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Ilya [14]
3 years ago
15

Solve using substitution-2x-y=-9. 5x-2y=18

Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
5 0
Equation 1)  -2x-y=-9
Equation 2)  5x-2y=18

Multiply all of equation 1 by 2, so that both equations have (2y) in them.

1)  2(-2x-y=-9)

Simplify.

1)  -4x-2y=-18
2)  5x-2y=18

Subtract equations with each other.

-9x=-36

Divide both sides by -9.

x=4

Plug in 4 for (x) into equation 1.

-2x-y=-9

-2(4)-y=-9

Simplify.

-8-y=-9

Add 8 to both sides.

-y=-1

Divide both sides by -1.

y=1

(4, 1)

~Hope I helped!~

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Which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?
sesenic [268]

Answer:  D. Two or zero

Step-by-step explanation: x=-7/6+-1/6√385

There isn't an exact place you could really solve this number, regardless of the way you break it down

5 0
3 years ago
I don’t understand please help!
nikklg [1K]

Answer:

x > 10/3

x will always be greater that 10/3 never the same nor less.

Step-by-step explanation:

3/5x + 1/3 < 4/5x - 1/3

3/5x - 4/5x + 1/3 < -1/3

-1/5x + 1/3 < -1/3

-1/5x < -1/3 - 1/3

-1/5x < -2/3

-1/5x/-1 < -2/3/-1   (Since it is both divided by a negative the sign switches, the sign also switches with multiplication. *Note: it only switches if it is negative!*)

1/5x > 2/3

5 • 1/5x > 2/3 • 5

x > 2/3 • 5/1

x > 10/3

6 0
3 years ago
Data on the blood cholesterol levels of 6 rats give mean = 85, s= 12. A 95% confidence interval for the mean blood cholesterol o
lana [24]

The <em><u>correct answer</u></em> is:

c)75.4 to 94.6

Explanation:

The formula for a confidence interval is:

\mu \pm z*(\frac{\sigma}{\sqrt{n}}),

where μ is the mean, z is the z-score associated with the level of confidence we want, σ is the standard deviation, and n is the sample size.

Our mean is 85, our standard deviation is 12, our sample size is 6, and since we want 95% confidence, our z-score is 1.96:

85\pm 1.96(\frac{12}{\sqrt{6}})=85\pm 9.6=85-9.6, 85+9.6=75.4, 94.6

4 0
3 years ago
Read 2 more answers
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})

6 0
3 years ago
Which ordered pairs make the equation true?
Nata [24]
(-4,-2)
You just plug in the numbers from the ordered pair, into your equation. Remember, the formula for ordered pairs are (x,y). :)
6 0
3 years ago
Read 2 more answers
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