find the arc length of a sector with a radius of 4 feet and a central angle of 6°

The sum of the triangular numbers is [tex]\frac{n(n+1)(n+2)}{6}[/tex]

According to the question, the series of triangular numbers is given as in the form of the number of dots constituting the equilateral triangles i.e.
1, 3, 6, 10, 15 . . . . .n

triangular number are the sequence and series of the numbers and each number represents and constitute in visualization of  series of  equilateral triangle.

given series in the figure
1, 3, 6, 10, 15, . . . . . .  ., n
each number represents the number of dots containing in triangle
now the series can be given by
[tex]S = \frac{n(n+1)}{2}[/tex]  for n = 1, 2, 3, 4,. . . . .n
now , according to the question the sum of the series can be given as
⇒  ∑S
⇒   ∑[tex]\frac{n^2+n}{2}[/tex]
⇒  [tex]\frac{1}{2}[\sum n^2+\sum n]\\\frac{1}{2}[\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}] \\\frac{n(n+1)}{4}[\frac{(2n+1)}{3}+1] \\\frac{n(n+1)}{4}[\frac{(2n+1+3)}{3}] \\\frac{n(n+1)}{4}[\frac{(2n+4)}{3}] \\\frac{n(n+1)}{4}2[\frac{(n+2)}{3}]\\\frac{n(n+1)(n+2)}{6}[/tex]

Thus, the sum of the triangular number is given by [tex]\frac{n(n+1)(n+2)}{6}[/tex]

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Answer:

Least, Median and Greatest height of boys are all higher then Least, Median and Greatest of girls height

Step-by-step explanation:

Least height of boys: 158cm > 150cm Least height of girls

Median height of boys: 168cm > 165cm Median height of girls

Greatest height of boys: 182cm > 170cm Greatest height of girls

The period of the graphed function is T = 8.

For a sinusoidal function, the period is the horizontal distance between two consecutive peaks.

Here we can see the first peak at x = 1, and the second peak is at x = 9.

The horizontal distance is: 9 - 1= 8.

Then we conclude that the period of the function is T = 8.

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Answer:

^ their right :)

Step-by-step explanation:

Its right on Acellus

have a great day!

The equation of volume will be V = [(1/2)t + 4]³. The surface area as a function of time will be A(s) = 3/2 t² + 24t + 96. The number of hours when the surface area equal 294 square inches will be 3 1/2 hours.

Functions are found all across mathematics and are required for the creation of complex relationships.

Part A: The equation that gives the volume at t hours after freezing begins will be

V = s³

V = [(1/2)t + 4]³

Part B: The surface area as a function of time, using composition, and determine its range will be

A(s) = 6(1/2 t + 4)²

A(s) = 6 (t²/4 + 4t + 16)

A(s) = 3/2 t² + 24t + 96

Part C: The number of hours when the surface area equal 294 square inches will be

294 = 6(1/2 t + 4)²

49 = (1/2 t + 4)²

7 = 1/2 t + 4

1/2 t = 3

t = 3 1/2 hours

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Answer:

258 km

Step-by-step explanation:

We can calculate the speed of the boat with (333km/7 hours) = 47.57 km/hr.

Assuming the same speed, the boat would travel (47.57 km/hr)*(6 hr) = 258 km

Answer:

this quantity refers to the amount that a container can hold.

Answer:

Step-by-step explanation:

Givens

x + y = 2

x - y = 6

Solution

Just add the two equations together. The y's will drop out.

x + y = 2

x - y = 6             Add

2x = 8                 Divide by 2

2x/2 = 8/2          Combine

x = 4                   Substitute x = 4 into the top equation

x + y = 2

4 + y = 2             Subtract 4 from both sides

4-4+y=2-4          Combine

y = - 2    

Answer

x = 4

y = -2

Answer:

54 = 2 × 3 × 3 × 3 = 2 × 3³

[tex] f(x) = 7(\sqrt[3]{54})^x [/tex]

[tex] f(x) = 7(\sqrt[3]{3^3 \times 2})^x [/tex]

[tex] f(x) = 7(3\sqrt[3]{2})^x [/tex]

Initial value: x = 0

[tex] f(0) = 7(3\sqrt[3]{2})^0 [/tex]

[tex] f(0) = 7(1) [/tex]

[tex] f(0) = 7 [/tex]

The initial value is 7.

The domain is all real numbers.

The range is all real numbers greater than zero.

Answer:3.5s2

Step-by-step explanation:

because I said so

Answer:

3.5s2

Step-by-step explanation:

because that guy said so and it was right

Answer:

4 days

Step-by-step explanation:

1) Derive a formula.

Let b = bicycle

Let x = the number of days

A set up equation: b = 6x + 15

2) If she pays 39 to hire a bicycle, substitute 39 into b, then solve for x.

39 = 6x + 15

39 - 15 = 6x

24 = 6x

24/6 = x

4 = x

x = 4

Since x is the number of days, she hired the bicycle for 4 days.

Answer:

B

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 1) and (x₂, y₂ ) = (- 4, 11) ← 2 ordered pairs from the table

m = [tex]\frac{11-(-1)}{-4-2}[/tex] = [tex]\frac{11+1}{-6}[/tex] = [tex]\frac{12}{-6}[/tex] = - 2

Step-by-step explanation:

[tex]f(x) = 2 {x}^{2} [/tex]

[tex] \: [/tex]

[tex] = (f \circ f)(x)[/tex]

[tex] = f(f(x))[/tex]

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

[tex] = 2 {(2 {x}^{2} )}^{2} [/tex]

[tex] = 2(4 {x}^{4} )[/tex]

[tex] = 2.4 {x}^{4} [/tex]

[tex] = 8 {x}^{4} [/tex]

The answer is A.

The measure of angle x will be 88 degrees. Then the correct option is C.

The complete question is attached below.

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

2ab cos θ = a² + b² – c²

The triangle is shown below.

Then the value of the variable x will be

2 · 7 · 10 · cos x = 7² + 10² – 12²

       140 · cos x = 49 + 100 – 144

                cos x = (149 – 144) / 140

                       x = 87.95 ≈ 88°

Then the correct option is C.

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The number of months before the complex would have 800 occupied units is 40 months.

The formula that can be used to determine the required value is:

(In FV / PV) / r

Where:

(In 800 / 15) / 0.1 = 40 months

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Answer: 47.3 months

Step-by-step explanation:

Answer:

D

Step-by-step explanation: the larger abs(r value) is, (abs of r closest to 1) the better the correlation. Negative values indicate a negative correlation (negative slope)

Answer:

since it talks about a ratio of margarine to flour, we should write it in this form:

Since we have a 50g margarine and a 200g flour, therefore, we write it as

➡️ 50 : 200 ➡️ 1 : 4

FINAL ANSWER SHOULD BE:

Step-by-step explanation:

Ratio of MARGARINE TO FLOUR

Given that margarine is 50g and flour is 200g. Therefore,

Margarine:Flour ➡️ 50:200 = 1:4

To check:

A:B= C:D ➡️ 50:200= 1:4

▶️AD= BC ➡️ (50) (4) = (200) (1)

➡️ 200 = 200

☑️

Hope it helps

Step-by-step explanation:

[tex]f(x) = 2 {x}^{2} + 3x - 3[/tex]

[tex]f( - 1) = 2. {( - 1)}^{2} + 3.( - 1) - 3[/tex]

[tex]f( - 1) = 2 - 3 - 3[/tex]

[tex]f( - 1) = - 4[/tex]

Considering the given scatter-plot, the line of best-fit is given by:

y = 0.77857t + 3.7.

To find the equation, we need to insert the points (t,y) in the calculator.

In this problem, considering the scatter-plot, we have that:

Hence, using the calculator, the equation is:

y = 0.77857t + 3.7.

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A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Here we have.

-3(2x - 5) < 5*(2 - x)

First, we need to isolate x in one side, let's expand both sides:

-6x + 15 < 10 - 5x

15 - 10 < 6x - 5x

5 < x

This will be represented with a number line where we have an open circle at 5, and an arrow that goes to the right. So the correct option is:

"A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right."

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Answer:

-22.2222222222%

Step-by-step explanation:

-0.4/1.8×100

Answer:

10. Ray ED and Ray EF (two rays)

11. DE and EF (two line segments)

Step-by-step explanation:

hope this helped

Answer:

Ray ED and Ray EF

DE and EF

Step-by-step explanation:

The answer is option D which is the range will be ( -∞, ∞ ).

After substituting the domain, the range of a function is the entire set of all possible values for the dependent variable (often y).

Given function is

u(x) = -2x²+3 and v(x) = ( 1 / x ).

The product of the function will give uv(x).

uv(x) = (-2x²+3 ) x  [tex]\dfrac{1}{x}[/tex]

uv(x) = [tex]\dfrac{-2x^2+3}{x}[/tex]

When we plot the graph of the function we found two opposite curved graphs and they are not intersecting at any point so the range will be from negative infinity to positive infinity. The graph of the function is attached with the answer below.

Therefore the answer is option D which is the range will be ( -∞, ∞ ).

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: E.\:\: \overline{DC}[/tex]

or

[tex]\qquad \tt \rightarrow \: F.\:\:\overline{CD}[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

A line with two dots at ends (two ends) represents a line segment.

And it can be represented as :

[tex]\qquad \tt \rightarrow \: \overline{DC}[/tex]

or

[tex]\qquad \tt \rightarrow \: \overline{CD}[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees

These method is used to determine the side and angles of a triangle

From the question given, we have the following parameters

Base of the building = 7feet (Adjacent side)

Height of the building = 18 feet (Opposite side)

Required

angle of elevation of the building

Using the SineOppositeHypotenuse CosineAdjacentHypotenuse TangentOppositeAdjacent identity

tanФ = opp/adj

tanФ = 18/7

Ф = 68.73 degrees

Hence the measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees

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The x-intercepts and the y-intercepts of the function is that determines the graph is:

The function of an absolute equation can be graphed by determining the values of x-intercepts and the y-intercepts of the function.

From the given equation:

y = 2|x+3| - 4

To determine the y-intercepts, we need to set the values of x to zero, and vice versa for x-intercepts.

By doing so, the x-intercepts and the y-intercepts of the function is:

Therefore, since we know the x and y-intercepts, the graph of the absolute value can be seen as plotted below.

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The pair of limits that would verify the existence of a vertical asymptote at x = –1 is:

[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

For a vertical asymptote at x = -1, the denominator is zero at -1, hence both lateral limits at x = -1 go to infinity, that is:

[tex]\lim_{x \rightarrow -1^-} = \infty, \lim_{x \rightarrow -1^+} = \infty[/tex]

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[tex]-3(x^{2} +5x+10)[/tex] is the standard form of the given expression

The given expression is:

[tex]=-3(x+3)^{2} -3+3x\\\\=-3*(x^{2} +2*3*x+3^{2} )-3+3x\\\\=-3x^{2} -3*6x-3*9-3+3x\\\\=-3x^{2} -18x-27-3+3x\\\\=-3x^{2} -15x-30\\\\=-3(x^{2} +5x+10)[/tex]

This is the standard form of the given expression.

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Answer:

∠ DCF = 39°

Step-by-step explanation:

the secant- secant angle DCF is half the difference of the measures of the intercepted arcs, that is

∠ DCF = [tex]\frac{1}{2}[/tex] (EG - DF) = [tex]\frac{1}{2}[/tex] (127 - 49)° = [tex]\frac{1}{2}[/tex] × 78° = 39°

Answer:

[tex]\frac{x}{12}[/tex] (x/12)

Step-by-step explanation:

if 12 pieces combine to make x, [we know they are identical], each piece must be 1/12 of x [1/12·x = x/12]

(think of it like this: "x" length must be divided amongst 12 pieces, so, we divide x/ 12)

Answer:

Timber=x/12

Step-by-step explanation:

12 pieces long is x, if the length of each one is same, so the length of each one is x/12.

Answer:

0 represents the ground level