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3 years ago

Through which angle of rotation does the image of a regular pentagon coincide with its preimage?

Mathematics

1 answer:

Cloud [144]3 years ago

5 0

Answer:

The correct answer option is B. 72°.

Step-by-step explanation:

A polygon is said to be a regular polygon when all its sides and angles are equal.

So a regular pentagon coincides with its pre-image when it is rotated at an angle of 72°.

When rotated at an angle of 72°, a regular pentagon produces the same pentagon regardless of being rotated clockwise or anticlockwise.

Therefore, option B is the right choice.

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Kallisto built a rectangular sign that measured 2 and 3/4. The width is 1 and 1/4 shorter than the length. To find the area, mul

prisoha [69]

Answer:

l = 1 5/16

w = 1/16

A = 21/16 x 1/16 = 21/256

Step-by-step explanation:

Perimeter = 11/4

l = length

w = l - 5/4

2l + 2(l - 5/4) = 11/4

2l + 2l - -5/2 = 1/4

multiply each side by 4

8l + 8l - 10 = 11

16l = 21

l = 21/16 or 1 5/16

width = 21/16 - 20/16 = 1/16

8 0

3 years ago

Help due today please

horsena [70]

Answer:

angle ABD =55 degree

angle BCD= 125 degree

Step-by-step explanation:

angle ABD and angle DBC are supplementary angles.

Hence, angle ABD +angle DBC = 180 --equation 1

angle ABD = (2x+15) ---equation 2

angle BCD = (4x+45) ------equation 3

ABD+DBC=180

(2x+15) + ( 4x+45 ) = 180

2x+4x+15+45=180

6x+60=180

6x=180-60

6x=120

x=120/6=20

angle ABD= 2x+15= 2(20) +15

=40+15= 55 degree

angle BCD= 4x+45 = 4(20) +45

= 80+45= 125 degree

Hence, angle ABD =55 degree

angle BCD= 125 degree

Hope this helps.

7 0

2 years ago

The ratio of boys to girls in Mr. Baker's social studies class is 2 to 3. If there are 30 total students in the class, how many

astraxan [27]

Answer:

Step-by-step explanation:

1st of all we should let the ration of boys to girls be 2x and 3x.

After that we should make the sum between 2x and3×and the sum of 2numbers is equal to 30

i.e.2x+3x=30

Then ,by solving this eqation we get the value of x=6

After that put the value of x in the number of boys

i.e.

2x=2×6=12

Hence ,the number of boys is 12

7 0

3 years ago

Read 2 more answers

Simplify the expression. Assume that all variables represent nonzero real numbers.StartFraction (4 n Superscript 4 Baseline q Su

Alja [10]

Answer:

$\frac{ - 3}{ 256 {q}^{10} {n}^{8} }$

Step by step explanation:

$\frac{ {(4 {n}^{4} {q}^{5})}^{2} {(8 {n}^{4} q)}^{-2} }{ {(- 3 {nq}^{9})}^{ - 1} {(4 {n}^{3} {q}^{9}) }^{3} }$

first we will change the terms with negative superscrips to the other side of the fraction

$\frac{{(4 {n}^{4} {q}^{5})}^{2}{(- 3 {nq}^{9})}^{ 1}}{{(4 {n}^{3} {q}^{9})}^{3} {(8 {n}^{4} q)}^{2} }$

then we will distribute the superscripts

$\frac{ {4}^{2} {n}^{2 \times 4} {q}^{2 \times 5} (- 3) {nq}^{9}}{ {4 }^{3}{n}^{3 \times 3} {q}^{9 \times 3} {8 }^{2}{n}^{4 \times 2} {q}^{2} }$

$\frac{ {4}^{2} {n}^{8} {q}^{10} (- 3) {nq}^{9}}{ {4 }^{3}{n}^{9} {q}^{27} {8 }^{2}{n}^{8} {q}^{2} }$

as when multiplying two powers that have the same base, we can add the exponents and, to divide podes with the same base, we can subtract the exponents

${4}^{2 - 3} {q}^{10 + 9 - 2 - 27} {n}^{8 + 1 - 8 - 9} {8}^{ - 2} { (- 3)}^{1}$

${4}^{ - 1} {q}^{ - 10} {n}^{ - 8} {8}^{ - 2} { (- 3)}^{1}$

then we will change again the terms with negative superscrips to the other side of the fraction

$\frac{ - 3}{ 4 \times {8}^{2} {q}^{10} {n}^{8} }$

$\frac{ - 3}{ 256 {q}^{10} {n}^{8} }$

4 0

3 years ago

PLS HELP ILL GIVE U BRAINLIST

SCORPION-xisa [38]

<h2>Answer:</h2>

B. |y| = 1.6

<h2>Step-by-step explanation:</h2>

A sketch of the vector is attached to this response.

As shown, the vector lies on the second quadrant and its horizontal and vertical components are given by x and y respectively.

Where;

|x| = v cos θ -----------------(i)

|y| = v sin θ -----------------(ii)

and

v = magnitude of the vector = 2.5km/hr

θ = angle that the vector makes with the +x axis = 90° + 50° = 140°

To get the magnitude of the vector's vertical component

Substitute these values into equation(ii) as follows;

|y| = 2.5 sin 140°

|y| = 2.5 x 0.6428

|y| = 1.607

|y| ≅ 1.6 km/hr

Therefore, the vertical component of the vector has a magnitude of 1.6 km/hr.

4 0

2 years ago