Just 2 questions.
Explaining the Converse of the Pythagorean Theorem
Task 1
Part A
The Pythagorean Theorem states that for any given right triangle, a2 + b2 = c2. Using the Pythagorean Theorem, what should be the relationship between the areas of the three squares?
Task 2
Part E What does this show about the relationship between the two triangles?

Answer:

B. domain is all integers 0 through 9

Step-by-step explanation:

Domain values area usually plotted along the horizontal axis. In this case, the number of days is the domain of the of the function.

The domain of the function that is plotted on the graph ranges from 0, 1, 2 to 9.

1, 2, 3 to 9 are all integers. Therefore, we can conclude that the "domain is all integers 0 through 9."

Answer:

75

Step-by-step explanation:

trust me bro

the total parcel size is 88 acres.

Let's denote the total parcel size as X acres.

According to the given information, 1/4 of the land is allocated to shopping, which amounts to 22 acres. Therefore, we can set up the following equation:

(1/4) * X = 22

To find the value of X, we need to solve this equation for X.

Multiplying both sides of the equation by 4, we get:

X = 22 * 4

X = 88

Therefore, the total parcel size is 88 acres.

what is equation?

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two sides, known as the left-hand side (LHS) and the right-hand side (RHS), connected by an equals sign (=).

The general form of an equation is:

LHS = RHS

The LHS and RHS can contain variables, constants, mathematical operations (such as addition, subtraction, multiplication, and division), functions, and other mathematical expressions.

The goal when working with equations is to find the values of the variables that satisfy the equation, making both sides equal. This process is often referred to as solving the equation.

For example, the equation "2x + 5 = 13" states that the expression "2x + 5" is equal to 13. To find the value of x that satisfies this equation, we can manipulate the equation to isolate the variable:

2x + 5 - 5 = 13 - 5  (subtract 5 from both sides)

2x = 8

2x/2 = 8/2  (divide both sides by 2)

x = 4

In this case, the value of x that satisfies the equation is 4.

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Answer:B

Step-by-step explanation:

Answer:

D, is the correct answer!!

Step-by-step explanation:

Answer:

I think you answer will be 7

The effect of this change on the function's values and the graph is the same.

Given `f(x) = x²` after performing the following transformations shift upward 40 units and shift 83 units to the right, the new function `g(x)` is: `g(x) = (x - 83)² + 40`

To understand the given problem statement, we need to know about the different transformations that can be performed on a function. Transformations of the function refer to changing the function's position or size without altering its shape. The following are the three main transformations of the function:

Translation: The graph of a function may be shifted up, down, right, or left using the translation method. We replace `x` by `(x-h)` in the equation to translate `h` units left and by `(x+h)` to translate `h` units right.Change in `x`:

The graph of a function may be stretched or compressed horizontally using the change in `x`. The new equation can be found by replacing `x` with `(x/a)`, where `a` is the stretch or compression factor.Change in `y`: The graph of a function may be stretched or compressed vertically using the change in `y`. The new equation can be found by multiplying the entire equation by the stretch or compression factor.In the given problem statement, the given function `f(x) = x²` is shifted 83 units to the right and 40 units upward, and the new function is `g(x) = (x - 83)² + 40`.

Therefore, g(x) = (x - 83)² + 40 is the new function after the given transformations.If the formula `y=x³` is changed by adding four (shown in red below), the new function will be `f(x) = x³ + 4`.

The addition of four in the function will cause the graph of the function to shift upward by four units.

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The answer is , new function would be: y = x³ + 4 , and The graph of the function is a shifted version of the original graph upward by 4 units.

Given f(x) = x² and after performing the following transformations:

shift upward 40 units and shift 83 units to the right, the new function

g(x) = g(x)

= (x - 83)² + 40.

If the formula y = x³ is changed by adding four (shown in red below), then the effect would be an upward shift of 4 units for the function's values.

The new function would be:

y = x³ + 4

The graph of the function would shift upward by 4 units as shown below:

Explanation:

The transformation of f(x) = x², after shifting 83 units to the right and upward 40 units can be shown below:

f(x) = x²g(x)

= (x - 83)² + 40

Note that g(x) is a parabola with vertex at (83, 40).

The transformation of y = x³ by adding four can be shown below:

y = x³ + 4

The graph of the function is a shifted version of the original graph upward by 4 units.

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Answer:

The balance after 6 years will be $10638.90

Step-by-step explanation:

in year 0, she had $7,500, and the interest is 6% (or 0.06 in decimal form) per year.

Then the amount of money in the bank can be described by the equation

M(y) = $7500*(1 + 0.06)^y

Where y is the number of years that passed. This equation says that the total amount of money increases by a factor of 1.06 each year.

We know that she can withdraw after 6 years, so we have y = 6

M(6) = $7500*(0.06)^6 = $10638.90

The balance after 6 years will be $10638.90

If this is helpful, please mark brainliest. Have a beautiful day.

$10638.9 is the answer.

The required correct answer is,

The area under P2 is 1, the area under P1 depends on the standard deviation of the dataset

i.e., Option d. is correct.

What is density curve ?

A density curve is a curve that illustrates the general shape of a data distribution. It is always above the x-axis; the area beneath it is always equal to one whole; the area beneath shows the percentage of all observations that fall in a given range. It is statistically easier to deal with a smooth curve than a histogram.

The bell-shaped density curve, which symbolizes the normal distribution, is the most well-known.

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Answer:

The numbers are 23,24, and 25 and the smallest one is 23.

=23

The marginal utility functions for the given utility function are \(U_{1} = 1 + Aaq_{1} ^{(a-1)}q_{2}^{b}\) and \(U_{2} = Abq_{1} ^{a} q_{2}^{(b-1)}+ 1\). The MRS is equal to the ratio of the marginal utilities, or MRS = U₁/U₂ = \(1 + Aaq_{1} ^{(a-1)}q_{2}^{b}\)/ \((Abq_{1}^aq_{2}^{(b-1)} + 1)\).

a) The marginal utility functions can be obtained by taking the partial derivatives of the utility function with respect to each good. For the given utility function U(q₁, q₂) = \(q_{1} + Aq_{1}^{(a)}q_{2}^{(b)} + q_{2}\) the marginal utility of good 1 (U₁) is equal to\(1 + Aaq_{1}^{(a-1)}q_{2}^{(b)}\), and the marginal utility of good 2 (U₂) is equal to \(Abq_{1}^{(a)}q_{2}^{(b-1)} + 1\).

b) The marginal rate of substitution (MRS) represents the rate at which a consumer is willing to exchange one good for another while maintaining the same level of utility. It is defined as the ratio of the marginal utilities of the two goods. In this case, the MRS can be calculated as MRS = U₁/U₂, which gives \(\frac{(1 + Aaq_{1}^{(a-1)}q_{2}^{(b)})}{(Abq_{1}^{(a)}q_{2}^{(b-1)} + 1)}\).

The explanation above summarizes the process of obtaining the marginal utility functions and the MRS for the given utility function. The utility function is differentiated with respect to each good to find the marginal utilities. The MRS is then calculated as the ratio of the marginal utilities. The specific expressions for the marginal utilities and the MRS are provided based on the given utility function.

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Answer:

See below:

Step-by-step explanation:

Hello! My name is Galaxy and I will be helping you today! I hope you are having a nice day.

So we can solve this in one single step, I'll start off with solving it.

So first we know that \(AB=DF\) and of which \(DF\) is the Hypotenuse of triangle \(DE F\).

Since the hypotenuse is equal to one of the legs of the 2nd triangle, we cannot use any rule that has Side in it as they are both not really getting us anywhere.

We do know that \(<ABC=<DE F\) as they are both 90 degrees.

As we don't have enough proof, these triangles are not congruent as we would need to do/prove rule RHS.

Cheers!

Answer:

x = -2 - sqrt(3), -2 + sqrt(3) 

Step-by-step explanation:

We can rewrite the equation as

x² + 4x + 1 = 0

Now we can use the quadratic equation.

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 1, b = 4, c = 1. Substituting these values ​​gives:

x = (-4 ± sqrt(4² - 4(1)(1))) / 2(1)

x = (-4 ± sqrt(16 - 4)) / 2

x = (-4 ± sqrt(12)) / 2

x = (-4 ± 2sqrt(3)) / 2

x = -2 ± sqrt(3)

So, from min to max, the solution is:

x = -2 - sqrt(3), -2 + sqrt(3) 

Hope this helps!

The probability that the number is in set B is 20 %.

The probability that the number is in the set A ∪ B is 30 %.

If a number is chosen at random from the universal set, the probability that the number is in set B is calculated as follows;

The total number of outcome = {1, 2, 3, 4, 5, 6, 7, 8, 9 , 10} = 10 numbers

The numbers in set B = { 3, 7}

The probability = 2/10 = 1/5 = 20%

The probability that the number is in the set A ∪ B is calculated as follows;

A ∪ B = { 2, 3, 7 }

The probability = 3/10  = 30%

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Answer:

The answer is A.

Step-by-step explanation:

X = 0

Therefore the answer is F(0)

Answer:

170

Step-by-step explanation:

Answer:

11/12

Step-by-step explanation:

The product of One-fourth times three and two-thirds will be 1 / 2.

Multiplication is the process of determining the product of two or more numbers in mathematics. A product, or an expression that specifies factors to be multiplied, is what happens when you multiply two numbers in mathematics.

Given that, the numbers are one-fourth times three and two-thirds. The product of the numbers will be calculated as,

Product =  ( 1 / 4 ) x ( 3 ) x ( 2 / 3 )

Product = 6 / 12

Product = 1 / 2

Therefore, the product of One-fourth times three and two-thirds will be 1 / 2.

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Based on the text, the primary source of primate endangerment today is habitat destruction.

Habitat destruction is considered the primary source of primate endangerment based on various factors mentioned in the text. Primates, like many other species, heavily rely on their natural habitats for survival, including food, shelter, and breeding. However, human activities such as deforestation, urbanization, and land conversion for agriculture or infrastructure development have significantly reduced and fragmented primate habitats.

Habitat destruction leads to the loss of critical resources and disrupts the ecological balance necessary for primate populations to thrive. As their habitats shrink, primates face increased competition for limited resources, reduced access to food and water sources, and decreased opportunities for successful reproduction and rearing of offspring. This loss of habitat also exposes primates to increased vulnerability to predation, disease transmission, and human-wildlife conflicts.

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a. The acceleration vector is a = (3 i + 12 j) units/s² when t = 2.

Differentiate dx/dt to get the x-component of acceleration, d²x/dt² = (d/dt)(dx/dt).

Differentiate dx/dt to get the x-component of acceleration, d²x/dt² = (d/dt)(dx/dt)d/dt(t² – t) = 2t – 1

Substitute t = 2 in the above equation to obtain the x-component of the acceleration.

d²x/dt² = 2(2) – 1 = 3i

Differentiate dy/dt to get the y-component of acceleration, d²y/dt² = (d/dt)(dy/dt)d/dt(3t² – 4) = 6t

This is the acceleration vector evaluated at t = 2. Hence,d²y/dt² = 6(2) = 12j

b. The equation of the tangent line to a curve y = f(x) at the point x = x₁ is given by y – f(x₁) = f'(x₁)(x – x₁).

Equation of the curve is given by y = y(t) and x = x(t) with y = f(x).

The slope of the tangent line is given by dy/dx = dy/dt ÷ dx/dt.

Differentiate y(t) and x(t) to get,dy/dt = 3t² – 4 and dx/dt = t² – t

Divide dy/dt by dx/dt to get the slope of the tangent line as follows: dy/dx = (dy/dt)/(dx/dt) = [3t² – 4]/[t² – t]

dy/dx = (3(2)² – 4)/[2² – 2] = 8/2 = 4

When t = 2, the object is at position (x,y) = (2,5).

x₁ = 2 and f(x₁) = y(2) = 5.

f'(x₁) = dy/dx = 4 when t = 2.

Equation of the tangent line at t = 2:y – 5 = 4(x – 2)

c. The speed of the particle at time t is given by the magnitude of the velocity vector at time t.

The velocity vector is given by v = dx/dt i + dy/dt j.

Therefore, the speed of the particle is given by v = √[dx/dt² + dy/dt²].

Substituting the given values, we getv = √[(t² – t)² + (3t² – 4)²]When t = 2,

the speed of the vector isv = √[(2² – 2)² + (3(2)² – 4)²]≈ 8.6 units/s

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Answer:

I am confused by the question no CAPPPPPP

Step-by-step explanation:

Answer:

V > -15

Step-by-step explanation:

\(\frac{V}{3} +12>7\\\\\frac{V}{3}>-5\\\\V>-15\)

Answer:

V > -15

Step-by-step explanation:

V/3 + 12 > 7

V/3 > -5

V > -15

One possible function of the form f(x) = 1/(x - 1/2) - 2/1 satisfies the conditions of having a vertical asymptote of x = 1/2 and a horizontal asymptote of y = -2.

A vertical asymptote occurs when the denominator of a fraction approaches zero, but the numerator does not, causing the function to approach infinity.

To have a vertical asymptote of x = 1/2, we need the denominator of the fraction to be equal to zero at x = 1/2. Therefore, we can write the denominator as (x - 1/2).

However, the function will not have a horizontal asymptote unless the degree of the numerator is less than or equal to the degree of the denominator.

To satisfy this condition, we can set the numerator to be a constant (i.e., degree zero). Let's call this constant k. Therefore, we can write the function as:

f(x) = k/(x - 1/2)

To find the value of k that satisfies the horizontal asymptote condition of y = -2, we can take the limit of the function as x approaches infinity or negative infinity:

lim x→∞ f(x) = lim x→-∞ f(x) = 0

This is because as x approaches infinity or negative infinity, the denominator becomes much larger than the numerator, causing the fraction to approach zero.

Therefore, we need to add a constant to the function to shift it downward by 2 units. Let's call this constant h. Therefore, the function becomes:

f(x) = k/(x - 1/2) + h

To find the value of k and h, we can use the fact that the function has a horizontal asymptote of y = -2 and substitute it into the function:

lim x→∞ f(x) = lim x→-∞ f(x) = -2

Substituting x = ∞ and x = -∞ into the function, we get:

k/(∞ - 1/2) + h = -2

k/(-∞ - 1/2) + h = -2

Since 1/∞ and 1/-∞ approach zero, we can simplify the equations to:

k/-1/2 + h = -2

k/1/2 + h = -2

Simplifying further, we get:

-k/2 + h = -2

k/2 + h = -2

Solving for k and h, we get:

k = 4

h = -2

Therefore, the function that satisfies the conditions of having a vertical asymptote of x = 1/2 and a horizontal asymptote of y = -2 is:

f(x) = 4/(x - 1/2) -2

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The dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

Let's assume that the width of the rectangle is x meters. According to the given information, the length of the rectangle is 3 meters less than double the width, which can be expressed as 2x - 3.

The area of a rectangle is given by the formula: Area = Length × Width. In this case, the area is given as 14 m². Therefore, we can write the equation:

(x)(2x - 3) = 14

Expanding the equation:

2x² - 3x = 14

Rearranging the equation to standard form:

2x² - 3x - 14 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 2, b = -3, and c = -14. Plugging in these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(2)(-14))) / (2(2))

x = (3 ± √(9 + 112)) / 4

x = (3 ± √121) / 4

x = (3 ± 11) / 4

Simplifying further:

x = (3 + 11) / 4 or x = (3 - 11) / 4

x = 14 / 4 or x = -8 / 4

x = 7/2 or x = -2

Since the width cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 7/2 meters.

Now, we can substitute the value of x into the expression for the length:

Length = 2x - 3

Length = 2(7/2) - 3

Length = 7 - 3

Length = 4 meters

Thus, the dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

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Answer: π/2

Step-by-step explanation:

3π/4 - π/4 = 2π/4

2π/4 = π/2

It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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Answer:

The answer is D

Step-by-step explanation:

To be a function, you cannot have the same x values.

If a force of 18 lb is required to hold a spring stretched 2 inches, the work done in stretching the spring from its natural length to 4 inches beyond is 72 lb*in.

To find the work done in stretching the spring from its natural length to 4 inches beyond, we need to first find the spring constant k.

Using Hooke's law, we know that F = kx, where F is the force applied, x is the displacement from the natural length, and k is the spring constant.

So, when the spring is stretched 2 inches beyond its natural length, we have:

18 lb = k * 2 in

Solving for k:

k = 9 lb/in

Now, to find the work done in stretching the spring from its natural length to 4 inches beyond, we use the equation for work:

W = (1/2)kx²

Where x is the displacement from the natural length, which in this case is 4 - 0 = 4 inches.

W = (1/2) * 9 lb/in * (4 in)²

W = 72 lb*in

So, the work done in stretching the spring from its natural length to 4 inches beyond is 72 lb*in.

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