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makvit [3.9K]
3 years ago
15

A square and a rectangle have the same perimeters.The lenght of a side of the suare is 4x-1.The lenght of the rectangle is 2x+2

and the widt is 2x.Wite and solve an euation to find x
Mathematics
1 answer:
Nina [5.8K]3 years ago
3 0

Answer:

x=1

Step-by-step explanation:

perimeter of the square is 4(4x-1)=16x-4

perimeter of the rectangle is 2(2x+2) + 2(2x)= 4x+4+4x=8x+4

As rectangle and square have the same perimeter, we get that:

16x-4=8x+4\\16x-8x=4+4\\8x=8\\x=\frac{8}{8} \\x=1

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Point P(-5,2) is translated using the rule (x + 3, y - 1) What is the x - coordinate of P'​
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Answer:

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Step-by-step explanation:

Since we are adding 3 to the x-coordinate and subtracting 1 from the y-coordinate, (-5, 2) becomes (-2, 1).

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Which of the following is a solution to sin x/2 = sqrt3/2 ?
Vera_Pavlovna [14]

Answer:

A. 60 degrees

Step-by-step explanation:

Solution to sin(x/2)=(\sqrt{3}/2)

By looking at this equation, I can identify that the answer must be within the first quadrant since the numerator and denominator are both positive.

Since it is in the first quadrant, the range of the value of the answer must be between 0 degrees less than or equal to x less than or equal to 90 degrees.

I can also identify that this is a 30, 60, 90 degree triangle because it has a \sqrt{3} and 2 as the numerator and denominator; in this case this tells us that we are dealing with a 30, 60, 90 degree triangle because that is the only triangle with those 2 respective sides.

Once identifying those two pieces of information, we can then determine the answer.

Since sin is equal Opposite/Hypotenuse, we can then substitute the sides of the triangle (\sqrt{3}, 2) to find the angle (unknown).

So the equation would look like this,

Sinx/2=\sqrt{3}/2 (\sqrt{3} representing the opposite side of the angle; 2 representing the Hypotenuse of the triangle)

We can then conclude that 60 degrees is the unknown angle, due to the nature of a 30 60 90 degree triangle.

*Use the attachment for reference

Therefore, the answer, 60 degrees, is a solution to the equation "sin(x/2)=(\sqrt{3}/2)"

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In how many ways can you seat 5 women and 5 men in a row if women must seat next to each other,men must seat next to each other,
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Answer: 288ways

Step-by-step explanation:

There are 5men and 5women to be arranged, since the men must seat together, they will be arranged in 5! ways. For the women, since they must also seat together but with siamese twins between them, they can be arranged in 4! ways instead of 5! ways and this is due to presence of the twins among them.

Note that Siamese twins cannot be separated as such both are taken as one making it 4!.

Since the women and men are always sitting together, they can be arranged in 2! ways i.e 2 sexes

The final seating arrangement can be done in 2!×(5!+4!) ways

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Note that the arrangement of the men and women are added because they can only be arranged differently to ensure different sex are not sitting together.

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