5.2: Bowling for Triangles (Part 2)
Here is a visual pattern of dots. The number of dots D(n) is a function of the step number n.

1. What values make sense for n in this situation? What values don't make sense for n?

The formula for the area of a circle is given as follows:

A = πr².

The area of a circle of radius r is given by the multiplication of the number π and the square of the radius, according to the equation presented as follows:

A = πr².

Hence, for example, for a circle of radius of 5 units, the area is given as follows:

A = π x (5 units)² = 25π units².

The diameter of a circle is twice the radius, hence the radius is half the diameter, and as a function of the diameter, the area will be given as follows:

A = 0.25πd².

As the diameter in the context of this problem is:

r² = (0.5d)² = 0.25d².

The problem is incomplete, hence the area of the circle was explained in general terms.

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The rate of change of function [tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex] for x = 4 and x = 9 is 7 / 30.

We know that the rate of change of a function is nothing but the slope of the line.

The slope of the line is given by;

Slope = Change in y-coordinate / change in x-coordinate

We are given;

[tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex]

We need to find the rate of change of function for x = 4 and x = 9.

Let us find the value of y or f(x) for the given value of x.

For x = 4, [tex]f(x) = \sqrt{4} - \frac{1}{\sqrt{4}}[/tex]   = 2 - 1/2 = 4 - 1 / 2 = 3 / 2

For x = 9, [tex]f(x) = \sqrt{9} - \frac{1}{\sqrt{9}}[/tex]   = 3 - 1/3 = 9 - 1 / 3 = 8 / 3

Put the values of x and y in the slope formula, we will get;

Slope = (8 / 3 - 3 / 2) / (9 - 4) = 7 / 6*5 = 7 / 30

So, the rate of change of function is 7 / 30.

Thus, the rate of change of function [tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex] for x = 4 and x = 9 is 7 / 30.

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Based on this information we can conclude that in one hour, Oliver and his sister would get all of the windows washed. This means that it would take 5/6 hours which is equal to 50 minutes) for them to get all of the windows washed.

Information is defined as the content of a message which is passed from a source to its receiver.

The number of hours it takes for Oliver to wash the house windows = 2 hours, so in an hour = 1/2

The number of hours it takes his sister to wash the same house windows = 3 hours, so in an hour = 1/3.

To calculate for one hour for both would be addition of the derived fractions;

= 1/2 + 1/3

= 3+2/6

= 5/6

When converter to minutes, multiple by 60;

= 5/6 × 60

= 300/6

= 50 minutes.

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Answer:

140

Step-by-step explanation:

It's 140 because 35 x 4 (4 TIMES) meaning you multiply. 35 x 4 is 140, meaning there are 140 alligators.

The quadratic equation 6 · x² + 13 · x + 6 = 0 has a positive discriminant and its roots are two distinct real numbers.

In this problem we must infer the features of the two roots of a quadratic equation of the form a · x² + b · x + c = 0, this can be done by means of the discriminant from the quadratic formula:

D = b² - 4 · a · c

Where a, b, c are real coefficients of the quadratic equation.

There are three possibilities for the results of the discriminant:

First, write the quadratic equation:

6 · x² + 13 · x + 6 = 0

Second, collect the real coefficients of the polynomial:

(a, b, c) = (6, 13, 6)

Third, calculate the discriminant:

D = 13² - 4 · 6²

D = 169 - 144

D = 25

The quadratic equation has two roots that are real and different.

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⇒In this case I will use the law of exponents that states:

[tex](x^{m} )^{n} \\=x^{m*n}[/tex]

⇒[tex]=(-3x)^{2y*4} \\=(-3x)^{8y}[/tex]

Answer: 81x^8y^4

Step-by-step explanation:

1. DISTRIBUTE EXPONENT by using the power rule: (ab)^n = (a^n)(b^n)

> Apply PRODUCT RULE: -3x^2y = (-3x^2)^4y^4

>Apply PRODUCT RULE: -3x^2 = (-3)^4 (x^2)^4y^4

2. RAISE -3 to the power of 4 = 81(x^2)^4y^4

3. MULTIPLY THE EXPONENTS in (x^2)^4

> Apply POWER RULE and MULTIPLY EXPONENTS, (a^m)^n = a^mn

(81x^2*4)(y^4)

> MULTIPLY 2 by 4 = 81x^8y^4

And that is your answer, 81x^8y^4

The amount of tax that the executive would pay on his income is; 20000 GBP

Tax is defined as a compulsory payment that is levied on the income or on the sales of specific goods and services. Tax is usually imposed by the government to get a variety of macroeconomic objectives.

Now, income tax is the tax that is levied on the income of an individual. There are different types of taxes, such as progressive tax which levies a higher tax percentage on those that earn higher incomes This means invariably that the tax rate increases as income increases.

We are given;

Gross Amount executive earns = 50,000 GBP.

We are told that any earnings between 33,500 GBP and 150,000 GBP are taxed at 40%.

Thus;

Tax that would be paid = tax rate * gross income

Tax that would be paid = 50000 * 0.4 = 20000 GBP

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Answer: 11,000

Step-by-step explanation:

The person earns 50,000 GBP, so they will stop at the tier 3 level of tax.

The first 11,500 GBP is tax free. They will be taxed 20% on (33,500−11,500)=22,000 GBP, and they will be taxed 40% on (50,000−33,500)=16,500 GBP. Hence the total tax (in GBP) they need to pay is

Total Income Tax=11,500×0%+22,000×20%+16,500×40%=0+22,000×20100+16,500×40100=0+4,400+6,600=11,000

The inverse of the function f(x) = (4x - 1)/(-2x +2) is equal to f⁻¹(x) = (2x + 1)/(4 + 2x).

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of this function f(x) = (4x - 1)/(-2x +2), we would interchange both the input value (x) and output value (y) as follows:

y = (4x - 1)/(-2x +2)

x = (4y - 1)/(-2y +2)

Cross-multiplying, we have:

x(-2y +2) = 4y - 1

2x - 2xy = 4y - 1

Next, we would rearrange the function by collecting like terms as follows:

4y + 2xy = 2x + 1

y(4 + 2x) = 2x + 1

Dividing both sides of the function by (4 + 2x), we have:

y = (2x + 1)/(4 + 2x)

y = f⁻¹(x) = (2x + 1)/(4 + 2x)

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Since fractions are the same as division, divide 617 by 50. The remainder will remain in fraction form.

617/50
600/50 = 12
617/50 = 12 17/50

Answer: 56 miles

Step-by-step explanation:

Tristan ran 7 miles, multiply by 4 because Kimberly ran 4 times as many miles as Tristan. 7x4=28

Next, 28x2=56 because Dominic ran 2 times as many miles as Kimberly, which is 28 times 2.
So Dominic ran 56 miles in total.

Using the straight line method, the depreciation expense in year 1 and 2 is $14,000.

Using the double declining method, the depreciation expense in year 1 is  $29,600 and $17,760 in year 2.

Using the unit of production method, the depreciation expense in year 1 is $18,000 and $19,000 in year 2.

The straight line depreciation method is a depreciation method in which the the depreciation amount each year of the asset's useful life is the same.

Straight line depreciation = (cost of the asset - salvage value) / useful life

Cost of the asset = $70,000 + $3000 + $1000 = $74,000

Straight line depreciation = ($74,000 - $4,000) / 5  = $14,000

The double declining method entails depreciating an asset at twice the rate of the straight line method.

Depreciation expense = cost of the asset x depreciation factor

Depreciation factor = 2 x (1/useful life)

Depreciation expense in year 1 = (2 /5) x  $74,000 = $29,600

Book value in year 2 = $74,000 = $29,600  = $44,400

Depreciation expense in year 2 = (2 /5) x  $44,400 = $17,760

The depreciation in the unit of production method depends on the output of the machine each year.

Depreciation = (output in a year / total output) x (cost of the asset - salvage value)

Depreciation in year 1 = ($74,000 - $4,000) x (36,000 / 140,000) = $18,000

Depreciation in year 2 = ($74,000 - $4,000) x (38,000 / 140,000) = $19,000

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Here is the rest of the question:

Units produced in Year 1 = 36,000 units

Units produced in Year 2 = 38,000 units.

well, from the end of year 5 to the end of year 6 is only 1 year later, so

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$3315.30\\ P=\textit{original amount deposited}\dotfill & \$3203.19\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 3315.30=3203.19[1+(\frac{r}{100})(1)] \implies \cfrac{3315.30}{3203.19}=1+\cfrac{r}{100} \\\\\\ \cfrac{3315.30}{3203.19}-1=\cfrac{r}{100}\implies 100\left( \cfrac{3315.30}{3203.19}-1 \right)=r\implies \stackrel{\%}{3.5}\approx r[/tex]

For the given function f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4 , the value of

(f -g)(x) =  2x³ + 6x² -8x + 1 .

As given in the question,

Function is given by :

f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4

Substitute the value in the given function and simplified it ,

( f - g )(x)

=  { 2x³ + 6x² - 5x - 3 } - { 3x - 4 }

= 2x³ + 6x² - 5x - 3 -3x + 4

= 2x³ + 6x² -5x -3x -3 + 4

= 2x³ + 6x² - 8x + 1

Therefore,  for the given function f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4 , the value of (f -g)(x) =  2x³ + 6x² -8x + 1 .

The complete question is:

If for the given function ,

f(x) = 2x³ + 6x² - 5x - 3 , g(x) = 3x - 4

Find the value of (f - g)(x).

a. 2x³ + 6x² -8x + 1

b. 2x³ + 6x² + 2x+1

c. 2x³ + 6x² + 2x -7

d. 2x³ + 6x² + 8x⁷

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Answer:

42.2 ft

Step-by-step explanation:

The given scenario can be modelled as a right triangle (see attached diagram), where the angle of elevation is 32°, and the length of the kite string (75 ft) is the hypotenuse.

We want to find the distance the kite is above the ground, so we want to find the side of the right triangle that is opposite the given angle. To do this, we can use the sine trigonometric ratio.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Substituting θ = 32° and H = 75 into the ratio, we get:

[tex]\sin 32^{\circ}=\dfrac{\sf O}{75}[/tex]

[tex]\textsf{O}=75\sin 32^{\circ}[/tex]

[tex]\textsf{O}=39.7439448...\; \sf ft[/tex]

The angle of elevation is the angle between the horizontal plane and the line of sight from an observer to an object located at a higher position.

In this scenario, the angle of elevation is measured from Savannah's hand, which is a distance of 2.5 ft above the ground. Therefore, we need to add 2.5 ft to the value of O found using the sine ratio.

[tex]\implies 39.7439448...+2.5=42.2\; \sf ft\;(nearest\;tenth)[/tex]

Therefore, the kite is 42.2 ft above the ground (rounded to the nearest tenth).

The number of ways he can form the teams would be = 336 ways.

Badminton is a type of racket game that makes use of single or double players where by they make use of a racket to hit a shuttlecock over the net to their opponents side.

The number of players available for the badminton game = 8

The number of teams to the formed = 4

To find the number of ways to form 4 double teams from these 8 players would be to find the factorials of 8 divided by factorial 4.

That is ;

8!/4! = 8×7×6×4×3×2×1/4×3×2×1

= 8064/ 24

= 336 ways.

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5.1 The amount of money received by the man at the end of 4 years is

$10,217.39

5.2 The rate of interest per annum is 94.56%/year.

Given:

P=5000

r = 18%

t= 4 years.

5.1 First, convert R as a percent to r as a decimal

r = R/100

r = 18/100

r = 0.18 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 5,000.00(1 + 0.18/12)(12)(4)

A = 5,000.00(1 + 0.015)(48)

A = $10,217.39

5.2 Given:

P = 3700

A = 8360,34

t = 7 years.

r =?

Solving for rate r as a decimal

r = n[(A/P)1/nt - 1]

r = 2 × [(836,034.00/3,700.00)1/(2)(7) - 1]

r = 0.945604

Then convert r to R as a percentage

R = r * 100

R = 0.945604 * 100

R = 94.56%/year

Hence we get the required answer.

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Answer: 50, 99

Step-by-step explanation:

we just have to substitute the values of x and y in the given expressions.

7(2)+4(9)=50

4(9)+7(9)=99

Answer:

Step-by-step explanation:

7x + 4y= 50 and 4y + 7y= 99

Since, x=2 and y=9

7x + 4y= 7*2 + 7*9= 14 + 36= 50

and similarly

4y + 7y= 4*9 + 7*9= 36 + 63= 99

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Answer:

A: Ira begins walking

B: Ira stops at a diner

C: Ira leaves the diner

D: Ira visits his grandmother

E: Ira walks from grandma’s house to home

Step-by-step explanation:

Hopes this helps please mark brainliest

The best course grade your friend can earn is 88%.

The minimum score your friend needs to have on the final to earn a 75% for the course is 35%.

If the final counts for 20% of the course grade, it means that the average of 85% counts for 80% (100 - 20%) of the total score.

The linear expression that can be used to determine the best course grade your friend can earn is:

(average that has already been accumulated x 80%) + (score on the finals x 20%)

(85% x 80%) + (20% x 100%)

(85% x 0.80) + (0.2 x 100%)

68 + 20 = 88%

The linear equation that can be used to determine the minimum score that can be earned on the final to have75% in the course is

Final grade = (total average before the final x 80%) + (score on the final x 20%)

75% = (85% x 80%) + (f x 20%)

75% = (85% x 0.80) + (0.20 x f)

75% = 68% + 0.20f

75% - 68% = 0.20f

7 =  0.20f

f = 7% / 0.20

f = 35%

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Answer: x = -10.7

Step-by-step explanation:

-10.7 + 4.3 = -6.4

Answer:

x = 15 , y = 4

Step-by-step explanation:

If 3 or more parallel lines are intersected by two or more transversals, the parallel lines divide the transversals proportionally. then

[tex]\frac{x}{5}[/tex] = [tex]\frac{18}{6}[/tex] = 3 ( multiply both sides by 5 )

x = 15

and

[tex]\frac{12}{y}[/tex] = 3 ( multiply both sides by y )

12 = 3y ( divide both sides by 3 )

4 = y

The missing measure is  ∠P =∠X = 122°

Given △ACP ≅ △LNX

XL = 13 cm, m∠L = 29°

AC = 21 cm, m∠C = 29°

PC = 13 cm, m∠Y = ??  (there is no angle Y)

On the right shows the triangles are isosceles, with XL = XN. That means also PA = PC. Those side lengths are all the same: 13 cm.

PA = PC = XL = XN = 13 cm

In the same way, ...

LN = AC = 21 cm

Of course, the angles have a similar relationship:

∠A = ∠C = ∠L = ∠N = 29°

The two base angles in the triangle add to 58°, so the third angle is ...

180° -58° = 122°

∠P =∠X = 122°

As is often the case in over-specified problems, the numbers shown are not consistent. The length LN is actually incorrect for the angle and side specified for triangle ACP, or the angles are incorrect for the side lengths specified. What this means is that the answers you get will depend on how you work the problem. Above, we have taken the given numbers and relationships at face value, even though we know they are incorrect.

Hence the answer is The missing measure is  ∠P =∠X = 122°

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The equation of the line passing through the points (9,9) and (1, 8) is 8y - x - 63 = 0 and the slope of the line is 1/8

Slope of the line that passes through the points (9,9) and (1, 8)

The equation of the line is

y -y₁ = ((y₂ - y₁)/ (x₂ - x₁)) (x - x₁)

y - 9 = ((8 - 9)/(1 - 9)) (x - 9)

y - 9 = (1/8) (x - 9)

8y - 72 = x - 9

8y - x - 63 = 0

8y = 1/8 (x + 63)

Therefpre, the equation of the line passing through the points (9,9) and (1, 8) is 8y - x - 63 = 0

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The graph of the given function is attached below.

We are given a function. A function connects an input and an output. It is analogous to a machine with an input and an output. And the output is somehow related to the input.

The coordinates of several points are given. We need to graph the function by plotting the ordered pairs (0, 0), (10, 125), (20, 250), (30, 375), and (40, 500).

The function is a straight line. A straight line is a one-dimensional figure with an infinite length. It is made up of an infinite number of points connected on both sides of a point. We also need to draw the line through the points. The graph is attached below.

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Numbers between 2.6×10^-1 and 29.5% are

2.6 × 10^-1 in exponential form written in decimal as 0.26

29.5% in percentage written in decimal as 0.295

2/7 in fraction written in decimal as 0.2857

2.8%  in percentage written in decimal as 0.028

0.2875 already in decimal form

the problem asks of numbers from 0.26 to 0.295

comparing the numbers shows that the numbers in this range are

0.2875 and 2/7

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Answer:

B. 12

Step-by-step explanation:

Answer:

7. what are the fold down options for this question exactly?

1. C and E

3. B and D

Step-by-step explanation:

7.

1. function 1 has a slope of 2/3 and function 2 has a slope of 3 so they are both positive rates of change, and the y intercept (the value that y has when it passes through x = 0) for function 1 is -6 while the y intercept for function 2 is -3.

3. K has a y intercept of 8 compared to the 3 that J has, and J has a slope of 5 compared to the 3 that K has.

The point slope form of equation is y- 3 = -4/3( x- (-3)).

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx

where, m is the slope

Given:

Points= (-3, 3) and (9, -13)

Now,

slope= (-13 - 3)/ (9 - (-3))

slope= -16 / 12

slope= -4/3

Now, the point slope form

y- [tex]y_1[/tex] = m (x- [tex]x_1[/tex])

y- 3 = -4/3( x- (-3))

y- 3= -4/3x - 4

y= -4/3x - 1

Hence, the point slope for of equation is y- 3 = -4/3( x- (-3)).

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If the square banquet has area = 3600m² then length of the room is 60 m .

The Area of the Square with side "s" can be calculated using the formula

Area = s × s

In the question ,

it is given that ,

the area of the Square banquet is = 3600m²  ,

let the length of the side of the room be "s" .

So , By the Area of the Square formula ,

we get ,

s × s = 3600

s² = 3600

taking quare root both the sides ,

we get

√s² = √3600

s = 60

the side = 60m

Therefore , If the square banquet has area = 3600m² then length of the room is 60 m .

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