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anyanavicka [17]

2 years ago

11

The graph below shows the relationship between the number of words typed and the number of minutes typed by a business secretary

.
Based on the information in the graph , what is the unit rate in words per minute?

A. 100 Words per minutes
B. 75 Words per minutes
C. 60 Words per minutes
D. 50 Words per minutes

Correct answer will get brainiest!

1 answer:

Tamiku [17]2 years ago

7 0

It is 75wpm because the slope is 3 up and 2 right which is 150/2

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Find the vertices and foci of the hyperbola. 9x2 − y2 − 36x − 4y + 23 = 0

Xelga [282]

Hey there, hope I can help!

NOTE: Look at the image/images for useful tips
$\left(h+c,\:k\right),\:\left(h-c,\:k\right)$

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1\:\mathrm{\:is\:the\:standard\:equation\:for\:a\:right-left\:facing:H}$
with the center of (h, k), semi-axis a and semi-conjugate - axis b.
NOTE: H = hyperbola

$9x^2-y^2-36x-4y+23=0 \ \textgreater \ \mathrm{Subtract\:}23\mathrm{\:from\:both\:sides}$
$9x^2-36x-4y-y^2=-23$

$\mathrm{Factor\:out\:coefficient\:of\:square\:terms}$
$9\left(x^2-4x\right)-\left(y^2+4y\right)=-23$

$\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}9$
$\left(x^2-4x\right)-\frac{1}{9}\left(y^2+4y\right)=-\frac{23}{9}$

$\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}1$
$\frac{1}{1}\left(x^2-4x\right)-\frac{1}{9}\left(y^2+4y\right)=-\frac{23}{9}$

$\mathrm{Convert}\:x\:\mathrm{to\:square\:form}$
$\frac{1}{1}\left(x^2-4x+4\right)-\frac{1}{9}\left(y^2+4y\right)=-\frac{23}{9}+\frac{1}{1}\left(4\right)$

$\mathrm{Convert\:to\:square\:form}$
$\frac{1}{1}\left(x-2\right)^2-\frac{1}{9}\left(y^2+4y\right)=-\frac{23}{9}+\frac{1}{1}\left(4\right)$

$\mathrm{Convert}\:y\:\mathrm{to\:square\:form}$
$\frac{1}{1}\left(x-2\right)^2-\frac{1}{9}\left(y^2+4y+4\right)=-\frac{23}{9}+\frac{1}{1}\left(4\right)-\frac{1}{9}\left(4\right)$

$\mathrm{Convert\:to\:square\:form}$
$\frac{1}{1}\left(x-2\right)^2-\frac{1}{9}\left(y+2\right)^2=-\frac{23}{9}+\frac{1}{1}\left(4\right)-\frac{1}{9}\left(4\right)$

$\mathrm{Refine\:}-\frac{23}{9}+\frac{1}{1}\left(4\right)-\frac{1}{9}\left(4\right) \ \textgreater \ \frac{1}{1}\left(x-2\right)^2-\frac{1}{9}\left(y+2\right)^2=1 \ \textgreater \ Refine$
$\frac{\left(x-2\right)^2}{1}-\frac{\left(y+2\right)^2}{9}=1$

Now rewrite in hyperbola standardform
$\frac{\left(x-2\right)^2}{1^2}-\frac{\left(y-\left(-2\right)\right)^2}{3^2}=1$

$\mathrm{Therefore\:Hyperbola\:properties\:are:}\left(h,\:k\right)=\left(2,\:-2\right),\:a=1,\:b=3$
$\left(2+c,\:-2\right),\:\left(2-c,\:-2\right)$

Now we must compute c
$\sqrt{1^2+3^2} \ \textgreater \ \mathrm{Apply\:rule}\:1^a=1 \ \textgreater \ 1^2 = 1 \ \textgreater \ \sqrt{1+3^2}$

$3^2 = 9 \ \textgreater \ \sqrt{1+9} \ \textgreater \ \sqrt{10}$

Therefore the hyperbola foci is at $\left(2+\sqrt{10},\:-2\right),\:\left(2-\sqrt{10},\:-2\right)$

For the vertices we have $\left(2+1,\:-2\right),\:\left(2-1,\:-2\right)$

Simply refine it
$\left(3,\:-2\right),\:\left(1,\:-2\right)$
Therefore the listed coordinates above are our vertices

Hope this helps!

8 0

3 years ago

What is the equation for the line that contains the points (-5 , 2) and (3 , 7)?

baherus [9]

Answer:

y= $\frac{5}{8} x+\frac{41}{8}$

Step-by-step explanation:

Hope this helps!

5 0

2 years ago

A circular pool has a radius of 12 feet. To the nearest square foot, what is the area of the trampoline?

svet-max [94.6K]

Answer:

452 ft.²

Step-by-step explanation:

πr² = 3.14 x 12²

= 452.16

= 452 ft.² (to the nearest square foot)

4 0

2 years ago

Read 2 more answers

Diane deposits $7000 into an account that pays simple interest at a rate of 6% per year. How much interest will she be paid in t

Mars2501 [29]

Answer:

1,260

Step-by-step explanation:

6x3=18 7000÷18=1,260

8 0

2 years ago

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List the following numbers in order from least to greatest. a) 3.5× 10/3 B) 3.5× 10-2 C) 5.3 × 10/3

Crazy boy [7]

Answer:

$3.5*10^{-2}, 3.5*10^3, 5.3*10^3$

B, A, C

Step-by-step explanation:

This is scientific notation. The numbers $3.5 * 10^3\\3.5 *10^{-2}\\5.3 * 10^3$ can be ordered least to greatest by looking at their digits and exponents. Since a -2 as an exponent is present, this means this is a small decimal and is the least. 3.5 and 5.3 have the same exponent of 3 but 5.3 is greater than 3.5 so its the greatest. The order is

$3.5*10^{-2}, 3.5*10^3, 5.3*10^3$

5 0

2 years ago