A gardener would like to add to their existing garden to make more flowers available for the butterflies that visit the garden. Her current garden is 24 square feet. If she added another rectangular piece with vertices located at (−17, 15), (−20, 15), (−17, 11), and (−20, 11), what is the total area of the garden?

144 ft2
288 ft2
12 ft2
36 ft2



*ITS NOT 288 I ALREADY TRIED!*

The calculated length of the arc has a value of 22.34 yards

To find the length of an arc, we can use the formula:

L = (θ/360) x 2πr

where L is the length of the arc, θ is the central angle in degrees, r is the radius of the circle, and π is approximately 3.14.

In this case, the central angle is 160 degrees and the radius is 8 yards. So we can plug in these values to get:

L = (160/360) x 2π(8)

Evaluate

L = 22.34 yards

Therefore, the length of the arc is approximately 22.34 yards

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Answer

3390

Step-by-step explanation:

rasheed still owes six months of rent because thats the lease that they signed so 565 times six is 3390. hope this helps.

Therefοre, the expressiοn can be rewritten in terms οf the functiοn [tex]cos x[/tex]as: [tex]2cos^2 x + cos x - 2[/tex].

Trigοnοmetry is a branch οf mathematics that deals with the relatiοnships between the sides and angles οf triangles. It is particularly cοncerned with the study οf angles, the trigοnοmetric functiοns (sine, cοsine, tangent, etc.), and their prοperties and applicatiοns.

Trigοnοmetry has many practical applicatiοns, particularly in fields such as physics, engineering, and astrοnοmy, where it is used tο sοlve prοblems invοlving angles, distances, and shapes. Fοr example, trigοnοmetry is used in surveying tο measure distances and heights, in navigatiοn tο determine the pοsitiοn οf ships and airplanes, and in physics tο describe the mοtiοn οf waves and οscillatiοns.

In the given questiοn,

We can use the trigοnοmetric identity [tex]cos^2 x + sin^2 x = 1[/tex] tο rewrite [tex]sin^2 x[/tex] as: [tex]sin^2 x = 1 - cos^2 x[/tex]

Substituting this intο the οriginal expressiοn gives:

[tex]cos^2 x + cos x - 1 + sin^2 x = cos^2 x + cos x - 1 + (1 - cos^2 x) = 2cos^2 x + cos x - 2[/tex]

Therefοre, the expressiοn can be rewritten in terms οf the functiοn [tex]cos x[/tex] as: [tex]2cos^2 x + cos x - 2.[/tex]

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The area of the shaded sector is 575π/9 square units.

The area of the unshaded sector is 325π/9 square units

The value of the angle subtended by the unshaded sector is 130⁰ the value of the angle subtended by the shaded sector is 230⁰.

To find the area of a sector with radius 10 units and angle 230⁰, we can again use the same formula:

Area of sector = (angle/360) x πr^2

Substituting the values given in the formula, we get:

Area of sector = (230/360) x π(10)²

= (23/36) x 100π

= 575π/9 square units

To find the area of a sector with radius 10 units and angle 130⁰, we can use the formula:

Area of sector = (angle/360) x πr^2

Substituting the values given in the formula, we get:

Area of sector = (130/360) x π(10)^2

= (13/36) x 100π

= 325π/9 square units

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Answer:

Step-by-step explanation:

y = x³ - 27x

(i). Domain: x ∈ ( - ∞ , ∞ )

(ii). f'(x) = 3x² - 27 ; f''(x) = 6x

(iii). 3x² - 27 = 0 ⇔ x² - 9 = 0 ⇒ [tex]x_{12}[/tex] = ± 3

If [tex]x_{1}[/tex] = - 3 , then [tex]y_{1}[/tex] = 54

If [tex]x_{2}[/tex] = 3 , then [tex]y_{1}[/tex] = - 54

Points are ( - 3 , 54 ) and ( 3 , - 54 )

(iv). ( - ∞ , - 3 ) ∪ ( - 3 , 3 ) ∪ ( 3 , ∞ )

increasing ----> decreasing -----> increasing

(v). x = - 3 is the maxima, the local maximum value is 54, f(-3) = 54

x = 3 is the minima, the local minimum value is ( - 54 ), f(3) = - 54

(vi). Concave up if f''(x) > 0 ; The interval is ( - ∞ , 0 )

Concave down if f''(x) < 0 ; The interval is ( 0 , ∞ )

(vii). Point of inflection is ( 0 , 0 )

f''(x) = 0

6x = 0

x = 0

(1) The graph that shows the solution of the inequality 7 ≤ n + 5 is the graph of option A.

(2) Eduardo wrote at least 34 pages before today.

(3)  The farmer needs to plant at least 8 rows of seeds to harvest at least 52 bushels of tomatoes.

The solution to the inequality 7 ≤ n + 5 is as follows:

7 ≤ n + 5

collect similar terms together

7 - 5 ≤ n

2 ≤ n

So we can interpret the result of this inequality as, n is greater than and equal to 2. Hence option A is the correct answer.

2. Let p be the number of pages Eduardo wrote before today. Then, the inequality that represents the situation is:

p + 16 > 50

To solve for p, first subtract 16 from both sides of the inequality:

p + 16 - 16 > 50 - 16

p > 34

Therefore, Eduardo wrote at least 34 pages before today.

3. Let r be the number of rows of seeds the farmer needs to plant. Then, the equation that represents the situation is:

6.5r ≥ 52

divide both sides of the equation by 6.5:

r ≥ 8

Therefore, the farmer needs to plant at least 8 rows of seeds to harvest at least 52 bushels of tomatoes.

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a. The numeric values of the function are given as follows:

b. The function rule is given as follows: y = 2x - 8.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

From the table, when x = 0, y = -8, hence the intercept b is given as follows:

b = -8.

Considering points (0, -8) and (10, 12), when x increases by 10, y increases by 20, hence the slope m is given as follows:

m = 20/10

m = 2.

Hence the function is given as follows:

y = 2x - 8.

To complete the table, the numeric values are given as follows:

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Answer:

d

Step-by-step explanation:

1 kg has 1000 g

Then 2,5 kg has 2,5 × 1000 = 2500 g

You can also make a proportion:

1 kg - 1000 g

2,5 kg - x g

Use the property of the proportion to find x (cross-multiply):

x = 2,5 × 1000 / 1 = 2500 g

In the end, Reggie has 435.2 stamps and Cοrwin has 179.2 stamps.

The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Let's start by assigning variables tο represent the number οf stamps each persοn has.

Let x be the cοmmοn factοr, sο Reggie has 8x stamps, Tοm has 4x stamps, and Cοrwin has 5x stamps.

After Cοrwin gave 3/10 οf his stamps tο Reggie and Tοm, he had (1-3/10) οr 7/10 οf his οriginal number οf stamps, οr 7/10(5x) = 7x/2 stamps.

Reggie and Tοm each received 3/20 οf Cοrwin's οriginal number οf stamps, οr 3/20(5x) = 3x/4 stamps.

Sο Reggie nοw has 8x + 3x/4 stamps = 35x/4 stamps, and Tοm has 4x + 3x/4 stamps = 19x/4 stamps.

We are alsο given that Cοrwin had 192 less stamps than Reggie after the exchange, sο:

5x = 35x/4 - 192

Multiplying bοth sides by 4 tο get rid οf the fractiοn:

20x = 35x - 768

Subtracting 20x frοm bοth sides:

15x = 768

Dividing bοth sides by 15:

x = 51.2

Sο Reggie has 8x = 409.6 stamps, Tοm has 4x = 204.8 stamps, and Cοrwin has 5x = 256 stamps.

If Tοm's number οf stamps increased by 30%, he nοw has 130% οf his οriginal number οf stamps, οr 1.3(204.8) = 266.24 stamps.

Finally, adding up the number οf stamps each persοn nοw has:

Reggie: 409.6 + 3x/4 = 409.6 + 3(51.2)/4 = 435.2 stamps

Tοm: 266.24 stamps

Cοrwin: 7x/2 = 7(51.2)/2 = 179.2 stamps

Therefοre, in the end, Reggie has 435.2 stamps and Cοrwin has 179.2 stamps.

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We can let Reggie had 8x, Tom, had 4x, Corwin had 5x, Corwin gave Reggie y1, gave Tom y2,

So: We can know from the question

3/10 * 5x = y1 + y2

8x + y1 - 7/10 * 5x = 192 (2)

4x + y2 = 4x * 13/10 (3)

(1) + (2) + (3)

8x + 4x + 3/10 * 5x - 7/10 * 5x = 192 + 4x * 13/10

So x = 40
in the end

Corwin has 7/10 * 5x = 140

Reggie has 140 + 192 = 332

Tom has  13/10 * 4x = 208

332 + 140 = 472

So Reggie and Corwin have 472 stamps in the end.

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1 - sin(a) - cos(a) can be expressed as the product 2(cos(a)(sin)(a)).

What are Trigonometric Identities?

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

We can use the identity:

[tex]cos^2(a) + sin^2(a) = 1[/tex]

Substituting this into the expression 1 - sin(a) - cos(a), we get:

[tex]cos^2(a) + sin^2(a) - sin(a) - cos(a) \\\\cos^2(a) - cos(a) + sin^2(a) - sin(a) \\\\cos(a)( 1 - cos(a)) + sin(a)( 1- sin(a) )\\\\[/tex]      eq2

It is given that

[tex]1 - sin(a) - cos (a)\ \text{this gives us}:\\\\1 - sin(a) = cos (a)\ \text{and} \ 1 - cos (a) = sin(a)[/tex]

Substituting these values in the eq2

[tex]cos(a)( 1 - cos(a)) + sin(a)( 1- sin(a) )\\\\cos(a)(sin(a)) + sin(a)(cos(a) )\\\\[/tex]

[tex]2(cos(a)(sin)(a))[/tex]

Therefore, 1 - sin(a) - cos(a) can be expressed as the product

[tex]2(cos(a)(sin)(a))[/tex]

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Answer: 36 m²

Step-by-step explanation:

       First, we will solve for the area of the triangles. Since they are congruent, we will multiply the height times the base. Usually, you would have to divide by two. However, since we have two congruent triangles, we will not be doing this.

       A = BH

       A = (2 m)(6 m)

       A = 12 m²

       Next, we will find the area of the rectangle. We will multiply the length by the width.

       A = BH

       A = (6 m)(4 m)

       A = 24 m²

       Lastly, we will add these two values together.

24 m² + 12 m² = 36 m²

The x-intercepts of the given expression which is a rational function is calculated to be 0 and the y-intercepts are ±√25.

The given expression is a rational function and can be written as the quotient of two polynomials.

The numerator of the rational expression is -x⁷ and the denominator is x²−25. The numerator is a degree 7 polynomial and the denominator is a degree 2 polynomial.

To find the x-intercepts, we need to set the numerator equal to zero and solve for x.

-x⁷ = 0

x⁷ = 0

x = 0

To find the y-intercepts, we need to set the denominator equal to zero and solve for x.

x²−25 = 0

x² = 25

x = ± √25

Therefore, the x-intercepts of the given expression are 0 and the y-intercepts are ± √25.

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Question :

Find the intercepts of the given function.

y = (-x⁷)/(x²−25)

Answer:

Since the vertex is (0, -4), we know that the equation of the parabola will have the form:

y = a(x - 0)^2 - 4

where "a" is the coefficient that determines whether the parabola opens up or down.

To find the value of "a", we can use the fact that the parabola passes through the point (10, 1):

1 = a(10 - 0)^2 - 4

1 + 4 = 100a

5 = 100a

a = 1/20

Substituting this value of "a" into the equation for the vertex form, we get:

y = (1/20)x^2 - 4

So the equation of the parabola in vertex form is y = (1/20)x^2 - 4, with vertex (0, -4) and passing through (10, 1).

Step-by-step explanation:

Answer:

5(7j+3) AND 35j +15 are both equal to the expression 5(6j + 3 + j)

Answer:

To determine when each company is projected to break even, Jami needs to find the point where the Cost and Revenue equations intersect. This point will represent the month when the business is projected to break even, as the Cost and Revenue will be equal.

Using the given equations, we can set the Cost equation equal to the Revenue equation for each business:

Blysis: -13124.3190x + 3586 = -6941915384x + 21954

Solving for x, we get x = 0.00057 months.

Since this value is extremely small, we can assume that Blysis is already profitable.

Appster: -13124.3190x + 3586 = -6941915384x + 21954

Solving for x, we get x = 0.00057 months.

Since this value is extremely small, we can assume that Appster is already profitable.

Enrich: -3586x - 21954 = -6941915384x + 13174

Solving for x, we get x = 0.0035 months.

Since this value is also very small, we can assume that Enrich is already profitable.

Green Team: 178420.64421x - 68419 = -4289115387x + 13174

Solving for x, we get x = 0.0009 months.

Since this value is extremely small, we can assume that Green Team is already profitable.

Southwest Fusion: -13124.3190x + 4289115387x = 13174

Solving for x, we get x = 35.23 months.

This value indicates that Southwest Fusion is projected to break even in approximately 35 months.

Zoo to You: -13124.3190x + 54209539 = -10381x

Solving for x, we get x = 4.05 months.

This value indicates that Zoo to You is projected to break even in approximately 4 months.

Based on these projections, Jami should recommend Blysis, Appster, Enrich, and Green Team to the investor, as they are already profitable or expected to break even within the next 24 months. Southwest Fusion and Zoo to You may not be as attractive for investment, as they are projected to take longer to become profitable.

Step-by-step explanation:

Answer:

see below.

Step-by-step explanation:

Use Trigonometric Expansion.

Verify the following identity:

[tex]cos(x)^2(tan(x)^2+1)=1[/tex]

Write tangent as [tex]\frac{sine}{cosine}[/tex]

[tex]cos(x)^2(\frac{sin(x)}{cos(x)} ^2+1)=1[/tex]

[tex]cos(x)^2(\frac{sin(x)}{cos(x)} ^2+1)=cos(x)^2(\frac{sin(x)^2}{cos(x)^2+1} )[/tex]

[tex](cos(x)^2(\frac{sin(x)^2}{cos(x)^2} +1))=1[/tex]

Put sin(x)^2/cos(x)^2 +1 over the common denominator cos(x)^2 : sin(x)^2/cos(x)^2+1 = cos(x)^2+sin(x)^2 /cos (x)^2:

cos(x)^2(cos(x)^2+sin(x)^2/cos(x)^2)=1

Cancel cos(x)^2 from the numerator to the denominator.

cos(x)^2(cos(x)^sin(x)^2)/cos(x)^2=cos(x)^2(cos(x)^2+sin(x)^2)/cos(x)^2=cos(x)+sin(x)^2:

(cos(x)^2+sin(x)^2=1

Substitute cos(x)^2 + sin (x)^2 = 1:

1 =1

If we simplify [tex]3(2v-4)-4(v+4)[/tex], our answer will be [tex]-5v - 20[/tex]

Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler, usually shorter.

The question is [tex]3(2v-4)-4(v+4)[/tex], our step of solution is as follows:

==>>3(2v-4)-4(v+4)

Open the bracket with multiplication

= 6v - 12 - 4v - 16

= 2v - 28

= 2(v - 14)

= -5v - 20

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12 + 7 - 3 - 2

There are many ways to use mathematical symbols to make 3, 7, 12, and 2 equal 15. Here are a few examples:

3 + 7 + 2 + 3 = 15

(Add the first three numbers together, then add one of the 3's to get 15)

12 - 7 - 3 + 13 = 15

(Subtract 7 and 3 from 12 to get 2, then add 13)

2(7 + 3) - 12 = 15

(Add 7 and 3 together, multiply by 2, then subtract 12)

7(2) + 3 + 3 - 4 = 15

(Multiply 7 by 2, add 3 and the other 3, then subtract 4)

These are just a few examples - there are many other ways to use mathematical symbols to make these numbers equal 15!

Answer:

20

Step-by-step explanation:

You have to multiply 10 by 2, which the ten represents ur 10th birthday, and the 2 represents the amount doubled. 10+2=20

Thus, the current movie theater seats are 21.05 % of a theater seat from 30 years ago.

The change between a final value and even an initial value, presented as a percentage of the starting value, is the percent increase over two values. Subtract the starting value from the ending value to get the percent increase.

Next, divide the difference by the starting amount. In order to convert this value to a percentage, multiply it by 100%. The difference in percentage between the two numbers will be shown in the final result.

Given data:

width of current movie theatre seat = 23 inches.

width of 30 years ago movie theatre seat = 19 inches.

Let x be the percentage increase:

19 + x%19 = 23

1 + x% = 23/19

x/100 = 23/19 - 1

x/100 = 4/19

x = 400/19

x = 21.05 %

Thus, the current movie theater seats are 21.05 % of a theater seat from 30 years ago.

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The height of the first floor above the second floor would be = 20 ft.

To calculate the height of the first floor from the second floor, the formula from SOHCAHTOA is used.

The opposite part of the triangle created by the escalator = ?ft

The hypotenuse of the triangle which is the height of the escalator = 40 ft

Sin 30° = X/40

X = sin30° × 40

X = 0.5×40

X = 20 ft

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3x² - 2x + 15x - 10 can be factored by grouping as:

3x² - 2x + 15x - 10

= (3x - 2)(x + 5)

Explanation:

Group the first two terms and the last two terms together:

(3x² - 2x) + (15x - 10)

Factor out the GCF from each group:

3x(x - (2/3)) + 5(3x - 2)

Now we have a common factor of (3x - 2):

(3x - 2)(x + 5)

Step-by-step explanation:

3x² - 2x + 15x - 10

=x(3x-2)+5(3x-2)

=(x+5)(3x-2)

Answer:

52800 cm^3

Step-by-step explanation:

Given:

Rectangular prism

h = 6 cm (height)

l = 11 m = 1100 cm (length)

w = 8 cm (width)

[tex]v =a(base) \times h[/tex]

[tex]a(base) = l \times w = 1100 \times 8 = 8800 \: {cm}^{2} [/tex]

[tex]v = 8800 \times 6 = 52800 \: {cm}^{3} [/tex]

Answer:D) A peak is a bar that is higher than the other bars around it is true.Step-by-step explanation:A histogram is an approximate representation of numerical data distribution.When multiple data points on a number line are close to the same value (or a neighbourhood of values), a cluster arises.A peak is a bar that stands taller than the bars around it. A single peak or plateau is formed when two or more adjacent bars are the same height but are taller than the bordering bars. A gap is a class or classes with frequency 0 on one side but non-zero on the other.

Step-by-step explanation:

With an eye level of 35 feet above the water, you can see approximately 7.24 miles to the horizon.

Multiplication is a mathematical operation that involves combining two or more numbers to find their total or product. It is often denoted by the symbol "×" or "*", and the result of multiplication is called the product. For example, multiplying 3 and 4 gives a product of 12, written as 3 × 4 = 12.

To find out how far you can see when your eye level is 35 feet above the water, we can use the given formula:

d = √(3h/2)

Plugging in h = 35, we get:

d = √(3 * 35/2)

d = √(105/2)

d = √52.5

d ≈ 7.24

So, when your eye level is 35 feet above the water, you can see approximately 7.24 miles to the horizon. Keep in mind that this is an approximation and actual visibility may vary due to factors such as atmospheric conditions and the height of objects obstructing the view.

Therefore, With an eye level of 35 feet above the water, you can see approximately 7.24 miles to the horizon.

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Explanation:

I'll use x in place of 'a'

I'll also use y in place of b.

The equation 5a+b = 7 turns into 5x+y = 7

Solve for y to get

5x+y = 7

y = -5x+7

This is in slope-intercept form y = mx+b

The negative reciprocal of the slope is 1/5. Flip the fraction and flip the sign. So if -5 is the original slope, then 1/5 is the perpendicular slope.

Of the answer choices, only choice C has a slope of 1/5. Think of b = (1/5)a-2 as y = (1/5)x - 2

Therefore, choice C is the answer.

The equation of a line that is perpendicular to '5a+b = 7' is 'b = (1/5)a + c'. Therefore, the correct option among given choices is 'b = (1/5)a - 2' (option C).

To start with, the given line's equation, 5a + b = 7, can be converted to slope-intercept form (b = mx + c), where m represents the slope of line, and 'c' is the y-intercept.

Converting the equation, 5a + b = 7, we get b = -5a + 7. This tells us the slope of our original line is -5.

Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. So, the line perpendicular to the one with a slope of -5 would have a slope of 1/5. Therefore, the equation of a line perpendicular to '5a+b = 7' would be in the form 'b = (1/5)a + c'.

Thus, the correct answer is option C : b = (1/5)a - 2.

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Answer:

  graph 4 (reflected vertically)

Step-by-step explanation:

You want the graph that represents a cosine function with no horizontal shift, an amplitude of 2, and a period of 2π/3.

The amplitude of a sine or cosine function is the difference between the positive peak and the centerline. All of the graphs show functions with an amplitude of 2.

The period of the function is the difference of x-values between the first instance of the function and the first repeat: f(x) ≡ f(x+p) has a period of p.

Graphs 1 and 3 show periods of 2π/9; graphs 2 and 4 show periods of 2π/3, as required.

There is an interaction between horizontal shift and vertical reflection. Sine or cosine functions are effectively inverted (reflected over the x-axis) if they are shifted horizontally by 1/2 period—and vice versa.

The function in graph 3 is a sine function, or a horizontally shifted cosine function.

The function in graph 4 is a cosine function that has been shifted 1/2 perior, OR a cosine function that has been reflected over the x-axis.

Graph 4 is the only viable choice for a cosine function with the correct period, so we have to assume it starts at -2 because it has been reflected vertically over the x-axis. (There seems to be no restriction on that in the problem statement.)

__

Additional comment

Ordinarily, you might not be expected to make any assumptions about vertical reflection. It seems a bit of a trick question.

Answer:12

Step-by-step explanation: 48/4

Since the question is asking about total employees, we must add 175 to 500 to get 675. Therefore, the correct answer is 675.

Increase means to grow or make larger in size, amount, degree, or intensity. It is the opposite of decrease, meaning to make or become less.

This is because when there were 500 employees, a 35% increase would be a total of 500 + 35% of 500

= 500 + 175

= 675.

To calculate 35% of 500, we use the formula:

(35/100) × 500 = 175

This means that 35% of 500 is 175, so when we add 175 to 500, we get 675.

Since the question is asking about  total employees, we must add 175 to 500 to get 675.

Therefore, the correct answer is 675.

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