The following options represent a proportion:

a) 37=25 3 7 = 2 5

b) 32=96 3 2 = 9 6

c) 2.515=212 This is not a proportion because it doesn't show the relationship between two or more quantities.

The intersection is - 7< <x<  4 after resolving the compound inequalities -20<  2x - 6 <2.

A relation between two terms or concepts that is equal in mathematics is referred to by the term inequality. Thus, disparity originates from imbalance. In economics, an inequality explains the connection between two non-equal numbers. Egality and equality are not the same. Use the same equal symbol most frequently when two results are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two aspects until only the variables are left, many straightforward inequalities can be solved. However, a range of variables support inequality: Both sides' negative values are split or added. Exchange the left and the right.

given

-20 < 2x - 6 < 2

Divide a system of inequalities into compound inequalities:

1) 2x - 6 > -20

2) 2x - 6 > 2

x> 7 and x < -4

the intersection, then: - 7 < x < 4

The intersection is - 7< x<  4 after resolving the compound inequalities -20<  2x - 6 <2.

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The complete question is :-

Solve the following compound inequality:

-20<  2x - 6 <2.

Note that where in the picture above PA = PD and AB = CD.

Since AB = CD

∠APB = ∠CPD  - open mouth theorem

Based on the above,

∠BPC = ∠APD - (∠APB +∠CPD)

Since points A, B, C and D are all on a straight line, thus, it is proven that

PB = PC - open mouth theorem.

The Hi. nge theorem (also known as the open mouth theorem) states in geometry that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is greater than the included angle of the second, the third side of the first triangle is longer than the third side of the second triangle.

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The work done is W = mgh = (15 lb)(32.2 ft/[tex]s^{2}[/tex])(10 ft) = 4830 ft-lb

This question uses the work-energy theorem, which states that the work done on an object equals its change in kinetic energy.

The kinetic energy of the chain is zero before it is lifted, and its kinetic energy is equal to its potential energy (mgh) after it is lifted, so the work done in lifting the chain is equal to mgh.

Step 1: Determine the mass of the chain. In this case, the mass of the chain is 15 lb.

Step 2: Determine the acceleration due to gravity.

The acceleration due to gravity is 32.2 ft/[tex]s^{2}[/tex].

Step 3: Calculate the height of the chain.

In this case, the height of the chain is 10 ft.

Step 4: Calculate the work done.

The work done in lifting the lower end of the chain to the ceiling is W = mgh = (15 lb)(32.2 ft/[tex]s^{2}[/tex])(10 ft) = 4830 ft-lb.

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The probability that a rivet is defective is 0.0247, and in ensuring that only 5% of all seams need reworking then the probability of a defective rivet is 0.0059.

Let p be the probability of a rivet being defective. The probability of a seam being defective is given by the binomial distribution:

P(defective) = 29Cx × p^x × (1-p)^(29-x)

where x is the number of defective rivets.

We know that 17% of seams are defective, so:

0.17 = ∑_{x=1}^{29} 29Cx × p^x × (1-p)^(29-x)

Solving for p, we have:

p = 0.0247

If only 5% of all seams need reworking, then:

0.05 = ∑_{x=1}^{29} 29Cx × p^x × (1-p)^(29-x)

Solving for p, we have:

p = 0.0059

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Therefore , the solution of the given problem of Inline view comes out to be this query is present in the FROM clause of other SELECT statement.

Inline view:-It is not a real view instead it is a sub-query or a SELECT statement in the FROM clause of the of another select statement. In the query provided we have a sub - query which is displaying category and Average of retail from the books table and this query is present in the FROM clause of other SELECT statement.

Here.

Given :

You can experiment with different ways of arranging these categories. Then, count the items in each category, and

record the information in the table

Thus , the solution of the given problem of Inline view comes out to be

this query is present in the FROM clause of other SELECT statement.

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