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2 years ago

Rewrite in rectangular form: r=5

Mathematics

1 answer:

SVETLANKA909090 [29]2 years ago

6 0

Answer:

x ^2+ y^ 2 = 25

Step-by-step explanation:

Square both sides:

r ^2 = 5^ 2

Substitute x ^2 + y^ 2 for r ^2 :

x ^2+ y ^2 = 5 ^2

Insert the center -0 into the x and y terms:

( x − 0 )^ 2 + ( y − 0 ) ^2 = 5 ^2

This is the standard form for a circle whose center is ( 0, 0 ) and the radius is 5.

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Write an equation of the line containing the point (6,-4) and perpendicular to.the line y=-2x-3

igor_vitrenko [27]

Answer:

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

Step-by-step explanation:

So we need to find an equation of a line that crosses the point (6,-4) and is perpendicular to y = -2x -3.

First, let's find the slope of the line we want to write. The line we want is perpendicular to y = -2x -3. Recall that if two lines are perpendicular to each other, their slopes are negative reciprocals of each other. What this means is that:

$m_1\cdot m_2=-1$

Plug -2 for one of the slopes.

$-2\cdot m_2=-1$

Divide by -2 to find the slope of our line.

$m_2=1/2$

Thus, our line needs to have a slope of 1/2.

Now, let's use the point-slope form. The point-slope form is given by:

$y-y_1=m(x-x_1)\\$

Plug in 1/2 for the slope m and let's let our point (6,-4) be x₁ and y₁. Thus:

$y-(-4)=\frac{1}{2}(x-6)\\$

Simplify and distribute:

$y+4=\frac{1}{2} x-3$

Subtract 4 from both sides:

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

The above is the equation that passes the point (6,-4) and is perpendicular to y = -2x -3.

5 0

3 years ago

Solve the simultaneous equation, 2p - 3q = 4 3p + 2q = 9

Kobotan [32]

Answer:

p = $\frac{35}{13}$ and q = $\frac{6}{13}$

Step-by-step explanation:

Given equations:

2p - 3q = 4 -----------(i)

3p + 2q = 9 ------------(ii)

Let's solve this equation simultaneously using the elimination method

(a) Multiply equation (i) by 3 and equation (ii) by 2 as follows;

[2p - 3q = 4] x 3

[3p + 2q = 9] x 2

6p - 9q = 12 -------------(iii)

6p + 4q = 18 -------------(iv)

(b) Next, subtract equation (iv) from equation (iii) as follows;

[6p - 9q = 12]

- [6p + 4q = 18]

-13q = -6 -----------------(v)

(c) Next, make q subject of the formula in equation (v)

q = $\frac{6}{13}$

(d) Now substitute the value of q = $\frac{6}{13}$ into equation (i) as follows;

2p - 3( $\frac{6}{13}$ ) = 4

(e) Now, solve for p in d above

Multiply through by 13;

26p - 18 = 52

Collect like terms

26p = 52 + 18

26p = 70

Divide both sides by 2

13p = 35

p = $\frac{35}{13}$

Therefore, p = $\frac{35}{13}$ and q = $\frac{6}{13}$

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2 years ago

Which shape is a continuous line of equal distance from its center?

natima [27]

A circle would be the answer

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2 years ago

I hate people who answer questions like this:

fiasKO [112]

Answer:

Oh wow

Step-by-step explanation:

Nice opinion xD

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2 years ago

Rob who has 13 girls phone number that are in his homeroom has 3 more than half the number that jay has what is the algebraic eq

Vikki [24]

Well Jay has 20 phone numbers.
20j=13r-3x2 im not sure but i hope that helped a little.

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3 years ago