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Ainat [17]
2 years ago
7

A regular pentagon and an equilateral triangle have the same perimeter...........

Mathematics
1 answer:
kondor19780726 [428]2 years ago
6 0

Answer:

Option 4: 45 units is the correct answer

Step-by-step explanation:

Let P_1 be the perimeter of Pentagon and

Let P2 be the perimeter of Triangle

So,

P_1 = 5(\frac{1}{2}x-1)\\P_2 = 3(x-5)

In order to find the perimeter of each figure we have to put both the expressions equal so that the value of x can be found and then perimeter.

So,

P_1 = P_2\\5(\frac{1}{2}x-1) = 3(x-5)\\\frac{5}{2}x-5 = 3x-15\\\frac{5}{2}x-3x = -15+5\\\frac{5x-6x}{2} = -10\\-\frac{x}{2} = -10\\-x = -10 * 2\\-x = -20\\x = 20

Putting x = 20 in 2nd perimeter

P_2 = 3(x-5) \\= 3(20-5)\\= 3(15)\\=45

As both the perimeters are same, the perimeter of pentagon will also be 45 units.

Hence,

Option 4: 45 units is the correct answer

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Find the length of the line segment formed by the points (2, 3) and (2, 5)
SCORPION-xisa [38]

Answer:

2 units

Step-by-step explanation:

Given data

The points are  (2, 3) and (2, 5)

x1= 2

y1= 3

x2= 2

y2= 5

substitute into the distance between two points formula

d=√((x_2-x_1)²+(y_2-y_1)²)

d=√((2-2)²+(5-3)²)

d=√(2)²)

d=√4

d= 2 units

Hence the length is 2 units

3 0
2 years ago
ABDE is a rectangle on coordinate axes, the sides of the rectangle are parallel to the axes,
Hitman42 [59]

The coordinates of B and D are the location of the vertices B and D in the rectangle

The coordinates of B and D are (55, 30) and (55, 14)

<h3>How to determine the coordinates of B and D?</h3>

From the figure of the rectangle, we have:

A = (25,30)

C = (40, 22)

Point B has the same y-coordinate as point A

So, we have:

B = (x, 30)

The x-coordinate is then calculated as:

Bx = 2Cx - Ax

This gives

Bx = 2*40 - 25

Bx = 55

So, the coordinates of B are:

B = (55, 30)

Point D has the same x-coordinate as point B

So, we have:

D = (55, y)

The y-coordinate is then calculated as:

Dy = Cy - (By - Cy)

This gives

Dy = 22 - (30 - 22)

Dy = 14

So, the coordinates of B are:

D = (55, 14)

Hence, the coordinates of B and D are (55, 30) and (55, 14)

Read more about rectangles at:

brainly.com/question/10737082

8 0
2 years ago
How is this solved using trig identities (sum/difference)?
GenaCL600 [577]
FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

cos \beta = -\frac{1}{2}  \sqrt{3}

tan \beta= \frac{1}{3}  \sqrt{3}

SECOND PART
Solve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
sin( \alpha + \beta )=(- \frac{12}{13} )( -\frac{1}{2}  \sqrt{3})+( -\frac{5}{13} )( -\frac{1}{2} )
sin( \alpha + \beta )=(\frac{12}{26}\sqrt{3})+( \frac{5}{26} )
sin( \alpha + \beta )=(\frac{5+12\sqrt{3}}{26})

Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )
cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )
cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )

Find tan (α - β)
tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha  tan \beta }
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}

Simplify the denominator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5\sqrt{3}}{24})}
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the numerator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }
tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the fraction
tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})
tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}

7 0
3 years ago
Which number line shows the solution to fx-5 &gt; 3?
sp2606 [1]

Answer:

8

Step-by-step explanation:

send <em>the</em><em> </em><em>-</em><em>5</em><em> </em><em>to</em><em> </em><em>where</em><em> </em><em>the</em><em> </em><em>+</em><em>3</em><em> </em><em>is</em><em> </em><em>then</em><em> </em><em>you</em><em> </em><em>can</em><em> </em><em>now</em><em> </em><em>add</em><em> </em><em>the</em><em> </em><em>value</em><em> </em><em>together</em><em>.</em>

7 0
3 years ago
Ardem collected data from a class survey. He then randomly selected samples of five responses to generate four samples.
scoundrel [369]

Solution: The sample mean of sample 1 is:

\bar{x}=\frac{4+5+2+4+3}{5}= \frac{18}{5}=3.6

The sample mean of sample 2 is:

\bar{x}=\frac{2+2+6+5+7}{5}= \frac{22}{5}=4.4

The sample mean of sample 3 is:

\bar{x}=\frac{4+6+3+4+1}{5}= \frac{18}{5}=3.6

The sample mean of sample 4 is:

\bar{x}=\frac{5+2+4+3+6}{5}= \frac{20}{5}=4

The minimum sample mean of the four sample means is 3.6 and maximum sample mean of the four sample means is 4.4.

Therefore, using  his four samples, between 3.6 and 4.4 will Ardem's actual population mean lie.

Hence the option 3.6 and 4.4 is correct

6 0
3 years ago
Read 2 more answers
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