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3 years ago

Which of the following expressions represents "The product of 9 and a number, diminished by 7"?

Mathematics

1 answer:

Arturiano [62]3 years ago

4 0

For this case we have to:

x: Be the variable that represents the unknown number

Then, the product of 9 and a number is represented as:

$9 * x$

If the product is reduced 7 units we have to:

$9x-7$

Finally the expression is:

$9x-7$

ANswer:

$9x-7$

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I need help with this one Eight cookies cost $12. At this rate, how much will 10 cookies cost?

mr Goodwill [35]

Answer:

$15

Step-by-step explanation:

12/8 = 1.5 = 1.50 per cookie

1.50* 10 = 15

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3 years ago

Ivory says that the equation 2x+2=x+1 has no solution because the left-hand side is double the right-hand side. Is Ivory Correct

lorasvet [3.4K]

Answer:

No, Ivory is incorrect. The equation does have a solution, and the solution is x = -1.

Step-by-step explanation:

We try to solve the equation first.

2x + 2 = x + 1

We want all variables on the left side and all numbers on the right side.

Subtract x from both sides.

x + 2 = 1

Subtract 2 from both sides.

x = -1

Check: Plug in -1 for x on both sides and see if it makes a true statement.

2x + 2 = x + 1

2(-1) + 2 = -1 + 1

-2 + 2 = 0

0 = 0

0 = 0 is a true statement, so the solution x = -1 is the correct solution.

Answer: Ivory is incorrect. The equation does have a solution, and the solution is x = -1.

8 0

3 years ago

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

Fiona wrote the linear equation y = x – 5. when henry wrote his equation, they discovered that his equation had all the same sol

djverab [1.8K]

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miss Akunina [59]

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Answer:

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Step-by-step explanation:

You can fill in the boxes from the table values as shown in the attachment.

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3 years ago

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