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Answer:

The area of rectangle BEFD is 180 square units.

Step-by-step explanation:

After checking the figure given, we have the following information:

[tex]AD = 15[/tex], [tex]AB = 12[/tex], [tex]BC = 15[/tex], [tex]CD = 12[/tex]

By Pythagorean Theorem, we determine the length of the line segment BD:

[tex]BD = \sqrt{AB^{2}+AD^{2}}[/tex] (1)

[tex]BD = \sqrt{12^{2}+15^{2}}[/tex]

[tex]BD = 3\sqrt{41}[/tex]

In addition, we know the following characteristics of the rectangle BEFD:

[tex]BD = EF[/tex], [tex]EF = EC + CF[/tex], [tex]BE = FD[/tex] (2), (3), (4)

By Pythagorean Theorem:

[tex]BC^{2} = BE^{2}+EC^{2}[/tex] (5)

[tex]CD^{2} = CF^{2}+DF^{2}[/tex] (6)

By (3), (4), (5) and (6):

[tex]BC^{2} = BE^{2} + EC^{2}[/tex] (7)

[tex]CD^{2} = (EF-EC)^{2} + BE^{2}[/tex] (8)

By (7) in (8):

[tex]CD^{2} = (EF-EC)^{2}+ (BC^{2}-EC^{2})[/tex]

[tex]CD^{2} = EF^{2}-2\cdot EF\cdot EC + EC^{2}+BC^{2}-EC^{2}[/tex]

[tex]CD^{2} = EF^{2}-2\cdot EF\cdot EC +BC^{2}[/tex]

Then, we clear [tex]EC[/tex]:

[tex]2\cdot EF\cdot EC = EF^{2} + BC^{2} - CD^{2}[/tex]

[tex]EC = \frac{EF^{2}+BC^{2}-CD^{2}}{2\cdot EF}[/tex]

If we know that [tex]EF = 3\sqrt{41}[/tex], [tex]BC = 15[/tex] and [tex]CD = 12[/tex], then the length of the segment [tex]EC[/tex] is:

[tex]EC = \frac{75\sqrt{41}}{41}[/tex]

And the length of the line segment [tex]CF[/tex] is:

[tex]CF = EF - EC[/tex]

[tex]CF = 3\sqrt{41}-\frac{75\sqrt{41}}{41}[/tex]

[tex]CF = \frac{48\sqrt{41}}{41}[/tex]

And the length of the line segment [tex]DF[/tex] is determined by Pythagorean Theorem:

[tex]FD = \sqrt{CD^{2}-CF^{2}}[/tex]

[tex]FD = \sqrt{12^{2}-\left(\frac{48\sqrt{41}}{41} \right)^{2}}[/tex]

[tex]FD = \frac{60\sqrt{41}}{41}[/tex]

And the area of the rectangle is determined by the following formula:

[tex]A = FD\cdot EF[/tex]

[tex]A = \left(\frac{60\sqrt{41}}{41} \right)\cdot (3\sqrt{41})[/tex]

[tex]A = 180[/tex]

The area of rectangle BEFD is 180 square units.

HOPE ITS HELPFUL ^_^

It's bottom left

It says let C represent the cost of a one-year membership.

C is 80 in order to represent the day you must divide it by 10.

which gives one box for day and 10 boxes for year

Answer: Approximately 17.69

Step-by-step explanation:

The formula needed to find the third side of this equation is the Pythagorean theorem. Which is as follows:

[tex]a^2+b^2=c^2\\c=\sqrt{a^2+b^2}[/tex]

The difference between the two is that the first one after you do [tex]a^2+b^2[/tex] you still need to square root the answer you get to get the third side, aka. the hypotenuse. If you do the second method, you get the answer after you do the calculation which is a lot easier.

Below are the calculations needed to be made in both ways:

[tex]12^2+13^2=313\\\sqrt{313}= 17.69[/tex]   17.69 was rounded to the hundredths place.

[tex]\sqrt{12^2+13^2}=17.69[/tex]   once again this answer was rounded to the hundredths place.

[tex]a^2+b^2[/tex] are respectively for the sides of the triangles.

[tex]c^2[/tex] is respectively for the hypothenuse, which is the longest side, and across from the right angle (located by a box).

Answer:

5 or 17.69

Step-by-step explanation:

1st case senario:

c^2=a^2+b^2

c^2=12^2+13^2

c^2=144+169

c^2=313

c^2=[tex]\sqrt{313}[/tex]

c=17.69

2nd case senario:

144+b^2=169

b^2=169-144

b^2=25

b^2=[tex]\sqrt{25}[/tex]

b+5

Answer:

Factored Form: y=(x+1) ( x+3)y=(x+1)(x+3)

X-intercepts: (-1,0), (-3,0)(−1,0),(−3,0)

Axis of Symmetry: x= -2x=−2

Vertex: (-2,-1)(−2,−1)

Domain: (\begin{gathered}(-\infty , \infty ), ( x | x ER)\\\end{gathered}

(−∞,∞),(x∣xER)

Range: y > =-1y>=−1

Answer:

Slope is (1/4)

Step-by-step explanation:

The slope is calculated by (6-5)/(5-1)=1/4

Answer:

Center ( 4 , -2) and r = 6

Step-by-step explanation:

x² - 8x + y² + 4y - 16 = 0

x² - 8x  + y² + 4 y = 16

x²- 2*4x + y² + 2 *2y = 16

(x² - 2*4x + 16 ) - 16 + (y² + 2*2y + 4) -4 = 16

(x - 4)² + (y + 2)² = 16 + 16 + 4

(x - 4)² + (y -[-2])² = 36

(x- 4)² + ( y - [-2] )² = 6²

Compare with (x - h)²+ (y - k)² = r²

Center ( 4 , -2) and r = 6

Answer:

Step-by-step explanation:

6 + 2 = 4,  given

6 + 5 = 11, correct

Answer:

B

Step-by-step explanation:

x((7/2)-(7/3))=y+x

x(7/6)=y+x

7x=6y+6x, x=6y. y/x=1/6

Answer:

Step-by-step explanation:

What are we supposed to do? You already have the answers and they’re all correct if that’s what you wanted to know

Answer:

58,59

Step-by-step explanation:

Let x be the first integer

x+1 be the next consecutive integer

x + x+1 = 117

2x+1 = 117

2x +1-1 =117-1

2x = 116

2x/2 = 116/2

x = 58

x+1 = 59

Answer: D. Angles that form a linear pair are sometimes supplementary.

That is not true, linear pairs are always supplementary.

Answer:

D. Angles that form a linear pair are sometimes supplementary.

~OAmalOHopeO

Answer:

33.80

Step-by-step explanation:

AB = BC = AD√2

AB = BC = 7√2

AD = DC

AC = 2AD

perimeter = AC + AB + BC

= 2AD  + 2AB

= 2(7) + 2(7√2)

= 14 + 14√2

≈ 33.80

Answer:

33.8

Step-by-step explanation:

45-45-90 degree triangle rules states that the sides that are opposite the angles measure 45 degrees have the same value. That means that BD has the same value as AD, which is 7. Since triangle BDC is also a 45-45-90 degree triangle, DC is equal to BD, which is 7. We have the value of AC, which is 7+7=14. Now, we can use the Pythagorean theorem to figure out BC and AB. We know that [tex]DC^2+BD^2=BC^2[/tex]. We know that DC and BD is equal to 7, so we can simplify that to [tex]49+49=BC^2[/tex], and we can further simplify that to [tex]BC=\sqrt{98}[/tex]. This is also equal to [tex]7\sqrt{2}[/tex]. Since BC is also equal to AB because of 45-45-90 degree triangle rules, we have the perimeter of the triangle as

[tex]7\sqrt{2} + 7\sqrt{2}+14[/tex], which is equal to [tex]14\sqrt{2} + 14[/tex]. We can simplify 14 times the square root of 2 as 19.8 (rounded to 2 decimal places). We have the answer as 19.8 + 14, which is 33.8.

Answer:

(3+3) / (2+3) = 6/5

:)))

..........

Answer:

8x^3/2

Step-by-step explanation:

(4x)^3/2 = ( 4^3/2 ) ( x^3/2 ) =8x^3/2

Answer:

y - 4 = 8/5 (x - 0)

Step-by-step explanation:

first, find the slope using the points given ((0,4) and (-5,-4))

use the following formula to find the slope:

m= y2 - y1/x2 - x1

using this formula you should get the following:

m= -4-4/-5-0 = -8/-5 = 8/5

using the point (0,4) and the slope, it into the slope-point form (y-y1=m(x-x1)

the answer should be: y - 4 = 8/5(x - 0)

Answer:

x = 14

Step-by-step explanation:

The sum of the interior angles of a six sided figure is 720

10x + 8x-16+12x-8 +7x+2 +9x+4 +6x+10 = 720

Combine like terms

52x-8=720

Add 8 to each side

52x-8+8 = 720+8

52x = 728

Divide by 52

52x/52 = 728/52

x = 14

Step-by-step explanation:

here's the answer for thy question

Answer:

Perimeter, P = 112 meters

Step-by-step explanation:

Translating the word problem into an algebraic expression, we have;

L = 6W  ...... equation 1

Given the following data;

To find the perimeter of the rectangle;

First of all, we would determine the dimensions of the rectangle using its area.

Mathematically, the area of a rectangle is given by the formula;

Area of rectangle = LW  ..... equation 2

Substituting eqn 1 into eqn 2, we have;

384 = 6W(W)

384 = 6W²

Dividing both sides by 6, we have;

W² = 384/6

W² = 64

Taking the square root of both sides, we have;

W = √64

Width, W = 8 meters

Next, we would find the length;

L = 6W

L = 6 * 8

Length, L = 48 meters

Lastly, we would determine the perimeter of the rectangle using the above dimensions;

Mathematically, the perimeter of a rectangle is given by the formula;

Perimeter = 2(L + W)

Substituting the values into the formula, we have;

Perimeter, P = 2(48 + 8)

Perimeter, P = 2(56)

Perimeter, P = 112 meters

Answer:

x/x∈R,x≤5 1/6

Step-by-step explanation:

Answer:

Create a function representing number of published articles per month:

[tex]a=12m+60[/tex]

Where:

Now substitute in the values of m to get the a-value:

Answer:

-5, - 2, 3

Step-by-step explanation:

y=2x+3, y=-7, x=-5; y=-1, x=-2, y=9, x=3

The area covered by the roof would be 84.5 square yards.

To calculate the area covered by the roof the formula that should be used would be the formula for the area of a square;

That is ;

Area = 2(length×width)

= 2(6.5×6.5)

= 2(42.25)

= 84.5 yards²

Learn more about area here:

https://brainly.com/question/28470545

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Answer:

n = 3

Step-by-step explanation:

Given

5 + 8n = 7(- 7 + 4n) - 6 ← distribute parenthesis on right side

5 + 8n = - 49 + 28n - 6 ( subtract 28n from both sides )

5 - 20n = - 55 ( subtract 5 from both sides )

- 20n = - 60 ( divide both sides by - 20 )

n = [tex]\frac{-60}{-20}[/tex] = 3

Answer:

42.1

Step-by-step explanation:

The height of the main triangle is,

h = 47√3/2 (since it's an 30-60-90 triangle)

so to find x,

tan(44) = h/x

x = h/tan(44)

x = 42.1 (rounded to the nearest tenth)

Answered by GAUTHMATH

Answer:

The volume of the cube is 21952.

Step-by-step explanation:

V = L x W x H

because a cube's sides are all the same, the length, width, and height are also the same. So we use the formula:

V= S^3

(S standing for side)

we know the height is 28 and as all sides measure the same we use the equation:

V= 28^3

28^3 = 21952

So, V= 21952

Answer:

total surface area  = 298.45105 m2

lateral surface area = 141.37155 m2

top surface area = 78.53975 m2

bottom surface area = 78.53975 m2

Step-by-step explanation:

Joanna will need approximately 298.3 square inches of frosting to cover the entire cake.

To calculate the amount of frosting Joanna will need for the entire cake, we first need to find the surface area of the cylindrical cake.

The formula for the surface area of a cylinder is given by:

Surface Area = 2πr² + 2πrh

Where r is the radius of the base and h is the height of the cylinder.

Given that the diameter of the cake is 10 inches, we can find the radius by dividing it by 2: r = 10/2 = 5 inches.

Plugging in the values, we have:

Surface Area = 2π(5)² + 2π(5)(4.5)

Simplifying the equation:

Surface Area = 2π(25) + 2π(22.5)

Surface Area = 50π + 45π

Surface Area = 95π

To find the actual numerical value, we can approximate π as 3.14:

Surface Area ≈ 95 * 3.14

Surface Area ≈ 298.3 square inches

To learn more about cylinder click on,

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