Explaining the Converse of the Pythagorean TheoremThe converse of the Pythagorean Theorem states that if the three sides of a triangle work for the equation a^2 + b^2 = c^2, then the triangle is a right triangle. To prove this, you can use what’s called a proof by contradiction. That is, you can prove something is true because it cannot be false.Start by assuming a triangle is not a right triangle and the sides work for the equation a^2 + b^2 = c^2. Here is a diagram of the triangle. Keep this diagram window open as you work on the tasks in this section.Now, create a right triangle with legs a and b. Call the hypotenuse n. Here is a diagram of the triangle. Keep this diagram window open as you work on the tasks in this section.questionsPart ASince triangle 2 is a right triangle, write an equation applying the Pythagorean Theorem to the triangle.Part BSince the equations for both triangles have a^2 + b^2, you can think of the two equations for c^2 and n^2 as a system of equations. Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation. After you substitute, what equation do you get?Part CNow, take the square root of both sides of the equation from part B and write the resulting equation.Part DIs there any way for this equation to be true? How?Part EWhat does this show about the relationship between the two triangles?Part FDoes this mean that triangle 1 is a right triangle? Why or why not?

Answer:

According to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.

What is the right angle triangle property?

In a right-angle triangle ratio of the opposite side to the adjacent side is equal to the tangent angle between the adjacent side and the hypotenuse side.

Here, (b) is the opposite side, (a) is the adjacent side, and is the angle made between the adjacent side and the hypotenuse side.

The sides of the triangle are 8, 15, and 17 units long and the measure of the angles of the right angle triangle is 62, 90, and 28 degrees.

Re-draw, the  Here in the given triangle, the base is the side which is 15 units long. Re-draw the triangle as shown below.

In the attached triangle below, the opposite side of the triangle is 15 units and the adjacent side of the triangle is 8 units long.

The angle between the opposite side and the adjacent side is 62 degrees. Thus using the right angle triangle property as,

Thus, according to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.

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Answer:

Step-by-step explanation:

Net pay = $1896.00

Amount can be spent on food:

Correct choice is B

Answer:

y = 2x - 4

Step-by-step explanation:

y = (slope)x + (y intersept)

y = (2)x + (-4)

y = 2x - 4

The equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. option B.

The equation y = ax² represents a parabola with its vertex at the origin. In this case, if the coefficient 'a' is negative, it determines the direction in which the parabola opens.

When 'a' is negative, the parabola opens downward. This means that the vertex, which is at the origin (0, 0), represents the highest point on the graph, and the parabola curves downward on both sides.

To understand this concept, let's consider the basic equation y = x², which represents a standard upward-opening parabola. As 'a' increases, the parabola becomes narrower. Conversely, when 'a' becomes negative, it flips the parabola upside down, resulting in a downward-opening parabola.

For example, if we have the equation y = -x², the negative coefficient causes the parabola to open downward. The vertex remains at the origin, but the shape of the parabola is now inverted.

In summary, when the equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. This can be visually represented as a U-shape curving downward from the origin. So Optyion B is correct.

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Step-by-step explanation:

If y varies directly as the square root of x, then we can express this relationship as:

y = k√x

where k is the constant of proportionality.

To find the value of k, we can use the initial values given in the problem:

y = 25 when x = 334

Substituting these values into the equation above, we get:

25 = k√334

Solving for k, we have:

k = 25/√334

Now we can use this value of k to find y when x = 247:

y = k√247

Substituting the value of k, we get:

y = (25/√334)√247

Using a calculator, we can evaluate this expression to two decimal places:

y ≈ 19.24

Therefore, when x = 247, y ≈ 19.24.

Answer:

2x + 15 = 37 - 2

Step-by-step explanation:

we know his age is the variable x

so (Two times his age plus fifteen equals thirty seven minus two) turns into:

2x (plus fifteen equals thirty seven minus two)

plus fifteen is +15 so now we have:

2x + 15 (equals thirty seven minus two)

equals is =, so now we have:

2x + 15 = (thirty seven minus two)

thirty seven is 37, so now we have:

2x + 15 = 37 (minus two)

minus two is -2, so now we have:

2x + 15 = 37 - 2

The parent function of the transformed function is y = f ( x ) = x

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

The transformed function is represented as y

where y = 2 ( x - 5 )

On simplifying , we get

y = 2( x - 10 )

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

The function is shifted horizontally left by 10 units and multiplied by a scale factor of 2 units.

Hence , the parent function is f ( x ) = x

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x² + 3x - 2

(5)² + 3 × 5- 2

25 + 15 - 2

40 - 2

38...

The type of distribution pictured in this histogram is skewed.

A skewed distribution is a statistical distribution that is not symmetrical around its mean or median.

In a skewed distribution, the tail of the distribution is pulled in one direction or the other, resulting in a longer tail on one side than the other.

There are two types of skewed distributions: positively skewed and negatively skewed.

The distribution in the image is positively skewed as its is pulled towards the left.

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Answer:

\(-11\sqrt5 - 11\sqrt6\)

Step-by-step explanation:

Hello!

To rationalize the denominator, we have to remove any root operations.

To do that, we can multiply the numerator and denominator by the conjugate of the denominator. A conjugate is simply the same terms but with opposite operations.

The answer is \(-11\sqrt5 - 11\sqrt6\).

Answer:

to the nearest tenth 30.2%

Answer:

Answer down bellow

Step-by-step explanation:

Q's Asked: A company determines an employee's starting salary according to the number of years of experience, as detailed in the table.

Years of experience Salary

0 $52,000

1 $53,150

2 $54,260

3 $55,285

4 $56,921

5 $57,126

---------------------------------------------------------------------------------------------------------

So based on the chart:

0 $52,000

1 $53,150

2 $54,260

3 $55,285

4 $56,921

5 $57,126

We can see for each year of experience the "Salary" goes up one thousands constantly. And that makes sense bc as you get used to the work u gradually get better meaning u work better and u also get paid better. ehmm... my bad

----------------------------------------------------------------------------------------------------------

So work side of things based on the chart we see the amount the amount change.  so from

0 to 1 yr

you will be paid $1,150 more.

and from 1 to 2 yrs you will be paid 1110.

and so on.

And btw i got it right on my test !

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The missing values are:

m∠1 = 36°

m∠2 = 122°

m∠3 = 122°

m∠4 = 38°

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The figure has two triangles.

58° and m∠3 is a straight angle.

58 + m∠3 = 180

m∠3 = 180 - 58

m∠3 = 122

Now,

m∠3 + m∠4 + 20 = 180

122 + m∠4 + 20 = 180

m∠4 = 180 - 122 - 20

m∠4 = 180 - 142

m∠4 = 38

m∠3 and m2 are opposite angles.

Opposite angles are equal.

m∠3 = m∠2 = 122

Now,

m∠1 + m∠2 + 22 = 180

m∠1 + 122 + 22 = 180

m∠1 = 180 - 144

m∠1 = 36

Thus,

The missing values are:

m∠1 = 36°

m∠2 = 122°

m∠3 = 122°

m∠4 = 38°

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\(3(x - 8) - 13x(x - 8) + 3 = 0 \\ 3x - 24 - 13 {x}^{2} + 104x + 3 = 0 \\ - 13 {x}^{2} + 107x - 21 = 0 \\ x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a } \\ a = - 13 \\ b = 107 \\ c = - 21 \\ x = \frac{ - 107 + - \sqrt{ {107}^{2} - 4(13)( - 21)} }{2( - 13)} \\ x1 = \frac{107 - \sqrt{10357} }{26} \\ x2 = \frac{107 + \sqrt{10357} }{26} \)

Hope it helps

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The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.

In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:

x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]

x = 284.372 mi

The distance x is equal to 284.372 miles.

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Exponential growth formula

where:

• f(x): exponential growth function

• a: initial amount

• r: growth rate, as a decimal

• x: time

In this case, f(x) models the expected population, the initial population is a = 200 deers, the growth rate is r = 0.07 (= 7/100), and x measures time in years. Substituting these values into the formula:

There are 56 numbers of schedules that are possible for Hannah.

Basically, A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.

Given Hannah, a roller coaster enthusiast has decided to ride 2 of the world's 8 most famous roller coasters this year.

total roller coasters = 8

since Hannah wants to ride 2 roller coasters,

that can be completed in a certain manner, after completing the first one she will go for the next,

total number of possibilities is calculated by permutation,

ⁿPₓ = n!/(n - x)!

n = 8,  x = 2

⁸P₂ = 8!/(8 - 2)!

⁸P₂ = 8*7*6!/6!

⁸P₂ = 56

Hence there are 56 different schedules are possible.

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The probability that a randomly selected point within the square falls in the red shaded square is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it is 100% in percentage.

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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Answer:

-1

Step-by-step explanation:

the slope of the line is given by the equation m=(y2-y1)/(x2-x1)

here the line passes with the coordinate (-2,0),(0,-2)

m=(-2-0)/(0-(-2))

 = -2/2

 = -1

Answer:

4

Step-by-step explanation:

Answer: Your answer is 23.5in²

Hope it helped :D

Good Luck!

The expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

Pascal's Triangle is a triangular array of numbers in which the value in each cell is the sum of the two numbers directly above it.

To expand the given expression (x²-3y)⁴ as per Pascal's triangle:

First, write down the fourth row of Pascal's Triangle as:

1 4 6 4 1

The above numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a is x² and b is -3y. Therefore, it can be written as,

1×(x²)⁴ + 4×(x²)³×(-3y) + 6×(x²)²×(-3y)² + 4×(x²)(-3y)³ + 1(-3y)⁴

Simplify each term,

x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸

Therefore, the expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

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Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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Answer:

\(J' = (14,-6)\)

Step-by-step explanation:

Given

\(J = (-14,6)\)

\(R_0 = 180^\circ\)

Required

Determine J'

When a point (x,y) is rotated 180 degrees around the origin, the new point is (-x, -y).

So:

\(J = (-14,6)\)

\(J' = (14,-6)\)

Answer:

30x

Step-by-step explanation:

Answer:

30x

Step-by-step explanation:

a negative multiplied by a negative is positive.

-5x x -6 =30x

Hope I helped!