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3 years ago

B is the midpoint of AC. What is the length of AB? AB is 9x+7 and BC is -3x+20

Mathematics

1 answer:

ahrayia [7]3 years ago

8 0

<h3>Answer:</h3>

$AB = \frac{67}{4}\\$

<h3>Step-by-step explanation:</h3>

If $B$ is the midpoint of $\overline{AC}$ then $AB$ is just half of $AC$ and also, $BC$ is just half of $AC$ . This means that $AB$ must be equal to $BC$ . Essentially, $9x +7 = -3x +20$ and we can solve for the of $x$ from that equation.

$9x +7 = -3x +20 \\ 9x +7 +3x = -3x +20 +3x \\ 12x +7 = 20 \\ 12x +7 -7 = 20 -7 \\ 12x = 13 \\ \frac{12x}{12} = \frac{13}{12} \\ x = \frac{13}{12}$

Now we can solve for $AB$

$AB = 9(\frac{13}{12}) +7 \\ AB = 3(\frac{13}{4}) +7 \\ AB = \frac{39}{4} +7 \\ AB = \frac{39}{4} +\frac{28}{4} \\ AB = \frac{67}{4}$

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Which of the following rational functions is graphed below?

vampirchik [111]

Answer:

The correct option is D.

i.e.

$f\left(x\right)=\frac{1}{x\left(x+4\right)}$ is the correct option.

The correct graph is shown in attached figure.

Step-by-step explanation:

Considering the function

$f\left(x\right)=\frac{1}{x\left(x+4\right)}$

$\mathrm{Domain\:of\:}\:\frac{1}{x\left(x+4\right)}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x$

$\mathrm{Range\:of\:}\frac{1}{x\left(x+4\right)}:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\le \:-\frac{1}{4}\quad \mathrm{or}\quad \:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-\frac{1}{4}]\cup \left(0,\:\infty \:\right)\end{bmatrix}$

$\mathrm{Axis\:interception\:points\:of}\:\frac{1}{x\left(x+4\right)}:\quad \mathrm{None}$

$\mathrm{Extreme\:Points\:of}\:\frac{1}{x\left(x+4\right)}:\quad \mathrm{Maximum}\left(-2,\:-\frac{1}{4}\right)$

So, the correct graph is shown in attached figure.

Therefore, the correct option is D.

i.e.

$f\left(x\right)=\frac{1}{x\left(x+4\right)}$ is the correct option.

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3 years ago

In Ryan Corporation, the first shift produced 5 1/2 times as many lightbulbs as the second shift. If the total lightbulbs produc

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Answer:

13750

Step-by-step explanation:

Let 'x' be the number of bulbs produced in second shift

Number of bulbs produced in 1st shift= 5.5x

Total number of bulbs= 5.5x+x

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3 years ago

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Answer:

Step-by-step explanation:

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4 years ago

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Step-by-step explanation:

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Divide 4 by 7 and you get...

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3 years ago

Read 2 more answers

Which points are the verticles of the ellipse? Equations of ellipse

Mashutka [201]

Answer:

This question is solved in detail below. Please refer to the attachment for better understanding of an Ellipse.

Step-by-step explanation:

In this question, there is a spelling mistake. This is vertices not verticles.

So, I have attached a diagram of an ellipse in which it is clearly mentioned where are the vertices of an ellipse.

Vertices of an Ellipse: There are two axes in any ellipse, one is called major axis and other is called minor axis. Where, minor is the shorter axis and major axis is the longer one. The places or points where major axis and minor axis ends are called the vertices of an ellipse. Please refer to the attachment for further clarification.

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$\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } = 1$

This is the case when major axis the longer one is on the x-axis centered at an origin.

$\frac{x^{2} }{b^{2} } + \frac{y^{2} }{a^{2} } = 1$

This is the case when major axis the longer one is on the y-axis centered at an origin.

where major axis length = 2a

and minor axis length = 2b

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3 years ago