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The rectangular equation for the curve is [tex]y = \frac{x^{2}}{2} -1[/tex].

In this question, we have a set of parametric equation which must be reduced into a single rectangular equation both by algebraic and trigonometric means, that is to say:

[tex]x = f(\theta), y = g(\theta) \to y = h(x)[/tex]

If we know that [tex]x = 2\cdot \cos \theta[/tex] and [tex]y = \cos 2\theta[/tex], then the rectangular equation is:

[tex]y = \cos 2\theta[/tex]

[tex]y = \cos^{2}\theta - \sin^{2}\theta[/tex]

[tex]y = 2\cdot \cos^{2}\theta -1[/tex]

[tex]\cos \theta = \frac{x}{2}[/tex]

[tex]y = 2\cdot \left(\frac{x}{2} \right)^{2}-1[/tex]

[tex]y = \frac{x^{2}}{2} -1[/tex]

The rectangular equation for the curve is [tex]y = \frac{x^{2}}{2} -1[/tex].

We kindly invite to check this question on parametric equations: https://brainly.com/question/23070611

Answer:

11 < x < 14

Step-by-step explanation:

Bleach ph value ranges from 11-13

Answer:

The final temperature was 9 degrees.

Step-by-step explanation:

You can first multiply 13x2, 7x2, and 9x2. Then you subtract 26 and 18 from 34. then add 14

Answer:

-23

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x² + c

f(4) = -7

Step 2: Solve for c

Answer:

8 METERS CUBES I THINK

Step-by-step explanation:

VOLUME IS LENGTH TIMES WIDTH TIMES HEIGHT

2 METERS TIMES 2 METERS TIMES 2 METERS IS 8 METERS

Answer:

5/3

Step-by-step explanation:

We need to rewrite the equation in slope intercept form

y =mx +b where m is the slope

-3x-5y = 7

Add 3x to each side

-5y = 3x+7

Divide by -5

y = -3/5 x -7/5

The slope of this line is -3/5

Perpendicular lines  have slopes that are negative reciprocals

-1 / (-3/5)

5/3

The slope of the perpendicular line is 5/3

Answer:

R is a function.

Step-by-step explanation:

Step-by-step explanation:

The angles a and b are congruent, also c and x are congruent.

Answer:

Step-by-step explanation:

Answer:

70 cents each snickers bar

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

cccccccc cccccccccdkdksksk

Step-by-step explanation:

1 _ 1.215

2_ 4.0608

3_1.5225

4_0.2875

5_3.6064

The correct quotient is -3

The mistake CJ likely made is multiplying using the reciprocal of -3/4. The correct option is d. He multiplied using the reciprocal of -3/4

From the question,

We are to determine the correct quotient.

The given division operation to be carried out is -3/4 divided by 1/4

The correct quotient can be determined as shown below

[tex]-\frac{3}{4} \div \frac{1}{4}[/tex]

Multiply [tex]-\frac{3}{4}[/tex] by the reciprocal of [tex]\frac{1}{4}[/tex]

The reciprocal of [tex]\frac{1}{4}[/tex] is  [tex]\frac{4}{1}[/tex]

Then, we get

[tex]-\frac{3}{4} \times \frac{4}{1}[/tex]

This gives

[tex]-\frac{12}{4}[/tex]

= -3

The correct quotient is -3

The mistake CJ likely made is multiplying using the reciprocal of -3/4.

Hence, the correct quotient is -3

The mistake CJ likely made is He multiplied using the reciprocal of -3/4. The correct option is d. He multiplied using the reciprocal of -3/4

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Answer:

17

Step-by-step explanation:

Let x be the number of books and y the number of CDs,

[tex]x+y=25\\[/tex]

The prices of the products are multiplied with the quantity bought, therefore:

[tex]1.5x + 5y = 65.50[/tex]

Multiplying the first equation by -5, then multiplying the two equations:

[tex]-3.5x=-59.5\\x=17[/tex]

Answer:

The answer is B

Step-by-step explanation:

Hope it helps

Answer:

I don't know sorry sorryy

Answer:

The ratios are proportional ratios

Answer:

Step-by-step explanation:

The ratios are proportional

[tex]\dfrac{5}{12}=\dfrac{5*2}{12*2}=\dfrac{10}{24}[/tex]

Answer:

y=4/5x-0.8

Step-by-step explanation:

Answer:

Granny is correct

Step-by-step explanation:

Hope it helps

Answer:

[tex] {x}^{4} - {x}^{2} {y}^{2} + {y}^{4} \\ {x}^{4} + {y}^{4} - {(xy)}^{2} [/tex]

Answer:

Step-by-step explanation:

Step-by-step explanation:

I can't see picture very well but as I see first angle is

-4x+5 and second is -13x+39 ( if it isn't, correct me)

sum of this angles is 180° because they are inner angles

(-4x+5) + (-13x+39) = 180

-4x+5 -13x+39=180

-17x+44=180

-17x = 180-44

-17x= 136

x= -8

angle -4x+5 will be:

-4*-8 + 5= 32+5= 37°

Answer:

II + III = 176

II = 44

III = 132

Step-by-step explanation:

Third round: 132

Second round: 3x=132

x=44 (second round)

2rounds: 132+44=176

Answer: the sun is 389.015069067 times further away from earth to the moon

Step-by-step explanation: 92935700/238990=389.015069067

Answer:

[tex]\sf\longmapsto \: 3.73 hours [/tex]

Step-by-step explanation:

[tex]\sf\longmapsto \: \frac{1}{7 } + \frac{1}{8} [/tex]

[tex]\sf\longmapsto \: \frac{15}{56} [/tex]

Now, Reciprocal–

[tex]\sf\longmapsto \: \frac{56}{15} [/tex]

[tex]\sf\longmapsto \: 3.73 hours [/tex]

The time taken together Marie and his sister to paint the living room are 3.73 hours or 3 hours and 43.8 minutes.

Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.

Another illustration of labor is when you finish your meal in an hour, which means that you finished your work in an hour.

Given that,

Marie take 7 hours to paint

1 work → 7 hour

1 hour → (1/7) work

Barbara takes 8 hour

1 work → 8 hour

1 hour → (1/8) work

Let's suppose together they take x hour

1 work → x hour

1 hour → (1/x) work

Now,

1-hour work together = 1-hour work of Marie + 1-hour work of Barbara

(1/x) = (1/7) + (1/8)

(1/x) = (7 + 8)/56

x = 56/15

x = 3.73

x = 3 hour and 0.73 × 60 = 43.8 minutes.

Hence "The time taken together Marie and his sister to paint the living room is 3.73 hours or 3 hours and 43.8 minutes".

For more information about the work and time relation,

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#SPJ2

The dish illustrates operations on a parabola.

The depth of the parabolish dish is 160 feet.

The bowl is said to be a parabola.

So, we have:

[tex]\mathbf{(x -h)^2 = 4p(y - k)}[/tex]

Where:

[tex]\mathbf{Focus: p = 40}[/tex]

[tex]\mathbf{Vertex:(h,k) = (0,0)}[/tex]

From the question, the diameter is 160 feet.

So, the radius (r) is:

[tex]\mathbf{r = \frac{160}{2} = 80}[/tex]

So, the coordinate of the depth of the parabola would be:

[tex]\mathbf{(x,y) = (60 + 100,y)}[/tex]

[tex]\mathbf{(x,y) = (160,y)}[/tex]

Substitute these values in [tex]\mathbf{(x -h)^2 = 4p(y - k)}[/tex]

So, we have:

[tex]\mathbf{(160 - 0)^2 = 4 \times 40 \times (y -0)}[/tex]

[tex]\mathbf{160^2 = 160y}[/tex]

Divide both sides by 160

[tex]\mathbf{160 = y}[/tex]

Rewrite as:

[tex]\mathbf{y = 160 }[/tex]

Hence, the depth of the parabolish dish is 160 feet.

Read more about parabolas at:

https://brainly.com/question/4074088

Answer:

x=5

Explanation:

y∝1x∴y=k⋅1x∴x⋅y=k;

When x=4;y=10∴4⋅10=kork=40.

So variation equation is x⋅y=40

When y=8;x=408=5∴x=5 [Ans]

Step-by-step explanation:

not surre

Answer:

6.67

Step-by-step explanation:

10=4

y=6

10×4/6

Step-by-step explanation:

[tex]6(y + 1) > 6 \\ 6y + 6 > 6 \\ 6y > 0 \\ y > 0[/tex]