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3 years ago

Angle BCA is congruent to angle DAC, and angle BAC is congruent to angle DCA by:

Mathematics

1 answer:

snow_tiger [21]3 years ago

6 0

Answer is the alternate interior angles theorem

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A 48-ounce bottle of soda costs $1.79. What is the unit price?

Lisa [10]

Answer:

a. $.04

Step-by-step explanation:

$1.79/48 = 0.037 = 0.04

6 0

3 years ago

What are the equations of the asymptotes of the graph of f(x)=(5/x+7)−8 ?

ludmilkaskok [199]

Answer:

$\mathrm{Vertical}:\:x=0,\:\mathrm{Horizontal}:\:y=-1$

The graph of the function is also attached.

Step-by-step explanation:

Considering the expression

$\:f\left(x\right)=\left(\frac{5}{x}+7\right)-8\:\:$

$\mathrm{Simplify}\:\frac{5}{x}+7-8:\quad \frac{5}{x}-1$

$\mathrm{Vertical\:asymptotes\:of\:}\frac{5}{x}-1:$

Go over every undefined point x = a and check if at least one of the following statement is true.

$\lim _{x\to a^-}f\left(x\right)=\pm \infty$

$\lim _{x\to a^+}f\left(x\right)=\pm \infty$

$\mathrm{Take\:the\:denominator\left(s\right)\:of\:}\frac{5}{x}-1\mathrm{\:and\:compare\:to\:zero}$

$x=0$

The following points are undefined

$x=0$

$\mathrm{The\:vertical\:asymptotes\:are:}$

$x=0$

$\mathrm{Horizontal\:Asymptotes\:of\:}\frac{5}{x}-1:$

$\mathrm{Check\:if\:at\:}x\to \pm \infty \mathrm{\:the\:function\:}y=\frac{5}{x}-1\mathrm{\:behaves\:as\:a\:line,\:}y=mx+b$

$\mathrm{Find\:an\:asymptote\:for\:}x\to -\infty \::$

$\lim _{x\to -\infty \:}\frac{f\left(x\right)}{x}=\lim _{x\to -\infty \:}\frac{\frac{5}{x}-1}{x}=0$

$\lim _{x\to -\infty \:}f\left(x\right)-mx=\lim _{x\to -\infty \:}\frac{5}{x}-1-0x=-1$

$y=-1$

$\mathrm{Find\:an\:asymptote\:for\:}x\to \infty:$

$\lim _{x\to \infty \:}\frac{f\left(x\right)}{x}=\lim _{x\to \infty \:}\frac{\frac{5}{x}-1}{x}=0$

$\lim _{x\to \infty \:}f\left(x\right)-mx=\lim _{x\to \infty \:}\frac{5}{x}-1-0x=-1$

$y=-1$

$\mathrm{The\:horizontal\:asymptote\:is:}$

$y=-1$

Therefore,

$\mathrm{Vertical}:\:x=0,\:\mathrm{Horizontal}:\:y=-1$

The graph of the function is also attached.

6 0

4 years ago

Read 2 more answers

How many solutions does this equation have?<br> (15x + 21) / 3<br> = 5x + 7

Lesechka [4]

Answer:

3*(5*x-7)-(15*x-21)=0

Step-by-step explanation:

3 • (5x - 7) - (15x - 21) = 0

Step 2 :

Equation at the end of step 2 :

0 = 0

Step 3 :

Equations which are always true :

7 0

3 years ago

Joshua spends 25 minutes of each day reading. He reads d days a week. Let m represent the number total minutes of reading a week

Rasek [7]

Answer:

25 x D = Y

Step-by-step explanation:

Example: Say he reads for three days a week.

25 x 3 = 75

or 6 days

25 x 6 = 150

or 4

25 x 4 = 100

4 0

3 years ago

Identify 2 composite numbers that each have 8 as a factor

suter [353]

2 composite numbers having 8 as factor:

8, 16, 24, 32, 40, 80, 800, 120 etc

7 0

3 years ago

Read 2 more answers