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Andrej [43]
3 years ago
10

Please help!! Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Which stateme

nt is correct?
a. The two tiles are not similar because SP:SR is 5 : 1 and MJ:ML is 2 : 3.
b. The two tiles are similar because PQ:QR is 1 : 3 and JK:KL is also 1 : 3.
c. The two tiles are similar because SR:SP is 3 : 2 and ML:MJ is also 3 : 2.
d. The two tiles are not similar because PQ:QR is 1 : 6 and JK:KL is 1 : 3.

Mathematics
1 answer:
Cerrena [4.2K]3 years ago
8 0

Answer: Statement B is correct; the two tiles are similar because PQ:QR is 1:3 and JK:KL is also 1:3

Step-by-step explanation: The two tiles as shown in the diagram has their dimensions given according to their position on the Cartesian plane. Tile SRQP has its width at coordinates (2,2) and (4,2) which means the width spans from 2 cm to 4 cm on the x-axis, that is a length of 4 minus 2 which is 2 cm. Similarly the length is at coordinates (2,2) to (2,8) which means the length spans from 2 cm to 8 cm on the y-axis, that is a length  of 8 minus 2 which is 6 cm. Therefore the dimensions of the first tile is 6 cm by 2 cm.

Similarly, we can derive the length and width of the smaller tile MLKJ, by applying the same procedure and what we would have is a tile measuring 3 cm by 1 cm.

The ratio of tile SRQP can be derived as

Ratio = 2 : 6

Ratio = 1 : 3

Also the ratio of the tile MLKJ can be derived as

Ratio = 1 : 3

Having calculated the ratio 1 : 3 for both tiles, then we can safely conclude that both are similar.

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Limit question: lim x-->pi ((e^sinx)-1)/(x-pi)
aleksandr82 [10.1K]
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f'(c):=\displaystyle\lim_{x\to c}\frac{f(x)-f(c)}{x-c}

So the value of this limit is exactly the value of the derivative of f(x)=e^{\sin x} at x=\pi.

You have

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4 0
3 years ago
28/29 and 30 please short explanation thanks
Bond [772]

Answer 28.

Possible values for the three factors of -3

  1. 1, -1 and 3
  2. -1.5, 1 and 2
  3. 1.5, -1 and 2  
  4. 1.5, 1 and -2

Answer 29.

The product of two nonzero integers will be less than or equal to both of the integers if they are multiplied by number itself and one or by number itself and one with negative sign.

Answer 30.

The sign of the product of three integers with the same sign will be positive or negative. If odd number of same sign is multiplied, the product will be of that sign.

(+)  (+)  (+) = (+)

(-)  (-)  (-) =  (-)

3 0
3 years ago
If f(1) = 0, what are all the roots of the function f(x)=x^3+3x^2-x-3? Use the Remainder Theorem.
Sophie [7]
There's no if about it, 

f(x)=x^3+3x^2-x-3


has a zero f(1)=0 so x-1 is a factor.   That's the special case of the Remainder Theorem; since f(1)=0 we'll get a remainder of zero when we divide f(x) by x-1.

At this point we can just divide or we can try more little numbers in the function.  It doesn't take too long to discover f(-1)=0 too, so  x+1 is a factor too by the remainder theorem.  I can find the third zero as well; but let's say that's out of range for most folks.

So far we have 

x^3+3x^2-x-3 = (x-1)(x+1)(x-r)

where r is the zero we haven't guessed yet.  Again we could divide f(x) by (x-1)(x+1)=x^2-1 but just looking at the constant term we must have

-3 = -1 (1)(-r) = r

so

x^3+3x^2-x-3 = (x-1)(x+1)(x+3)

We check f(-3)=(-3)^3+3(-3)^2 -(-3)-3 = 0 \quad\checkmark

We usually talk about the zeros of a function and the roots of an equation; here we have a function f(x) whose zeros are

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8 0
3 years ago
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Reika [66]
57+23 = 80
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