Two students each write a function, C(n), that they think can be used to find the number of circles needed to make the nth figure in the pattern shown.

Use the drop-down menus to explain why each function does or does not represent the number of circles needed to make the nth figure in the pattern.

Answer:

[tex] \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} }[/tex]

[tex]LHS = \displaystyle{ \sqrt{ \frac{1 + cos \: {30}^{ \circ} }{1 - cos \: {30}^{ \circ} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{1 + \frac{ \sqrt{3} }{2} }{1 - \frac{ \sqrt{3} }{2} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{ \frac{2 + \sqrt{3} }{2} }{ \frac{2 - \sqrt{3} }{2} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{2 + \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } } }[/tex]

[tex] \displaystyle{ \sqrt{ \frac{(2 + \sqrt{3} {)}^{2} }{4 - 3} } }[/tex]

[tex] \displaystyle{2 + \sqrt{3} }[/tex]

[tex]RHS = sec \: {60}^{ \circ} + tan \: {60}^{ \circ} [/tex]

[tex] = 2 + \sqrt{3} [/tex]

[tex] \rm\therefore{LHS=RHS,proved. }[/tex]

Answer:

778ft

Step-by-step explanation:

[tex]\mathsf\pink{♧ANSWER♧}[/tex]

[tex] \mathsf \purple{0.85 = \frac{85}{100} = \frac{17}{20} }[/tex]

85/100 = 17/20

first we write the fraction from of 0.85 which is 85/100

then for simplifying it, we divide both 85 and 100 by 5

then we get to 17/20 which is our final answer

Answer:

  see attached

Step-by-step explanation:

The values are plotted on the number line attached.

__

Each value is represented on the list both as a fraction and as a decimal. Equal values map to the same point on the number line.

  0.27 = 27/100

  0.49 = 49/100

  0.75 = 75/100

The location on the number line is found by effectively dividing the distance between 0 and 1 into 100 parts, then locating the point on the corresponding division. The attached number line shows the interval divided into 50 parts, so the given values will lie halfway between the grid marks on this number line.

Answer:

5x+3

Step-by-step explanation:

[tex]\left[Thank\;you\;for\;Joining\;Brainly!][/tex]

Answer:

5x + 3

Step-by-step explanation:

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

[tex]\mathrm{Expand\;2(4x+3)}:8x+6[/tex]

[tex]=8x+6-3\left(x+1\right)[/tex]

[tex]\mathrm{Expand\;-3(x+1)}:-3x-3[/tex]

[tex]=8x+6-3x-3[/tex]

[tex]\mathrm{Group\:like\:terms}[/tex]

[tex]=8x-3x+6-3[/tex]

[tex]\mathrm{Subtract\:the\:numbers:}\:6-3=3[/tex]

[tex]=8x-3x+3[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:8x-3x=5x[/tex]

[tex]=5x+3[/tex]

Hence, your answer is 5x + 3

[RevyBreeze]

Answer:

y = -2x - 2

Step-by-step explanation:

Answer:

2880 cubic meters.

Step-by-step explanation:

To find the area of a rectangular prism, multiply the length width and height.
20*12*12=144*20=2880

The volume of the Rectangular Prism is 2880 cubic meters.

Rectangular prism can be defined as a" 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid".

According to the question,

Length of the rectangular prism = 20 meters

Height of the rectangular prism = 12 meters

Width of the rectangular prism = 12 meters

Formula for Rectangular Prism = length × breadth × height

= 20 × 12 × 12

= 2880 cubic meters.

Hence, the volume of the Rectangular Prism is 2880 cubic meters.

Learn more about Rectangular Prism here

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Step-by-step explanation:

We can Show that ∆ABC is congruent to∆A'B'C' by a translation of 1 units(s) to the left and a reflection across the X -axis.

We can show that ΔABC is congruent to ΔA'B'C' by a translation of 2 units to the left and reflection across the x-axis.

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given that the two triangles ABC and A'B'C'.

The points are A(8, 8), B(10, 4) and C(2, 6).

And A'(6, -8), B'(8, -4), and C'(0, -6).

The translation rule 2 units to the left and reflection across the x-axis.

We can show that ΔABC is congruent to ΔA'B'C' by a translation of 2 units to the left and reflection across the x-axis.

Therefore, the required translation rule is given above.

To learn more about the reflection;

https://brainly.com/question/11232423

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Hi there!

Part D:

We can use the Taylor Polynomial expansion for a second-degree polynomial:

[tex]P_3(x) = g(c) + \frac{g'(c)}{1!}(x - c) + \frac{g''(c)}{2!}(x - c)^2[/tex]
Where c is the value that the polynomial is centered about.

We are given that:
[tex]g(c) = 1\\\\g'(c) = 0\\\\g''(x) = 2[/tex]

Therefore:
[tex]P_3(x) = 1 + \frac{0}{1}(x - 2) + \frac{2}{2!}(x - 2)^2\\\\\boxed{P_3(x) = 1 + (x - 2)^2}[/tex]

Answer:

-5x+7y+25=0

Step-by-step explanation:

vecto AB= (7;5)

vecto n = (-5;7)

line through the points (-2;5) and (5;0) :

-5*(x+2)+7*(y+5)=0

-5x+7y+25=0

Answer:

x = 15

Step-by-step explanation:

the easiest way to do this is 5 times 3 and with that we get 15 :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

Step-by-step explanation:

answer: x = 15

explanation in picture

[tex]4x^2+12x=32\\\\\implies x^2+3x=8\\\\\implies x^2 +2 \cdot \dfrac 32 \cdot x+\left(\dfrac 32 \right)^2 - \left(\dfrac 32\right)^2 =8\\ \\\implies \left(x+\dfrac 32 \right)^2 = 8 + \dfrac 94 = \dfrac{41}4\\\\\implies x+\dfrac 32 = \pm\dfrac{\sqrt{41}}2\\\\\implies x = \pm \dfrac{\sqrt {41}}2 - \dfrac 32\\\\\text{The roots are}~ x = -\dfrac 32-\dfrac{\sqrt{41}}2~ \text{and}~~ x = -\dfrac 32+\dfrac{\sqrt{41}}2[/tex]

Answer:

No No No No No No No No No No No No No

c = 25(h)

dependent variable : They must give $25 per hour.

independent variable: time is independent as no specific time given.

total cost = $25 * hours taken

c = 25 * h

c = 25(h)

Answer:

See below ↓

Step-by-step explanation:

Given

Solving

Answer:

Step-by-step explanation:

Answer:

a = 5, b = -12

Step-by-step explanation:

By basic factoring, you get 9 - 12i + [tex]4i^2[/tex]. Since [tex]i^2[/tex] is simply -1, the expression evaluates to 9 - 12i - 4, which is 5 - 12i.

Answer:

x = 12

Step-by-step explanation:

Becuase 6/12 = 2 and 9 + 2 = 11

12

Answer:

Step-by-step explanation:

Essentially, recall what an absolute value function is.

When you plug number into an absolute value function, or make it an absolute value, you will ALWAYS get a positive version of that number.

When the question asks, what number could be the absolute value of another number, it's asking you what is a possible outcome of making a number an absolute value.

Since we know that making any number an absolute value, makes that number positive. We can get rid of all of the negative answers.

You are left with B.

Answer:

B. 1200

Step-by-step explanation:

Absolute value is the non-negative version of a number/variable. Whether the sign is negative or positive, the absolute value is always positive.

Example:

|-4|=4
|2|=2

Answer:

v = length x width x hight

Answer:

y = -3x + 1

Step-by-step explanation:

as we can see the y intercept is 1 because on the y- axis (0,1)

for slope it is 3 because rise over run. We rise 3 and run 1 = 3/1 = 3

the slope is negative because of the line

Hope this helps!!

Answer:

y=-3x+1

Step-by-step explanation:

Answer:

D. x< -6

Step-by-step explanation:

Divide both sides by −2. Since −2 is negative, the inequality direction is changed.

x < 12/-2

Divide 12 by −2 to get −6.

x < -6

Answer: B,D,C,A

Step-by-step explanation:

I hope that helps

Please mark me the brainiest !

Answer:

Alex = No B.

Step-by-step explanation:

1) Use Quotient Rule: [tex]\frac{x^{a} }{x^{b} } =x^{a-b}[/tex]

[tex]n^{1-3}[/tex]

2) Simplify 1 - 3 = 2

[tex]n^{-2}[/tex]

3) Use Negative Power Rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex]

[tex]\frac{1}{n^{2} }[/tex]

Answer:

x=23

Step-by-step explanation:

An inscribed angle is half of the intercepted arc.

Answer:

x > 8

Step-by-step explanation:

5x > 40

40/5 = 8

x> 8

subtract 14

divide by 5

Answer:

x = 44.5 due to the Triangle Angle Sum Theorem

Step-by-step explanation:

This is the Triangular Angle Sum Theorem.

This rule states that every angle inside the triangle has to equal 180.

This is a solve for x situation

2x + x + x + 2 = 180

Add all the x's first

3x + x + 2 = 180

4x + 2 = 180

Now subtract 2 both sides

4x = 180 -2

4x = 178

Divide 178 by 4

x = 44.5

You could verify by plugging 44.5 into the x's

2(44.5) + 44.5 + 44.5 + 2 = 180

89 + 44.5 + 46.5 = 180

Answer:

x = 44.5

Step-by-step explanation:

2x + x + (x+2) = 180

4x + 2 = 180

4x = 178

x = 44.5

Just saw your last comment :)

Let me know if you have any questions!

Answer: The domain of this function is any real number. More mathematically it is put as

-∞ < x <+∞

Answer:

The domain of this function is any real number. More mathematically it is put as

-∞ < x <+∞

Step-by-step explanation:

Answer:

7 nights

Step-by-step explanation:

If he does 1/3 every night then you must turn 2 1/3 into a mixed fraction.

7/3

Then divide.

7/3 by 1/3

your answer is 7/1 or just 7 nights

Just divide

No of nights

He need 7 nights

Answer:

65 degrees

Step-by-step explanation:

The angles will sum up to 360, just do 360 - all known angles

360 - 90 - 128 - 77 = 65

Answer:

Step-by-step explanation:

Sum of all angles is 360 degrees

Let the measure of angle M equal x.

x+90+77+128=360

x=65

Measure of angle M is 65 degrees