Please answer the both questions in the photos below ( will mark brainliest if available + 30p )

Answer:

[tex]y^2 = x^3 / 2^{3/2}[/tex] or [tex]y = x^{3/2} / 2^{3/4}[/tex]

Step-by-step explanation:

We can use the identity [tex]cos^3(t) = cos(t)*cos^2(t) and sin^3(t) = sin(t)*sin^2(t)[/tex] to rewrite the given parametric equations in terms of x and y:

[tex]x = 2cos(t)*cos^2(t) = 2x^2 - 2y^2[/tex]

[tex]y = 2sin(t)*sin^2(t) = 2xy^2[/tex]

Solving for y in terms of x, we get:

[tex]y = x^{3/2} / 2x^{3/4}[/tex]

Therefore, the cartesian equation of the curve is:

[tex]y = x^{3/2} / 2^{3/4}[/tex]

or, equivalently:

[tex]y^2 = x^3 / 2^{3/2}[/tex]

Polynomial multiplication is the process of multiplying two polynomials together to get a new polynomial that represents the product of the two original polynomials.

It should be noted that to multiply two polynomials, you need to perform a distributive operation. You take each term of the first polynomial and multiply it by each term of the second polynomial. Then, you add all the resulting terms together to get the final polynomial.

For example, let's say you want to multiply the polynomials (x + 2) and (x - 3).

First, you multiply the x term in the first polynomial by the x term in the second polynomial:

(x) * (x) = x²

Next, you multiply the x term in the first polynomial by the -3 term in the second polynomial:

(x) * (-3) = -3x

Then, you multiply the 2 term in the first polynomial by the x term in the second polynomial:

(2) * (x) = 2x

Finally, you multiply the 2 term in the first polynomial by the -3 term in the second polynomial:

(2) * (-3) = -6

Now, you add up all the resulting terms to get the final polynomial:

x² - x - 6

Therefore, the product of (x + 2) and (x - 3) is x² - x - 6.

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The true statements about the functions A and B are

Given that

Function B: y = 3x + 4

A linear equation is represented as

y = mx + c

Where

Rate of change = m

y-intercept = c

Using the above definition, we have the following summary for function B

Rate of change = 3 and y-intercept = 4

For function A (the table), we have

Rate of change = (10 - 2)/(3 - 1)

Rate of change = 4

While the y-intercept is

y-intercept = 2 - 4

y-intercept = -2

So, we have

                                             Function A                Function B

Rate of change                         3                                4

y-intercept                                4                                -2

By comparing the features, we have the following true statements

C. The y-intercept of Function A is greater than the y-intercept of Function B.

E. The rate of change of Function A is less than the rate of change of Function B.

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Complete question

Function A and Function B are linear functions. Function A is represented by the table of values. Function B is represented by the equation.

Function A

x 1   3    4    7

y 2  10  14 26

Function B

y = 3x + 4

Which statements about the properties of Function A and Function B are true? Select each correct statement.

A. The y-intercept of Function A is equal to the y-intercept of Function B. B. The y-intercept of Function A is less than the y-intercept of Function B. C. The y-intercept of Function A is greater than the y-intercept of Function B.

D. The rate of change of Function A is equal to the rate of change of Function B.

E. The rate of change of Function A is less than the rate of change of Function B.

F. The rate of change of Function A is greater than the rate of change of Function B.

Answer:

The probability of selecting a face card or a spade when randomly selecting one card from a standard deck of cards is 11/26 or approximately 0.423.

Step-by-step explanation:

Part A

No, selecting a face card and selecting a spade when randomly selecting one card from a standard deck of cards are not mutually exclusive events. This is because there are face cards that are also spades, so there is an overlap between the two events.

Part B

The probability of selecting a face card or a spade when randomly selecting one card from a standard deck of cards can be calculated as follows

P(face card or spade) = P(face card) + P(spade) - P(face card and spade)

Part C

The probability of selecting a face card or a spade when randomly selecting one card from a standard deck of cards can be calculated as follows

P(face card or spade) = P(face card) + P(spade) - P(face card and spade)

P(face card or spade) = 12/52 + 13/52 - 3/52

P(face card or spade) = 22/52

P(face card or spade) = 11/26

Hence, the probability of selecting a face card or a spade when randomly selecting one card from a standard deck of cards is 11/26 or approximately 0.423.

(x + 2)2 + (y - 4)2 - 11 = 0

The equation of the circle in standard form is x2 + y2 + 36x - 72y + 11 = 0. To arrive at this answer, you need to complete the square for both the x and y terms in the equation. First, divide the equation by 9 to get the following:

x2 + y2 + 4x - 8y + 1 = 0

To complete the square for the x terms, add and subtract (4/2)2 = 16/4 = 4 to the equation:

x2 + 4 + y2 + 4x - 8y + 1 - 4 = -4

Simplifying gives you:

(x + 2)2 + y2 - 8y + 5 = 0

To complete the square for the y terms, add and subtract (8/2)2 = 64/4 = 16 to the equation:

(x + 2)2 + (y - 4)2 + 5 - 16 = -11

Simplifying gives you:

(x + 2)2 + (y - 4)2 - 11 = 0

This is the equation in standard form.

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Situation 1:

Dependent variable: Distance traveled (d)

Independent variable: Speed (s)

Situation 2:

Dependent variable: Speed (s)

Independent variable: Distance traveled (d)

The dependent variable is the variable being studied or measured in an experiment or observation. It is the output or response that is being examined based on changes in the independent variable.

An independent variable is a variable that is manipulated or controlled by the experimenter in order to observe the effect on the dependent variable. It is also sometimes called the predictor variable.

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Answer:

it goes by minus 8 each time so just put the number and negative 8 each time on a paper and the 20th term would be your answer

The answer is 4.4753, i.e. the critical value of the statistic upto four decimal places.

Null hypothesis (H0): σ21 = σ22

Alternative hypothesis (H1): σ21 > σ22

Round your answer(s) to four decimal places.

Critical value = 4.4753

Test statistic = 34.66/6.3 = 5.5

The test statistic (5.5) is greater than the critical value (4.4753), so we reject the null hypothesis and accept the alternative hypothesis.

We conclude that the variance in performance from the sixth grade class is greater than the variance in performance from the seventh grade class at a 0.1 level of significance.

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Answer:

c ≈ 11.2

Step-by-step explanation:

Using the distance formula, we have:

c = √[(x2 - x1)² + (y2 - y1)²]

c = √[(-7 - 3)² + (1 - (-4))²]

c = √[(-10)² + 5²]

c = √(100 + 25)

c = √125

c ≈ 11.2

Therefore, the distance between the two points is approximately 11.2 units.

[tex]\sqrt{(-7-3)^{2} + (1-(-4))^{2} } = \sqrt{(-10)^{2} + (5)^{2} } = \sqrt{100 + 25} \\[/tex]

[tex]= \sqrt{125} = 5\sqrt{5} =11.2[/tex]

The book value at the end of the third year is (A) $1,690.

The depreciation of an asset is the difference between the cost of the asset and the estimated resale value at the end of its useful life.

The straight-line method of depreciation is used to calculate the annual depreciation of an asset.

In this case, the computer system cost $3,500 and was estimated to have a resale value of $525 after five years.

This means that the computer system will depreciate $595 each year.

To calculate the book value at the end of the third year, subtract the depreciation for the first three years from the cost of the asset:

Cost of Computer System: $3,500

Annual Depreciation: -$595

Book Value at End of 3rd Year= $3,500 - ($595 x 3) = $1,690

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According to the data given in the question, the book value at the end of the third year is (A) $1,690.

The depreciation of an asset is the difference between the cost of the asset and the estimated resale value at the end of its useful life.

The straight-line method of depreciation is used to calculate the annual depreciation of an asset.

In this case,

the computer system cost= $3,500

estimated resale value after five years= $525

depreciation  of the computer system each year= $595

To calculate the book value at the end of the third year, subtract the depreciation for the first three years from the cost of the asset:

Cost of Computer System: $3,500

Annual Depreciation: $595

Book Value at End of 3rd Year

= $3,500 - ($595 x 3)

= $1,690

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Answer:

Proved

Step-by-step explanation:

In triangles ABD and CBD,

Angle CDB = Angle ADB (given in Question)
Angle CBD = Angle ABD ( Angle Bisector Therom)
BD = BD ( Common side)

Therefore Triangle ABD is congruent to Triangle CBD by ASA

Hope it helps :)

Answer:

Add to eliminate X

Step-by-step explanation:

To eliminate a variable, we need to make its coefficient equal and opposite in the two equations. In this case, we can see that the coefficient of x in both equations is the same (6x), so we can eliminate x by adding the two equations.

When we add the two equations, the x term will cancel out, leaving us with the equation:

9y = 36

We can then solve for y by dividing both sides by 9:

y = 4

Now that we know the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:

6x + 5y = 12

6x + 5(4) = 12

6x + 20 = 12

6x = -8

x = -4/3

Therefore, the solution to the system of equations is x = -4/3, y = 4.

The workman's hourly rate of pay for a 40-hours week is 380.

Hourly rate of pay = Total pay ÷ Total hours worked

Hourly rate of pay = 15, 200 ÷ 40 = 380

Therefore, the workman is paid 380 per hour for a 40-hours week. To calculate the hourly rate of pay, the total pay is divided by the total hours worked. In this case, the total pay is 15, 200 and the total hours worked is 40, so when we divide 15, 200 by 40, we get 380. This is the hourly rate of pay for the workman for the 40-hours week.

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Answer: 5/81

Step-by-step explanation:

F(4) = 5 * (1/3) ^ 4

F(4) = 5 * 1/81

F(4) = 5/81

As a result, it takes around 0.25 minutes for the oven to reach 300°F, or equation roughly 15 seconds. Rounded to the closest minute, the answer is 0 minutes.

A math equation is a mechanism for connecting statements and indicating equivalence with both the equals symbol (=). An equation is an algebraic claim that asserts the equivalency of two formulae in algebra. In the calculation 3x + 5 = 14, for example, the equivalence sign separates the numbers 3x + 5 and 14. To explain the relationship among the two words on each surface of a letter, a formula can really be employed. The software and the logo are usually interchangeable. For instance, 2x - 4 equals 2.

Set T = 300 in the equation and solve for t to discover the number of minutes it takes for the oven's temperature to reach 300°F:

T = 400 - It

300 = 400 - It / subtraction T = 300

It = 400 - 300

It = 100

t = 100 / I

T = 400 minus It I = (400 minus T) / t

When we substitute T = 0 and T = 1, we get:

I = (400 - 0) / 1\sI = 400

Now we can substitute I = 400 into the equation we found before for t:

t = 100 / I\st = 100 / 400\st = 0.25

As a result, it takes around 0.25 minutes for the oven to reach 300°F, or roughly 15 seconds. Rounded to the closest minute, the answer is 0 minutes.

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Answer: 20.1 m

Step-by-step explanation:

using  the formula circumference = 2pi r:

[tex]126=2\pi r[/tex]

divide 2 pi on both sides

[tex]r=\frac{126}{2\pi }[/tex]

r = 20.05

r = 20.1 m

Here is the stem and leaf plot :

0    8, 9

1      1, 3, 4, 7, 7, 8, 9

2      0, 2, 3 5

A stem-and-leaf plot is a table that is similar to a histogram. A stem-and-leaf plot divides a number into a stem and a leaf.

The stem is the first number in the digit. In this question, the stem is the tens value.  While the leaf is the last number. In this question, it is the units digit. For example in the number 20, 2 would be the stem and 0 would be the leaf. All the numbers that have the same stem would occupy the same row.

An advantage of a stem and leaf plot is that it is easy to create while a disadvantage is that it can be tedious when the dataset is large.

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Answer:

B.   51 in²

Step-by-step explanation:

The area of a sector which has a central angle of θ degrees is given by
Area of circle x θ/360

where
area of circle = πr² with r being the radius

So area of sector = πr² x θ/360

here r = 14 in and θ=30°

Area of sector
= π x 14² x 30/360

= 51.31268 in²

≈ 51 in²

Option B

Answer:

[tex]y-x=1[/tex]

Step-by-step explanation:

All the other choices are incorrect because when put in slope-intercept form (y = mx + b), the slope is not equal to 1. The slope of the lines for the other equations are [tex]-\frac{1}{2} , 2, and -1[/tex]. Only the first choice has a slope of 1 like the given equation.

Answer: Its B.) −5 ≤ y ≤ 2

Step-by-step explanation: The graph shows one part of the interval increasing which is the y value and stops at 3. The X interval which is the decreasing interval stops at -5. So this would be -5 greater then or equal to y greater then or equal to 2.

Sorry if wrong! Have a nice day :)

Answer:5f+6g+12

Step-by-step explanation:

10f-5f=5f

8+4=12

5f+6g+12

1 kilogram of soil will fit in the container, since 1 kilogram is less than 27/5 kilograms.

We can start by using ratios to solve this problem.

From the information given, we know that:

We want to know how much soil will fit in the entire container (which is equivalent to 3 times the amount that fills 1/3 of the container)

To find out how much soil fills the entire container, we can set up a ratio:

(3/5 kg of soil) : (1/3 of container) = (x kg of soil) : (1 container)

We can cross-multiply to solve for x:

(3/5 kg of soil) * (1 container) = (1/3 of container) * (x kg of soil)

Multiplying both sides by 3/1 gives:

(3/5) * 3 * (1 container) = (1/3) * x

Simplifying gives:

9/5 = 1/3 * x

Multiplying both sides by 3 gives:

27/5 = x

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The complete question is below:

3/5 kilogram of soil fills 1/3 of a container can, 1 kilogram of soil fit ? in the container

By answering the given question, we may state that Therefore, the equivalent inequality is: x < 2

A relationship between two terms or values which is not equal is known as an inequality in mathematics. Inequality follows imbalances, therefore. In mathematics, an inequality makes a link among two quantities that are not equal. Egality and inequality are different. Use the not similar symbol most frequently when two components are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two parts until only the variables are left, one can solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left & right.

inequality using basic algebraic operations:

5(2x-6)+6(3-x)<2x+4

10x-30+18-6x < 2x+4

4x - 8 < 0

4x < 8

x < 2

Therefore, the equivalent inequality is:

x < 2

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Step-by-step explanation:

disculpa, te recomiendo acercar más la foto para porder

te ayudar

Step-by-step explanation:

Im not at a great place to answer them all, but hope this helps on answering them

So the first is 5/2. When you found that, you essentially found the 2 other sides of the "triangle".

You can use Pythagoras to find the length of PQ.

[tex] {2}^{2} + {5}^{2} = {x}^{2} [/tex]

[tex]4 + 25 = 29[/tex]

[tex] \sqrt{29} = x[/tex]

You can either keep it like that, or use a calculator to find that value. im not sure how the system accepts it. you'll do that for each one

Answer:

Dry your hands from the soap and try twisting the lid of the pan. This will cause it to start to turn. If you put it in the freezer it will be harder to take it off. My guess is by twisting the lid, you would be able to cause enough friction to take the lid off.

Step-by-step explanation:

If this doesn't work try tilting the lid and then lifting it

Answer:

Try soaking it in hot water. The pot only if possible. The top is smaller and if the  pan expands it should loosen up

Answer: -2x(x-5)(x+4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

add it up and then multiply and then you divide and you got the answer so may i please have brinliest. sir

so its x27

The coordinates of the fourth vertex of the parallelogram are given as follows:

(-5,0).

To find the coordinates of the fourth vertex of the parallelogram, we need to use the fact that opposite sides of a parallelogram are parallel and equal in length. We can use the given three vertices and their coordinates to find the vector representing one of the sides of the parallelogram, and then use this vector to find the fourth vertex.

For the fourth vertex, we have that:

Hence the coordinates of the vertex are of:

(-5,0).

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Answer:

The measure which changes the most is the mean and the new value is 84°

The correct answer option is option B

Step-by-step explanation:

How to calculate mean and median?

Given data set:

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Median = (100 + 105) / 2

= 205/2

= 102.5°

Mean = (58 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12

= 965 /12

= 80.4°

Range = Highest value - lowest value

= 105 - 57

= 48°

Interquartile range = Third quartile - First quatile

= 88.5° - 74°

= 14.5°

If 58° is changed to 101°

101, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

Median = (100 + 105) / 2

= 205/2

= 102.5°

Mean = (101 + 61 + 71 + 77 + 91 + 100 + 105 + 102 + 95 + 82 + 66 + 57) / 12

= 1008 /12

= 84°

Range = Highest value - lowest value

= 105 - 57

= 48°

First quartile = (71 + 77) / 2

= 148/2

= 74°

Third quartile = (95 + 82)/2

= 177/2

= 88.5°

Interquartile range = Third quartile - First quatile

= 88.5° - 74°

= 14.5°

Therefore, the new mean is 84°

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