= OPEN ENDED QUESTION Example 2 t) The local furniture store pays $110 for a chest of drawers and sells it with a 40% markup. What is the selling price of the chest of drawers?

The Distance the handler will move from the starting point to the return point will be approximately 439.8204 feet.

The distance the handler will move from the starting point to the return point when creating an arc of a circle with a radius of 70 feet, we need to find the length of the arc.

The formula to calculate the length of an arc is given by:

Length of arc = (θ/360) * 2πr

Where:

θ is the central angle of the arc (in degrees)

r is the radius of the circle

In this case, since the handler is creating a full circle, the central angle is 360 degrees.

Length of arc = (360/360) * 2π * 70

Length of arc = (1) * 2π * 70

Length of arc = 2π * 70

Length of arc = 140π

To find the approximate value in feet, we can use the approximation π ≈ 3.14159.

Length of arc ≈ 140 * 3.14159

Length of arc ≈ 439.8204 feet

Therefore, based on the given theory and using a circle with a radius of 70 feet, the distance the handler will move from the starting point to the return point will be approximately 439.8204 feet.

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Irene has 49 Books, and Alejandro has 24 books.

Let's assume that Irene has x books, and Alejandro has y books. According to the given information, we can form the following equations:

1. Irene has twice as many books as Alejandro plus 1:

  x = 2y + 1

2. The total number of books between Irene and Alejandro is 73:

  x + y = 73

We can now solve this system of equations to find the values of x and y.

Substituting the value of x from equation (1) into equation (2), we have:

(2y + 1) + y = 73

3y + 1 = 73

3y = 72

y = 24

Now, we can substitute the value of y into equation (1) to find x:

x = 2(24) + 1

x = 49

Therefore, Irene has 49 books, and Alejandro has 24 books.

To verify our solution, we can check if the sum of their books equals 73:

49 + 24 = 7

So, our solution is correct.

In conclusion, Irene has 49 books, and Alejandro has 24 books.

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Answer:

0

Step-by-step explanation:

A formula that describes the average revenue per person is:

average revenue per person = 1.4w

Average revenue per person is the ratio of the total revenue received to the number of people. It is calculated by dividing total revenue by the number of people.

We have:

Total revenue formula, M = 350w⁴

Total number of people formula, T = 250w³

Thus,

Average revenue per person = M/T

Average revenue per person = 350w⁴/250w³

Average revenue per person = 1.4w

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Answer: You can do this!

Step-by-step explanation: For D. The x= -1 and the y= 1 for E same thing the x= 7 and the y= 1 so look for the 7 on the x-axes and the one on the y-axes get it. I believe that you got this!

Hope this helped love<3

The area of this composite figure made from placing a sector of a circle on a triangle is 95.55 square cm

The sector area

The area of the sector is calculated as

Area = x/360 * πr²

Where

r² = 8² + 6²

So, we have

r² = 100

This means that

Area = 82/360 * π * 100

Evaluate

Area = 71.55

The triangle area

This is calculated as

Area = 0.5bh

So, we have

Area = 0.5 * 8 * 6

Evaluate

Area = 24

So, the area of the figure is

Figure = 24 + 71.55

Figure = 95.55

Hence, the area is 95.55

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The height of the projectile after 4 seconds is 421.28 ft.

The projectile is in the air for 8.015 seconds.

The horizontal distance traveled by the projectile is 881.77 ft.

The maximum height of the projectile is 464.1 ft.

To solve this problem, we can use the kinematic equations of motion for a projectile.

Let's assume that the initial height of the projectile is zero.

What is the height of the projectile after 4 seconds:

We can use the equation:

\(y = yo + vot + 1/2at^2\)

where

y = height of the projectile

yo = initial height (zero in this case)

vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec

a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)

t = time = 4 sec

Plugging in the values, we get:

\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)

Therefore, the height of the projectile after 4 seconds is 421.28 ft.

Long is the projectile in the air:

The time of flight of a projectile can be calculated using the equation:

t = 2vo sinθ / g

where θ is the launch angle and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 2(220 sin(60°)) / 32.2 = 8.015 sec

Therefore, the projectile is in the air for 8.015 seconds.

Horizontal distance traveled by the projectile:

The horizontal distance traveled by the projectile can be calculated using the equation:

\(x = xo + vot + 1/2at^2\)

where

x = horizontal distance traveled

xo = initial horizontal position (zero in this case)

vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec

a = acceleration due to gravity (zero in the horizontal direction)

t = time = 8.015 sec

Plugging in the values, we get:

\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)

Therefore, the horizontal distance traveled by the projectile is 881.77 ft.

Maximum height of the projectile:

The maximum height of a projectile can be calculated using the equation:

\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)

Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)

Therefore, the maximum height of the projectile is 464.1 ft.

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An arrangement of more than one repeating shape with no spaces or overlapping between shapes is a semi-regular tessellation

Given data ,

Let the semi-regular tessellation be represented as A

Now , the value of A is

A semi-regular tessellation is a tiling of the plane by two or more regular polygons in such a way that every vertex has the same configuration of polygons in the same order

Therefore , an arrangement of more than one repeating shape with no spaces or overlapping between shapes

Hence , the semi-regular tessellation is solved

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Answer:

gradient = 2

Step-by-step explanation:

calculate the gradient ( slope ) m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (2, 2) and (x₂, y₂ ) = (5, 8) ← 2 points on the line

m = \(\frac{8-2}{5-2}\) = \(\frac{6}{3}\) = 2

Answer:

Step-by-step explanation:

the gradient means the tan value of the line

tan = y/x

= 6/ 3 = 2

El supplemento y el complemento de cada ángulo son, respectivamente:

Caso A: m ∠ A' = 43°

Caso B: m ∠ A' = 31°

De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:

Ángulo y su complemento

m ∠ A + m ∠ A' = 90°

Ángulo y su suplemento

m ∠ A + m ∠ A' = 90°

Donde:

Ahora procedemos a determinar cada ángulo faltante:

Caso A: Complemento

47° + m ∠ A' = 90°

m ∠ A' = 43°

Caso B: Suplemento

149° + m ∠ A' = 180°

m ∠ A' = 31°

El enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.

The statement is written in Spanish and its answer is written in the same language.

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The inequality states that Jayda's age (j) is greater than 12 i.e., j > 12.

Let j represent Jayda's age.

Since Jayda is older than her 12-year-old sister, we can write the inequality:

j > 12

Thus, the inequality states that Jayda's age (j) is greater than 12.

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9514 1404 393

Answer:

  x = 19

Step-by-step explanation:

Corresponding sides are proportional.

  full length/right segment = 36/20 = (x+5+30)/30

Multiplying by 30 gives ...

  54 = x +35

  19 = x . . . . . . . subtract 35

The rate of change of the simple index over one day is approximately 12.78%.

To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.

On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:

Total value of Stock A on Monday = 5000 * $2.75 = $13,750

Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:

Total value of Stock B on Monday = 3000 * $4.30 = $12,900

The total value of the index on Monday is the sum of the values of Stock A and Stock B:

Total value of the index on Monday = $13,750 + $12,900 = $26,650

On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.

The total value of Stock A on Tuesday is:

Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500

The total value of Stock B on Tuesday is:

Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550

The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:

Total value of the index on Tuesday = $15,500 + $14,550 = $30,050

To calculate the percent change in the index, we use the formula:

Percent Change = ((New Value - Old Value) / Old Value) * 100

Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%

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The polynomial f(x) with real coefficients and the given zeros is:

f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)

To form a polynomial with degree 5 and the given zeros, we can start by writing the factors corresponding to each zero.

The zero 3 gives us the factor (x - 3).

The zero -i gives us the factor (x + i) since complex zeros always come in conjugate pairs.

The zero 9+i gives us the factor (x - (9+i)).

Now, we can multiply these factors together to obtain the polynomial:

f(x) = (x - 3)(x + i)(x - (9+i))

Next, we simplify the expression:

f(x) = (x - 3)(x + i)(x - 9 - i)

Expanding the product, we have:

f(x) = (x^2 + xi - 3x - 3i)(x - 9 - i)

Multiplying further:

f(x) = (x^3 - 9x^2 - ix^2 + xi - 3x^2 + 27x + 3ix - 3xi - 27i - 3x + 27 + 3i)

Combining like terms:

f(x) = x^3 - (9 + i)x^2 - 3x^2 + (x - 3 - 3i)x + 27x + (27 + 3i)

Simplifying:

f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)

The polynomial f(x) with real coefficients and the given zeros is:

f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)

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Because ∠DAC equals ∠BAD, we can conclude that triangles ΔABC and ΔACD are similar according to the Angle-Angle (AA) similarity criterion. Then the length of the CD is 8.3.

To find the length of the CD, we can use the similarity of triangles ΔABC and ΔACD. Since∠ DAC is equal to ∠ BAD, we can conclude that triangles ΔABC and ΔACD are similar by the Angle-Angle (AA) similarity criterion.

Using the given information:

AB = 5.7

AC = 5.1

BD = 3.6

Let's set up the proportion based on the similarity of triangles  ΔABC and ΔACD:

AB/AC = BC/CD

Substituting the given values:

5.7/5.1 = (5.7 + 3.6)/CD

Simplifying the equation:

1.1176 = 9.3/CD

Cross-multiplying:

CD = 9.3 / 1.1176

Calculating CD:

CD ≈ 8.3214

Therefore, Rounding the CD to one decimal place, the length of the CD is approximately 8.3.

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The algebraic property illustrated is the commutative property of multiplication

The properties of algebra are those properties mostly used in simplifying algebraic expressions.

Algebraic properties are:

From the expression given we have

4/5 • 5/4 = 1

= 4/ 5 × 5/ 4

= 1

Thus, the algebraic property illustrated is the commutative property of multiplication

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Answer:

x=158

Step-by-step explanation:

109=-x+267

-267     -267

-158=-x

x=158

(also i noticed part of your question says x=(?)*5 and 31.6*5 is 158 so that would be 31.6)

∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°

→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°

→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°

angle Y and W are supplementary angles

so

→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°

angle X and Z are supplementary angles

so

→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

Therefore, the answer is

Answer: 18x

___________________________________

The difference in the circumference of the circles is 4π / x + 2

The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle.

The formula of circumference of a circle is given as;

C = 2πr

Subtracting the circumference of B from A

C = [8π / x + 2] - [4π/ x + 2]

Since both fractions have the same denominators;

C = 8π - 4π / x + 2

C = 4π / x + 2

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The angles are formed by a transversal and two parallel lines in the figure. By applying congruent angles and vertical opposite angle property, ∠1 ≅∠3 ≅ ∠5 ≅ ∠7; ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8. Therefore option B is correct.

Congruent angles are identical to each other and have the same measure. The angles formed by the transversal in corresponding corners are called corresponding angles and they are congruent.

Therefore, ∠1 ≅ ∠5, ∠3 ≅ ∠7----------(1)

At a vertex if two angles are opposite to each other, then they are vertically opposite angles, they are equal and congruent to each other.

Therefore, ∠1 ≅ ∠3, ∠5 ≅ ∠7----------(2)

Combining (1) and (2), we get:

∠1 ≅∠3 ≅ ∠5 ≅ ∠7
Similarly we can find,

∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8.

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Answer:

22

Step-by-step explanation:

The ratio tells us 2/5 of the swimmers are indoor swimmers.

55(2/5)=22

The percentage decrease in the pictures taken from last year to this year is 20.5%

Percentage decrease formula finds the decrease from one amount to another as a percentage of the first amount.  The percent decrease formula gives the decrease in quantity with respect to its initial value. To calculate the decrease in percentage, we first need to find the difference in the values. Then, divide the difference by the initial value and multiply it by 100.

In the problem, we have our data as;

The percentage decrease will be calculated using the formula;

Percentage decrease = [last year - this year / last year] * 100

Percentage decrease = [(780 - 620) / 780] * 100

Percentage decrease = 20.5%

The percentage decrease between last year and this year is 20.5%

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The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:

tan² x · sec² x + 2 · sec² x - tan² x = 2

Second, use trigonometric formulas to reduce the number of trigonometric functions:

tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2

Third, expand the equation:

tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2

tan⁴ x + 2 · tan² x = 0

Fourth, factor the expression:

tan² x · (tan² x - 2) = 0

tan² x = 0 or tan² x = 2

tan x = 0 or tan x = ± √2

Fifth, determine the solutions to trigonometric equation:

x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

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The required value of trigonometric ratios is,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

We know that,

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

Therefore,

sin 45° = 1/\(\sqrt{2}\)

cos 30 = \(\sqrt{3}\)/2

tan 60 = 1/  √3

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Answer:

12

Step-by-step explanation:

G(2)= 2^2 +4(2)

Solve via order of operations

G(2)=4 +8

G(2)=12

Answer:

710/3×31/10

\(reduce \: fraction \: to \: the \: lowest \\ term \: by \: canceling \: the \: greatest \\ common \: factor \: \\ = \frac{71 \times 31}{3} \\ calculate \: the \: first \: two \: terms \\ = \frac{2201}{3} \: is \: the \: answer\)