help solve a problem

Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

Answer:

A

Step-by-step explanation:

Because square root of 30 is 5.4 rounded, and square root of 6 is 2.4 rounded, so 5.4 divided 2.4 is 2.25, and square root of 5 (Answer choice A) is 2.25 rounded as well. They are more accurate when not rounded btw u can check yourself:) HAVE A GREAT DAY/NIGHTT!

If Mira had spent the same total amount of time but an equal amount of time on each problem, each problem would have taken around 2.36 minutes.

In the given plot, Mira spent varying amounts of time on each of the 55 math problems. To find out how many minutes each problem would have taken if Mira had spent an equal amount of time on each problem, we need to calculate the total time she spent and divide it by the number of problems.

Looking at the plot, we can estimate the total time Mira spent by counting the dots above each tick mark and multiplying them by the corresponding time interval. Let's break it down step by step:

The tick marks on the plot are at 7, 7.5, 8, 8.5, 9, 9.5, and 10 minutes per problem.

There are 2 dots above the unlabeled tick mark between 8 and 8.5 minutes per problem. We can assume it represents 8.25 minutes.

There are 3 dots above the 9.5 minutes per problem tick mark.

Now, let's calculate the total time Mira spent:

(7 * 2) + (7.5 * 2) + (8 * 2) + (8.25 * 2) + (9 * 2) + (9.5 * 3) + (10 * 2) = 129.5 minutes.

Since Mira spent a total of 129.5 minutes on 55 problems, each problem would have taken approximately 2.36 minutes (rounded to two decimal places) if she had spent an equal amount of time on each problem.

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Answer:

-225

Step-by-step explanation:

-30(7)-15

-210-15

-225

Answer:

  220

Step-by-step explanation:

You want to use differences to find the pattern and the next term in the sequence 3, 8, 15, 28, 51, 88, 143.

Subtracting each term from the next, we find the sequence of first differences to be ...

  5, 7, 13, 23, 37, 55

The first differences are not constant, so we know the sequence is not linear. They are not in an arithmetic progression, so we know the sequence is not quadratic. They do not have a common ratio, so we know the sequence is not exponential.

The second differences are the differences of the sequence of first differences. They are ...

  2, 6, 10, 14, 18

The differences of the terms of the 2nd-difference sequence are constant: 4.

  4, 4, 4, 4, 4

Constant 3rd differences mean the original sequence can be described by a 3rd degree polynomial. The coefficients found by a calculator are shown in the attachment.

Since we know the third differences are constant, we can work our way back up the chain of differences to find the next term of the original sequence.

  next 2nd difference = 18 +4 = 22

  next 1st difference = 55 +22 = 77

  next sequence term = 143 +77 = 220

The eighth term should be 220.

__

Additional comment

The n-th term is ...

  f(n) = 2/3n^3 -3n^2 +28/3n -4

We can write g in terms of f as: g(x) = f(x) - 3 = x² - 3

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

To write g in terms of f, we can use function composition, which involves plugging the function f(x) into g(x) wherever we see x.

So, we have:

g(x) = f(x) - 3

where f(x) = x².

Substituting f(x) into g(x), we get:

g(x) = (x²) - 3

Therefore, we can write g in terms of f as:

g(x) = f(x) - 3 = x² - 3.

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Answer:

just multiply everything together, to get volume.

Answer:

The general volume of a pyramid formula is given as: Volume of a pyramid = 1/3 x base area x height.

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

The vertical distance between the sinusoidal axis and the maximum or minimum value of the function.

Trust

It is the last one ...................

A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;

g(x) = kf(x)

g(x) = 1/2f(x)

\(g(x) = \frac{1}{2} e^x -4\)

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Answer:

22 sides

Step-by-step explanation:

The expression to find an interior angle of a polygon is:

\(\frac{(n-2)*180}{n}\)

The expression to find an exterior angle of a polygon is:

\(\frac{360}{n}\)

Please note that "n" represents the number of sides the polygon has.

We can use these two expressions to set up an equation.

\(\frac{(n-2)*180}{n}=10(\frac{360}{n})\)

Multiply both sides by "n":

\((n-2)*180=10n(\frac{360}{n})\)

Now, distribute:

\(180(n)-180(2)=\frac{3600n}{n}\\180n-360=3600\)

Divide both sides by 10:

\(\frac{180n}{10}-\frac{360}{10}=\frac{3600}{10}\\\)

\(18n-36=360\)

Add 36 to both sides:

\(18n=360+36\\18n=396\)

Divide both sides by 18:

\(n=22\)

The polygon has 22 sides

Answer:

solution

4%=260

100%=?

=(100x260)/4

=6500

Percentage of fans in the stadium who were teenagers = 4%

Number of teenagers in the match = 260

Let the total number of people at the stadium be x.

Which means :

\( =\tt 4\% \: \: of \: \: x = 260\)

\( =\tt \frac{4}{100} \times x = 260\)

\( =\tt \frac{4 \times x}{100} = 260 \)

\( = \tt \frac{4x}{100} = 260\)

\( = \tt4x = 260 \times 100 \\ \tt \: \: \: = 26000\)

\( =\tt x = \frac{26000}{4} \)

\(\color{plum} =\tt x = 6500\)

▪︎Therefore, number of people at the stadium = 6500

Answer: 9

Step-by-step explanation:

3/4mile takes 1/12 hours

so a whole hour is 3/4 / 1/12 = 3/4*12 = 9miles/hour

Answer:

3/2 miles per hour

Step-by-step explanation:

To find his average speed, divide 3/4 mile by 1/2 hour:

 3        2

----- *  ------ = 3/2 miles per hour

 4         1

Answer:

102.0625 square units

Step-by-step explanation:

First determine the length of each side using the distance formula  for two points. Then use Heron's formula to determine the area of a triangle given three sides

Distance Formula

The distance between two points is the length of the path connecting them

The distance between points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean theorem:

\(d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

Let's compute the lengths of the sides FH, FG and HG

The three vertices are F(-2, 5)   G(7, -10) and H(-9, -6)  as indicated on the graph

So length FG between (-2,5) and (7,-10)

\(FG= \sqrt {(7 - (-2))^2 + (-10 - 5)^2}\)

\(= \sqrt {(9)^2 + (-15)^2}\)

\(= \sqrt {{81} + {225}}\)

\(= \sqrt {306}\)

FG \(= 17.492856\)  (round to 17.5)

Length FH between(-2,5) and (-9, -6) is

\(FH = \sqrt {(-9 - (-2))^2 + (-6 - 5)^2}\)

\(= \sqrt {(-7)^2 + (-11)^2}\)

\(= \sqrt {{49} + {121}}\)

\(= \sqrt {170}\)

FH \(= 13.038405\)  (can be rounded to 13.04

Length GH between (7, -10) and (-9, -6) is

\(GH = \sqrt {(-9 - 7)^2 + (-6 - (-10))^2}\)

\(= \sqrt {(-16)^2 + (4)^2}\)

\(= \sqrt {{256} + {16}}\)

\(= \sqrt {272}\)

GH \(= 16.492423\)   (can be rounded to 16.5)

Determining the area of a triangle given 3 sides

Heron's formula allows us to find the area of a triangle given 3 sides If the sides are a, b and c the general form of Heron's formula is

\(Area = \sqrt {s(s-a)(s-b)(s-c)}\)

where s is the semi-perimeter = \(\frac{a+b+c}{2}\)

Substituting values we get

s = \(\frac{17.5+13.04+16.5}{2} = 23.52\)

\(Area = \sqrt {23.52(23.52-17.5)(23.52-13.04)(23.52-16.5)}\)

\(= \sqrt{23.52\cdot6.02\cdot10.48\cdot7.02}\)

\(102.0625\)  square units

9514 1404 393

Answer:

  (c)  -3/4

Step-by-step explanation:

Subtracting a positive number moves you to the left on the number line. Subtracting a negative number moves you in the opposite direction, to the right.

Here, we start at -2 1/2 = -5/2, and we move 1 3/4 = 7/4 to the right from there. Each mark on this number line is 1/4 unit, so we move 7 marks. The results is ...

  -2 1/2 -(-1 3/4) = -5/2 +7/4

  = -10/4 +7/4 = -3/4

The asked consecutive even integers are -4,-2,0,2

Consecutive integers are whole numbers that follow each other without gaps. For example, 15, 16, 17 are consecutive integers.

Given that, what are four consecutive even integers if the first integer is −4

We know that, Consecutive even integers are even integers that follow each other, and they differ by 2. If x is an even integer, then x + 2, x + 4 and x + 6 are consecutive even integers.

Therefore, here x = -4,

-4+2 = -2

-4+4 = 0

-4+6 = 2

Hence, the asked consecutive even integers are -4,-2,0,2

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Answer:1.5

Step-by-step explanation:

Y=1/2 of x

Answer: 23

Step-by-step explanation:

Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

When budgeting for housing, it is generally recommended to allocate a certain percentage of your income towards housing expenses. The recommended percentage varies depending on factors such as location, personal financial goals, and individual circumstances.

A common guideline is to spend no more than 30% of your monthly income on housing expenses. To determine the maximum amount Freya should budget for housing, we can calculate 30% of her monthly income:

Maximum housing budget = 30% of $1575

Maximum housing budget = 0.30 × $1575

Maximum housing budget = $472.50

Therefore, Freya should budget a maximum of $472.50 for housing expenses based on the guideline of spending 30% of her monthly income.

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Answer:

root(x+6) +3

Step-by-step explanation:

so you see that it is moved 2 left and 5 up

so root (x+6) +3

The location of L″ is (-5, 0).

To find the location of L″, we first need to apply the first translation rule to the coordinates of trapezoid JKLM:

J': (x, y) → (x + 3, y - 3) => J'(-2+3, 1-3) = J(1, -2)

K': (x, y) → (x + 3, y - 3) => K'(1+3, 1-3) = K(4, -2)

L': (x, y) → (x + 3, y - 3) => L'(3+3, -2-3) = L(6, -5)

M': (x, y) → (x + 3, y - 3) => M'(-4+3, 2-3) = M(-1, -1)

Now, we need to apply the second translation rule to the coordinates of J', K', L', and M':

J'': (x, y) → (x - 1, y + 1) => J''(1-1, -2+1) = J''(0, -1)

K'': (x, y) → (x - 1, y + 1) => K''(4-1, -2+1) = K''(3, -1)

L'': (x, y) → (x - 1, y + 1) => L''(6-1, -5+1) = L''(5, -4)

M'': (x, y) → (x - 1, y + 1) => M''(-1-1, -1+1) = M''(-2, 0)

Therefore, the location of L″ is (-5, 0).

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Answer:

(5,-4)

Step-by-step explanation:

Answer:

(4 1/2 , 1 1/2)

Step-by-step explanation:

to find midpoint follow the formula (x1 +x2/2 , y1+y2/2)

so (2+7/2 , 8 + -5/2)

(9/2 , 3/2)

(4.5 , 1.5)

Answer:

x2-4=0 and 4x 2 = 16

The second derivative of f(x) = 2x3 + 9x2 -60x + 70 is f''(x) = 6x2 + 18x - 60, and its sign chart shows that f is concave up for x> -3/2; concave down for x< -3/2; inflection point at x=-3/2, option d is true, and f is concave up for x> -3/2; concave down for x< -3/2; inflection point at x=-3/2.

The second derivative of \(f(x) = 2x3 + 9x2 -60x + 70 is f''(x) = 6x2 + 18x - 60.\) This means that the sign chart for f''(x) is + for x> -10/3, 0 for x= -10/3 and - for x< -10/3. This means that the function is concave up for x> -10/3, concave down for x< -10/3, and has an inflection point at x = -10/3. This means that option d is true, and f is concave up for x> -3/2; concave down for x< -3/2; inflection point at x=-3/2.

To determine this, we need to calculate the second derivative of f(x). The derivative of a polynomial is calculated using the power rule, which states that the derivative of f(x) = axn is f'(x) = anxn-1. Therefore, the second derivative of f(x) = 2x3 + 9x2 -60x + 70 is f''(x) = 6x2 + 18x - 60. We can then plot a sign chart of the second derivative, which will show us the intervals where the function is increasing or decreasing. For f''(x), the sign chart is + for x> -10/3, 0 for x= -10/3 and - for x< -10/3. This means that the function is concave up for x> -10/3, concave down for x< -10/3, and has an inflection point at x = -10/3, which is the same as saying that f is concave up for x> -3/2; concave down for x< -3/2; inflection point at x=-3/2.

The second derivative of f(x) = 2x3 + 9x2 -60x + 70 is f''(x) = 6x2 + 18x - 60, and its sign chart shows that f is concave up for x> -3/2; concave down for x< -3/2; inflection point at x=-3/2.

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Answer: \(r(s(5))=-26\)

Step-by-step explanation:

\(s(5)=5^2 +2=27\\\\r(s(5))=r(27)=-27+1=-26\)

The solution of the equation 4x - 3  = 5 is not extraneous .

Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.

Therefore, let's solve the equation to know whether it is extraneous solution.

Hence,

4x - 3  = 5

add 3 to both sides of the equation

4x - 3 + 3 = 5 + 3

4x = 8

divide both sides of the equation by 4

4x / 4 = 8 / 4

x = 2

Therefore, it is not extraneous solution.

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