In order for a triangle to be acute, what relationship must c2 have with a2 + b2?
group of answer choices

c2>a2+b2




c2



c2=a2+b2

To find the equation of the circle with center at (6,3) and tangent to the y-axis, we need to determine the radius of the circle.The distance from the center of the circle to the y-axis is equal to the radius of the circle. Since the circle is tangent to the y-axis, the x-coordinate of the center (6) is also the distance to the y-axis. Therefore, the radius is 6.

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

Substituting the values for the center (6,3) and the radius 6 into the equation, we have:

(x - 6)^2 + (y - 3)^2 = 6^2

Simplifying the equation gives:

(x - 6)^2 + (y - 3)^2 = 36

Therefore, the equation of the circle with center at (6,3) and tangent to the y-axis is (x - 6)^2 + (y - 3)^2 = 36.

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Explanation

For the given question, we have the formula that relates the Celsius scale to the Fahrenheit scale

This is given by

In our case, we have C= 9

so the value of F will be

Therefore, our answer is 48.2°F

To the nearest cent, the minimum cost for such a box is 337.5 dollars.

To find the minimum cost for the box, we need to minimize the total cost of the materials used for the top, bottom, and sides. Let the length, width, and height of the box be x, y, and z, respectively.

We know that the volume of the box is 17 cubic feet, so:

x * y * z = 17

We want to minimize the cost, so we need to minimize the total surface area of the box. The surface area is made up of the top, bottom, and 4 sides, so:

Surface area = 2xy + 2xz + 2yz

Substituting z = 17/xy from the volume equation, we get:

Surface area = 2xy + 34/x + 34/y

To find the minimum surface area, we need to take the partial derivatives of this equation with respect to x and y, and set them equal to zero:

d(Surface area)/dx = 2 - 34/x² = 0
d(Surface area)/dy = 2 - 34/y² = 0

Solving these equations, we get:

x = √(17/2)
y = √(17/2)

Substituting these values into the surface area equation, we get:

Surface area = 2 * √(17/2) * √(17/2) + 34/√(17/2) = 44

Now we can calculate the cost of the materials:

Top: 10 * √(17/2)² = 85 dollars
Sides: 2 * 2 * 44 = 176 dollars
Bottom: 9 * √(17/2)² = 76.5 dollars

Total cost = 85 + 176 + 76.5 = 337.5 dollars

Therefore, the minimum cost for the box is 337.5 dollars.

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The critical numbers of f(x) are x = -1 and x = 1. The function is increasing on the intervals (-∞, -1) and (1, +∞), and decreasing on the interval (-1, 1). The local maximum is at x = -1, the local minimum is at x = 1. The function is concave up on the intervals (-∞, -√3) and (√3, +∞), and concave down on the interval (-√3, √3). The inflection point is at x = 0.

(a) To find the critical numbers of f(x), we need to find the values of x where the derivative f'(x) is either zero or undefined.

First, let's find the derivative of f(x):

\(f'(x) = (x^2 + 1)^2 / (1 - x^2)\)

Setting f'(x) equal to zero:

\((x^2 + 1)^2 / (1 - x^2) = 0\)

The numerator \((x^2 + 1)^2\) can never be equal to zero since it is always positive. Therefore, there are no critical numbers of f(x) in this case.

Next, let's consider when f'(x) is undefined. This occurs when the denominator \((1 - x^2)\) equals zero:

\(1 - x^2 = 0\)

Solving for x:

\(x^2 = 1\)

x = ±1

So, the critical numbers of f(x) are x = -1 and x = 1.

(b) To determine where f(x) is increasing or decreasing, we need to analyze the sign of the derivative f'(x) in different intervals.

Considering the intervals (-∞, -1), (-1, 1), and (1, +∞):

For x < -1, f'(x) is positive since both the numerator and denominator are positive. Therefore, f(x) is increasing in the interval (-∞, -1).

For -1 < x < 1, f'(x) is negative since the numerator is positive but the denominator is negative. Therefore, f(x) is decreasing in the interval (-1, 1).

For x > 1, f'(x) is positive again since both the numerator and denominator are positive. Therefore, f(x) is increasing in the interval (1, +∞).

(c) To find the x-coordinates of local minima and local maxima, we need to examine the behavior of the derivative f'(x) around the critical numbers.

For x = -1, f'(x) is positive on the left side and negative on the right side. Therefore, there is a local maximum at x = -1.

For x = 1, f'(x) is negative on the left side and positive on the right side. Therefore, there is a local minimum at x = 1.

(d) To determine the intervals of concavity, we need to analyze the sign of the second derivative f''(x) in different intervals.

Considering the intervals (-∞, -√3), (-√3, 0), (0, √3), and (√3, +∞):

For x < -√3 and √3 < x, f''(x) is positive since both the numerator and denominator are positive. Therefore, f(x) is concave up in the intervals (-∞, -√3) and (√3, +∞).

For -√3 < x < √3, f''(x) is negative since the numerator is positive but the denominator is negative. Therefore, f(x) is concave down in the interval (-√3, √3).

(e) To find the x-coordinates of inflection points, we need to determine where the concavity changes. This occurs when the second derivative f''(x) equals zero or is undefined.

The second derivative f''(x) is undefined when the denominator 2\(x(x^2 - 3)\) equals zero:

\(2x(x^2 - 3) = 0\)

This equation is satisfied when x = 0.

Therefore, the x-coordinate of the inflection point is x = 0.

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Lindsay's cookie recipe recipe calls for 4.5 cups of flour and makes 6 dozen cookies. Lindsay has 3 cups of flour, so she will be able to make 4 dozen. If she wants to make 1 dozen cookies, she needs 3/4 cups of flour.

Arithmetic is a branch of mathematics in which we study numbers and their relations using various properties and apply them to solve examples.

The term "arithmetic" is derived from "arithmos," a Greek word for numbers. Arithmetic is one of the oldest and most fundamental mathematical principles. It is all about numbers and the basic operations (addition, subtraction, multiplication, and division) that can be performed on them.

If 4.5 cups make 6 dozen cookies

Then 1 cup makes dozen cookies = 6/4.5

                                              = 4/3

And 3 cups of flour will make dozen cookies =  3 × 4/3

                                                                           = 4

And 4 dozen cookies is made from 3 cup of flour

Then 1 dozen cookies is made by 3/4 cup of flour.

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There are 128 number of bit string of length 7.

For the data given in question-

7-character string with two possible values for each (0 or 1).

a) For strings with an average length of 7 bits:

The 7-digit string contains two possibilities for each digit.

As, a bit is a 0 or a 1.

The 7-digit number is;

N = 2×2×2.... = 2^7 = 128

Thus, there are 128 number of bit string of length 7.

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The tangent at any point on the curve x=(eᵗ)cost, y=(eᵗ)sint, z=eᵗ makes a constant angle with the Z-axis, which is equal to the arctan of the square root of 2.

To show that the tangent at any point on the curve makes a constant angle with the Z-axis, we need to show that the dot product of the tangent vector and the unit vector along the Z-axis is constant.

Let P be a point on the curve, and let t be the parameter value at P. The position vector of P is given by r(t) = (eᵗ)cost i + (eᵗ)sint j + eᵗ k.

Taking the derivative with respect to t, we get the tangent vector T(t) = ((eᵗ)cos(t) - (eᵗ)sin(t)) i + ((eᵗ)sin(t) + (eᵗ)cos(t)) j + (eᵗ) k.

The dot product of T(t) and the unit vector along the Z-axis, k/|k|, is given by:

T(t) · (k/|k|) = (eᵗ) k · (k/|k|) = eᵗ |k|/|k| = eᵗ.

Therefore, the tangent vector T(t) makes a constant angle with the Z-axis, and the angle is given by the inverse tangent of eᵗ.

Hence proved.

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The rocket will take 1.5 seconds to reach its maximum height.

Additionally, the rocket can reach a height of 39 feet.

A function of the form f(x) = ax² + bx + c is called a parabolic function.

The given parabolic function is,

h(t) = -16t²+48t+3       (1),

Initial velocity is 48 feet per second,

And initial height = 3 feet

Differentiate with respect to t,

h'(t)= -32t+48

To find time to substitute this expression to zero.

-32t+48=0

t = 1.5 seconds

For maximum height, substitute this value in equation (1).

h(t) = -16(1.5)²+48(1.5)+3

     = -36+72+3

     = 39ft

As a result, the rocket achieves its maximum height in 1.5 seconds, reaching a height of 39 feet.

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The solution to the system of equations −5y = 10 − 5x and −2y = 8 − 4x is x =2 and y = 0

What is a system of equations?

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Here, we have

Given: The solution to the system of equations −5y = 10 − 5x and −2y = 8 − 4x

From the question, we have the following parameters that can be used in our computation:

−5y = 10 − 5x and −2y = 8 − 4x

Multiply the first equation by 2 and the second by -5

So, we have

−10y = 20 − 10x and 10y = -40 + 20x

Add the equations

So, we have the following representation

0 = -20 + 10x

Evaluate the like terms

10x = 20

So, we have

x =2

Substitute x =2 in −2y = 8 − 4x

−2y = 8 − 4 × 2

Evaluate

−2y = 0

So, we have

y = 0

Hence, the solution is x =2 and y = 0

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one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.

What is eigenvalue?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

\(A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\\)

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

\(A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right]\)

and by taking the determinant:\(\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}\)

and the roots of this polynomial is:

\(\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}\)

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

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Complete Quetion

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.

Answer:

x=the total amount of money the manager had in the beginning

y represents the total amount of the money at the end and x represents the total amount of money at the beginning.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

A store manager begins each shift with the same total amount of money.

She keeps $200 in a safe and distributes the rest equally to the 5 cashiers in the store.

This situation can be represented by the function y = (x − 200)5.

y represents the total amount of money at the end and x represents the total amount of money at the beginning.

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The shape of the distribution of water bills can be described as skewed right.

Here's a step-by-step explanation:
1. Analyze the histogram: 100-125 (1), 125-150 (2), 150-175 (5), 175-200 (10), 200-225 (13), 225-250 (8).
2. Observe that the frequency increases as the monthly water bill increases, reaching a peak at the 200-225 range.
3. Notice that after the peak, the frequency decreases as the monthly water bill increases further (from 225-250).
4. Based on this pattern, we can conclude that the distribution is not uniform (equal frequency across all ranges) or roughly symmetric (equal frequency on both sides of a central point).
5. Since the frequency increases as we move to the right and then decreases, the shape of the distribution is skewed right.

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Answer:

25 gallons

Step-by-step explanation:

The equation to plot in the complex Cartesian plane is 2Re(z) - |z²| ≥ -3Im(iz).

To plot the equation 2Re(z) - |z²| ≥ -3Im(iz) graphically, you can follow these steps:

1. Represent the complex number z in terms of its real and imaginary parts, z = x + yi, where x is the real part and y is the imaginary part.

2. Substitute the values of x and y into the equation and simplify it.

3. Separate the equation into real and imaginary parts.

4. For each part, plot the corresponding inequality on the Cartesian plane.

- For the real part, plot the inequality 2x - |(x + yi)²| ≥ -3y.

- For the imaginary part, plot the inequality 0 ≥ 0 (as -3Im(iz) = 0 for all values of x and y).

5. Determine the common region that satisfies both inequalities. This region represents the solution to the original equation.

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Answer:

148

Step-by-step explanation:

148

Answer:

w= -11

Step-by-step explanation:

1. Subtract 2.8 from the right side and add it to the left side. Now you have 2+6.6=1.4.

2. Subtract 2 from the left side and add it to the right side. Now you have 6.6= -.6

3. Divide both sides by -.6. You will get -11=w

Answer:

Q=-8

Step-by-step explanation:

Q-2-6

Answer:

x = -27

Step-by-step explanation:

x(x+3)=2(x+15)

x+3=2x+30

x+3-2x+30

x-2x=30-3

-x=30-3

-x=27

x = -27

Answer:

The product of two numbers is 0 - hypotheses

At least one of the numbers must be 0 -conclusion

Step-by-step explanation:

The statement given in the question is a conditional statement because of the if and then factors attached to it. From this conditional statement, a hypothesis and conclusion can be derived. A hypothetical statement unlike a conclusive statement does not have a tone of finality to it. A hypothetical statement is subject to tests to prove its trueness after which a conclusion can be made.

It is indeed true that one of the numbers must be zero if the product of two numbers is zero.

Example: a * 0 =0

110 * 0 = 0

Answer:

9) 28/36 = 7/9

10) Total animals = 84

36/84= 3/7

The logarithmic form is written as logₐ(X)=b. It is a rearrangement of the exponential form, aᵇ=X.

What is Logarithmic Form?

The logarithmic form is written as logₐ(X)=b. It is generally the rearrangement of the exponential form, aᵇ=X. Any exponential equation can be written as a logarithm. The logarithmic form is mostly used to calculate an exponent of an equation. The logₐ(X)=b. is read as “log base a of X equals b“.

The logarithmic form is simply a rearrangement of an equation written in exponential form. The same numbers are used but they are written in a different order. The word log is written which implies that the logarithm function is being used.

Therefore, If the logarithmic form is logₐ(X)=b. then it is a rearranged as the exponential form as aᵇ=X.

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The volume of the solid generated when the trapezoid is rotated about side DA is approximately 1586.6 cubic units (rounded to the nearest tenth).

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

Given:

DC = 7

DA = 6

DE = 6

AB = 14

Height of the trapezoid:

ED = (DC/AB) * EA = (7/14) * EA = 0.5 * EA

Height = EA - ED = EA - 0.5 * EA = 0.5 * EA

Circumference of the cylindrical shell:

Circumference = 2 * π * AB = 2 * π * 14

Thickness of the cylindrical shell:

Since the trapezoid is being rotated about side DA, the thickness (Δx) will vary along DA. We'll integrate with respect to x from 0 to 6 (the length of DA).

Volume of the solid generated:

Volume = ∫(0 to 6) [2 * π * 14 * 0.5 * EA * Δx]

Substituting EA = DE + DA = 6 + 6 = 12Volume = ∫(0 to 6) [2 * π * 14 * 0.5 * 12 * Δx]

Integrating:

Volume = 2 * π * 14 * 0.5 * 12 * [x] from 0 to 6

Volume = 2 * π * 14 * 0.5 * 12 * (6 - 0)

Volume = 504 * π

Approximating to the nearest tenth:

Volume ≈ 504 * 3.14 ≈ 1586.6 cubic units (rounded to the nearest tenth)

Therefore, the volume of the solid generated when the trapezoid is rotated about side DA is approximately 1586.6 cubic units (rounded to the nearest tenth).

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The error in the proportion is the second line should be 2x + 18 = 3x making the final answer 18 = x

The error in the solution of the proportion shown can be calculated as follows:

Therefore, let's solve the equation to know the error made.

2 / 3 = x / x + 9

cross multiply

2(x + 9) = 3x

open the brackets

2x + 18 = 3x

subtract 2x from both sides of the equation

2x + 18 = 3x

2x - 2x + 18 = 3x - 2x

x = 18

Therefore, he made mistake in the second line, it should be  2x + 18 = 3x making the final answer 18 = x

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Answer:

lol im guessing b?

Step-by-step explanation:

tell me if i got it wrong if so ill try to fix my answer

Answer:

216.32 cm²

Step-by-step explanation:

Given that the scale factor is 5.2 then the area scale is

(5.2)² , thus

area of B = area of A × (5.2)² = 8 × (5.2)² = 216.32 cm²

The profit margins (return on sales) for each division are approximately :Division A = 10.85%,Division B = 9.11% and The calculations for the year would be:Net Income = $85,428,Return on Assets = 18.9%.

To compute the profit margins (return on sales) for each division, we divide the profit by the sales and multiply by 100 to express the result as a percentage.

For Division A:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($230,000 / $2,120,000) * 100

Profit Margin ≈ 10.85%

For Division B:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($34,700 / $381,000) * 100

Profit Margin ≈ 9.11%

To calculate the net income and return on assets for Polly Esther Dress Shops Inc., we use the given information.

Net Income = Profit Margin * Sales

Net Income = 7% * $1,220,400

Net Income = $85,428

Return on Assets = Profit Margin * Asset Turnover

Return on Assets = 7% * 2.7

Return on Assets = 18.9%

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If z is a standard normal random variable , then the value of z for which P(Z≤z)=0.2580 is -0.65 .

A standard normal random variable is a continuous random variable that follows a normal distribution with a mean of 0 and a standard deviation of 1.

We can use a standard normal distribution table to find the value of z for which P(Z ≤ z) = 0.2580.

By using the standard normal distribution table, we can find the value that is closest to 0.2580, which is 0.2580 itself, and locate the corresponding z-value in the table,

Which is approximately z = -0.649523 ,

⇒ z ≈ -0.65 .

Therefore , the required value of z is -0.65 .

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The given question is incomplete , the complete question is

Given that z is a standard normal random variable, the value z for which P(Z≤z)=0.2580 is

Using cross-multiplication we know that the team played 20 total matches.

One might cross-multiply an equation between two fractions or rational expressions in mathematics, more specifically in elementary arithmetic and elementary algebra, to make the equation simpler or to find the value of a variable.

To cross multiply them, simply multiply the denominator of the first fraction by the numerator of the second, then record the result.

You next multiply the number in the denominator of your first fraction by the numerator of the second fraction, and you record the result.

So, now we know that:

17 wins are 85% of the match.

Let the remaining matches be x and the percentage would be:

100 - 85 = 15%

Now, write as follows:

17/85 = x/15

Perform cross-multiplication:

17/85 = x/15

85x = 17*15

x = 17*15/85

x = 255/85

x = 3

Then, the rest 15% of matches were 3 matches.

Total matches would be: 17 + 3 = 20

Therefore, using cross-multiplication we know that the team played 20 total matches.

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Answer:don’t worry u not dum and also im sorry that’s not a function.

Step-by-step explanation:

Give me brainliest!