4. Find the area of the following figure.
10 cm
16 cm
10 cm
12 cm

[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ n=10\\ a_1=4\\ r=\frac{1}{4} \end{cases}[/tex]

[tex]{\displaystyle\sum_{n=1}^{10}}~4\left( \frac{1}{4} \right)^{n-1}\implies 4\left( \cfrac{1-\left( \frac{1}{4} \right)^{10}}{1-\frac{1}{4}} \right)\implies 4\left( \cfrac{\frac{1048575}{1048576}}{\frac{3}{4}} \right) \\\\\\ 4\left( \cfrac{349525}{262144} \right) \implies \cfrac{349525}{65536} ~~ \approx ~~ 5.33[/tex]

Answer:

Sin 60°

Sin 60°

Cos 30°

Cos 30°

Answer:

[tex](-6)^{7}[/tex]

Step-by-step explanation:

using the rule of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

then

[tex](-6)^{5}[/tex] × (- 6)²

= [tex](-6)^{(5+2)}[/tex]

= [tex](-6)^{7}[/tex]

Answer:

two are supplementary. the measure of one of these angles is 12 degrees less than one-third the measure of the other.what is the measure of each angle

Let's call the measures of the two angles x and y, where x is the larger angle. We know that the two angles are supplementary, which means they add up to 180 degrees:

x + y = 180

We also know that one of the angles (let's say y) is 12 degrees less than one-third the measure of the other angle (x):

y = (1/3)x - 12

Now we can substitute the second equation into the first equation to solve for x:

x + (1/3)x - 12 = 180

Multiplying both sides by 3 to get rid of the fraction, we have:

3x + x - 36 = 540

Combining like terms, we get:

4x - 36 = 540

Adding 36 to both sides, we get:

4x = 576

Dividing both sides by 4, we get:

x = 144

Now we can use the first equation to solve for y:

144 + y = 180

Subtracting 144 from both sides, we get:

y = 36

Therefore, the measures of the two angles are 144 degrees and 36 degrees.

The sum of the sides of a regular polygon is 96ft, find the measure of it side.

Let's say that the regular polygon has n sides, and each side has length s. The formula for the sum of the sides of a regular polygon is:

sum of sides = n * s

We know that the sum of the sides is 96ft, so we can write:

96 = n * s

We want to find the length of each side, so we need to isolate s on one side of the equation. We can do this by dividing both sides by n:

s = 96/n

Now we can substitute this expression for s into the formula for the perimeter of a regular polygon:

Perimeter = n * s

Perimeter = n * (96/n)

Simplifying this expression, we get:

Perimeter = 96

We know that the perimeter of a regular polygon is the sum of the lengths of all its sides, so we can divide the perimeter by the number of sides to find the length of each side:

s = Perimeter / n = 96 / n

Therefore, the length of each side of the regular polygon is 96/n feet. We cannot determine the value of n from the given information in the problem.

The second x - intercept on the graph of a car that has been travelling for 8 hours, represents the end of the car's journey.

To show a car's journey on a graph with two x-intercepts, determine the scale for your x-axis and y-axis based on the range of values for your car's journey.

The x-intercepts represent the points where the car starts and ends its journey. These points should be plotted on the x-axis at the appropriate values based on your scale. Once you have plotted the x-intercepts and any intermediate points, connect them with a line to show the car's journey.

In conclusion, the second x - intercept shows the end of the car's journey.

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The pattern fοr the given rule is 5, 6, 7, 8, 9 and sο οn.

What is a pattern?

A pattern is a regular arrangement οf symbοls, such as numbers, geοmetric fοrms, οr cοlοurs. Sοmetimes the term "series" is used tο describe patterns.

We are given a rule as a + 4, where a = 1, 2, 3, 4, 5, ...On substituting the value οf a in the rule, we get

When a = 1, then a + 4 = 5

When a = 2, then a + 4 = 6

When a = 3, then a + 4 = 7

When a = 4, then a + 4 = 8

When a = 5, then a + 4 = 9

and the pattern cοntinues.

Hence, the pattern fοr the given rule is 5, 6, 7, 8, 9 and sο οn.

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Complete question:

This is the only question:

Create a pattern for the rule a + 4.

Answer: 2/7 as a decimal rounded to the nearest thousandth is 0.286.

The commercial message that need to be run on every medium to maximize the audience is x = 15, y = 7 and z = 12.

A mathematical method called linear programming is used to maximise a linear objective function under the restrictions of linear equality and inequality. Finding choice variable values that maximise or decrease the objective function while meeting the limitations is required.

Let us suppose the number of advertisement run on television = x.

Let us suppose the number of advertisement run on radio = y.

Let us suppose the number of advertisement run on online = z.

Then,

140,000x + 18,000y + 30,000z

The constraints on the ads run on are as follws:

1,500x + 200y + 550z <= 24,100 (budget constraint)

x <= 15 (television usage limit)

y <= 19 (radio usage limit)

z <= 12 (online usage limit)

y <= 0.45(x+y+z) (radio usage limit as a percentage of total usage)

x >= 0.15(x+y+z)

Using the linear programming model we have:

x = 15, y = 7 and z = 12.

Substitute the value of x, y, and z:

140,000(15) + 18,000(7) + 30,000(12) = 2,910,000

Hence, the commercial message that need to be run on every medium to maximize the audience is x = 15, y = 7 and z = 12.

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[tex]\cfrac{\sqrt[5]{1024h^{-8}s^5}}{\sqrt[5]{h^{-5}s^9}}\implies \sqrt[5]{\cfrac{1024h^{-8}s^5}{h^{-5}s^9}}\implies \left( \cfrac{2^{10}h^{-8}s^5}{h^{-5}s^9} \right)^{\frac{1}{5}}\implies \left( \cfrac{2^{10}}{h^{-5}h^8s^{-5}s^9} \right)^{\frac{1}{5}}[/tex]

[tex]\left( \cfrac{2^{10}}{h^{8-5}s^{9-5}} \right)^{\frac{1}{5}}\implies \left( \cfrac{2^{10}}{h^3 s^4} \right)^{\frac{1}{5}}\implies \cfrac{2^{10\cdot \frac{1}{5}}}{h^{3\cdot \frac{1}{5}}s^{4\cdot \frac{1}{5}}} \\\\\\ \cfrac{2^2}{h^{\frac{3}{5}}s^{\frac{4}{5}}}\implies {\Large \begin{array}{llll} \stackrel{k ~ ~~ ~ r ~~~ t }{4h^{-\frac{3}{5}}s^{-\frac{4}{5}}} \end{array}}[/tex]

Answer:

These distances show that AB, which is only 10 nautical miles apart, and AB are the closest pair of islands.

Step-by-step explanation:

We must first locate the three pairs of islands in order to establish which pair is nearest before determining the safest route for the ship.

Give the three islands the letters A, B, and C. The three island groups are designated as AB, AC, and BC. Finding the closest pair is necessary.

We can leverage the separation between the islands to do this. Assuming that the islands are separated by the following distances:

A and B are separated by 10 nautical miles.

A and C are separated by 15 nautical miles.

B and C are separated by 12 nautical miles.

These distances show that AB, which is only 10 nautical miles apart, and AB are the closest pair of islands.

Answer:

Solve:

y = 2x+5

x+y=8

x-x+y=8-x

y = -x + 8

Now:

y = 2x+5

y = -x+8

SUBSTITUTE

-x+8=2x+5 add x on both sides 8 -5 =3x+5 -5

3 = 3x
x= 1
Now for y :

Substitute:

y=2(1)+5

y=7

SOLUTION: )1,7)

Answer:

X= 135°

Step-by-step explanation:

Let y be equal to x

45° + y = 180°

Y = 180 - 45

Y = 135°

Therefore y = X

Answer:

x ≈ 10.4

Step-by-step explanation:

using the tangent ratio in the right triangle

tan41° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{x}[/tex] ( multiply both sides by x )

x × tan41° = 9 ( divide both sides by tan41° )

x = [tex]\frac{9}{tan41}[/tex] ≈ 10.4 ( to the nearest tenth )

Answer:

x=10.34

Step-by-step explanation:

tanФ=opposite ÷ adjacent

tan41°=9/x

0.87=9/x

x=9/0.87

 =10.34

Answer: Let's call the base of the triangle "b" and the height of the triangle "h". We are given that the sum of the base and the height is 22 cm, so we can write:

b + h = 22

We want to find the dimensions for which the area of the triangle is a maximum. The formula for the area of a triangle is:

A = (1/2)bh

We can use the equation b + h = 22 to solve for h in terms of b:

h = 22 - b

We can substitute this expression for h into the formula for the area:

A = (1/2)b(22 - b)

Simplifying this expression, we get:

A = 11b - (1/2)b^2

To find the value of "b" that maximizes the area, we can take the derivative of this expression with respect to "b" and set it equal to zero:

dA/db = 11 - b = 0

Solving for "b", we get:

b = 11

Substituting this value of "b" back into the equation b + h = 22, we get:

h = 22 - b = 22 - 11 = 11

Therefore, the dimensions for which the area of the triangle is a maximum are:

base = 11 cm

height = 11 cm

And the maximum area is:

A = (1/2)bh = (1/2)(11 cm)(11 cm) = 60.5 square cm

Step-by-step explanation:

Therefore , the solution of the given problem of function comes out to be  (g - f)(-1) = 29.

The math lesson covers an extensive variety of subjects, including geometry, integers, one's divisions, construction, and both real and imagined geographic places. A work covers the connections between various variable that all work together to produce the same result. A utility is made up of a variety of distinctive components that cooperate to create distinct results for each input.

Here,

We must first evaluate g(-1) and f(-1) before subtracting the results to obtain (g - f)(-1).

We possess

=> g(x) = 5x + 18

=>  g(-1) = 5(-1) + 18 = 13

=>  f(x) = x² - 17

=>  f(-1) = (-1)² - 17 = -16

Therefore:

=>  (g - f)(-1) = g(-1) - f(-1) = 13 - (-16) = 29

So, (g - f)(-1) = 29.

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Answer:

Step-by-step explanation:

Let the profit in 2020 be P.

The profit in 2021 would then be 1.20P (20% increase).

The profit in 2022 would be 0.83(1.20P) = 0.996P (17% decrease from 2021).

We can see that the profit in 2020 was P, while the profit in 2022 was less than P (0.996P).

Therefore, the higher profit was in 2020.

The solution is, the higher profit was in 2020.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Let the profit in 2020 be P.

The profit in 2021 would then be 1.20P (20% increase).

The profit in 2022 would be 0.83(1.20P) = 0.996P (17% decrease from 2021).

We can see that the profit in 2020 was P, while the profit in 2022 was less than P (0.996P).

Therefore, the higher profit was in 2020.

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Answer:

-7 in binary is -0b111.

-5 in binary is -0b101.

Step-by-step explanation:

Answer:

-111

-101

Step-by-step explanation:

Binary uses powers of 2.

2^0 = 1

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16

7 = 4 + 2 + 1

7 = 1 × 2^2 + 1 × 2^1 + 1 × 2^0

7 in binary is 111

-7 in binary is -111

5 = 4 + 1

5 = 1 × 2^2 + 0 × 2^1 + 1 × 2^0

5 in binary is 101

-5 in binary is -101

Answer: The range is the best measure of variability for the given data set and its value is 500.

The range is the difference between the maximum and minimum values in a data set, and in this case, the maximum value is 1100 and the minimum value is 600, so the range is 1100-600=500. The range gives us an idea of how spread out the data is, but it can be affected by outliers. In this case, it seems like a reasonable measure of variability since there are no extreme values that would greatly affect the range.

Step-by-step explanation:

From the data of the number of meters swam by students , range is the best measure of variability and equals 500

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the data set be represented as A

Now , the value of A is

A = { 600, 750, 800, 850, 900, 1100 }

The appropriate measure of variability for the given data is the range. The range is the difference between the largest and smallest values in the data set.

And , range = 1100 - 600

R = 500

Hence , the range of the data set is R = 500

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Answer:

£6.8

Step-by-step explanation:

to make 1 litre of drink juice and lemonade are in the ratio

= 1: 4

juice costs £6 per litre

lemonade costs 50p per litre

to make 1 litre lemonade will cost 4 * 50p = 200p

1£ = 250p

thus, 200p = £.8

thus, cost to make 1 litre of the fruit drink is £6.8

Answer:

Step-by-step explanation:

zachary climed 9.5 m

erin climed 8.8m

to 2 dp

zachary-9.51

erin-8.76

The trigonometry equations when evaluated are ∅ = 82π/125 and ∅ = 28π/23

Equation 1

Given that

cos ∅ = -8/17, π/2 < ∅ < π

Take the arc cos of both sides of the equation

So, we have the following

∅ = 82π/125

Equation 2

The trigonometry equation from the question is given as

tan ∅ = 2/5

The domain of the function is given as

π < ∅ < 3π/2

This means that the definition of the function is

tan ∅ = 2/5, π < ∅ < 3π/2

Take the arc tan of both sides of the equation

So, we have the following

∅ = tan⁻¹(2/5), π < ∅ < 3π/2

Express fraction as decimal

This gives

∅ = tan⁻¹(0.4), π < ∅ < 3π/2

Evaluate the arc tan

∅ = 28π/25

Hence, the measure of the angle is approximately 28π/23

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SOLUTION

Total no of ties = 45

Number of ties that he feels goes well with jacket = 34

Number of ties that he feels does not go well with jacket = 45 - 34 = 11

a) Probability that tie goes well with jacket =

[tex]\dfrac{\text{Number of ties that goes well with jacket}}{\text{Total number of ties}}[/tex]

                                [tex]=\dfrac{34}{45}[/tex]

b) Probability that a tie does not go well with jacket

[tex]\dfrac{\text{Number of ties that doe not goes well with jacket}}{\text{Total ties}}[/tex]

                                [tex]=\dfrac{11}{45}[/tex]

Answer:

Step-by-step explanation:

x

x  - 1

(x - 1 ) × 3

(x - 1 ) × 3 =

3x - 3

Answer:

i don't know

Step-by-step explanation:

good luck bro

(alright I'm just here for the points so yeah bye)

Answer:

no sé talvez sería

bueno no sé jajaja

To find zx and zy, we need to take partial derivatives of z with respect to x and y. Taking z with respect to x, we get zx = 3x2 + 12xy and zy = 6x + 16y. Taking z with respect to y, we get zy = 6x + 16y and g(x, y) = 3xy - 7x. Therefore, gx = 3y - 7 and gy = 3x.

A derivative is a measure of how much a function changes as its input changes. More specifically, the derivative of a function at a particular point is the slope of the function at that point, which describes how quickly the function is changing at that point.

Geometrically, the derivative of a function at a given point can be thought of as the slope of the tangent line to the function at that point.

To find zx and zy, we need to take partial derivatives of z with respect to x and y, respectively.

Given z = [tex]x^3 + 6x^2y + 8y^2[/tex],

Taking partial derivative of z with respect to x, we get:

zx = [tex]3x^2 + 12xy[/tex]

Taking partial derivative of z with respect to y, we get:

zy = 6x + 16y

Therefore, zx = 3x^2 + 12xy and zy = 6x + 16y.

Given g(x, y) = 3xy - 7x,

Taking partial derivative of g with respect to x, we get:

gx = 3y - 7

Taking partial derivative of g with respect to y, we get:

gy = 3x

Therefore, gx = 3y - 7 and gy = 3x.

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The equation y = (-2/3)x + 6 represents a line that is decreasing from left to right and intersects the y-axis at the point (0, 6).

The slope refers to the measure of the steepness of a line or a curve. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or the curve.

The equation of a line can be written as with the help of slope intercept form is given by:

y = mx + b

Where "b" is the y-intercept and "m" is the line's slope of the line.

In the equation y = (-2/3)x + 6, we can see that the slope 'm' is -2/3, which means that for every unit increase in x, the y-value decreases by 2/3 of a unit. This tells us that the line represented by this equation is decreasing (i.e., sloping downwards) from left to right.

The y-intercept 'b' is 6, which means that the line intersects the y-axis at the point (0, 6). This is the starting point of the line, where the value of y is 6 when x is 0.

Therefore, the equation y = (-2/3)x + 6 represents a line that is decreasing from left to right and intersects the y-axis at the point (0, 6).

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The statement "Square both sides twice and then solve the resulting linear equation." describes the correct process to solve √(3x+4)=√3x+4

Given equation:

[tex]\sqrt{3x} + 4= \sqrt[]3{x} + 4[/tex]

Square both sides :

[tex]3x+4=3x + 16+8\sqrt{3x}[/tex]

= [tex]8\sqrt{3x} =-12[/tex]

Square both sides again

[tex]64[/tex] × [tex]3x[/tex][tex]=144[/tex]

=  x=3\4

Linear equations are mathematical expressions that describe a straight line on a coordinate plane. They are used to model relationships between variables that have a constant rate of change or a constant slope.

Linear equations are fundamental and essential in many areas of mathematics, science, and engineering, and are used extensively in algebra, geometry, calculus, statistics, and physics.

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Complete question:

Which statement describes how to solve √(3x+4)=√3x+4?