Calculate the area of the figure below using the following information:


Area of triangle ABC = 31.8 square units


Area of triangle ACD = 39.2 square units


Area of triangle AED = 35.5 square units


Image of irregular pentagon with vertices points A, B, C, D, and E starting at upper left moving clockwise. Two dotted diagonal lines, one connecting vertices A and C, and the second connecting vertices A and D.

Check the picture below.

Answer:

64 m

Step-by-step explanation:

100.5% is the probability .

What is included in a probability simple definition?

The likelihood or possibility that a particular event will occur is expressed mathematically as a probability. Probabilities can be expressed as fractions between 0 and 1, as well as percentages between 0% and 100%.

                              The likelihood of an event happening or of something else happening is measured by probability. When we toss the coin into the air, we calculate the probability that it will land with the heads side up using the probability concept.

Probability that sharpshooter hit the target p = 90/100  = 9/10

         p + q = 1

        q = 1 - p = 1 - 9/10  = 1/10

a) The probability that she misses all the shots

Using binomial theorem

                = 9C₀P⁰1/10⁹

               =     100.5%

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After filling 1,295 bags of 6 ounces each, there will be 1 ounce of cookies left.

To find out how many bags of cookies can be filled, we need to divide the total number of ounces of cookies by the size of each bag:

7,771 ounces ÷ 6 ounces/bag = 1,295.1667 bags

We can't have a fraction of a bag, so we need to round down to the nearest whole number:

1,295 bags

Now we can find out how many ounces of cookies will be left by subtracting the total number of ounces used for the filled bags from the total number of ounces produced:

Total ounces produced - (number of bags filled × size of each bag)

= 7,771 ounces - (1,295 bags × 6 ounces/bag)

= 7,771 ounces - 7,770 ounces

= 1 ounce

Therefore, there will be 1 ounce of cookies left after filling as many 6-ounce bags as possible.

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The quotient using a synthetic method of division is 3x⁴ - 8x³ + 16x² - 31x + 46

The quotient expression is given as

(3x⁵ - 2x⁴ + x² - 16x - 132) divided by x + 2

Using a synthetic method of quotient, we have the following set up

-2 |   3    -2   0  1    -16    -132

     |__________

Bring down the first coefficient, which is 3:

-2 |   3    -2   0  1    -16    -132

     |__________

        3

Multiply -3 by 1 to get -3, and write it below the next coefficient and repeat the process

-2 |   3    -2    0     1    -16    -132

     |____-6__16_-32_62__-92__

        3    -8    16   -31   46   -224

So, the quotient is 3x⁴ - 8x³ + 16x² - 31x + 46 and the remainder is -224

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We have the equation to represent the relationship between books and dollars, i.e. y = 5x

The slοpe οf a line is a measure οf its steepness. Mathematically, the slοpe is calculated as "rise οver run" (change in y divided by change in x).

Assuming that the first cοlumn οf the matrix represents the number οf bοοks and the secοnd cοlumn represents the cοrrespοnding cοst in dοllars, we can write a linear equatiοn tο represent the relatiοnship between bοοks and dοllars.

Here, When the number of books is 1, the price 5

Same, When the number of books is 2, the price 10

let the number of books be x and price of books be y

Now, the linear equation with two variables forms = y = mx

5 = m1

m = 5/1 = 5

Lets check again

10 = m2

m = 10/2 = 5

Therefore

y = 5x

Thus, m = 5 where m is a constants, And we have the equation to represent the relationship between books and dollars, i.e. y = 5x

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Answer:

Step-by-step explanation:

We know that (a−b)2=a2+b2−2ab. . Thus, we have AC=AB. Hence, we have proved that if two medians of a triangle are equal, then the triangle is isosceles.

Answer:

a.9π

b.v=54πcm^3

c.54(π)=169.56

Step-by-step explanation:

a. area of circle = πr^2

3^2π

9π

b. V=πr^2h

v=π(9)(6)

v=54πcm^3

c. 54(π)=169.56

Answer:

Step-by-step explanation:

Let's assume that the width of the floral mosaic flag is "x" ft.

According to the problem, the length of the flag is 320 ft greater than the width. So, the length will be x+320 ft.

The perimeter of the flag is given as 2,400 ft.

As the perimeter of a rectangle is given by the formula 2(length + width), we have:

2(x + x+320) = 2400

Simplifying the equation:

2(2x+320)=2400

4x+640=2400

4x=1760

x=440

So, the width of the floral mosaic flag is 440 ft.

And the length of the flag is x+320 = 440+320 = 760 ft.

Therefore, the width of the floral mosaic flag is 440 ft and the length is 760 ft.

Jοsiah mistake is He did nοt multiply the numeratοr and denοminatοr by the cοrrect number tο equal 1,500.

A fractiοn, which is derived frοm the Latin wοrd fructus, which means "brοken," is a cοmpοnent οf a whοle οr, mοre brοadly, any number οf equal pieces. When emplοyed in cοnversatiοnal English, a fractiοn denοtes the quantity οf cοmpοnents οf a specific size, as in οne-half, eight-fifths, and three-quarters.

It cοnsists οf a nοn-zerο denοminatοr that is shοwn belοw (οr after) a line and a numeratοr that is shοwn abοve the line. Numeratοrs and denοminatοrs are used in cοmmοn fractiοns such as cοmpοund fractiοns, cοmplex fractiοns, and mixed numerals.

It is said as fοllοws: 10/20 = x/1500

1500 divided by bοth sides : (10/20)x1500 = (x/1500)x1500

Or,(10x1500) /20 = x

Or, x=750

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Anthοny cοuld be expected tο make 64 pars οr better οn the remaining 160 hοles.

We can use a prοpοrtiοn tο determine hοw many pars οr better Anthοny cοuld be expected tο make οn the remaining 160 hοles:

par οr better οn remaining hοles / tοtal remaining hοles = par οr better οn first 80 hοles / tοtal first 80 hοles

Let x be the number οf pars οr better Anthοny cοuld be expected tο make οn the remaining 160 hοles. Then we can set up the prοpοrtiοn as:

x / 160 = 32 / 80

Simplifying the right side οf the equatiοn, we get:

x / 160 = 2 / 5

Crοss-multiplying, we get:

5x = 320

Dividing by 5, we get:

x = 64

Therefοre, Anthοny cοuld be expected tο make 64 pars οr better οn the remaining 160 hοles.

So the answer is 64 pars.

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Step-by-step explanation:

We can simplify the expression using trigonometric identities:

cot(x) - csc^2(x) / cot(x)

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

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

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

= -sin^2(x) / sin(x)

= -sin(x)

Therefore, cot(x) - csc^2(x) / cot(x) simplifies to

-sin(x).

The amount of pesos that you need to purchase $100,000 is 793,651.

A buy is when something is obtained in exchange for some type of payment, such as products or services. The usual forms of payment are cash or credit (to be paid later). A purchase could also be made in exchange for taking on an obligation or as part of a barter exchange where various non-cash assets are traded. However, when a noun form is required, you should use "buy," as in: You made a wise purchase when you bought petrol before the price increased. Use "buy" for straightforward activities and "purchase" for more formal exchanges of money for products.

Solve: 100,000/.126 = 793,650.79

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Answer:

225π+362.5 should be your answer. Make sure to round it up!

Step-by-step explanation:

Answer:

275.81 ft²

Step-by-step explanation:

So we need to find the area of this figure. First, break down the figure into two distinct shapes, a triangle and a semicircle. Form an area equation that includes these two formulas.

Area = Area of triangle + Area of Semicircle

Now translate this into numbers and variables.

A = (0.5)bh + (0.5)pi(r)²

The problem suggests we use 3.14 to represent pi.
b = 25 ft
h = 15 ft
r = 7.5 ft

So now rewrite the total area equation with our given values and simplify as much as possible.

A = (0.5)(25)(15) + (0.5)(3.14)(7.5)²

  = 187.5 + 88.3125

  = 275.8125 ft²

The problem statement asks for the answer rounded to the nearest hundredth, so the area if the figure is 275.81 ft².

Answer:

20

Step-by-step explanation:

from: BODMAS

Bracket

Of

Division

Multiplication

Addition

Subtraction

We first deal with brackets, division and then subtraction last.

13 - 2 (1- 15) ÷ 4

13 - 2(-14) ÷4

13 -(-28÷4)

13 - (-7)

13 +7

= 20

Answer:

Nancy invested her money for 2.5 years.

Step-by-step explanation:

We can use the formula for simple interest to solve for the time (in years) that Nancy invested her money:

Interest = Principal x Rate x Time

Here, the principal is $6000, the rate is 3%, and the interest earned is $450. Substituting these values into the formula, we get:

$450 = $6000 x 0.03 x Time

Simplifying, we get:

Time = $450 / ($6000 x 0.03)

Time = 2.5 years

Therefore, Nancy invested her money for 2.5 years.

For more help:

Identify the given variables:

Principal (P) = $6000

Annual interest rate (r) = 3%

Interest earned (I) = $450

Use the formula for simple interest to solve for time (t):

I = P * r * t

where t is the time in years

Substitute the given values into the formula:

$450 = $6000 * 0.03 * t

Solve for t:

$450 = $180t

t = $450 / $180

t = 2.5 years

Extra information:

The simple interest formula is a mathematical formula used to calculate the interest earned on a principal amount of money, given a fixed interest rate and time period. The formula is:

I = P * r * t

where:

• I is the interest earned

• P is the principal amount

• r is the annual interest rate (as a decimal)

• t is the time period (in years)

Using this formula, you can calculate the amount of interest earned on a given principal amount, at a given interest rate, for a certain amount of time. It is called "simple" interest because it assumes that the interest is calculated only on the principal amount, without compounding (i.e., without adding the interest earned back into the principal amount).

Hoped this help! I'm sorry if it's wrong. If you need more help, ask me! :]

Yes, the triangles must be cοngruent. This can be justified by the Cοnverse οf the Pythagοrean Theοrem

Cοngruency refers tο the prοperty οf having the same size and shape. Twο geοmetric figures are said tο be cοngruent if they have identical measurements οf angles and sides.

Yes, the triangles must be cοngruent. This can be justified by the Cοnverse οf the Pythagοrean Theοrem, which states that if a perpendicular line is drawn frοm the vertex οf the right angle οf a right triangle tο the hypοtenuse, then the twο smaller triangles fοrmed are similar tο the οriginal triangle and tο each οther.

Since an isοsceles triangle can be cοnsidered a special case οf a right triangle where the hypοtenuse is alsο a leg, the Cοnverse οf the Pythagοrean Theοrem applies and the twο smaller triangles fοrmed by the perpendicular line are cοngruent.

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Therefore , the solution of the given problem of angle comes out to be the distance between the vessels is roughly 66.71 metres.

The top as well as bottom of the wall separate the two circle lines that, in Cartesian coordinates, make up a skew's ends. A junction point may be created when two rays collide. Another result of two objects interacting is an angle. They most closely approach dihedral shapes. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.

Here,

The boats and the points immediately beneath them make two right triangles with the tower when viewed from the tower.

We can determine d1 and d2 using the tangent function:

=> d1 = 75 tan(12°) = tan(12°) = d1/75

=> d2/75 = 75 tan(7°) = tan(7°) = d2/75

Using these formulas as a substitute for d = d2 - d1, we obtain:

=> 75 Tan(7°) - 75 Tan(12°) = d

Calculating the values of these tangents yields the following results:

=> d ≈ 161.65 - 94.94

=> d ≈ 66.71

Consequently, the distance between the vessels is roughly 66.71 metres.

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The number of chairs sold must be a non-negative integer, we can round up -10 to 0. Therefore, the minimum number of chairs the store must sell is 0.

Given the constraints in the problem, we can set up the following system of inequalities:

c + t ≤ 30 (the store can ship no more than 30 pieces of furniture)

Rc + Rt ≥ 6500 (the store must sell a minimum of $6500 worth of chairs and tables)

Rc = 150c (the price of a chair is $150)

Rt = 400t (the price of a table is $400)

We know that 10 tables were sold, so we can substitute t = 10 into the first two inequalities:

c + 10 ≤ 30

150c + 4000 ≥ 6500

Simplifying the first inequality, we get c ≤ 20. So the store can sell at most 20 chairs in addition to the 10 tables.

We can set up the following optimization problem:

Maximize 150c

Subject to c + t ≤ 30

Rc + Rt ≥ 6500

Rt = 400t

t = 10

Using substitution, we can rewrite the second constraint as:

150c + 4000 + 400t ≥ 6500

150c + 4000 + 400(10) ≥ 6500

150c + 8000 ≥ 6500

150c ≥ -1500

c ≥ -10

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Answer:

the shape includes a curve

By answering the presented question, we may conclude that This inequality indicates that his practise time must be larger than or equal to the difference between 45 and his homework time.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many basic inequalities may be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are split or added on both sides. Exchange left and right.

If Jamaal spends x minutes playing his guitar and y minutes on schoolwork, his total time is x + y minutes.

x + y ≥ 45

x + y - y ≥ 45 - y

x ≥ 45 - y

As a result, the disparity representing Jamaal's practise time is:

x ≥ 45 - y

This indicates that his practise time must be larger than or equal to the difference between 45 and his homework time.

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The answer of the given question based on finding the length of EF from the triangle is, the length of EF is approximately 1.2. The answer is (d).

The Law of Sines is a trigonometric rule that relates the angles and sides of a triangle. Specifically, it states that for any triangle ABC, the ratio of the length of a side of the triangle to the sine of the angle opposite that side is equal to the same ratio for any other side and its opposite angle:

a/sin(A) = b/sin(B) = c/sin(C) ,where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the opposite angles, respectively. This law is useful in solving problems involving triangles, such as finding the length of a side or the measure of an angle when given certain other information about the triangle.

To find the length of EF, we can use the Law of Sines,

Let x be the length of EF. Then we have:

sin(75°)/3 = sin(50°)/x

Solving for x, we get:

x = 3*sin(50°)/sin(75°) ≈ 1.2

Therefore, the length of EF is approximately 1.2. The answer is (d).

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Mrs. Rodriguez purchased 10 boxes of colored pencils and 25 boxes of plain pencils, for a total of 35 boxes of pencils costing a total of $50.

Mrs. Rodriguez purchased 10 boxes of colored pencils and 25 boxes of plain pencils. This can be expressed as an equation: 10 boxes of colored pencils + 25 boxes of plain pencils = 35 boxes of pencils. This is because there are 35 boxes of pencils in total. Each box of colored pencils is counted as one unit, and each box of plain pencils is counted as one unit, so the total number of boxes purchased is 35.The cost of the purchase can be calculated by multiplying the number of boxes of each type of pencils purchased by the cost per box. For example, if each box of colored pencils costs $2 and each box of plain pencils costs $1, the total cost of the purchase is 10 x $2 + 25 x $1 = $50.In summary, Mrs. Rodriguez purchased 10 boxes of colored pencils and 25 boxes of plain pencils, for a total of 35 boxes of pencils costing a total of $50.

Question:

Mrs Rodriguez buys 10 boxes of colored pencils and 25 boxes of plain pencils.How many boxes of pencils does Mrs Rodriguez buy in total? or How much does Mrs Rodriguez need to pay for 10 boxes of colored pencils and 25 boxes of plain pencils?

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The value of a, b and c are found as 6, 10 and 2 respectively.

Values for exponents, commonly referred to as powers, indicate how many often to multiply a quantity by itself.

The given expression is;

[tex]4x^{8} y^{c} = \frac{24x^{b}y^{-3} }{ax^{2} y^{-5} }[/tex]

Solving expression using the law of indices.

[tex]x^{8} y^{c} = \frac{6x^{b-2}y^{-3+5} }{a}[/tex]

[tex]ax^{8} y^{c} = {6x^{b-2}y^{2} }[/tex]

Comparing powers of both sides:

a = 6

8 = b-2 : b = 10

c = 2

Thus, the value of  a, b and c are found as 6, 10 and 2 respectively.

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Answer:

The simplified version of 68/84 is 17/21.

Step-by-step explanation:

To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common factor (GCF). In this case, the GCF of 68 and 84 is 4. Dividing both numbers by 4 gives:

68/4 = 17

84/4 = 21

Therefore, 68/84 simplifies to 17/21.

The simplest form of [tex]\dfrac{63}{84}[/tex] is [tex]\dfrac{3}{4}[/tex].

Find the GCD (or HCF) of numerator and denominator

GCD of 63 and 84 is 21

Divide both the numerator and denominator by the GCD

[tex]63 \div 21[/tex]

[tex]84 \div 21[/tex]

Reduced fraction:

[tex]\dfrac{3}{4}[/tex]

Therefore, [tex]\dfrac{63}{84}[/tex] simplified to lowest terms is [tex]\dfrac{3}{4}[/tex].

The graph of the image point S' is (2.24, -6.93) on the coordinate plane.

A graph is a visual representation of data that shows the relationship between different variables or sets of data. Graphs can be used to display information in a way that is easy to understand and interpret, and they are often used to summarize complex data sets.

There are many different types of graphs, including:

Line graphs: These graphs show changes in data over time by connecting data points with straight lines.

Bar graphs: These graphs use bars to represent different categories or data sets, with the height or length of each bar indicating the value of the data.

Pie charts: These graphs use slices of a circle to represent different proportions of a data set, with each slice representing a different category or value.

Scatter plots: These graphs show the relationship between two different variables by plotting each data point on a two-dimensional plane.

To graph the image of S(-7,-1) after a rotation of 270° clockwise around the origin, we can use the following steps:

Therefore, the graph of the image point S' is (2.24, -6.93) on the coordinate plane.

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Answer:

6,075

Step-by-step explanation:

Substitute 81 for x

x (x -6)

81(81-6)

81(75)

6075

Helping in the name of Jesus.

Answer: B. 6,075

Step-by-step explanation:

1. Substitute x = 81 into x(x - 6): 81 x (81 - 6)

2. Calculate: 81 x (81 - 6): 6,075

Answer: a) Write an equation that represents the amount of water in the first pool after t minutes, assuming water is only being added and not removed.

We can use the formula for uniform motion to represent the amount of water in the first pool after t minutes:

amount of water = initial amount + rate * time

The initial amount of water in the first pool is 872 liters. The rate at which water is being added to the first pool is 18.25 liters per minute. Therefore, the equation that represents the amount of water in the first pool after t minutes is:

A(t) = 872 + 18.25t

b) Write an equation that represents the amount of water in the second pool after t minutes, assuming water is only being added and not removed.

Similar to part (a), we can use the formula for uniform motion to represent the amount of water in the second pool after t minutes:

amount of water = initial amount + rate * time

The initial amount of water in the second pool is 0 liters, since it is initially empty. The rate at which water is being added to the second pool is 45.5 liters per minute. Therefore, the equation that represents the amount of water in the second pool after t minutes is:

B(t) = 0 + 45.5t

c) How long will it take until the two pools have the same amount of water?

To find the time when the two pools have the same amount of water, we can set the two equations from parts (a) and (b) equal to each other:

A(t) = B(t)

872 + 18.25t = 45.5t

Subtracting 18.25t from both sides, we get:

872 = 27.25t

Dividing both sides by 27.25, we get:

t ≈ 32 minutes

Therefore, it will take approximately 32 minutes until the two pools have the same amount of water.

Step-by-step explanation: