Eliminate the parameter to complete the statements describing the equations
x = 3cos(t) - 2 and y = 2sin(t) + 1.
The rectangular form of this equation is
A. 4(x + 2)2 + 9(y – 1)2 = 36
B. 9(x + 2)2 + 4(y - 1)2 = 36
C. 4(x - 2)2 + 9(y + 1)2 = 36
D. 9(x - 2)2 + 4(y + 1)2 = 36
The equations represent a/an

Step-by-step explanation:

Consider this polynomial,

[tex]8 {x}^{2} + 2x - 3[/tex]

First, I do the AC memethod. To find my two numbers,

That is to find two numbers that multiplied will equal my leading coeffeicent, A times my constant, C

And that will also add to 2, my middle term.

So using that

[tex]8 \times - 3 = - 24[/tex]

So let find factors of-24:

Factors can be positve or negative

The factors of 24 are : 1,2,3,4,6 8,12,24.

So which one of these add up to 2.

[tex]6 + ( - 4) = 2[/tex]

and

[tex]6 \times - 4 = - 24[/tex]

So six and negative four is our numbers.

Now, let set up our binomials

Step 1: Rewrite the orginal equation by using 6x and -4x instead of 2x.

Disclaimer: The placement of these numbers doesn't matter.

So we have

[tex]8 {x}^{2} + 6x - 4x - 3[/tex]

Step 2: Group the first two terms and last two terms

[tex](8 {x}^{2} + 6x) + ( - 4x - 3)[/tex]

Factors the first group by finding the GCF.

x is the greatest common variable, and 2 is the gcf so we have

[tex]2x(4x + 3) + ( - 4x - 3)[/tex]

Next, factor the next group by -1.

[tex]2x(4x + 3) - 1(4x + 3)[/tex]

Combine the outside factors.

[tex](2x - 1)(4x + 3)[/tex]

So those are the factors.

Answer:

B

Step-by-step explanation:

No these triangles are not congruent.

Left triangle

Shortest side = 6 cm

Longest side = 13 cm

3rd side = unknown but < 13

Right triangle

Shortest side = 6 cm

Longest side = unknown but > 13

3rd side = 13 cm

Although the shortest side of both triangles is 6 cm, the longest side of the left triangle is 13 cm, whereas the longest side of the right triangle is unknown but will be more than 13 cm.

We do not know if any of the angles are congruent.  If they were congruent, we would expect to see this marked by the same angle line(s) on each triangle.

Answer:

234 mm^2

Step-by-step explanation:

These questions are tricky but to make them easier, try to break down the shape into smaller regular shapes and work them out.

I would divide this shape into 2 rectangles and one triangle

Area of small bottom rectangle: 4 x 11 = 44mm^2

Area of rectangle in the middle: 14 x 8 = 112mm^2

Area of triangle: 12 x 13/2 = 78mm^2

Add all the areas together = 44+112+78 = 234mm^2

Answer:

2(x - 2)

Step-by-step explanation:

- 4(x + 1) + 6x ← distribute parenthesis by - 4

= - 4x - 4 + 6x ← collect like terms

= 2x - 4 ← factor out 2 from each term

= 2(x - 2)

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

Let's simplify this expression.

The first step is to use the distributive property, which states:-

[tex]\bigstar{\boxed{a(b+c)}[/tex]

Simplify:-

[tex]\bigstar{\boxed{-4(x+1)}[/tex]

[tex]\longmapsto\sf{-4x-4}[/tex]

Add 6x:-

[tex]\longmapsto\sf{-4x+6x-4}[/tex]

Combine Like Terms:-

[tex]\longmapsto\sf{2x-4}[/tex]

Now, we should write our answer in factored form, so we factor 2 out:-

[tex]\longmapsto\sf{2(x-2)}[/tex]

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

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

y=-2x-1

Step-by-step explanation: This is because of rise/run. This means rise, count up or down until you hit the line that is horizontal to where your line intersects a whole point. Then run, what you count horizontal matches with your rise count. This means we can count 2/1 and since it's going down it's negative. So the slope is -2 and the y-intercept is -1 because it intersects through the y-intercept -1.

[tex]\qquad\qquad\huge\underline{{\sf Answer}}☂[/tex]

Let's solve, using Trigonometry ~

[tex]\qquad \sf  \dashrightarrow \: \tan(x) = \frac{54}{72} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \tan(x) = \frac{3}{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \tan { }^{ - 1} ( \frac{3}{4} ) [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 37 \degree[/tex]

Answer:

[tex]\displaystyle 36,9[/tex]

Step-by-step explanation:

[tex]\displaystyle 1\frac{1}{3} = cot\:x \hookrightarrow cot^{-1}\:1\frac{1}{3} = x \hookrightarrow 36,869897646...° = x \\ \\ 36,9° ≈ x[/tex]

OR

[tex]\displaystyle \frac{3}{4} = tan\:x \hookrightarrow tan^{-1}\:\frac{3}{4} = x \hookrightarrow 36,869897646...° = x \\ \\ 36,9° ≈ x[/tex]

Information on trigonometric ratios

[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ[/tex]

I am joyous to assist you at any time.

Answer:

Scale factor = 3

Step-by-step explanation:

A - B = 1-3

3 - 1 = 2

A' - B' = 3-9

9 - 3 = 6

6 / 2 = 3

Step-by-step explanation:

area of triangles

1/2*9*8= 36

area of.rectangle

8*9= 72

36+72=108 square inches

Answer:

12%, 0.12, 5/17, or as a ratio: 5:17

Step-by-step explanation:

To find the percentage:

Take the 40 students who prefer cheese and divide it by 340:

0.11764705882 rounded would be 0.12.

Convert 0.12 into 12% of students prefer cheese pizza.

To find the decimal, to the same exact thing I did up there, but, don't turn it into a percent, just leave it as 0.12.

To find the fraction, turn it into:

40/340

Then simplify it:

5/17 prefer cheese pizza.

For ratio, do the same as fraction, but, instead of the slash mark, turn it into a colon like this: 5:17.

:)

Answer:

Step-by-step explanation:

[tex]y=ab^x\\x=0,y=4\\4=ab^0\\4=a(1)\\a=4\\y=4b^x\\x=2,y=256\\256=4b^2\\b^2=\frac{256}{4} =64\\b=\pm8\\y=4(8)^x\\or\\y=4(-8)^x[/tex]

Answer:

The sandbox is most likely in the shape of a kite. As it has only two right angles, it cannot be a square or other form of rectangle. It also cannot be a parallelogram, which has no right angles, nor is it a rhombus- all four sides are not of the same length.

A kite, however, has two pairs of equal-length sides that are adjacent to each other. It also has two sets of equal-measure angles, one of which can be 90° if it is a cyclic kite.

[11]

Equation: 180° - 75°

Measure: 105°

      A straight line has an angle measurement of 180°. Since we have GFB, 75°, we can find EFB this way.

[12]

Equation: 90° - 40°

Measure: 50°

      The little box in the angle shows that it is equal to 90°. Since they give us HGB, 40°, we can solve for EFB using this information.

Answer:

64 cm^3

Step-by-step explanation:

V = lwh

V = 4 x 4 x 4

V = 64 cm^3

Hope this helps!

[tex] \huge\fbox\orange{ANSWER} [/tex]

[tex] \mathsf \purple{volume \: of \: square = {x}^{3} }[/tex]

[tex] \mathsf \pink{v = {4}^{3} }[/tex]

[tex] \mathsf \purple{v = {64cm}^{3} }[/tex]

Answer:

C

Step-by-step explanation:

Remark

The way to solve the problem is to figure out how many cubic feet would be present if the window was not there and then calculate the volume of the window and subtract it. That is the general method used to obtain the answer to the question you have asked.

Volume Original Shape

Each side of the figure is one side of a square.

So the volume of the square face is 6 by 6 or 6*6 = 36 (no window)

The window is 2*2 which is 4.

The volume of the original shape is 36 - 4 = 32

Volume new shape

Each side of the figure is 12 by 12 = 144    With no window

The size of the window is 4 by 4 =   16   With the window (Subtract)

The size of the modified figure is    128

Answer and discussion

The question is a bit ambiguous. I think the question means that the wall has gone from 32 to 128 cubic feet.  So you need Subtract to find the difference..

Answer: 128 - 32 = 96 which is C.

Answer:

150ft^2

Step-by-step explanation:

FINDING THE LENGTHS

50 = x + 5 + x + x + 5 + x

50 = 4x + 10

50 - 10 = 4x

40 = 4x

40/4 = x

10ft = x

AMOUNT OF FLOORING

area = l x b

= (10 + 5) x 10

= 15 x 10

= 150ft^2

Answer:

I don't know sir actually I didn't understand your question no need to reply to my answer bye

Answer:

13

Step-by-step explanation:

if you read through the paragraph and pot your data on the table, the answer will show and is 13

[tex]5^{7/3} = 42.75[/tex] (approximately)

using the formula [tex]x^{a/b}=\sqrt[b]{x^a}[/tex] we can solve the problem

so we rewrite it as [tex]\sqrt[3]{5^7}[/tex] and get ~42.75

The amount Don must pay on his card without  going over the credit limit is $125.

Don's credit limit is $500. If Don does not want to go over the limit, he must not exceed the $500 limit. In order to determine the amount he should pay, add the sum of the charges and subtract it from the credit limit.

Amount to be paid = (425 + 200) - 500 = $125

To learn more about addition, please check: https://brainly.com/question/19628082

Answer:

B 24 million years old

Step-by-step explanation:

i did this quiz a long time ago tho so it might be B or D

Answer: 1.56

Step-by-step explanation:

Add all the cost together, the subtract the ten dollars.

2.18 + 2.28+ 3.98 = 8.44

10.00 - 8.44 = 1.56

[tex]\huge\underline\mathtt\colorbox{cyan}{37✅✅✅}[/tex]

Step-by-step explanation:

Answer:

Third option: An infinite geometric series converges if −1<r<1 is true.

Step-by-step explanation:

An infinite geometric series contains an infinite number of terms. A convergent infinite geometric series can go to infinity on a graph. An infinite geometric series can converge if the ratio "r" is true in the equation " –1 < r < 1".

Answer:

between 222 and 223 days

Step-by-step explanation:

This relation includes the point (0, 2).

A proportional relation must include the point (0, 0).

This is not proportional, but it may be linear.

Points: (0, 2), (2, 20)

y = mx + b

20 = (20 - 2)/(2 - 0) × 2 + b

20 = 18/2 × 2 + b

b = 2

y = 18x + 2

When 4000 people know, y = 4000.

y = 18x + 2

4000 = 18x + 2

3998 = 18x

x = 3998/18

x = 222.111...

Answer: between 222 and 223 days

Answer:

<N and <K

Step-by-step explanation:

Alternate exterior angles are a pair of angles on the outer side of the two parallel lines and are opposite of each other yet their measure is equal to each other.

The pair of angles that meet these requirements mentioned above are angle N and angle K.

Answer:

(a) 8000 times 5 times 2 = 800

The value of n will the terminal side fall on the y-axis at n=3

The terminal side of an angle fall along the positive portion of the y-axis,

If it can written in the form of [tex](90^0)a[/tex]

Where a = positive odd integer,

We hyave given the given angle is,

[tex](870n)^0,[/tex]

The terminal side of an angle theta drawn in angle standard position is the side which isn't the initial side

Now for n=3

[tex](870(3))^0=2610^0[/tex]

The  angle will be 2610°

Its terminal side fall along the positive portion of the y-axis,

[tex]2610^0 = (90^0)a \implies a = 29[/tex]......( Positive odd integer )

Therefore  for n = 3,  the terminal side of the angle (870n)° falls along the positive portion of the y-axis,

For n = 4,

Our angle will be 3480°

Its terminal side fall along the positive portion of the y-axis,

[tex]3480^0 = (90^0)a \implies a = 38.6667 ( Not possible )[/tex]

Therefore for n = 4, the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis

Next is for n = 5,

Our angle will be 4350°

Its terminal side fall along the positive portion of the y-axis,

[tex]4350^0 = (90^0)a \implies a = 48.333.. ( Not possible )[/tex]

Thus, for n = 5,  the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis,

For n = 6,

Our angle will be 5220°

Its terminal side fall along the positive portion of the y-axis,

[tex]5220^0 = (90^0)a \implies a = 58..... ( Not possible )[/tex]

Thus, for n = 6,  the terminal side of the angle (870n)° does not fall along the positive portion of the y-axis.

Therefore,the value of n will the terminal side fall on the y-axis at n=3.

To learn more about the terminal side visit:

https://brainly.com/question/24680641

Answer:

a

Step-by-step explanation:

x=3 on edge

Answer:

x = -3

Step-by-step explanation:

A vertical line has an equation of the form

x = a

where a is the x-coordinate of every point on the line.

Every point on the line has x-coordinate -3, so the equation is

x = -3

I got -7. I tried probably wrong