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3 years ago

A square of 81cm² is cut to make two rectangles, A and B

Mathematics

2 answers:

grandymaker [24]3 years ago

8 0

Answer:

Length of A: 9

Width of A: 6

Length of B: 9

Width of B: 3

Step-by-step explanation:

If you look at the diagram, you can see that the length of rectangles A and B are the same, and are also the same as they were in the original square. We can find the length of each side by finding the square root of the area of the square to give us the length and width of the square which is 9. Now that we know that the length of both rectangles A and B, we can find the width of both rectangles by taking 9, and splitting it into 3 portions of 3. Since the ratio of area is 2:1, we could also do this with the area, but since we know the lengths are the same, we know the widths are proportional to the area. Using the ratio of 2:1, and the 3 portions of 3, you can combine 2 of these portions to get 6, and since the ratio 6:3 is proportional to 2:1, these measurements can be used as the width of each rectangle. Thus, the answer given above.

katen-ka-za [31]3 years ago

8 0

Answer:

Length of A: 9

Width of A: 6

Length of B: 9

Width of B: 3

Step-by-step explanation:

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What is the center and radius of x^2+6x+y^2-4y =-4?

Nat2105 [25]

Answer:

The center of this circle is at $(-3,\, 2)$ . The radius of this circle is $3$ .

Step-by-step explanation:

A circle with center $(a,\, b)$ and a radius of $r$ ( $r > 0$ ) could be expressed as:

$(x - a)^{2} + (y - b)^{2} = r^{2}$ .

(In other words, a point is on this circle if and only if the distance between that point and the center is equal to the radius.)

Rearrange this equation using binomial expansion to match the equation given in this question:

$(x^{2} - 2\, a\, x + a^{2}) + (y^{2} - 2\, b\, y + b^{2}) = r^{2}$ .

$x^{2} + (-2\, a)\, x + y^{2} + (-2\, b)\, y = -a^{2} - b^{2} + r^{2}$ .

The equation in this question is:

$x^{2} + 6\, x + y^{2} + (-4)\, y = -4$ .

Match up the coefficients of $x$ and $y$ in the two equations.:

Coefficient of $x$ : $(-2\, a) = 6$ .
Coefficient of $y$ : $(-2\, b) = (-4)$ .

Thus, $a = (-3)$ and $b = 2$ .

The constants of the two equations should also match up:

$(-a^{2} - b^{2} + r^{2}) = (-4)$ .

Substitute in $a = (-3)$ as well as $b = 2$ and solve for $r$ :

$r^{2} = 9$ .

$r = 3$ (since $r > 0$ .)

Therefore, the center of this circle is $(-3,\, 2)$ . The radius of this circle is $3$ .

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2 years ago

Write the equation of the ellipse using the given information:

horsena [70]

We know, equation of ellipse is given by :

$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$

Here,

(h,k) is centre of the ellipse = (0,0).

a = major axis = 8.

b = minor axis = 4.

Putting all given value in above equation, we get :

$\dfrac{(x-0)^2}{8^2}+\dfrac{(y-0)^2}{4^2}=1\\\\\dfrac{x^2}{8^2}+\dfrac{y^2}{4^2}=1\\\\\dfrac{x^2}{64}+\dfrac{y^2}{16}=1$

Hence, this is the required solution.

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3 years ago

X²- 12x + a = (x-b)² <br>Find the Value of a and value of b <br>

maxonik [38]

Answer:

a = 36 , b = 6

Step-by-step explanation:

expand the right side using FOIL and compare coefficients with like terms on left side.

(x - b)²

= x² - 2bx + b² , compare to x² - 12x + a , then

- 2b = - 12 ( divide both sides by - 2 )

b = 6

and a = b² = 6² = 36

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2 years ago

What is the slope of a line that is perpendicular to the line shown on the graph?

Anvisha [2.4K]

The answer is C. 1/2

Hope this helps!

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3 years ago

In a recent year, 304 of the approximately 300,000,000 people in the United States were struck by lightning. Estimate the prob

umka2103 [35]

Answer:

$\frac{19}{18,750,000}=0.0000010133333333$

Step-by-step explanation:

We have been given that in a recent year, 304 of the approximately 300,000,000 people in the United States were struck by lightning.

$\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}$

$\text{P( A randomly selected person in the United States will be struck by lightning this year)}=\frac{304}{300,000,000}$

$\text{P( A randomly selected person in the United States will be struck by lightning this year)}=\frac{19}{18,750,000}$

$\text{P( A randomly selected person in the United States will be struck by lightning this year)}=0.0000010133333333$

Therefore, the probability that a randomly selected person in the United States will be struck by lightning this year is $\frac{19}{18,750,000}=0.0000010133333333$ .

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4 years ago

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