Find the exact length of the curve.x = 5 cos(t) − cos(5t), y = 5 sin(t) − sin(5t), 0 ≤ t ≤

The scale factor can alter an object's size, either making it bigger or smaller.

By multiplying the x and y coordinates of the original figure by the scale factor, you may locate locations on the dilated image when a dilation in the coordinate plane has the origin as the centre of dilation. (X, Y) is how the dilation is expressed algebraically for scale factor k.

An object's size can be changed by the scale factor, either making it larger or smaller. To determine a dilated figure's scale factor, use the following simple formula: Scale factor is the product of the old shape's dimension and the new shape's dimension.

By constructing the new function f (x) → f (x), it is possible to dilate a function f (x) in the vertical direction by a scale factor of a. The function's roots and the x-coordinates of any turning points remain unaltered when a function is dilated vertically.

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Triangles which are similar to triangle ABC is the triangle having same corresponding angles.

A) triangle DEF where angle D is 35º and angle E is 20°.

C) triangle JKL where angle J is 35º and angle L is 125°.

D) triangle MNO where angle N is 20° and angle O is 125°.

Triangle can be defined as a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.

We know the sum of all the interior angles in a triangle is 180°.

A triangle ABC, angle A is 35º and angle B is 20º.

∴ m∠C is 180° - (35 + 20)°.

m∠C = 180° - 55°.

m∠C = 125°.

∴ Triangles which are similar to triangle ABC is the triangle having the same corresponding angles.

Triangle DEF where angle D is 35º and angle E is 20°.

Triangle JKL where angle J is 35º and angle L is 125°.

Triangle MNO where angle N is 20° and angle O is 125°.

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The equation of the line with given slope and passing through the given point is y = -5x - 6.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Slope can also be defined as the tangent of the angle that the line is making with the positive X axis.

General form of slope intercept form of line is,

y = mx + d

Here d is the y intercept, which is the value of y coordinate when x coordinate is 0. And m is the slope.

Given that slope, m = -5

Also we have a point on the line (-2, 4)

Substituting these,

4 = (-5 × -2) + d

4 = 10 + d

d = -6

So the equation is y = -5x - 6.

Hence the equation of the line is y = -5x - 6.

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Answer:

Translation, then Rotation

Step-by-step explanation:

It is first moved(translation), then rotated(rotation) around the left meeting point of the graph by about 90 degrees to the right.

The definite integral by u-substitution: [tex]$$\int_0^2 x^3 \sqrt{x^4+1} dx$$[/tex] will be 11.515

The region beneath a curve between two set limits is a definite integral. For a function f(x), defined with reference to the x-axis, the definite integral is written as baf(x)dx a b f (x) d x, where an is the lower limit and b is the upper limit.

The upper limit and lower limit are the two stated limits that make up the definite integral.

As per the question,

We have the value: [tex]$$\int_0^2 x^3 \sqrt{x^4+1} dx$$[/tex]

Given:-

[tex]I=\int_0^2 x^3 \sqrt{x^4+1} dx[/tex]

Let [tex]x^4+1=t[/tex]

[tex]\\& 4 x^3 d x=d t \\& x^3 d x=\frac{d t}{4}[/tex]

x=0, t=0^4+1=1

x=2,

t=2^4+1

t=16+1=17

Now evaluating the value of integration:

[tex]$$\begin{aligned}I & =\int_{t=1}^{17} \sqrt{t} \frac{d t}{4} \\I & =\frac{1}{4} \int_1^{17} t^{1 / 2} d t \\& =\frac{1}{4}\left[\frac{t^{1 / 2+1}}{\frac{1}{2}+1}\right]_q^{17} \\& \left.=\frac{1}{4}\left[\frac{17^{3 / 2}-1^{3 / 2}}{\frac{3}{2}}\right]^{17 \sqrt{17}-1}\right] \\& =\frac{1}{4} \times \frac{2}{3} \times[120]\end{aligned}$$[/tex]

[tex]I=\frac{1}{6}[17 \sqrt{17}-1]=11.51546594[/tex]

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The correct questions should be:

Evaluate the definite integral by u-substitution: [tex]$$\int_0^2 x^3 \sqrt{x^4+1} dx$$[/tex]

The correct answer is D. The station's faulty prediction is a result of bias. Only people watching the news will respond, and their preference may differ from that of other voters. The sampling method may systematically produce samples that do not represent the population of interest.

The TV station's "Pulse-Poll" method of collecting data is not a random sample of the population of interest, which is the entire voter population. Instead, it only captures the opinions of people who are watching the evening news and choose to text in their vote. This group of people may not be representative of the entire voter population, as it only includes viewers of that specific TV station and those who are motivated enough to text in their vote. The sample is not representative of the population of interest, and therefore the results are biased and should not be used to make predictions about the election outcome.

This self-selected group of people may have different characteristics and opinions than the general voter population. For example, viewers of the specific TV station may have different political leanings than the general population, and those who are motivated enough to text in their vote may have different levels of political engagement. As a result, the sample is not representative of the population of interest, and therefore the results are likely to be biased.

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Establish,Set a condition and Include an iteration are the three action.

Looping math is a part of lion that starts and end at the same point. It can refer to a continuous curve like Circle or a or to a sequence of discrete Point like a polygonal line.

1. Establish a loop control variable - This is a variable that will be used to control the loop. It is typically assigned an initial value before the loop starts, and is then modified each time the loop runs.

2. Set a condition - The loop should include a condition that will be evaluated each time the loop runs. If the condition is true, the loop will continue, and if the condition is false, the loop will end.

3. Include an iteration - The loop should include an instruction that will be executed each time the loop is run. This instruction can modify the loop control variable, or it can perform some other action.

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Function A have a greater initial value compared to function B

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the initial value

For function A, from the table, using the point (0, 4) and (2, 0):

y - 4 = [(0 - 4)/(2 - 0)](x - 0)

y - 4 = -2x

y = -2x + 4

Function A have an initial value of 4

Function B have an initial value of 3

Function A have a greater initial value.

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For the given mean and other values the value of data point will be 131.6.

What is mean?

The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.

The formula for the z-score is

z = (x - μ)/σ

x = data point

μ = mean

σ = standard deviation

Now

Given

Mean=102.8

standard deviation=15.4

z-value=1.87

putting the values in the formula

z = (x-μ)/σ

where x is the data point , μ is the population mean, and σ is the population standard deviation

1.87=(x-102.8)/15.4

Hence,

x=131.6

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The solution of the given equation is (i) x = 3 ,(iii) x=-1/2 .

Quadratic equation's roots The roots of a quadratic equation are the values of the variables that satisfy the equation. In other words, if f() = 0, therefore x = is a root of the quadratic equation f(x). The x-coordinates of the points where the curve y = f(x) intersects the x-axis are the real solutions of an equation f(x) = 0.

So we can find the root of 2[tex]x^2[/tex]— 5x —3 = 0 by factorising them.

=> 2x² - 5x - 3 = 0

=> 2x² - 6x + x - 3 = 0

=> 2x(x - 3) + (x - 3) = 0

=> (x-3)(2x+1) = 0

so the value of x = 3 , - 1/2

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Complete question :

For 2[tex]x^2[/tex]— 5x —3 = 0, determine which of the following are solutions?

(i) x = 3 (ii) x= –2

(iii) x=-1/2 (iv) x=-1/3

Colleen's velocity increased from the first section to the second section, while it remained constant from the second section to the third section.

The measures in this problem are obtained considering the relation between velocity, distance and time.

The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:

v = d/t.

In which:

For session 1, considering decimal numbers, the parameters are given as follows:

Hence the velocity is of:

v = 9.9/2.2 = 4.5 miles per hour.

For session 2, the parameters are given as follows:

Hence the velocity is of:

v = 11.875/2.5 = 4.75 miles per hour.

For session 3, the parameters are given as follows:

Hence the velocity is of:

v = 15.4375/3.25 = 4.75 miles per hour.

The table is given by the image presented at the end of the answer.

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Answer: OK IM HURRYING LOL

its y = -3x+2

Step-by-step explanation:

NO TIME

Answer:

5 _12 5947272950381_8294

The 53rd term of the arithmetic sequence is 584

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2

The nth term of an arithmetic sequence is given as : a(n) = a+(n-1) d

where a is the first term and d is the common difference.

The first term in the sequence is -12 and the common difference is -1-(-12) = 11

a(53) = -12+( 53-1) 11

= -12+ 52×11

= 12+ 572

a(53) = 584

Therefore the 53rd term is 584

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Answer:

The original number is 8.

Step-by-step explanation:

(x + 8) x 3 = 48

x + 8 = 48/3

x = 16 - 8

x = 8

So, on solving the provided question, we cans ay that value o the  quadratic equation (x+1)(x+1) => x = -1, -1

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation will be

[tex]y=(x+1)^2[/tex]

so,

(x+1)(x+1)

x = -1, -1

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The correct question is -

What is the restricted domain of the quadratic(y=(x+1)^2) that would ensure that the inverse is a function?

This means that C-Town flour is more expensive because it is only $1.88 per pound compared to Food Bazaar's $2.25 per pound.

Cost is the amount of money or resources needed to acquire, maintain, or produce something. It can refer to either the expense of buying a good or service, the expense of labor, or the expense of resources such as time and materials. In a business context, cost is often used to refer to the total amount of money a company has spent on a particular activity or product.

C-Town's smaller bag size may make it a more convenient purchase, but it is not a good price compared to Food Bazaar.

In order to get the best deal, the shopper needs to compare prices and consider all of the factors. The size and quantity of the bags, the number of servings in each bag, the cost per serving, and the store's location are all important considerations. For example, C-Town may be closer geographically, but if the shopper needs more servings for their recipe, the extra cost to buy multiple bags at C-Town may be more expensive than buying a larger bag of flour at Food Bazaar.

In addition to the cost of the flour, other costs such as the cost of transportation to the store, the cost of any necessary packaging, the cost of any other ingredients needed for the recipe, and the cost of any other items purchased should also be taken into account.

Finally, shoppers should take the quality of the product into consideration. The type of flour, the freshness and shelf life of the product, and any special features of the product should also be taken into account. A low-cost bag of flour may be far less desirable than a more expensive bag of flour with higher quality ingredients.

Overall, to get the best deal on flour, shoppers need to consider all of these factors and compare prices between stores.

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A quadratic equation x² = 16 has two solutions, x = 4 and x = -4.

A quadratic equation has standard form:

ax² + bx + c = 0

There are several methods to solve a quadratic equation:

- using factorization

- by completing the square

The given quadratic equation is: x² = 16

Method 1: Using factorization

x² = 16

x² - 16 = 0

(x + 4) (x - 4) = 0

Hence, the solution is x = 4 and x = -4

Method 2: By completing the square

x² = 16

This is already a perfect square. Hence,

x = ±√16

x = ±4

Hence, the solution is x = 4 and x = -4

Conclusion: there are two solutions of  x² = 16,  x = 4 and x = -4

There was typos in your question, most likely your question was:

How many solutions does x² = 16 have?

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Answer: If 20% of a farmer's harvest had to be given to Pharaoh, and the farmer had to give 40 bushels, we can set up the equation:

(x * 0.2) = 40 bushels

where x represents the number of bushels the farmer harvested. To find the value of x, we can divide both sides of the equation by 0.2:

x = 40 bushels / 0.2

x = 200 bushels

Therefore, the farmer harvested 200 bushels of grain that year.

Step-by-step explanation:

why, it's clearly D stoopid

Answer:

  d = 8.24

Step-by-step explanation:

You want the measure of d, the side opposite the 31° angle in the right triangle shown as having a hypotenuse of length 16.

The mnemonic SOH CAH TOA was invented to remind you of the relations between sides and trig functions in a right triangle. In the triangle shown, you have an angle, the side opposite (O), and the hypotenuse (H). The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

Filling in the values shown, this tells you ...

  sin(31°) = d/16

Multiplying by 16 gives the value of d:

  d = 16·sin(31°)

Your calculator can tell you what this value is, rounding it if you want.

The value of d is 8.24.

__

Additional comment

The other parts of the mnemonic tell you ...

You will notice the flag in the lower left corner of the calculator display tells you the mode is set to Degrees (DEG), rather than radians (RAD) or grads (GRA). This is required in order for sin(31) to be properly interpreted.

Answer:

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

Step-by-step explanation:

first get everything onto one side

5x^2+13x-6=0

then multiply 5 by 6 to get 30 and 15 times 2 is thirty and 15-2=13

5x^2+15x-2x-6=0

then split in half and factor both sides

5x^2+15x factored is 5x(x+3)

-2x-6 factored is -2(x+3)

so the answer is (x+3) and (5x-2)

Answer:

[tex]\huge\boxed{\sf x = -100}[/tex]

Step-by-step explanation:

[tex]\displaystyle -\frac{x}{5} -8=12\\\\Add \ 8 \ to \ both \ sides\\\\-\frac{x}{5} = 12+ 8\\\\-\frac{x}{5} = 20\\\\Multiply \ both\ sides \ by \ 5\\\\-x = 20 \times 5\\\\-x = 100\\\\Multiply\ both \ sides \ by\ -1\\\\x = -100\\\\\rule[225]{225}{2}[/tex]

The cost of each t-shirt is $20 and cost of each pair of pant is $12.

In the given question a shopper purchased 8 t shirts and 5 pairs of pants for $220

The next day he purchased 5 t shirts and 1 pair of pants for $112. We have to find the cost of each pair of t-shirts and pants.

Suppose that t is the price of a T-shirt and p is the price of a pair of pants.

For $220, a customer bought 5 pairs of pants and 8 T-shirts:

8t + 5p = 220...…..(1)

He spent $112 on 5 T-Shirts and 1 pair of slacks the following day:

Now the equation should be

5t + p = 112...…..(2)

From the equation 2, p = 112 - 5t

Now putting the value of p in equation (1)

8t + 5(112 - 5t) = 220

8t + 560 - 25t = 220

Subtract 560 on both side, we get

-17t = -340

Divide by -17 on both side, we get

t = 20

Now putting the value of t in p = 112 - 5t

p = 112 - 5(20)

p = 112 - 100

p = 12

Hence, the cost of each t-shirt is $20 and cost of each pair of pant is $12.

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The line created by Alexa is not a good representation for this data

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

The graph

On the graph, we can see that the line divides the points on the line unevenly

A good line of best fit would have equal number of points on either sides

Hence, the line is not a good representation

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The Simplification of the rational expression n[1/x - 1/(x + 2) / 2] gives 1/[x(x+2)] or 1/(x²+2x)

Simplification of a rational expression as a way of writing an expression in the most efficient and compact form without affecting the value of the original expression

[1/x - 1/(x+2)] /2

The LCM of x and (x+2) is x(x+2). Thus, we have:

[1/x - 1/(x+2)] /2 = [(x+2 - x) / x(x+2)] /2

                        = [ 2 / x(x+2)] /2

                        = 1 / [x(x+2)]

                        = 1/(x²+2x)

Thus, the expression simplifies to 1/[x(x+2)] or 1/(x²+2x)

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So the sin(z) is approximately 0.4866.

In a right triangle, the two non-right angles are complementary, meaning that their measures add up to 90 degrees.

So, if ∠x is complementary to ∠z, then we can write the equation ∠x + ∠z = 90°

We also know that in a right triangle, the cosine of one angle is equal to the ratio of the adjacent side to the hypotenuse.

And the sine of one angle is equal to the ratio of the opposite side to the hypotenuse.

Given that cos(x) = 0.6.

We can find sin(z) by using the trigonometric identity, sin²(z) + cos²(z) = 1

sin²(z) = 1 - cos²(x)

sin²(z) = 1 - 0.6²

sin²(z) = 0.24

sin(z) = √0.24

sin(z) = 0.4866

So the sin(z) is approximately 0.4866.

It's important to note that the result is an approximation since the value of cos(x) is given as 0.6, which is not exact.

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The area of the wall is 80.7293 square feet. The number of cans that Asher needs is 4.

What is a pentagon?

A pentagon is a five-sided polygon with five angles. The term "pentagon" is made up of two terms, Penta and Gonia, both of which mean five angles. All of the sides of a pentagon meet end to end to form a shape.

Given the wall on a storage shed is a pentagonal shape.

The area of a pentagon can be divided into two shapes. The shapes are one is a rectangle and another is a triangle.

The length of the rectangular shape is (1+1+1) = 3 meters.

The width is (1+1) = 2 meters.

The area of the rectangular shape is 3 × 2 = 6 square meters.

The length of the base of the triangle is 3 meters.

The height of the triangle is 1 meter.

The area of the triangle is 1/2× base× height = 1/2 × 3×1 = 3/2 square meter.

Total area of the pentagon is  6 + 3/2 = 7.5 square meters.

1 square meter = 10.7639 square feet

7.5 square meters = (7.5×10.7639) square feet

                              = 80.7293 square feet

1 can of paint covers an area of 24 square feet.

Therefore to cover 80.7293 square feet, he needs 80.7293/24 = 3.36.

Thus he needs a minimum 4 cans of paint.

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