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3 years ago

A living room has a circular rug. According to a small tag, the rug has a circumference of 6.28 yards. What is the rug's area?

Mathematics

1 answer:

cluponka [151]3 years ago

6 0

Answer:

A = 3.14 yd^2

Step-by-step explanation:

The circumference is given by

C = 2 * pi * r

Letting pi be approximated by 3.14

6.28 = 2 * (3.14) *r

6.28 = 6.28 r

Divide each side by 6.28

6.28/6.28 = 6.28r/6.28

1=r

We can find the area by

A = pi r^2

A = 3.14 (1)^2

A = 3.14

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3 years ago

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D’Quan’s grandmother made a quilt for his bed. The quilt is

damaskus [11]

One Square Meter= 10.764 Square Feet.
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3 years ago

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What is an equation of the line that passes through the point (2,−6) and is parallel to the line x-2y=8

lana [24]

Answer:

$y=\frac{1}{2}x-7$ , or x-2y=14

Step-by-step explanation:

Hi there!

We want to find the equation of the line that passes through the point (2, -6) and is parallel to the line x-2y=8

First, we need to find the slope of x-2y=8, since parallel lines have the same slopes

We can convert the equation from standard form (ax+by=c) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept), in order to help us find the slope of the line

Start by subtracting x from both sides

-2y=-x+8

Divide both sides by -2

y= $\frac{1}{2}x$ -4

The slope of the line x-2y=8 is 1/2

It's also the slope of the line parallel to it.

Since we know the slope of the line, we can plug it into the equation for slope intercept form:

$y=\frac{1}{2}x+b$

Now we need to find b.

As the equation of the line passes through (2, -6), we can use it to help solve for b

Substitute -6 as y and 2 as x:

$-6=\frac{1}{2}(2)+b$

Multiply

-6=1+b

Subtract 1 from both sides

-7=b

Substitute -7 as b into the equation:

$y=\frac{1}{2}x-7$

The equation can be left as that, or you can convert it into standard form if you wish.

In that case, you will need to move 1/2x to the other side:

$-\frac{1}{2}x+y=-7$

A rule about the coefficients a, b, and c in standard form is that a (coefficient in front of x) CANNOT be negative, and every coefficient must be an integer (a whole number, not a fraction or decimal).

So multiply both sides by -2 in order to clear the fraction, as well as change the sign of a

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5x^2=11x-2 quadratic equation

hjlf

Given data:

The given equation is 5x^2= -11x-2.

The given equation can be written as,

$\begin{gathered} 5x^2=-11x-2 \\ 5x^2+11x+2=0^{} \\ 5x^2+10x+x+2^{} \\ 5x(x+2)+1(x+2)=0 \\ (5x+1)(x+2)=0 \\ x=-\frac{1}{5},\text{ x=-2} \end{gathered}$

Thus, the values of x are x=-1/5, and x= -2.

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