x = 3 - 2y
y = -1/2x+3/2

Answer:

hope you can understand

The parametric equation that represents the same path as the original equation is x = 3 + cos(2θ) and y = 2sin(2θ).

The given parametric equation can be expressed as follows;

x = 3 + cosθ

y = 2sinθ

From the given options, a plot of the various equation can be used to determine the paths of the equation.

For; x = 3 + cos(2θ) and y = 2sin(2θ), its parametric plots is same as original equation since the equation [3 + cos(2θ) and y = 2sin(2θ)] changed at equal rate of the angles.

Thus, the parametric equation that represents the same path as the original equation is x = 3 + cos(2θ) and y = 2sin(2θ).

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Check the picture below.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{6^2 - 4^2}=a\implies \sqrt{36-16}=a\implies \sqrt{20}=a\implies 2\sqrt{5}=a \\\\[-0.35em] ~\dotfill\\\\ sin(A )=\cfrac{\stackrel{opposite}{2\sqrt{5}}}{\underset{hypotenuse}{6}}\implies sin(A)=\cfrac{\sqrt{5}}{3} \\\\\\ cos(B )=\cfrac{\stackrel{adjacent}{2\sqrt{5}}}{\underset{hypotenuse}{6}}\implies cos(B)=\cfrac{\sqrt{5}}{3}[/tex]

Answer:

6+8x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:d

Step-by-step explanation:

The vertices of ABCD after 90 degrees clockwise rotation about point C are: A' (0,6), B' (3,7), C' (4,6) and D' (4,3)

The image of the polygon ABCD is not given; however, the question can still be answered because the coordinates are known.

The vertices of polygon ABCD are given as:

A = (4, 6)

B = (5, 3)

C = (4, 2)

D = (1, 2)

The rule of rotation about point C is:

(x,y) = (a + b - y, x + b - a)

Where:

(a, b) = (4, 2) --- the point of rotation.

So, we have:

(x,y) = (4 + 2 - y, x + 4 - 2)

(x,y) = (6 - y, x + 2)

The above means that:

A' = (6 - 6, 4 + 2) = (0,6)

B' = (6 - 3, 5 + 2) = (3,7)

C' = (6 - 2, 4 + 2) = (4,6)

D' = (6 - 2, 1 + 2) = (4,3)

Hence, the image of the rotation and their vertices (i.e. coordinates) are:

A' = (0,6)

B' =  (3,7)

C' = (4,6)

D' =  (4,3)

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Answer:

1 solution

Key:

Assume x is the the range x > 0 ≥ 1, in other words, assume x is equal to 1.

Step-by-step explanation:

[tex]y = -x - 8x - 16\\= -x - 8x\\= 9x\\= 9x - 16[/tex]

Answer:

xy = - 8

Step-by-step explanation:

note that

(x - y)² = x² + y² - 2xy , that is

6² = 20 - 2xy

36 = 20 - 2xy ( subtract 20 from both sides )

16 = - 2xy ( divide both sides by - 2 )

- 8 = xy

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

Therefore

[tex]6^2=20-2xy\\36=20-2xy\\2xy=-16\\xy=-8[/tex]

Answer:

x = 1

y = -3

Step-by-step explanation:

cos(pi) = -1

so many ways :

sqrt(0.5/2) = sqrt(0.5/2 × 8/8) = sqrt(4/16)

= sqrt(0.5/2 × 18/18) = sqrt(9/36)

= sqrt(1/4) = 1/2

"nicest" approach (all integers) :

3x² = sqrt(9)

3x² = 3

x² = 3/3 = 1

x = 1

2y = sqrt(36)

2y = 6

y = 6/2 = 3

one of them has to be negative (because cos(pi) = -1), so it has to be y, because 3x² cannot be negative with real numbers.

so, y = -3

-1 × 3×1²/(2×-3) = sqrt(0.5/2) = 1/2

-1 × 3/-6 = 1/2

3/6 = 1/2

1/2 = 1/2

correct

Answer:

1/2  /   50% chance

Step-by-step explanation:

There are 10 yellow out of 20 (6 + 4 + 10 = 20) balls.

So, the probability is 10 / 20

Or, 1 / 2 (which is the same thing as 50% chance)

(chance = probability)

Answer:

C

Step-by-step explanation:

Formula for the volume of a cone :

Volume (cone) = 1/3πr²h

===========================================================

Given :

⇒ r = 4 units

⇒ h = 21 units

============================================================

Solving :

⇒ Volume (cone) = 1/3 × π × (4)² × 21

⇒ Volume (cone) = 16 × 7 × π

⇒ Volume (cone) = 112π units²

Answer:

[tex]\sf C. \quad 112 \pi \:units^2[/tex]

Step-by-step explanation:

[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substituting the given values into the formula:

[tex]\implies \sf Volume=\dfrac{1}{3} \cdot \pi \cdot 4^2 \cdot 21[/tex]

[tex]\implies \sf Volume=112 \pi \:units^2[/tex]

Answer:A

Step-by-step explanation:

Good luck on the exam!

Answer:

the 3rd one ez clapppppppp

The area of a circle is defined as [tex]\pi(r^{2})[/tex], where r = 4.3 here. 4.3^2 ≅ 18.49, so the area of the full circle is 18.49π.
The shaded section covers 12 degrees of the full 360 degrees in a circle, or 1/30th of the area. Therefore, the area of the shaded section is equal to [tex]\frac{18.49\pi}{30}[/tex], or about 1.936. In this question's context, that would be 1.936[tex]in^{2}[/tex].

The linear equation that models the cost for having x additional family members added is:

c(x) = $75 + $10.99*x

Here we know that the plan has a fixed price of $75 plus $10.99 for each family member added beyond the primary account holder.

Then if there are x family members added, the cost will be:

$75 + $10.99*x

Then the linear equation that models the cost for having x additional family members added is:

c(x) = $75 + $10.99*x

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Answer:

(3,0)

Step-by-step explanation:

Answer:

57 f

Step-by-step explanation:

-16t² + vt + h

-16(4 s)² + (72 f/s)(4 s) + (25 f)

-256 + 288 + 25 = 57

Answer:

Step-by-step explanation:

If you roll an even number it doesn't just get rid of the number off the cube, it still exists

Events A and B are independent.

These events have no outcomes in common,

Option C is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

Events A and B are independent because the outcome of one event does not affect the probability of the other event.

The fact that 6 is an even number is not relevant to the independence of the events.

Event A is the event of rolling an even number on the first cube, which has three even and three odd numbers.

Event B is the event of rolling a 6 on the second cube, which has one 6 and five non-6 numbers.

These events have no outcomes in common, and the outcome of the first roll does not affect the outcome of the second roll.

Therefore,

Events A and B are independent.

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Answer:

Step-by-step explanation:

B is at (-3,-2) Multiply by 3: (-9,-6)

O is at (2,-1)  Multiply by 3: (6,-3)

T is at (-3,3) Multiply by 3: (-9,9)

Hope this helps!!

After 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have a line of best fit:

y = 2.5 + 1.25x

Plug x = 7 weeks

y = 2.5 + 1.25(7)

y = 11.25 units

Thus, after 7 weeks the plant will 11.25 units tall if the equation for the best-fit line to be y = 2.5 + 1.25x.

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We will see that f'(x) > 0, which means that f(x) is an increasing function.

For any function f(x), if f'(x) > 0, then f(x) is increasing for any value of x.

Here we have the cubic function:

f(x) = x³ + 4x

If we differentiate this, we get:

f'(x) = df(x)/dx = 3x² + 4.

And notice that x² is always positive, then f'(x) > 0, which means that f(x) is an increasing function.

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Answer:

Step-by-step explanation:

_________________________________________________

initial number of sweets               |   18                   |      18

                                                       |                          |

Sue gives Tony x sweets              |   18 - x              |      18 + x

                                                       |                          |

Sue ,eats 5 of her sweets. and   |  18 - x - 5 =       |      (18 + x)/2 =

Tony ,eats half of his sweets        | 13 - x                |     9 + x/2

Step-by-step explanation:

n + 5 = -16

n = -21

The correct option is -21

Answer:

Answer: -3/2

Step-by-step explanation:

#KEEPSAFE

#GOODLUCK

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Answer:

an accounting metric used to represent the average number of days between a credit sale date and the date when the purchaser remits payment.

Answer:

Step-by-step explanation:

2x^3 + 5x^3 + 2 + 3 = 7x^3 + 5

Answer:$3.25

Explanation:

Since the 7 min phone call is at 1.75, that means that one minute of phone call time is 0.25. 13 minutes would be 0.25*13=3.25

hope this helps

The first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.

The first term of an arithmetic progression can be calculated using the following expression:

Sn = n/2 [2a + (n − 1)d]

Where;

100 = 2 [2a + (4 - 1)4]

100 = 4a + 24

4a = 100 - 24

a = 76/4

a = 19

Therefore, the first term of an arithmetic progression of 4 terms and ratio equal to 4 whose sum is 100 is 19.

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