Something divided by4 =9

What is the equation of a circle centered at the origin with radius 20?

Colt1911 [192]

We know that
the equation of a circle is
(x-h)²+(y-k)²=r²
where
(h,k)-----> is the center
r--------> is the radius

is the center is the point (0,0) and radius r=20
then
(h,k) is (0,0)

(x-0)²+(y-0)²=20²---------> (x)²+(y)²=400

the answer is
the option D.) x2 + y2 = 400

3 0

2 years ago

Which two statements contradict each other?

TiliK225 [7]

II. Triangle ABC is obtuse and III. Triangle ABC is acute, because acute is less than 180° and obtuse is between 180° and 270°

3 0

3 years ago

A coordinator will select 6 songs from a list of 9 songs to compose an event's musical entertainment lineup. How many different

g100num [7]

Answer:

84 different lineups are possible

Step-by-step explanation:

The order in which the songs are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question:

6 musics from a set of 9. So

$C_{9,6} = \frac{9!}{6!(9-6)!} = 84$

84 different lineups are possible

4 0

3 years ago

Add [1/-4 3/5] [-2/6 -2/4]

brilliants [131]

Answer:

25/138

Step-by-step explanation:

1 Convert 4\frac{3}{5}4

5

3

to improper fraction. Use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

c

b

=

c

ac+b

.

\frac{1}{-(\frac{4\times 5+3}{5})}(-\frac{2}{6}-\frac{2}{4})

−(

5

4×5+3

)

1

(−

6

2

−

4

2

)

2 Simplify 4\times 54×5 to 2020.

\frac{1}{-(\frac{20+3}{5})}(-\frac{2}{6}-\frac{2}{4})

−(

5

20+3

)

1

(−

6

2

−

4

2

)

3 Simplify 20+320+3 to 2323.

\frac{1}{-(\frac{23}{5})}(-\frac{2}{6}-\frac{2}{4})

−(

5

23

)

1

(−

6

2

−

4

2

)

4 Simplify \frac{2}{6}

6

2

to \frac{1}{3}

3

1

.

\frac{1}{-(\frac{23}{5})}(-\frac{1}{3}-\frac{2}{4})

−(

5

23

)

1

(−

3

1

−

4

2

)

5 Simplify \frac{2}{4}

4

2

to \frac{1}{2}

2

1

.

\frac{1}{-(\frac{23}{5})}(-\frac{1}{3}-\frac{1}{2})

−(

5

23

)

1

(−

3

1

−

2

1

)

6 Find the Least Common Denominator (LCD) of \frac{1}{3},\frac{1}{2}

3

1

,

2

1

. In other words, find the Least Common Multiple (LCM) of 3,23,2.

LCD = 66

7 Make the denominators the same as the LCD.

-\frac{1\times 2}{3\times 2}-\frac{1\times 3}{2\times 3}−

3×2

1×2

−

2×3

1×3

8 Simplify. Denominators are now the same.

-\frac{2}{6}-\frac{3}{6}−

6

2

−

6

3

9 Join the denominators.

\frac{-2-3}{6}

6

−2−3

10 Simplify -\frac{1}{3}-\frac{1}{2}−

3

1

−

2

1

to -\frac{5}{6}−

6

5

.

\frac{1}{-(\frac{23}{5})}\times \frac{-5}{6}

−(

5

23

)

1

×

6

−5

11 Move the negative sign to the left.

-\frac{1}{\frac{23}{5}}\times \frac{-5}{6}−

5

23

1

×

6

−5

12 Invert and multiply.

-\frac{5}{23}\times \frac{-5}{6}−

23

5

×

6

−5

13 Use this rule: \frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}

b

a

×

d

c

=

bd

ac

.

-\frac{5\times -5}{23\times 6}−

23×6

5×−5

14 Simplify 5\times -55×−5 to -25−25.

-\frac{-25}{23\times 6}−

23×6

−25

15 Simplify 23\times 623×6 to 138138.

-\frac{-25}{138}−

138

−25

16 Move the negative sign to the left.

-(-\frac{25}{138})−(−

138

25

)

17 Remove parentheses.

\frac{25}{138}

138

25

7 0

2 years ago

Write an equation of the line that is perpendicular to 3x - 4y equals 9 + contains (-4, -5)

Inga [223]

Slope-Intercept Form: y = mx+b, with m = slope and b = y-intercept

So perpendicular lines have slopes that are negative reciprocals to each other, but firstly we need to find the slope of the original equation. The easiest method to find it is to convert this standard form into slope-intercept.

Firstly, subtract 3x on both sides of the equation: $-4y=-3x+9$

Next, divide both sides by -4 and your slope-intercept form of the original equation is $y=\frac{3}{4}x-\frac{9}{4}$

Now looking at this equation, we see that the slope is 3/4. Now since our new line is perpendicular, this means that its slope is -4/3.

Now that we have the slope, plug that into the m variable and plug in (-4,-5) into the x and y coordinates to solve for the b variable as such:

$-5=-\frac{4}{3}*-4+b\\\\-5=5\frac{1}{3}+b\\\\-10\frac{1}{3}=b$

In short, your new equation is y = -4/3x - 10 1/3.

3 0

2 years ago

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