Question 10
Here is a figure made of a circle inscribed in a square.
36 m
(a circle within
a square)
What is the area of the shaded region?

(You may round answer to a whole number)

Answer:

Step-by-step explanation:

here goes your solution down

The given system of equations can be written as a matrix equation and solved by using the inverse coefficient matrix. The inverse coefficient matrix is 1/10 [4 -2], [3  5], and when multiplied by the vector of variables [x, y] the vector of constants [4, 10] is obtained. This gives the solution x = 6 and y = 2.

Given system:

x + 2y = 4

3x + 4y = 10

Matrix equation:

[x  y]   [1  2]   [4]

[    ] = [    ] x [  ]

[3  4]   [3  4]   [10]

Inverse coefficient matrix:

1/10 [4 -2]

    [3  5]

Solution:

1/10 [4 -2] [x]   [4]

    [3  5] [y] = [10]

x = 6

y = 2

The given system of equations can be written as a matrix equation which can be solved by using the inverse coefficient matrix. This inverse coefficient matrix is found by calculating the inverse of the matrix of coefficients of the variables. In this case, the matrix of coefficients is [1, 2], [3, 4], and the inverse of this matrix is 1/10 [4 -2], [3  5]. Multiplying this inverse coefficient matrix by the vector of variables [x, y] will give the vector of constants [4, 10]. This allows us to solve for the variables, giving x = 6 and y = 2. Therefore, the solution of the given system of equations is x = 6 and y = 2.

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The volume of the fish tank is 633,957.5 cubic cm or 0.634 cubic meter.

The formula for calculating the volume of a cuboid is

=  length  × breadth ×height

Given :

the length of fish tank = 105 cm

The width of fish tank= 75 cm

The height of fish tank= 80.5 cm

So, the volume of the fish tank =105×75 ×80.5

                                                =633,957.5 [tex]cm^{3}[/tex]

In metric units ;

1 meter = 100 cm

So, converting all the dimensions into metric units.

length of fish tank = 1.05 m

width of fish tank = 0.75 m

height of fish tank = 0.805 m

So, the volume of fish tank = 1.05 x 0.75 x 0.805

                                         = 0.6339575 [tex]m^{3}[/tex] or

                                         = 0.634 [tex]m^{3}[/tex]

The equation y = 5x for x ≤ 2 and y = 10 + 2.5(x-2) for x ≥ 2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

In other words, an equation is a set of variables that are constrained through a situation or case.

Given that,

First, the two-hour rate of charge is $5 per hour

y = 5x for x ≤ 2

Over the 2 hours, the rate of charge is $2.5 per hour

y = 10 + 2.5(x-2) for x ≥ 2.

Hence "The equation y = 5x for x ≤ 2 and y = 10 + 2.5(x-2) for x ≥ 2".

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Answer:

- 4x^3 + 17

Step-by-step explanation:

14 - 4x^3 + 3

- 4x^3 + 17

Step-by-step explanation:

70% = 0.7

15% = 0.15

65% = 0.65

x = gallons of the 70% solution.

0.7x + 0.15×20 = 0.65(x + 20)

70% + 15% solution = 65% solution (which has a many gallons as the combination of x and 20 gallons).

0.7x + 3 = 0.65x + 0.65×20

0.05x + 3 = 13

0.05x = 10

x = 10/0.05 = 200 gallons

so, 200 gal of the 70% pesticide solution is needed to make combined with 20 gal of the 15% solution a final solution that is 65% pesticide.

The operations of functions results in another function which are shown as below.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

There are two functions given.

f(x) = x² + 7

g(x) = 2x + 1

7. Addition of functions

   (f + g)(x) = f(x) + g(x)

                 = x² + 7 + 2x + 1

                 = x² + 2x + 8

8. Subtraction of functions

    (f - g)(x) = f(x) - g(x)

                 = (x² + 7) - (2x + 1)

                 = x² - 2x + 6

9. (g - f)(x) = g(x) - f(x)

                 = (2x + 1) - (x² + 7)

                 = -x² + 2x - 6

10. Multiplication of Functions

     (f . g)(x) = f(x) . g(x)

                  = (x² + 7) . (2x + 1)

                  = 2x³ + 14x + x² + 7

                  = 2x³ + x² + 14x + 7

11. Division of functions

   [tex]\frac{f}{g}[/tex](x) = [tex]\frac{f(x)}{g(x)}[/tex]

          = (x² + 7) / (2x + 1)

12.  [tex]\frac{g}{f}[/tex](x) = [tex]\frac{g(x)}{f(x)}[/tex]

            = (2x + 1) / (x² + 7)

Hence the operations of the functions are done.

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A convex pentagon has five exterior angles, and the sum of the measures of these angles is equal to 360 degrees.

We know that the measures of the exterior angles of a convex pentagon are 75°, 62°, 68°, and 101°, we need to find the measure of the last exterior angle.

To find the measure of the last exterior angle, we can use the formula:

Sum of all exterior angles = (n-2) x 180

where n is the number of sides in the polygon.

For a pentagon, n = 5, so the sum of all exterior angles is (5-2) x 180 = 540 degrees

So we can use this information to find the measure of the last exterior angle:

75 + 62 + 68 + 101 + x = 540

x = 244

Therefore, the measure of the last exterior angle is 244 degrees.

Total number of monthly payments, not including the final balloon payment is $1,195.77

The monthly payment is the sum that must be paid each month for the duration of the loan to cover the principal balance. When a loan is taken out, not only the principal—the amount that was initially loaned out—but also the interest—which accrues—must be repaid.

Step1

M = 350,000(0.071/12)(1+0.071/12)² /(1+0.071/12)¹² =3,618.02

M = P(r/12) (1+r/12)¹²×n/(1+r/12)¹²×n -1

Step2:

3,618.02 × 12 × 12 = 520,994.88

The total paid is the product of the monthly payment and the number of payments.

520,994.88 - 350,000 = 170,994.88

= 170,994.88÷143

= 1,195.77

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A rectangle's perimeter is 40 cm. The rectangle's length is 2 cm longer than its width. Find the rectangle's length and width, which are both 6 cm.

Perimeter of rectangle [tex]$=40 \mathrm{~cm}$[/tex] (given)

condition :- length [tex]=2 \times$ breadth $+2$[/tex]

[tex]$\Rightarrow 1=2 \mathrm{~b}+2[/tex]

perimeter [tex]$\mathrm{p}=2(1+\mathrm{b})=40$[/tex]

[tex]& \Rightarrow 2(2 b+2+b)=40 \\[/tex]

[tex]& \Rightarrow 2(3 b+2)=40 \\[/tex]

[tex]& \Rightarrow 6 b=40-4=36 \\[/tex]

[tex]& \therefore b=6 \mathrm{~cm}[/tex]

[tex]1=2 \times 6+2=12+2=14 \mathrm{~cm}[/tex]

[tex]\therefore \text { length }=14 \mathrm{~cm} \text {, breadth }=6 \mathrm{~cm}[/tex]

The complete question is:

The perimeter of a rectangle is 40 cm. The length of rectangle is more than double its breadth by 2 cm. Find the length and breadth of rectangle .

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The value of the cost of a swimming class is $20.

Given that,

The amount to pay for swimming and yoga classes this month = $200

And, the one yoga class price is $30.

Here, the equation is,

[tex]Qy = 12 - 4Qs[/tex]

Since there are only 2 swimming classes for attending.

Hence substitute Qs = 2,

[tex]Qy = 12 - 4(2)[/tex]

[tex]Qy = 12 - 8[/tex]

[tex]Qy = 4[/tex]

Since The total cost of yoga classes = 4.

So, the cost of yoga classes is,

[tex]4 \times \$40 = \$160.[/tex]

Hence, the cost of swimming classes;

[tex]\text {Total budget - Total cost of yoga classes } = \$200 - \$160[/tex]

[tex]= \$40[/tex]

It will cost the following to take two swimming lessons:

[tex]\text {Cost of swimming classes } = \dfrac{\text { Total cost of swimming classes}}{\text {Number of swimming classes cost of swimming classes}}[/tex]

                                    [tex]= \dfrac{40}{2}[/tex]

                                    [tex]= 20[/tex]

Therefore, the total cost of a swimming class is $20.

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Both questions can be answered by using the function f(x).The function f(x) represents the total output of a farm in tons in the week of 2015, and the value of x is known. This means that by using the value of x, the total output of the farm in 2015 and the output of the farm in the week of 2015 can both be calculated.

The function f(x) is a mathematical representation of the total output of a farm in tons for the week of 2015. The value of x is known, which means that by using this value, the total output of the farm in 2015 as well as the output of the farm in the week of 2015 can both be calculated. Therefore, both of the questions can be answered by using the function f(x). Knowing the total output of the farm in 2015 can help to better understand the production of the farm over the course of the year, while the output of the farm in the week of 2015 can be used to gain insights into the weekly production of the farm. With this information, decisions can be made to improve the production and efficiency of the farm.

The function f(x) can be used to answer both questions regarding the total output of a farm in 2015 and the output of the farm in the week of 2015.

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∴  Coordinates of B & D are [tex](\frac{9}{2} ,\frac{1}{2} ) & (-\frac{1}{2} ,\frac{4}{2} )[/tex] respectively.

What are coordinates of graph?

Coordinates X and Y axes are present in every graph. Positions on a graph are indicated using coordinates, which are expressed as an ordered pair of numbers.

ABCD is a square with A(-3,2) & C(0,5).

To find out-

The coordinates of B & D

Solution-

Let the coordinates of B=(x,y).

Since ABCD is a square,

[tex]AB=BC=AB^2=BC^2.[/tex]

Using distance formula,

[tex](x-3)^2+(y-2)^2=(x-0)^2+(y+5)^2[/tex]

⟹2x+8y−6=0

⟹x=([tex]\frac{6-8y}{2}[/tex] ) .........(i).

Now, in ΔABC,

[tex]AB ^2+BC ^2=AC ^2[/tex]

[tex](x-3)^2+(y-2)^ 2+(x-0) ^2 +(y+5)^ 2=(3-2) ^2+(0+5) ^2[/tex]

⟹[tex]x^ 2+y ^2 -3x-3y=0.[/tex]

Substituting for x from (i),

[tex](\frac{6-8y}{2} )^2+y ^2 -3(\frac{6-8y}{2} )-3y=0[/tex]

⟹[tex]3y^2-9y+4=0[/tex]

⟹[tex](2y-1)(2y-4)=0[/tex]

⟹[tex]y=( \frac{1}{2},\frac{4}{2} ).[/tex]

Substituting for y in (i),

[tex](x,y)=( \frac{9}{2},\frac{1}{2} ) & (-\frac{1}{2} , \frac{4}{2} )[/tex]Now abscissae of A & C are 3 & 1, respectively.

∴  Abscissa of B will be in between 1 & 3.

So here,  [tex]\frac{9}{2}[/tex] will be the abscissa of B.

 Coordinates of B & D are [tex](\frac{9}{2} ,\frac{1}{2} ) & (-\frac{1}{2} ,\frac{4}{2} )[/tex] respectively.

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The coordinates of the remaining vertices B and D are (0, 2) and (-3, 5) respectively.

What are the coordinates of the vertices?

The unit square precisely refers to the square on the Cartesian plane having four corners.

Since square ABCD has a diagonal with the given vertices A(-3, 2) and C(0, 5), we know that the other two vertices of the square will be B and D, and that all four sides of the square are congruent.

We can use the coordinates of A and C to find the coordinates of B and D.

First, we know that the x-coordinate of B must be the same as the x-coordinate of C because the side BD is parallel to the x-axis.

Therefore, the x-coordinate of B is 0.

Next, we know that the y-coordinate of B must be the same as the y-coordinate of A because the side AB is parallel to the y-axis.

Therefore, the y-coordinate of B is 2.

So, the coordinates of B are (0, 2).

Finally, we know that the x-coordinate of D must be the same as the x-coordinate of A because the side AD is parallel to the x-axis.

Therefore, the x-coordinate of D is -3.

Next, we know that the y-coordinate of D must be the same as the y-coordinate of C because the side CD is parallel to the y-axis.

Therefore, the y-coordinate of D is 5.

So, the coordinates of D are (-3, 5)

Therefore, the coordinates of the remaining vertices B and D are (0, 2) and (-3, 5) respectively.

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The level of the sound with the given properties is 200

From the question, we have the following parameters that can be used in our computation:

I0 = 10^-12

I = 10^-8

Also, we have the equation to be

β = 10log(I I0)

Substitute the known values in the above equation, so, we have the following representation

β = 10 * log(10^-12 * 10^-8)

Evaluate

β = -200

Hence, the level of sound is -200

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Complete question

use the following information for determining sound intensity. The level of sound β in decibels, with an intensity of I, is given by β = 10log(I I0), where l0 is an intensity of 10^-12 watt per square meter, corresponding roughly to the faintest sound that can be heard by the human ear find the level of sound β. l = 10^-8 watt per m^2 (quiet radio)

The triangles ∆AEC ≅ ∆AFC by Side-Angle-Side theorem

The complete question is added as an attachment

With the given information and the image attached below, we can state that the two triangles are congruent by SAS,

Then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.

The proof is given as:

Statement Reason

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9^10 divided by 9 can be simplified to 9^(10-1) = 9^9

This is because when dividing a power by the same base, we can subtract the exponent by one.

In other words, 9^10 / 9 = (9999999999) / (9) = 99999999*9 = 9^9.

So, 9^10 divided by 9 is equal to 9^9.

Another way to think about this is that dividing a number by itself is the same as multiplying that number by 1, and 9^10 / 9 = 9^10 * 1 / 9 = 9^10 / 9^1 = 9^(10-1) = 9^9

In terms of real numbers, 9^10 is equal to 387420490 and 9^9 is equal to 3486784401. So 9^10 divided by 9 is equal to 3486784401.

[tex]\it \dfrac{9^{10}}{9}=9^{10}:9^1=9^{10-1}=9^9[/tex]

A direct variation equation that relates x and y is y = (5/2)x.

What is the direct variation equation?

Direct variation is a linear function defined by an equation of the form y = kx when x is not equal to zero. Inverse variation is a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant.

When two variables are directly proportional, they vary directly with each other.

The relationship between the variables can be represented by a direct variation equation of the form:

y = kx

where k is the constant of proportionality.

Given that y = 5 and x = 2, we can use these values to find the value of k:

y = kx

5 = k(2)

k = 5/2

So the direct variation equation that relates x and y is:

y = (5/2)x

This equation shows that for every value of x, the value of y is 5/2 times that value.

For example, if x = 3, then y = (5/2) * 3 = 7.5, and if x = 4, then y = (5/2) * 4 = 10.

Hence, A direct variation equation that relates x and y is y = (5/2)x.

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According to the given statement, 37.9 cups of tomatoes in each jar.

A system of linear equations is a set of equations with two or more variables. A linear equation is one that can be expressed as ax + b = c, where x is a variable and a, b, and c are constants.

A group of two or more linear equations that share the same variables is known as a system of linear equations. As an illustration, consider the set of linear equations below:

2x + 3y = 10

4x + 6y = 20

x and y are the same variables, and the equations are linear equations. The solution to this system of linear equations is x = 2, y = 2.

This question can be solved using the system of linear equations.

Solving the system of equations gives:

T = 7.4 cups of tomatoes in each jar

Step 1: Calculate the total amount of tomatoes used.

Total tomatoes = 8 jars x cups of tomatoes per jar

Total tomatoes = 8 x (41.6 - 2.1)

Total tomatoes = 303.2 cups

Step 2: Divide the total amount of tomatoes by the total number of jars.

Cups of tomatoes per jar = Total tomatoes ÷ 8

Cups of tomatoes per jar = 303.2 ÷ 8

Cups of tomatoes per jar = 37.9 cups

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Answer: [tex]3q+1[/tex]

Step-by-step explanation:

[tex](q+3)+(2q-2)=q+3+2q-2=(q+2q)+(3-2)=3q+1[/tex]

x/40 = 48/60

x= 4/5 × 40

x= 4 × 8

x = 32

Answer:

32

Step-by-step explanation:

by use of similarity and enlargement the answer can be evaluated.

use the formula: IMAGE LENGTH ÷OBJECT LENGTH.

Answer:

  54

Step-by-step explanation:

You want the mean of the positive 2-digit multiples of 4.

The 2-digit multiples of 4 form an arithmetic sequence whose first term is 12, and whose last term is 96. The arithmetic mean of the numbers in the sequence will be the average of the first and last numbers:

  (12 +96)/2 = 108/2 = 54

The average of the 2-digit multiples of 4 is 54.

Answer:

These ratios are equivalent

Step-by-step explanation:

We can put both ratios into fraction form:

For 3 cookies and 7 glasses of milk, the fraction will be [tex]\frac{3}{7}[/tex]

For 27 cookies and 63 glasses of milk, the fraction will be [tex]\frac{27}{63}[/tex]

Both fractions in decimal form will be equal to 0.428571, so they are equivalent.

Yes because If you times both of them by 9 then they are equivalent

Contour Interval: The contour interval is the difference in elevation between two adjacent contour lines. In this case, the contour interval is 50 feet, as indicated in the bottom-left corner of the map.

Contour lines are lines on a map that connect points of equal elevation above a reference surface, usually sea level. They indicate the steepness of a terrain or landform and are often used to represent hills, valleys, and other relief features.

Ridge Line: A ridge line is a line formed by two or more contour lines that form a peak. In this map, the ridge line is marked by the contour lines labeled 1200 and 1250.
Valley: A valley is a line formed by two or more contour lines that form a low point. In this map, the valley is marked by the contour lines labeled 950 and 1000.

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The equation that shows the number of pounds of celery(y) the cook will use each day is 8y+17= 31 and y = 1 ¼

A linear equation is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

For each day , the cook will use 2 1/8 pounds of carrot and y pounds of celery

therefore total = 17/8 +y

for 5 days the total carrot and celery used =( 17/8 + y) ×5

for 5 days 19 3/8 pounds of carrot and celery is used . Therefore;

155/8 = 5(17/8+y)

for each day, divide both sides by 5

155/8×1/5 = 17/8+y

31/8 = 17/8+y

collect like terms

y = 31/8-17/8

multiply through by 8

8y = 31-17

8y+17 = 31

therefore the equation that can be used to find the pound of celery used per day is 8y+17= 31

and y = 14/8 = 7/4 = 1 ¼

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On average, 15-20% of the cost is left as a gratuity. Add the desired decimal percentage tip to the total amount of the check and multiply the result to determine the tip.

How much should you leave for tip?

15% to 20% of the tab is typically left as a gratuity. Add the decimal % tip you want to leave to the total check amount to compute the tip. You would multiply 1 by 0.20 to reach 1.20 if you wanted to leave a 20% tip. To calculate the total amount you would tip, multiply the bill by 1.20.

It is advised that you leave at least 10% of your tip, even if the service was subpar. * Because some restaurants tack on a gratuity, carefully review your tab. Whether or not you should add to that is up to you. In sit-down restaurants, the tip for the wait staff should be between 15 and 20 percent of the pretax total.

To find out the tip amount, we need to first calculate 15% of the bill:

$40.94 x 0.15 = $6.14.

Rounding this amount to the nearest cent, we get $6.14 as the tip amount.

Therefore, the tip total is$ 7.00

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Answer:

Step-by-step explanation0.275 of 20 is 20*0.275 = 5.5

52% of $10 is (0.52)*10 = 5.2

So the expression 0.275 of 20 and 52% of $10 can be simplified to 5:

The length of the side BC of right triangle ABC can be found by applying the Pythagorean theorem with AC = 12 and DC = 4. The length of BC can be expressed in simplest radical form.

Using the Pythagorean Theorem, BC^2 = AC^2 - DC^2

= 12^2 - 4^2

= 144 - 16

= 128

Therefore, BC = [tex]\sqrt{128}[/tex]= 2[tex]\sqrt{32}[/tex] = 8[tex]\sqrt{2}[/tex]

The length of the side BC of a right triangle ABC can be found by applying the Pythagorean theorem. The Pythagorean theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, AC = 12 and DC = 4, so BC^2 = AC^2 - DC^2 = 144 - 16 = 128. Therefore, which is the length of \overline{BC}BC in its simplest radical form. This result can be verified by calculating the length of the hypotenuse AC and confirming that it is equal to the square root of the sum of the squares of BC and DC.

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The piecewise function for the price of n gallons of diesel at Buc-ee’s would be = $1.00

The price paid for 3 gallons or less = $2.68 per gallon

That is, $2.68 =/< 3 gallons

Therefore $x= 1 gallon

Make X the subject of formula;

X = 2.68/3

X= $0.89

The price paid for 4 gallons or less = $2.41 per gallon

That is, $2.41 per =/< 4 gallons

Therefore $y = 1 gallon

Make y the subject of formula;

y = 2.41/4

y = $0.60

From the both outcomes, it can be concluded that the n gallons of diesel at Buc-ee’s would be approximately $1.00.

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Answer:

Step-by-step explanation:

The distance traveled by the plane can be represented by the expression: distance = speed x time

In this case, the speed of the plane is given as x-110 mph and the time it travels is 3.5 hours.

So the expression for the distance traveled is:

distance = (x-110) * 3.5 miles

This expression represents the distance traveled in miles. The variable x represents the speed of the plane in mph.

Answer:

Domain:  (-∞, ∞)

Range:  [2, ∞)

Input:  (f) = 2

Output:  f(1) = 3

Step-by-step explanation:

The domain is the set of all possible input values (x-values).

There are arrows at both endpoints of the graphed continuous line, indicating that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  

The range is the set of all possible output values (y-values).

Assuming that each square is 1 unit, from inspection of the graph, the minimum y-value is y = 2.

The arrow at the endpoint in quadrant I indicates that the line continues horizontally at y = 2.

The arrow at the endpoint in quadrant II indicates that the line continues indefinitely towards y = ∞.

Therefore, the range of the relation is restricted:  

To find the value of f(4), find x = 4 and trace up to the line then read the y-value at that point.  Therefore:

To find the x-value when y = 3, find y = 3 and trace horizontally to the line then read the x-value at that point.  Therefore: