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2 years ago

Solve the compound inequality 10 + x < 20 and 4x > -24

Mathematics

1 answer:

kotykmax [81]2 years ago

6 0

Answer:

Step-by-step explanation:

1.) move all terms that are not x to the right side.of the inequalities.

10+x≤20 <u>4x</u>≥<u>-24</u>

-10 -10 4 4

x≤10 x≥-6

2.) combine the two equations to make -6≤x≤10

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find the centre and radius of the following Cycles 9 x square + 9 y square +27 x + 12 y + 19 equals 0

Citrus2011 [14]

Answer:

Radius: $r =\frac{\sqrt {21}}{6}$

$Center = (-\frac{3}{2}, -\frac{2}{3})$

Step-by-step explanation:

Given

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Solving (a): The radius of the circle

First, we express the equation as:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

So, we have:

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Divide through by 9

$x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0$

Rewrite as:

$x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}$

Group the expression into 2

$[x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}$

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

Next, we complete the square on each group.

For $[x^2 + 3x]$

1: Divide the $coefficient\ of\ x\ by\ 2$

2: Take the $square\ of\ the\ division$

3: Add this $square\ to\ both\ sides\ of\ the\ equation.$

So, we have:

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

$[x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Factorize

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Apply the same to y

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}$

Add the fractions

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}$

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

By comparison:

$r^2 =\frac{7}{12}$

Take square roots of both sides

$r =\sqrt{\frac{7}{12}}$

Split

$r =\frac{\sqrt 7}{\sqrt 12}$

Rationalize

$r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}$

$r =\frac{\sqrt {84}}{12}$

$r =\frac{\sqrt {4*21}}{12}$

$r =\frac{2\sqrt {21}}{12}$

$r =\frac{\sqrt {21}}{6}$

Solving (b): The center

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

From:

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

$-h = \frac{3}{2}$ and $-k = \frac{2}{3}$

Solve for h and k

$h = -\frac{3}{2}$ and $k = -\frac{2}{3}$

Hence, the center is:

$Center = (-\frac{3}{2}, -\frac{2}{3})$

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2 years ago

Please help, Geometry I have NO idea how to do this. Both pictures! (#12, #16)

Dvinal [7]

180 degrees in a triangle. so 180-90-31=59

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2 years ago

to make hummingbird nectar you must use 4 cups of water and 1 cup of sugar. what is the ratio of water to sugar

Nutka1998 [239]

Your ratio is 4:1 because it takes 4 cups of water for every cup of sugar.

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2 years ago

H(x)=4|x+4|+3 what’s the answer

MatroZZZ [7]

Answer:

To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.

Parent Function:

g(x)=|x|

Horizontal Shift: Right 4 Units

Vertical Shift: Up 1 Units

Reflection about the x-axis: None

Vertical Compression or Stretch: None

Step-by-step explanation:

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2 years ago

Kayla buys two pairs of jeans for j dollars each and one shirt for 15 dollars. she has 60 dollars to spend. The equation 2j+ 15-

weeeeeb [17]

Kayla buys two pairs of jeans for j dollars each and one shirt for 15 dollars. The cost of one pair of jeans is $22.5 (twenty-two dollars and fifty cents)

From the given information

Let the cost of two pairs of jeans be 2j
The cost of 1 shirt = 15
Total amount to spent = $60

∴

The equation is said to be expressed as:

2j + 15 - 60 = 0

Collect like terms

2j = 60 - 15
2j = 45

Divide both sides by 2

$\mathbf{\dfrac{2j}{2}= \dfrac{45}{2}}$
j = 22.5

Therefore, we can conclude that the cost of one pair of jeans is $22.5 (twenty-two dollars and fifty cents).

Learn more about cost here:

brainly.com/question/13910351?referrer=searchResults

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1 year ago