NOTE: Angles not necessarily drawn to scale.

The area of the patio is 192 [tex]m^{2}[/tex]

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The word "area" refers to a free space. A shape's length and width are used to compute its area.

Length of swimming pool=18 m

Width of swimming pool=8 m

Area of swimming pool= 18*8 = 144[tex]m^{2}[/tex]

Width of patio=3m

Total length of swimming pool=18+2(3)=24 m

Total width of swimming pool=8+2(3)=14 m

Total area=24*14=336 [tex]m^{2}[/tex]

Area of patio= total area - Area of swimming pool

                     =336-144

                     =192 [tex]m^{2}[/tex]

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[tex]f(x) = 3(x + 2)(x - 5)[/tex]

[tex]solving \: f(x) = 0 \\ 3(x + 2)(x - 5) = 0 \\ (x + 2)(x - 5) = \frac{0}{3} \\ (x + 2)(x - 5) = 0 \\ x + 2 = 0 \: \: \: \: \: \: \: \: \: \: x - 5 = 0 \\ x = - 2 \: \: \: \: \: \: \: \: \: \: x = + 5[/tex]

The sum of the numbers is 7.69 * 10^6

The expression is given as:

(1.54 times 10 superscript 6 baseline) (6.15 times 10 superscript 6 baseline)

Rewrite properly

(1.54 * 10^6) + (6.15 * 10^6)

Factor out 10^6

(1.54 + 6.15) * 10^6

Evaluate the sum

7.69 * 10^6

Hence, the sum of the numbers is 7.69 * 10^6

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Answer:

a

Step-by-step explanation:

Find the sum. Express the answer in scientific notation.

(1.54 times 10 Superscript 6 Baseline) + (6.15 times 10 Superscript 6 Baseline)

7.69 times 10 Superscript 6

9.471 times 10 Superscript 6

7.69 times 10 Superscript 12

9.471 times 10 Superscript 12

Answer: B

[tex]x + 2y \leq 4 \textrm{ and } 3x + y \leq 4[/tex]

Step-by-step explanation:

Insert the values of x and y for any point in the heavily shaded region and see if it satisfies both inequalities

We can see that the origin (0,0) is inside the shaded region so use these values because they are the easiest to compute

Plug in x = 0 and y = 0 into the first inequality
0 + 2.0 = 0 which is greater than 5.

So we can eliminate both A and D since they both contain incorrect inequalities

Now, test the second inequality with x = 0 and y = 0

For B we get

3.0 + 0 = 0 which is indeed less than 4

C is not applicable since 0 is not greater-than-equal to 4

Hence B is the correct solution

This can be verified using a graphing tool (see image)

Answer:

Step-by-step explanation:

The amplitude of a sine function is equal to one-half the distance between the maximum and minimum values of the function.

In this case, the maximum value is approximately 84 customers, and the minimum value is approximately 30 customers

Therefore, the value that is closest to the amplitude of the transformed function is 27 customers.

Answer:

{x:x is a real number}

Since any value can replace x to give an integer.

{x:x is a real number}

Answer:The radius is √16.

Step-by-step explanation:

The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation of the parabola passing through (0, 0), (-3, 9) and (3, 9) is y = x²

The equation of the parabola with vertex at (4, 22) passing through (0, 6), (8, 6) and (3, 9) is y < -x² + 8x + 6

The solution to the system of equation is the darker region and it contains the point (-1, 6)

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Answer:

(2,9)

Step-by-step explanation:

Got it on FlVS

The length of the shortest side is DC

As a general rule in triangle;

The smallest angle in a triangle is opposite the shortest side.

Similarly, the largest angle in a triangle is opposite the largest side.

From the given figure of triangles, the smallest angle is angle CBD with a measure of 47 degrees.

The side opposite this angle is side length DC

Hence, the length of the shortest side is DC

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The perimeter of the rectangle is 70 Inches square

The formula for perimeter of a rectangle is given as;

Perimeter = 2 ( l + w)

length = 20 inches

width = 15 inches

Perimeter = 2 ( 20 + 15 )

Perimeter = 2 ( 35)

Perimeter = 70 Inches square

Thus, the perimeter of the rectangle is 70 Inches square

Note that it is a general knowledge on the given question.

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Answer:

C. 9

Step-by-step explanation:

The cubed root of 729 is the number that is multiplied 3 times to get 729. In this case, it's 9.

9*9*9 = 81*9

81*9 = 729

Answer: 9

Step-by-step explanation:

Answer:

9 songs

Step-by-step explanation:

a quarter is basically a fourth of a number so you need to just divide the number by four

What is one major limitation of the Social Readjustment Rating Scale?

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❄ Hi there,

let us revise the rounding rules and then, get down to rounding the number.

[tex]\sf{Rounding \ Rules:}[/tex]

Now we can start the rounding process.

Reading the problem & the directions, we notice that we need to round to 3 decimal places (3 numbers after the decimal point).

Looking at the fourth number, we notice that it's less than 5.

∴ we need to round down ↡

↬[tex]\sf{18.57631 \ rounded \ to \ 3 \ DP \ = \bf{18.576}}[/tex]

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

❄

1003 more square feet of wallpaper for the living room than the family room when family room is with dimensions (l = 3x, b = 3x, h = x), living room is with dimensions (l = 5x, b = 3x, h = x) and doors are with dimension (b =3,    h = 7) {where x = 8}. This can be obtained by forming equations for the given figures.

Given that,

dimensions (l = 3x, b = 3x, h = x) and there is one door (b =3, h = 7)

expression of square feet of wallpaper for family room,

⇒ area of four walls - area of one door= [(3x)(x)+(3x)(x)+(3x)(x)+(3x)(x)] - [3×7]

                                                               =[3x²+3x²+3x²+3x²] - 21

                                                               =12x² - 21 square feet

Given that,

height and width are same as of the family room but length is 5 times more than height [length = 5(height) ⇒ l = 5x]

dimensions (l = 5x, b = 3x, h = x) and there is two doors (b =3, h = 7)

expression of square feet of wallpaper for family room,

area of four walls - area of two doors= [(3x)(x)+(5x)(x)+(3x)(x)+(5x)(x)] - 2[3×7]

                                                               =[3x²+5x²+3x²+5x²] - 2(21)

                                                               =16x² - 42 square feet

total amount of wallpaper needed

⇒wallpaper for family room + wallpaper for living room = 12x²-21 + 16x²-42

                                                                                        =28x²-63 square feet

Area of wallpaper of living room - area of wallpaper of family room

= 1750 - 747

= 1003 square feet

Hence 1003 more square feet of wallpaper for the living room than the family room when family room is with dimensions (l = 3x, b = 3x, h = x), living room is with dimensions (l = 5x, b = 3x, h = x) and doors are with dimension (b =3,    h = 7) {where x = 8}.

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The perimeter of the triangle whose coordinates are A (2, 2), B (3, 3), and C (4, 2) is 4.828

We can determine the perimeter of a triangle with vertices by utilizing the distance formula.

Given that, we have the vertices (x₁,y₁), (x₂, y₂), (x₃, y₃). Then the length of each sides can be expressed as follows:

SIde AB = [tex]\mathbf{\sqrt{(x_1 -x_2)^2 +(y_1 -y_2)^2}}[/tex]

Side AC = [tex]\mathbf{\sqrt{(x_1 -x_3)^2 +(y_1 -y_3)^2}}[/tex]

Side BC = [tex]\mathbf{\sqrt{(x_2 -x_3)^2 +(y_2 -y_3)^2}}[/tex]

Replacing the values of the coordinates into the given formula above the perimeter of the triangle is 4.828

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The total surface area of a regular square pyramid having slant height of 10units and base length of 6 units is 168 square inches which is fifth option.

Given that slant height is 10 units and base lengths of 6 units.

We are required to calculate total surface area of regular square pyramid.

We know that total surface area of regular square based pyramid is equal to [tex]s^{2} +s\sqrt{s^{2} +4h^{2} }[/tex] in which s is side of base length and h is slant height of regular square pyramid.

Total surface area=[tex]6^{2} +6\sqrt{6^{2} +4*10^{2} }[/tex]

=36+6[tex]\sqrt{36+400}[/tex]

=36+6[tex]\sqrt{436}[/tex]

=36+6*20.88

=36+125.28

=161.28

Nearest option is 168 square inches.

Hence the total surface are of regular square based pyramid is option 5 which is 168 square inches.

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The metallurgist must use 5.538 pounds of an alloy with 39 % copper and 42.462 pounds of an alloy with 62 % copper.  

Herein we must create a new alloy by using correct quantities of two alloys with distinct copper concentrations. All required information can be found by concept of weighted averages:

(62/100) · (48 lb) = (39/100) · x + (65/100) · (48 - x)

62 · 48 = 39 · x + 65 · 48 - 65 · x

3 · 48 = 26 · x

x = 5.538 lb

The metallurgist must use 5.538 pounds of an alloy with 39 % copper and 42.462 pounds of an alloy with 62 % copper.  

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It's kind of self-evident. Any power of 21 will have a 1 in the units place, and adding 9 to it makes it 0 and hence the number is divisible by 5.

To prove the claim by induction, first establish the base case. I assume [tex]n\in\Bbb N[/tex], so for [tex]n=1[/tex] we have

[tex]21^1 + 9 = 21 + 9 = 30[/tex]

and of course 30 = 5×6 is divisible by 5.

Assume the claim is true for [tex]n=k[/tex], that [tex]5 \mid 21^k + 9[/tex]. This means that for some integer [tex]\ell[/tex], we can write

[tex]21^k + 9 = 5\ell[/tex]

Now the induction step: when [tex]n=k+1[/tex], we have

[tex]21^{k+1} + 9 = \bigg(21\times(21^k + 9) - 9\times21\bigg) + 9 \\\\ ~~~~~~~~~~~~~~ = 21\times5\ell - 9\times20 \\\\ ~~~~~~~~~~~~~~= 5\times(21\ell - 9\times4)[/tex]

which is divisible by 5. QED

The area of the actual building lot is 5040 square ft

This factors are used to enlarge or diminish the given figure. Given the  scale model of a rectangular building lot measures 7 feet by 5 feet. If the actual house will be built using a scale factor of 12, the new length and width is expressed as:

Length = 12 * 7 = 84ft

Width = 5*12=60 ft

Determine the area

Area = 84 * 60

Area = 5040 square feet

Hence the area of the actual building lot is 5040 square ft

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The laterals surface area of the given hexagonal prism is: 250 cm².

Lateral surface area = 5ah, where:

Given the following:

a = 5 cm

h = 10 cm

Lateral surface area of the hexagonal prism = 5ah =  5(5)(10)

Lateral surface area of the hexagonal prism = 250 cm²

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Answer:

y = 2/5x -4

Step-by-step explanation:

Point-Slope Form formula

y - y1 = m (x - x1)

slope = m = 2/5

(-5, -6)

y - -6 = 2/5 (x - -5)

y + 6 = 2/5x + 2

y = 2/5x - 4

patrickJMT

The wonderful waffle cone holds more ice cream than super sundae cone.

In this question,

The ice cream cone is the shape of hemisphere at the top and cone shape at the bottom.

Volume of ice cream cone = volume of hemisphere + volume of cone

Volume of ice cream cone = [tex]\frac{2}{3}\pi r^{3} +\frac{1}{3} \pi r^{2} h[/tex]

Volume of super sundae cone:

Radius of hemisphere = height of hemisphere = 0.5 in

Depth of the ice cream cone = 4 in

Volume of super sundae cone = [tex]\frac{2}{3}\pi (0.5)^{3} +\frac{1}{3} \pi (0.5)^{2} (4)[/tex]

⇒ [tex]\frac{2}{3}(3.14)(0.125) +\frac{1}{3} (3.14)(0.25)(4)[/tex]

⇒ 0.2616+1.0466

⇒ 1.3082 ≈ 1.31 cubic in.

Volume of wonderful waffle cone:

Radius of hemisphere = height of hemisphere = 0.9 in

Depth of the ice cream cone = 3 in

Volume of wonderful waffle cone = [tex]\frac{2}{3}\pi (0.9)^{3} +\frac{1}{3} \pi (0.9)^{2} (3)[/tex]

⇒ [tex]\frac{2}{3}(3.14)(0.729) +\frac{1}{3} (3.14)(0.81)(3)[/tex]

⇒ 1.526+2.5434

⇒ 4.0694 ≈ 4.07 cubic in.

Thus volume of wonderful waffle cone > volume of super sundae cone.

Hence we can conclude that the wonderful waffle cone holds more ice cream than super sundae cone.

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The measure of angle E is (b) 50°

The given parameters are:

The similarity of the triangles implies that:

From the figure, we have:

angle A = 50

Substitute angle A = 50 in angle A = angle E

angle E = 50

Hence, the measure of angle E is (b) 50°

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The weight of a 36-inch piece of PVC pipe is 0.20 pounds

The given parameters about the 36-inch piece of PVC pipe are

Height, h = 36 inches

Outside diameter, D = 0.82 inches

Inside diameter, d= 0.75 inches

The volume of the PVC pipe is then calculated as:

V = πh(D/2)^2 - πh(d/2)^2

Substitute the known parameters in the above equation

V = 3.14 * 36 * (0.82/2)^2 - 3.14 * 36 * (0.75/2)^2

Evaluate the quotients

V = 3.14 * 36 * 0.41^2 - 3.14 * 36 * 0.375^2

Evaluate the exponents

V = 3.14 * 36 * 0.1681 - 3.14 * 36 * 0.140625

Evaluate the products

V = 19.002024 - 15.89625

Evaluate the difference

V = 3.105774 cubic inches

From the question, we have:

Weight =  0.063 pounds per cubic inch

So, the total weight is

Total weight = 3.105774 cubic inches * 0.063 pounds per cubic inch

Evaluate the product

Total weight = 0.195663762 pounds

Approximate

Total weight = 0.20 pounds

Hence, the weight of a 36-inch piece of PVC pipe is 0.20 pounds

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False, Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.

What animals evolved during Cambrian period?

When did animals evolve in the Cambrian?

What long lived group of arthropods went extinct at the end of the Permian?

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The complete question is -

True or false . Whales evolved in the early Cambrian and include transitional species such as Kutchicetus and Rodhocetus.

The surface area of the prism according to the segment labels is; 480mm².

The prism given in the task content is five-faced and hence, its surface area can be evaluated as follows;

Surface area = 2(0.5×15×8)+(15×9)+(8×9) + (17×9).

Hence, the surface area of the prism upon evaluation is; 480mm².

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Answer:

A= 16

P=16

Step-by-step explanation:

A=h^bxb/ 2

P= side+base+side

The points are (0,0) Minimum and (1/6, 1/18) is the saddle point.

What is the saddle point?

To solve the question we have:

f(x,y) = xy(1-2x-6y)

Therefore, f(x,y) = xy-2x²y-6xy²

Finding the partial derivative of the above gives:

fₓ = y - 4xy-6y²

= x - 2x²-12xy

Therefore, when the above equations are set to 0 we get:

y - 4xy-6y² = 0.......(1)

x - 2x²-12xy  = 0......(2)

Dividing equations (1) and (2) by y and x respectively give:

1 - 4x - 6y = 0

1 - 2x - 12y = 0  

Solving gives:

x = 0.167 = 1/6

y = 0.056 = 1/18

When we place x in equation (1) we have:

y - 4(1/6)y-6y² = 0

y = 0 or y = 1/18

Similarly, x = 0 or 1/6

Therefore, the four critical points are:

(0,0) (1/6,1/18)

When x = 0 and y = 0

f(x,y) = 0 Hence this is a minimum

When x = 1/6 and y = 1/18

f (x,y) = 1/324 Which is a saddle point.

Therefore, the points are (0,0) Minimum, and (1/6, 1/18) is the saddle point.

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The question you are looking for is here:

(1 point) The function f(x,y)=xy(1−2x−6y) has 4 critical points. List them and select the type of critical point. Points should be entered as ordered pairs and listed in increasing lexicographic order. By that, we mean that (x,y) comes before (z,w) if x

Answer: [tex]y=2x+2[/tex]

Step-by-step explanation:

[tex]2x+4y=8\\\\x+2y=4\\\\2y=-x+4\\\\y=-\frac{1}{2}x+2[/tex]

So, the slope of the given line is -1/2, meaning the slope of the line we want to find is 2.

Since the y-intercept is the given line is (0,2), the equation is [tex]y=2x+2[/tex]