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Arturiano [62]
2 years ago
8

Simplify

" align="absmiddle" class="latex-formula"> ÷ \frac{9X}{x^{2}- 9x -10}
Mathematics
1 answer:
mr Goodwill [35]2 years ago
4 0

In the second fraction, factorize the denominator:

x^2-9x-10=(x-10)(x+1)

Then we have, as long as x\neq10,

\dfrac1{x-10}\div\dfrac{9x}{x^2-9x-10}=\dfrac{\frac1{x-10}}{\frac{9x}{(x-10)(x+1)}}=\dfrac1{\frac{9x}{x+1}}=\dfrac{x+1}{9x}

which you could also write as

\dfrac{x+1}{9x}=\dfrac x{9x}+\dfrac1{9x}=\dfrac19+\dfrac1{9x}

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a parabola has an x-intercept at 2, its axis of symmetry is the line x=4, and the y-coordinate of its vertex is 6. Determine the
nlexa [21]

Answer:

The standard equation of the parabola is:

y=-\frac{3}{2}x^2+12x-18

Step-by-step explanation:

An x intercept of 2 means that the point (2, 0) is in the graph of the parabola.

We can also write the general expression for the parabola in vertex form, since we can use the information on the coordinates of the vertex: (4, 6) - recall that the axis of symmetry of the parabola goes through the parabola's vertex, so the x-value of the vertex must be x=4.

y-y_{vertex}=a\,(x-x_{vertex})^2\\y-6=a\,(x-4)^2

Now we can find the value of the parameter "a" by using the extra information about the point (2, 0) at which the parabola intercepts the x-axis:

y-6=a\,(x-4)^2\\0-6=a\,(2-4)^2\\-6=a\,4\\a=-\frac{6}{4} =-\frac{3}{2}

Then the equation of the parabola becomes:

y-6=-\frac{3}{2} \,(x-4)^2\\y-6=-\frac{3}{2} (x^2-8x+16)\\y-6=-\frac{3}{2}x^2+12x-24\\y=-\frac{3}{2}x^2+12x-18

7 0
3 years ago
Which expressions are equivalent to, 8m + 6 *
guajiro [1.7K]

Answer:

4m + 4m + 6

3+3+5+3

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Step-by-step explanation:

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4 0
3 years ago
HELP ME PLEASE! A representation of a linear equation in two variables is graphed below.
Kamila [148]

Option C, y = 1/2 x -2 is the correct answer

4 0
2 years ago
Help ASAP! I’m confused. Thanks!!
KATRIN_1 [288]

Answer:

B

Step-by-step explanation:

3 0
2 years ago
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The nearest perfect square that is less than 22 is
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Answer:

16

Step-by-step explanation:

The square numbers are

1² = 1

2² = 4

3² = 9

4² = 16 ← this is the closest perfect square

5² = 25 (not applicable, over 22)

5 0
2 years ago
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