A vegetable garden and a surrounding path are shaped like a square that together is 12 ft wide. The path is 1 foot wide. Find the total area of the vegetable garden and path.

Answer:

b=58

Step-by-step explanation:

b-12=46

b=46+12

b=58

Answer:

Fourth answer choice.

Step-by-step explanation:

Start by factoring the numerator and the denominator:

(x - 1)(x + 1)

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

(x + 1)(x + 4)

Note that x can be neither -1 nor -4, since either results in an undefined quotient.  These two x-values are critical values because of this.  If we cancel the (x + 1) terms, we obtain the result

(x - 1)

--------- for x ≠ -1 and x ≠ - 4

(x + 4)

The next step is to evaluate the given quotient on the three intervals defined by {-4, -1}:  (-∞, -4), (-4, -1), (-1, ∞ ).  We choose an x-value from within each interval and evaluate the given function at each.  Suitable test values include {-10, -3, 0}:

At x = -10, the reduced given quotient (x - 1) / (x + 4) takes on the value  (-10 - 1) / (-10 + 4) = -11/(-6), which is positive.  Reject this interval, as we want and expect the quotient value to be 0 or less.

At x = -3, we get (-3 - 1) / (-3 + 4), which is negative.  The given inequality is true on the interval (-4, -1) (or -4 < x < -1).

At x = 0, we get (0 - 1) / (0 + 4), which is negative, so the inequality is true on (-1, ∞ ).

So the fourth answer choice is the correct one.

Answer:

Answer D

Step-by-step explanation:

Answer: 398cm²

Step-by-step explanation:

Surface area of a Rectangular Prism: 2lw+2lh+2wh

l= 5cm

w= 9cm

h= 11cm

Area= (2x5x9)+(2x5x11)+(2x9x11)

      =398cm²

Answer:

D

Step-by-step explanation:

Any ellipse has the following equ

ation:

[tex] \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

where

(as in the picture)

So it should be like:

[tex] \frac{ {x}^{2} }{ { (\frac{6}{2} )}^{2} } + \frac{ {y}^{2} }{ {( \frac{4}{2} )}^{2} } = 1 \\ \frac{ {x}^{2} }{ 9} + \frac{ {y}^{2} }{ 4 } = 1[/tex]

Since it should be moved to the right and up, the answer would be:

[tex]\frac{ {(x - 5)}^{2} }{ 9} + \frac{ {(y - 1)}^{2} }{ 4 } = 1[/tex]

Option D. (x - 5)²/9 + ( y - 1 )²/4 = 1

An ellipse has the following equation:

x²/a² + y²/ b² = 1

where

2b = vertical axis length

2a = horizontal axis length

So it should be like:

x²/(6÷2)² + y²/ (4÷2)² = 1

x²/9 + y²/4 = 1

Since it should be moved to the right and up, the answer would be:

(x - 5)²/9 + ( y - 1 )²/4 = 1

Please check the attached diagram for more details.

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Answer:

339.35

Step-by-step explanation:

The amount of money the credit card customer still owes to pay is $339.35.

We are given that,

The amount the credit card customer owes = $523.85.

The amount the credit card customer paid = $184.50.

We have to find the amount of money the credit card customer still owes to pay.

The amount of money the credit card customer still owes to pay :

= The amount the credit card customer owes - The amount the credit card customer paid

= $523.85 - $184.50

= $339.35

Thus, the amount of money the credit card customer still owes to pay after paying $184.50 is $339.35.

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Answer:

80

Step-by-step explanation:

Simply radical 16 which will give you 4, then multiply 4 by 20 which equals 80

Answer:

Part A is Answer C

C=2pi * r

D= 2r

C= 2 * 3.14 * 31.5

C= 197.82

__________________________

Part B is 3115.67 sq cm

A = 3.14 * r*r

A= 3.14 x 31.5x31.5

A=3115.665

Rounded: 3115.67

The circumference of the circle is C = 197.82 cm

The area of the circle is A = 3,115.67 cm²

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the diameter of the circle be d = 63 cm

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle and π is the mathematical constant pi, approximately equal to 3.14159.

C = π(63)

C = 197.92 cm

The area of a circle is given by the formula

A = πr²

where r is the radius of the circle. Since we are given the diameter, we can find the radius by dividing the diameter by 2:

r = d/2

r = 63/2

r = 31.5 cm

Substituting the radius r = 31.5 cm into the formula for the area, we get:

A = 3.14159 x 31.5²

A = 3.14159 x 992.25

A = 3,117.15 cm²

Hence , the area of the circle is 3,117.15 cm²

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[tex]\frac{9\pi }{5}[/tex] radians is equal to [tex]324[/tex]° .

Step-by-step explanation:

Degrees are a unit of angle measure. A full circle is divided into 360 degrees. For example, a right angle is 90 degrees. A degree has the symbol ° and so ninety degrees would written 90°. Another unit of angle measure is the radian.

The radian is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.

We know that 1 radian = 180°/[tex]\pi[/tex] . So [tex]\frac{9\pi }{5}[/tex] radians is equal to :

⇒ [tex]\frac{9\pi }{5}(\frac{180}{\pi } )[/tex]

⇒ [tex]\frac{9(180) }{5}[/tex]

⇒ [tex]9(36)[/tex]

⇒ [tex]324[/tex]°

Therefore , [tex]\frac{9\pi }{5}[/tex] radians is equal to [tex]324[/tex]° .

To convert 9pi/5 radians to degrees, multiply by the conversion factor of 180°/π, resulting in 324 degrees.

To convert the angle 0 = 9pi/5 radians to degrees, we need to use the relationship between radians and degrees. Recall that 360° = 2π radians. Consequently, to convert radians to degrees, we can multiply by a conversion factor of 180°/π. Using this conversion factor, the computed angle in degrees is:

9π/5 radians × (180°/π) = 9/5 × 180° = 9 × 36° = 324°

Therefore, the angle of 9π/5 radians is equivalent to 324 degrees.

Since both have the same interquartile range, the inference made would be: types of cars sold in the two months typically get about the same gas mileage.

The interquartile range is a measure of variability, which can be used in comparing two data distribution.

Interquartile range = Q3 - Q1.

Interquartile range for gas mileage of cars sold in June = 33 - 21 = 12.

Interquartile range for gas mileage of cars sold in December = 26 - 14 = 12.

Therefore, since both have the same interquartile range, the inference made would be: types of cars sold in the two months typically get about the same gas mileage.

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Answer: Its C.

Step-by-step explanation:

Edge 2022

Answer:

Step-by-step explanation:

Let b and s represent the weights of the big and small boxes, respectively. Then the two delivered weights can be summarized as ...

  5b +6s = 187

  3b +2s = 87

We can eliminate the "s" variable by subtracting the first equation from 3 times the second:

  3(3b +2s) -(5b +6s) = 3(87) -(187)

  4b = 74 . . . . . collect terms

  b = 18.5 . . . . . divide by 4

Using this value in the second equation, we find ...

  3(18.5) +2s = 87

  2s = 31.5 . . . . . . . . subtract 55.5

  s = 15.75 . . . . . . . . divide by 2

The large box weighs 18.5 kg; the small box weighs 15.75 kg.

The length of EF in the given triangle is 8.80 m.

Step-by-step explanation:

Step 1:

In the given triangle, the opposite side's length is 16.2 m, the adjacent side's length is x m while the triangle's hypotenuse measures 16.2 m units.

The angle given is 90°, this makes the triangle a right-angled triangle.

So first we calculate the angle of E and use that to find x.

Step 2:

As we have the values of the length of the opposite side and the hypotenuse, we can calculate the sine of the angle to determine the value of the angle of E.

[tex]sinE = \frac{oppositeside}{hypotenuse} =\frac{13.6}{16.2} = 0.8395.[/tex]

[tex]E = sin^{-1} (0.8395), E = 57.087.[/tex]

So the angle E of the triangle DEF is 57.087°.

Step 3:

As we have the values of the angle and the hypotenuse, we can calculate the cos of the angle to determine x.

[tex]cos E = \frac{adjacentside}{hypotenuse} = \frac{x}{16.2} .[/tex]

[tex]cos(57.087) = 0.5433, x = 16.2 (0.5433) = 8.8014.[/tex]

Rounding this off to the nearest hundredth, we get x = 8.80 m.

Answer:

a) 8x

b)2+12y

Step-by-step explanation:

Answer:

5X+3X & 8X For the first one

and 2+12y for the second one i believe those are correct let me know in the comments below

Step-by-step explanation:

hope this helps have a great day

Answer:

the answer is  about 4.243

Step-by-step explanation:

Squares mean all sides would have the same length. So you just need to find the square root of the area (18)  which is about 4.243 and just to check multiply 4.243 by itself and you would get 18.

Final answer:

The length of one side of the table top with an area of 18 square feet is approximately 4.24 feet, as calculated by taking the square root of the area.

Explanation:

To find the length of one side of a table top with an area of 18 square feet, we should understand that a square has all sides of equal length. Therefore, to find the side length of a square, we take the square root of the area. In this case, we have an area of 18 square feet, so the calculation would be √18, which is approximately 4.24 feet. Thus, the length of one side of the table top is approximately 4.24 feet.

Answer

34.5 inches

Step-by-step explanation:

Answer: The equations are as follows;

5p + 4d = 43.25 ————(1) and

3p + 2d = 24.25 ————(2)

Also a bag of popcorn costs $5.25

Step-by-step explanation: We start by assigning letters to the unknown variables. Let a bag of popcorn be p and let one drink be d. The clues given in the question include the cost of buying five bags of popcorn and four drinks which is a total of $43.25. This can be expressed as

5p + 4d = 43.25 ————(1)

Another clue is that three bags of popcorn and two drinks cost $24.25. This also can be expressed as

3p + 2d = 24.25 ————(2)

Now we have a pair of simultaneous equations as follows

5p + 4d = 43.25 ————(1)

3p + 2d = 24.25 ————(2)

We shall use the elimination method since all the unknowns have coefficients greater than 1. Multiply equation one by 3, and multiply equation two by 5 (so as to eliminate ‘p’)

5p + 4d = 43.25 ——— x3

3p + 2d = 24.25 ——— x5

15p + 12d = 129.75 ———(3)

15p + 10d = 121.25 ———(4)

Subtract equation (4) from equation (3) and we have

2d = 8.5

Divide both sides of the equation by 2

d = 4.25.

That means each drink costs $4.25

We can now substitute for the value of d into equation (2)

3p + 2d = 24.25

When d = 4.25

3p + 2(4.25) = 24.25

3p + 8.5 = 24.25

Subtract 8.5 from both sides of the equation

3p = 15.75

Divide both sides of the equation by 3

p = 5.25. This means a bag of popcorn costs $5.25

Answer: 49.8 is the answer

Step-by-step explanation:

Answer:

C) Going from A to C to D and it is shorter by 3 miles.

Step-by-step explanation:

Angles  

AB is 6 miles

BD is _12__ miles

AC is 5 miles

CD is 10 miles

First you need to find BD, so AB times CD. 6(10) = 60. then divide 60 with AC. 60/5 = 12. So  BD = 12.  

Now add  

AB and BD,  

{ 6+ 12 = 18} ABD = 18

Now add  

AC and CD

{ 5 + 10 = 15 } ACD = 15

18 - 15 = 3  

So ACD is 3 miles shorter then ABD.

Got right on the test

The shortest route is to take segment AD which is 8 miles long.

To determine the shortest route, we need to find the length of segment AD and compare it to the combined length of segments AC and CD. Since segment AD bisects LA, we can use the properties of a line segment bisector to find its length.

Since segment AD bisects LA, we can say that AC = CD

Therefore, the shortest route is to take segment AD, which is 8 miles long, since it is equal to the combined length of segments AC and CD.

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Answer:

(-4, -1)

Step-by-step explanation:

x = 4y

-4x - y = 17

Plug in 4y for x in the second equation:

-4(4y) - y = 17

Simplify. Remember to follow PEMDAS. Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other.

First, multiply 4y with -4:

-4(4y) = -16y

-16y - y = 17

Simplify. Combine like terms:

-16y - y = 17

-17y = 17

Isolate the variable, y. Divide -17 from both sides:

(-17y)/-17 = (17)/-17

y = 17/-17

y = -1

Plug in -1 for y in the first equation:

x = 4y

x = 4(-1)

x = -4

x = -4, y = -1

Answer: (-4, -1)

~

Answer:

D) Each additional day is associated with an additional 17.5 grams of mass.

Step-by-step explanation:

Slope = 17.5

= change in mass/change in day

Which is 17.5 g increase in 1 day

Answer:

its d!

Step-by-step explanation:

Answer:

(3, -2) or (3, 2)

Step-by-step explanation:

Please see the attached pictures for full solution.

Answer:

x = [tex]\frac{12}{17}[/tex] or 0.706

[tex]y = \frac{59}{34}[/tex] or 1.735

Step-by-step explanation:

5x + 2y=7    ----->(eq 1)

- 2x + 6y=9 ----->(eq 2)

Multiply (eq 1) with 3

3×(5x + 2y) = 3×7  

15x + 6y = 21  ----->(eq 3)

substract (eq 3) from (eq 2)

- 2x + 6y - (15x + 6y) = 9-21

- 2x + 6y - 15x - 6y = 9-21

- 2x - 15x + 6y - 6y = 9-21

-17x = -12

x = -12 ÷ -17

x = [tex]\frac{12}{17}[/tex]

put x = [tex]\frac{12}{17}[/tex] in (eq 1)

[tex]5*\frac{12}{17} + 2y = 7[/tex]

[tex]2y = 7- 5*\frac{12}{17}[/tex]

[tex]2y = \frac{7*17 - 60}{17}[/tex]

[tex]2y = \frac{119- 60}{17}[/tex]

[tex]2y = \frac{59}{17}[/tex]

[tex]y = \frac{59}{17*2}[/tex]

[tex]y = \frac{59}{34}[/tex]

Answer:

[tex]SA=54\pi\ units^2[/tex]

Step-by-step explanation:

we know that

The surface area of the cone is given by the formula

[tex]SA=\pi r^{2}+\pi rl[/tex]

where

r is the radius of the base

l is the slant height

we have

[tex]r=3\ units\\l=15\ units[/tex]

substitute

[tex]SA=\pi (3)^{2}+\pi (3)(15)[/tex]

[tex]SA=54\pi\ units^2[/tex]

984′, 1,063′ to tip.

the ' is feet

The required height of the Eiffel Tower is given as 327.27 meters.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Let the height of the Eiffel tower be x,
According to the question,
The ratio of the height to the base of the Eiffel tower is equal to the ratio of  height to the

base of men,
x / 500 = 1.8 / 2.75
x = 327.27 meters

Thus, the required height of the Eiffel Tower is given as 327.27 meters.

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[tex]\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-6)}}}\implies \cfrac{-15}{3+6}\implies \cfrac{-15}{9}\implies -\cfrac{5}{3}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{-\cfrac{5}{3}}[x-\stackrel{x_1}{(-6)}]\implies y-8=-\cfrac{5}{3}(x+6) \\\\\\ y-8=-\cfrac{5}{3}x-10\implies y = -\cfrac{5}{3}x-2[/tex]

Answer:

[tex]m=\frac{-5}{3}[/tex]

Step-by-step explanation:

Step 1: Let's find the slope between your two points.

[tex](-6,8); (3,-7)\\\\(x_{1} ,y_{1} )=(-6,8)\\\\(x_{2} ,y_{2} )=(3,-7)[/tex]

Step 2: Use the slope formula

[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }\\\\=\frac{(-7) - 8}{3- (-6)} \\\\=\frac{-15}{9}\\\\= \frac{-5}{3}[/tex]

Therefore, the equation is [tex]\frac{-5}{3}[/tex]

Answer: approximately 102.8 times farther

Step-by-step explanation: If you divide the distance of Mercury to the Sun (3.6E7) from the distance of Pluto to the Sun (3.7E9) you get 102.777777. That is the approximate distance. Rounded you get 102.8

Answer:

No, not a solution

Step-by-step explanation:

Step 1:  Check if solution

y = 3x + 5

-1 = 3(4) + 5

-1 = 12 + 5

-1 = 17

DOES NOT EQUAL

Answer: No, not a solution

The volume of the ball is 24,400 cm³

Step-by-step explanation:

Volume of the ball = 4/3 πr³

                               = 4/3 × 3.14 × (18)³

                               = 24,416.64 cm³ ≈ 24,400 cm³ (nearest hundredth)

Answer:

21.75

Step-by-step explanation:

i hoped this helped.  14.50 divide-by 2 = 7.25 so 14.50 + 7.25= 21.75

In physics, work is defined force that causes displacement. So this can be expressed by the following equation:

[tex]W=Fs[/tex]

Where:

[tex]F:Force \\ \\ s:Displacement[/tex]

The force can be found as:

[tex]F=ma \\ \\ F=5(10)=50N[/tex]

And for the displacement:

[tex]s=6-2=4m[/tex]

The force (weight) is down and the displacement is up, then the work must be negative. So:

[tex]W=-(50)(4) \\ \\ \boxed{W=-200J}[/tex]

Answer:

Slope = [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

Slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

Slope = [tex]\frac{2 - 12}{-8 - 4}[/tex]

Slope = [tex]\frac{-10}{-12}[/tex]

Slope = [tex]\frac{5}{6}[/tex]

Answer:  Slope = [tex]\frac{5}{6}[/tex]