Determine the two equations necessary to graph the hyperbola with a graphing calculator, y2-25x2 = 25 OA. y=5+ Vx? and y= 5-VR? ОВ. y y=5\x2 + 1 and y= -5/X2+1 OC. and -y=-5-? D. y = 5x + 5 and y= -

a) By strong induction, any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

b) By strong induction, any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

c) By strong induction, any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

a. Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

Base case: For postage worth 8 cents, we can use two 4-cent stamps, which can be made using a combination of one 3-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 8, can be made from 3-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 8, we can use the induction hypothesis to make k cents using 3-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with a 5-cent stamp to get the same value. If the last stamp we added was a 5-cent stamp, we can replace it with two 3-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3-cent or 5-cent stamps.

b. Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

Base case: For postage worth 24 cents, we can use three 8-cent stamps, which can be made using a combination of one 7-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 24, can be made from 7-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 24, we can use the induction hypothesis to make k cents using 7-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 5-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with three 5-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 7-cent or 5-cent stamps.

c. Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

Base case: For postage worth 12 cents, we can use one 3-cent stamp and three 3-cent stamps, which can be made using a combination of two 7-cent stamps.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 12, can be made from 3-cent or 7-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 12, we can use the induction hypothesis to make k cents using 3-cent or 7-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with one 3-cent stamp and two 7-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3

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The density of glycerin at 60°C is approximately 19.9592 g/cm³.

To find the density of glycerin at 60°C, we can use the volume expansion coefficient and the given density at 20°C.

The formula for volume expansion is:

ΔV = β * V₀ * ΔT

where:

ΔV is the change in volume,

β is the volume expansion coefficient,

V₀ is the initial volume, and

ΔT is the change in temperature.

In this case, we want to find the change in density, so we can rewrite the formula as:

Δρ = -β * ρ₀ * ΔT

where:

Δρ is the change in density,

β is the volume expansion coefficient,

ρ₀ is the initial density, and

ΔT is the change in temperature.

Given:

ρ₀ = 20 g/cm³ (density at 20°C)

β = 5.1 x 10⁻⁴ °C⁻¹ (volume expansion coefficient)

ΔT = 60°C - 20°C = 40°C (change in temperature)

Substituting the values into the formula, we have:

Δρ = - (5.1 x 10⁻⁴ °C⁻¹) * (20 g/cm³) * (40°C)

Calculating the expression:

Δρ = - (5.1 x 10⁻⁴) * (20) * (40) g/cm³

≈ - 0.0408 g/cm³

To find the density at 60°C, we add the change in density to the initial density:

ρ = ρ₀ + Δρ

= 20 g/cm³ + (-0.0408 g/cm³)

≈ 19.9592 g/cm³

Therefore, the density of glycerin at 60°C is approximately 19.9592 g/cm³.

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The answer is:

\(\large\textbf{They aren't equivalent.}}\)

In-depth explanation:

To determine the answer to this problem, we will use one of the exponent properties:

\(\sf{x^{-m}=\dfrac{1}{x^m}}\)

And

\(\sf{\dfrac{1}{x^{-m}}=x^m}\)

Now we apply this to the problem.

What is 4⁻³ equal to? Well according to the property, it's equal to:

\(\sf{4^{-3}=\dfrac{1}{4^3}}\)

And this question asks us if 4⁻³ is the same as 1/4⁻3.

Well according to the calculations performed above, they're not equivalent.

Answer:

B!

Step-by-step explanation:

you have to simply the 2/6 to 1/3

Answer:

7/12

Step-by-step explanation

Write all numerators above the LCD (least common denominator) 12

Answer: B,C,D

21

Step-by-step explanation:

(21-21)+(21-21)+21 = 0+0+21 = 21

Answer:

A = 0; B = -9/2

Step-by-step explanation:

To have no solutions, you need parallel lines with equal slopes and different y-intercepts.

3x + 4y = A      Eq. 1

Bx - 6y = 15     Eq. 2

In Eq. 1, notice that the coefficient of x is 3/4 of the coefficient of y.

We must have the same ratio for the coefficients in Eq. 2.

B/(-6) = 3/4

4B = -6(3)

4B = -18

B = -9/2

Now we have

3x + 4y = A      Eq. 1

-9/2 x - 6y = 15     Eq. 2

How do we change the left side of the second equation into the left side of the first equation? -6/4 = -3/2 and also -9/2 ÷ 3 = -3/2

To change the left side of the second equation into the left side of the first equation, divide the left side by -3/2.

If we divide 15 by -3/2 we get -10.

The equation -9/2 x - 6y = -10 is the same as Eq. 1, so that would create a system of equations with only one equation and an infinite number of answers.

To have no equations, the y-intercepts must be different, so A can be any number other that -10.

Answer: A = 0; B = -9/2

Answer:

Hi! Based on your question, you would like to know the best measure of center to represent the data in a dot plot. Here are the options to consider:

1. Mode
2. Mean
3. Range
4. Median
5. Interquartile Range

However, without an actual dot plot to analyze, I am unable to provide specific advice on which measure(s) of center would be best for representing the data. If you can provide a dot plot or specific data points, I will gladly help you determine the best measure(s) of center for your data.

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The options that describe the best measure of center to represent the data in the dot plot are Mode and Median.

Based on the information provided, the best measure of center to represent the data in the dot plot would be:

Mode: The mode represents the value(s) that appear most frequently in the data and can be a good measure of center when there are clear peaks or modes in the distribution.

Median: The median represents the middle value in a dataset when it is arranged in ascending or descending order. It is a robust measure of center that is not affected by extreme values or outliers.

Both the mode and median are suitable measures of center for representing the data in a dot plot. However, the dot plot alone does not provide information about the mean, range, or interquartile range.

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Answer:

y = 2x + b

I dont know what b is but the slope is 2 I think

Answer:

The factored form is,

\((4a^2+2a+1)(4a^2-2a-1)\)

Step-by-step explanation:

We have,

\(16a^4-4a^2-4a-1\\factoring,\\We\ can \ write \ 16a^4 \ as \ (4a^2)^2\\Also,\\then we have,\\(4a^2)^2-(4a^2+4a+1)\\Now, 4a^2 + 4a + 1 \ is \ a \ perfect \ square,\\4a^2 + 4a + 1 = (2a)^2 + 2(2a) + 1\\= (2a + 1)^2\\so, we \ have,\\(4a^2)^2 - (2a + 1)^2\\\)

Using the difference of square formula,

\(x^2 - y^2 = (x+y)(x-y)\\with,\\x = 4a^2,\\y = 2a+1,\\we \ get,\\(4a^2+2a+1)(4a^2-2a-1)\)

Which is the factored form,

Answer:

D.

Step-by-step explanation:

205.296/3.12 = 65.8

Answer:

:D

Step-by-step explanation:

The possible values of two consecutive even integers, of which the sum of their squares is 1684, are 28 and 30 for positive integers, while for negative integers, they are  -28 and -30.

The difference between two consecutive even integers is 2.

Let the integers be a and (a+2). Then,

a² + (a + 2)² = 1684

a² + a² + 4a + 4 = 1684

2a² + 4a - 1680 = 0

a² + 2a -840 = 0

Hence, we get a quadratic equation.

There are three methods of solving a quadratic equations: by factoring, completing the square, and by using the abc formula.

Use the factoring method:

a² + 2a -840 = (a - 28) (a + 30)

a = 28  and a = -30

Hence, if the integers are positive, they are: 28 and 30.

If the integers are negative, they are -28 and -30.

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Step-by-step explanation:

x² = 36/121

move terms to left side

x² - 36/121 = 0

1/121 (121x² - 36) = 0

121x² - 36 = 0

Use quadratic formula

x= -b + √b² - 4ac / 2a

a = 121

b= 0

c= 36

x = -0 + √0² - 4.121 (-36) / 2.121

x = + 132/ 242

sperate the equation

x = 131/242

x = -131/242

x = 6/11

x= -6/11

it's essential to use Leibniz notation when using separation of variables to solve differential equations.

When using separation of variables to solve a differential equation, we begin by separating the variables, typically denoted as y and x. This involves isolating all y terms on one side of the equation and all x terms on the other side.

At this point, we have an equation of the form f(y)dy = g(x)dx, where f(y) and g(x) are some functions of y and x, respectively. To solve for y, we integrate both sides of the equation with respect to their respective variables. However, it's important to use Leibniz notation (i.e., dy and dx) to keep track of which variable we are integrating with respect to.

Specifically, we write ∫ f(y)dy = ∫ g(x)dx, which means that we integrate f(y) with respect to y and g(x) with respect to x. If we were to use prime notation instead (i.e., y' and x'), it would be unclear which variable we were integrating with respect to, since both y' and x' represent derivatives.

After integrating both sides, we obtain an equation in terms of y and x that we can use to solve for y. This is why it's essential to use Leibniz notation when using separation of variables to solve differential equations.

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The slope of the line on this graph is equal to 1/4.

In Mathematics, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (50 - 30)/(90 - 10)

Slope (m) = 20/80

Slope (m) = 1/4.

In this context, we can reasonably infer and logically deduce that the slope of the line on this graph is equal to 0.25 or 1/4.

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The probability of getting a number less than 5 or greater than 9 is:

P = 0.583

The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes.

The numbers that are less than 5 or greater than 9 are:

{1, 2, 3, 4, 10, 11, 12}

So 7 out of the total of 12 outcomes make the event true, then the probability we want to get is the quotient between these numbers:

P = 7/12 = 0.583

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Answer:

Two shapes are congruent if there length and size or breadth are same

The maximum volume of the rectangular box is 975,000 cubic cm, and the minimum volume is 405,000 cubic cm.

Let's solve the problem step by step. We are given that the surface area of the rectangular box is 9000 square cm and the sum of the lengths of all edges is 520 cm. We need to find the maximum and minimum volumes of the box.

To find the maximum volume, we need to consider the case where the box is a cube. In a cube, all sides have equal lengths. Let's assume the length of each side is 'a'.

The surface area of a cube is given by 6a^2, and in this case, it is equal to 9000 square cm. So we have:

\(6a^2 = 9000\)

Dividing both sides by 6, we get:

\(a^2 = 1500\)

Taking the square root of both sides, we find:

\(a = \sqrt{1500} \\= 38.73 cm\)

The sum of the lengths of all edges of a cube is given by 12a, so we have:

12a = 12 * 38.73

= 464.76 cm

The maximum volume of the cube-shaped box is:

\(a^3 = 38.73^3\)

= 975,000 cubic cm.

To find the minimum volume, we need to consider the case where the box is not a cube. In this case, let's assume the lengths of the sides are 'x', 'y', and 'z'. We know that the sum of the lengths of all edges is 520 cm, so we have:

4(x + y + z) = 520

Dividing both sides by 4, we get:

x + y + z = 130

We need to maximize the volume of the box, which occurs when the sides are as unequal as possible.

In this case, let's assume x = y and z = 2x. Substituting these values into the equation above, we have:

2x + 2x + 2(2x) = 130

Simplifying, we get:

6x = 130

x = 21.67 cm

Substituting the values of x and z back into the equation, we find:

y = 21.67 cm and z = 43.33 cm

The minimum volume of the rectangular box is:

x * y * z = 21.67 * 21.67 * 43.33

= 405,000 cubic cm.

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(100, 600)

1/6 or 100/600 is the slope. You can find the Y intercept where X = 0, so the Y intercept would be 0. The equation would be Y = 1/6 + 0

Answer:

2x² - xy - 15y²

Step-by-step explanation:

(2x + 5y)(x - 3y)

Each term in the second factor is multiplied by each term in the first factor, that is

2x(x - 3y) + 5y(x - 3y) ← distribute parenthesis

= 2x² - 6xy + 5xy - 15y² ← collect like terms

= 2x² - xy - 15y²

Sophia did Calculus test better ompared to the rest of her class, as her z-score for Statistics  was lower than her z-score for Calculus

We know that the formula for the z-score is: \(z=\frac{x-\mu}{\sigma}\)

where x is the observed value

μ is the mean of the sample

σ is the standard deviation of the sample

Sophia got a 95% on her statistics. The grades had a mean of 87%, with a standard deviation of 7%

So, her z-score for statistics would be:

\(z_s=\frac{95-87}{7}\\\\z_s=1.14\)

She got a 91% on her calculus mid-term. The grades had a mean of 85%, with a standard deviation of 47%

So, her z-score for statistics would be:

\(z_c=\frac{91-85}{4}\\\\z_c=1.5\)

Since her z-score for Statistics  was lower than her z-score for Calculus,  she did Calculus test better.

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Answer:

3c +11 .........................

Answer:

A histogram would be the most appropriate graph to display the distribution of scores and identify clusters and gaps.

Step-by-step explanation:

Answer:

y = 29

Step-by-step explanation:

y = (3x)2 + 17

y = (3(2))2 + 17

y = (6)2 + 17

y = 12 + 17

y = 29

Answer:

5

Step-by-step explanation:

The ones place is the one most to the right that isn't after a decimal point.

Answer:

5, since it is all the way to the right

Step-by-step explanation:

if you ever have a big number, the number in thes ones place is ALWAYS on the far right, except if its a decimal !

i hope this helps !! :D

Answer:

A)  y = 2x

Step-by-step explanation:

Answer

search how they got the answer

Step-by-step explanation:

#look pic for detailed info

180° - 125° = 55°

180° - 115° = 65°

180° - 55° - 65° = 60°

180° - 60° = 120°

180° - 120° = 60°

Answer:

x = 120°

Step-by-step explanation:

you can draw a perpendicular base betweeen the two parallel segments and form a pentagon, which has 540 degrees inside.

the two base angles will each be 90°, and we have known values for the other two.

as far as 'x', that angle is vertical to the top angle of the pentagon so we add up all the known values and solve for 'x':

90 + 90 + 125 + 115 + x = 540

180 + 240 + x = 540

x = 540 - (180 + 240)

x = 540 - 420

x = 120

Answer:

40 coats don't have hoods