in parallelogram ABCD, AB= x, BC= x+y, CD= y-x and AD= 15. solve for x and y

For the first graph

A = (-5, 2)

B = (5, -4)

To calculate the slope we will use the following formula

The answer would be m = -3/5

For the second graph

A = (-1, -1)

B = (3, 0)

To calculate the slope we will use the following formula

The answer would be m = 1/4

For the third graph

In the third graph, we have a vertical slope at point x = 2

In this case the slope would be equal to infinity and the equation of the line would be equal to x = 2

Answer:

24

Step-by-step explanation:

a circle is 360

we can divide 360 by 15

360 divided by 15 =

24

Verifying that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c = 2  such that f'(c) = 0.

Given:

Consider the function f(x) = x2 - 4x + 8 on the interval 0, 4. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0.

f(x)=x^2−4x+8, [0,4]

when, x = 0

f(x) = x^2 -4x +8

f(0) = y = 0 - 0 + 8 = 8

when, x=4

f(5) = y = 16 - 16+8 =

thus, we have 2 points (0, 8) ; (4, 8)

slope,m = {8-(8)} / {4-0} = 0

hence, we have to calculate all the points,x where 0<x<8 and slope=0

f '(x) = 2x - 4 = 0

or, f '(c) = 2c - 4 = 0

c = 4/2 =2 ( 0<x<4)

hence, the there is only one solution c=2 which satisfies Rolle's theorem.

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Answer: (x+2)(x−7)

Step-by-step explanation: I'm built different

Answer:

(x-7)(x+2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

We have $3, we need more money $x, so that the sum will be $12 or more

                3                      +                    x                                        ≥12

the inequality is 3+x ≥ 12

solve for x

3+x ≥ 12, subtract 3 from both sides of the equation

3-3+x ≥1 2-3

x ≥ 9, we need $9 or more to purchase a ticket

The time series component that exhibits a repeating pattern over successive periods, often one-year intervals, is called the seasonal component. It represents the regular and predictable variations in the data that occur due to seasonal factors, such as weather patterns, holidays, or annual events.

The seasonal component typically follows a consistent pattern, where the values tend to rise and fall in a similar manner within each season. For example, retail sales may experience higher values during the holiday season each year and lower values during other times.

Identifying and analyzing the seasonal component is crucial in many fields, including economics, finance, marketing, and forecasting. By understanding and accounting for the seasonal patterns, analysts and decision-makers can make more accurate predictions, adjust for seasonality in data, and develop strategies to optimize operations or sales during specific periods.

Methods such as seasonal decomposition or seasonal adjustment techniques are used to separate the seasonal component from other components, such as trend and irregular fluctuations, in order to better understand the underlying patterns and make informed decisions based on the data.

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Answer:

is it -8r

Step-by-step explanation:

L(t) = (2/3)t + 3, (-1/2)t + 4, t + 2.

The curve of intersection of the cylinders x² + y² = 25 and y² + z² = 20 can be found by setting the two equations equal to each other:

x² + y² = y² + z² = 20

The intersection of the two cylinders is a circle.

To determine the radius of this circle, we use either of the two equations and solve for one variable in terms of the other two:

y² + z² = 20y²

= 20 - z²y

= ±sqrt(20 - z²)

If we substitute this expression for y into the equation x² + y² = 25, we can solve for x in terms of z:

x² + (20 - z²)

= 25x²

= 5 + z²x

= ±sqrt(5 + z²)

Thus, the curve of intersection can be expressed parametrically as follows:

r(t) = (x(t), y(t), z(t)) = (sqrt(5 + t²), sqrt(20 - t²), t)for -2sqrt(5) ≤ t ≤ 2sqrt(5)

At the point (3, 4, 2), t = 2.

To find the tangent vector to the curve at this point, we take the derivative of the position vector:

r'(t) = (x'(t), y'(t), z'(t)) = (t/sqrt(5 + t²), -t/sqrt(20 - t²), 1)

at t = 2:r'(2) = (2/sqrt(9), -2/sqrt(16), 1) = (2/3, -1/2, 1)

Finally, we obtain the vector equation of the tangent line by using the point-normal form of the equation of a line:

L(t) = r(2) + t r'(2)L(t)

     = (3, 4, 2) + t (2/3, -1/2, 1)L(t)

     = (2/3)t + 3, (-1/2)t + 4, t + 2

Therefore, a vector equation for the tangent line to the curve of intersection of the cylinders x² + y² = 25 and y² + z² = 20 at the point (3, 4, 2) is:

L(t) = (2/3)t + 3, (-1/2)t + 4, t + 2.

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1230\\ r=rate\to 3.19\%\to \frac{3.19}{100}\dotfill &0.0319\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 1230[1+(0.0319)(3)] \implies \stackrel{balance}{\boxed{A \approx 1347.71}}~\hfill \underset{interest}{\stackrel{1347.71~~ - ~~1230}{\boxed{117.71}}}\)

To identify the slope and y-intercep of a line, you need to write the equation in slope intercpet form:

m is the slope

b is the y-intercept (the value of y when the line cross the y-axis)

To write the equation in slope-intercept form, leave the variable y in one side of the equation.

-Substract 7x in both sides of the equation:

-Divide both sides of the equation into 2:

The solution to the initial value problem is x = (t - 1) ln(t) - 1 + ln(t) + 8\(e^{(-t)\).

To solve the initial value problem given by the differential equation dx/dt + x = t ln(t) and the initial condition x(1) = 8, we can use an integrating factor.

Rewrite the equation in the standard form for a first-order linear differential equation:

dx/dt + x = t ln(t)

Identify the integrating factor. The integrating factor is given by the exponential of the integral of the coefficient of x. In this case, the coefficient of x is 1, so the integrating factor is \(e^t\).

Multiply the entire equation by the integrating factor \(e^t\):

\(e^t\) dx/dt + \(e^t\)x = t ln(t) \(e^t\)

Notice that the left side is now the derivative of the product \(e^t\) x with respect to t:

d/dt (\(e^t\)x) = t ln(t) \(e^t\)

Integrate both sides with respect to t:

∫ d/dt (\(e^t\) x) dt = ∫ t ln(t) \(e^t\) dt

Apply the fundamental theorem of calculus to the left side and integrate the right side by parts:

\(e^t\) x = ∫ t ln(t) \(e^t\) dt

Solve the integral on the right side using integration by parts. Let u = ln(t) and dv = t \(e^t\) dt. Then, du = (1/t) dt and v = \(e^t\) (t - 1). Applying integration by parts, we have:

∫ t ln(t) \(e^t\) dt = \(e^t\) (t - 1) ln(t) - ∫ \(e^t\) (t - 1) (1/t) dt

Simplify and solve the remaining integral:

∫\(e^t\) (t - 1) (1/t) dt = ∫ \(e^t\) (1 - 1/t) dt

= ∫ \(e^t\) dt - ∫ \(e^t\)/t dt

= \(e^t\) - ln(t)\(e^t\) + C

Substituting the result of the integral back into the equation, we have:

\(e^t\) x = \(e^t\) (t - 1) ln(t) - \(e^t\) + ln(t) \(e^t\) + C

Simplify the equation:

x = (t - 1) ln(t) - 1 + ln(t) + C\(e^{(-t)\)

Apply the initial condition x(1) = 8 to find the value of the constant C:

8 = (1 - 1) ln(1) - 1 + ln(1) + C\(e^{(-1)\)

8 = C * \(e^(-1)\)

Solving for C:

C = 8 * e

Substitute the value of C back into the equation:

x = (t - 1) ln(t) - 1 + ln(t) + 8\(e^{(-t)\)

Therefore, the solution to the initial value problem is x = (t - 1) ln(t) - 1 + ln(t) + 8\(e^{(-t)\).

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Answer:

pi is irrational

if I remember correctly it's irrational

The number of cups of vinegar that Mike used lies between the whole numbers 2 and 4

If Mike used one cup of vinegar for each salad dressing recipe, then he used a total of 3 cups of vinegar (1 cup x 3 recipes = 3 cups).

However, the question states that he used "a cup of vinegar" in each recipe, which could mean that he used slightly less than one cup, exactly one cup, or slightly more than one cup.

Assuming that Mike used at least 3/4 cup of vinegar in each recipe (which is still close to "a cup"), then he used a minimum of 2 and 1/4 cups of vinegar in total (3/4 cup x 3 recipes = 2 and 1/4 cups).

Assuming that Mike used at most 1 and 1/4 cups of vinegar in each recipe (which is still close to "a cup"), then he used a maximum of 3 and 3/4 cups of vinegar in total (1 and 1/4 cups x 3 recipes = 3 and 3/4 cups).

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If someone wants the product of two line segments to be represented as another line segment, they can make use of similar triangles

The correlation between the lengths of line segments can be established by creating a geometric shape comprising of two triangles that are identical and share one side.

If the legs of the triangles are used to represent the two line segments and their shared side represents the resulting line segment, it is possible for the lengths to be proportional through the similarity of the triangles.

To represent the product of the two original line segments, it is necessary to ensure that they and the resulting line segment are a collection of similar triangles. This is because the length of the resulting line segment can represent the product of the initial segments.

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It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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ok for what i got is 3468750

I don't know how I got it but I think you need to multiply the area

please forgive me if I am wrong.

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

Answer:

4. 5.6 5. 7/8

Step-by-step explanation:

Answer:

C 60 inches

Step-by-step -

60 x 2 = 120, which is both lengths, and since he width is half the length, then 30 x 2 = 60. So 130 (length) + 60 (width) = 180. So 60 inches would be the maximum length for both sides.

Answer:

C

Step-by-step explanation:

I just took the unit test

A) The exponential function that models the mass show many grams remain from a 480-gram sample after t minutes is G(t) = 22(1/2)^(t/5.5)

B) The grams that remain after 2 hours is 51.42 grams.

A substance's half-life is the amount of time needed for half of a radioactive substance to decay. It is a word that is used in nuclear chemistry to describe how quickly unstable atoms undergo radioactive decay into other nuclear species by emitting particles or the amount of time needed for the rate of disintegrations per second of radioactive material in order to reduce by half of its initial value.

Given:

The half-life of goo is 22 minutes/4 = 33.75 minutes

b) A formula for the amount remaining could be ...

G(t) = 22(1/2)^(t/5.5)

c) After 2 hours, the amount remaining is ...

G(120) = 135(1/2)^(47/33.75) ≈ 51.42 . . . grams

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A). After t minutes, the exponential function used to describe the mass remaining from a 480-gram sample is \(G(t) = 22(\frac{1}{2} )^{(t/5.5)}\)

B). 51.42 grammes are still there after two hours.

The amount of time required for a radioactive substance to decay by half is known as its half-life. It is a term used in nuclear chemistry to describe how quickly unstable atoms transform into different nuclear species by emitting particles or how long it takes for the rate of radioactive material's disintegrations per second to fall by half of its initial value.

Given:

The half-life of goo is 22 minutes/4 = 33.75 minutes

b) The amount left could be calculated using the method...

\(G(t) = 22(\frac{1}{2} )^{(t/5.5)}\)

c) The amount left after two hours is...

\(G(120)=135(\frac{1}{2} )^{(\frac{47}{33.5} )}\) ≈ 51.42 . . . grams

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The shortest horizontal shift of a sine curve that will turn it into a cosine curve is a shift of 90°( π/2 radians).

The function y = sin x defines a sine wave as a geometric waveform that oscillates (moves up, down, or side to side) frequently. It is an s-shaped, smooth wave that oscillates above and below zero, to put it another way.

Technical analysis and trading both employ sine waves to assist spot oscillator-related patterns and cross-overs.

Similar to the sine graph, the cosine graph is an up-down graph. The sine graph and cos graph are identical except that the sine graph begins at 0, whereas the cos graph begins at 90° (or π/2). The cosine (cos) graph shown below starts at 1 and drops to -1 before rising once again.

Thus, the shortest horizontal shift of a sine curve that will turn it into a cosine curve is a shift of 90°( or π/2 radians).

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Answer:

D

Step-by-step explanation:

Because the line would be solid, since y is greater than or equal to, and the shaded region would be above, since y is greater than.

Answer:

D

Step-by-step explanation:

The line is solid, because y is greater  than or equal to. So that means it's B or D. The shaded region would be in the upper quadrant, because y is greater than. :)

Answer:

T would represent touchdowns, E or P would represent extra points, and F or FG would represent fiels goals.

Step-by-step explanation:

Hope this helps :)

T would represent touchdowns, E or P would represent extra points, and F or FG would represent field goals.

240 gallons of a 50% antifreeze solution must be mixed with 80 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

Let's call the amount of 50% antifreeze solution that we want to mix with the 80 gallons of 10% antifreeze "x".

The total volume of the mixture after mixing x gallons of 50% antifreeze solution with 80 gallons of 10% antifreeze solution is given by (x + 80) gallons.

The concentration of antifreeze in the mixture is given by the weighted average of the antifreeze concentrations in the two solutions, where the weight for each solution is proportional to its volume:

(0.5x) + (0.1 * 80) = (0.4 * (x + 80))

Expanding and solving for x, we get:

0.5x + 8 = 0.4x + 32

0.1x = 24

x = 240

Therefore, we need to mix 240 gallons of 50% antifreeze solution with 80 gallons of 10% antifreeze solution to get a mixture that is 40% antifreeze.

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Answer:

d. All of the above are true

Step-by-step explanation:

All of the following statements,

a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1.

b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative.

C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant.

are true

The total length of a boundary defines the perimeter of an equilateral triangle.

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Answer:

The equation for scenario is 2(l + b) = 3a

The rectangle’s perimeter is 2(l + b)

The equilateral triangle’s perimeter is 3a

What is perimeter ?

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

According to question

The perimeters of a rectangle and an equilateral triangle are equal.

So

let,

The length and breadth of the rectangle are l & b

And

Side of an equilateral triangle is a

Now

The rectangle’s perimeter = 2(length + breadth)

⇒ 2(l + b)

And

The equilateral triangle’s perimeter = Sum of All sides

⇒ a + a + a

⇒ 3a

Therefore

    perimeters of a rectangle = perimeters an equilateral triangle

              2(l + b) = 3a

hence, 2(l + b) = 3a is the equation which show that perimeter of rectangle and equilateral triangle is equal.

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Answer:

Step-by-step explanation:

They are different numbers:

0.269 + 50.9 = 51.169

0.26 + 50.9 = 51.16