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3 years ago

What is the slope of (12,10),(12,5)

2 answers:

7 0

To figure the slope of a line, you can either use $\frac{rise}{run}$ or $m = \frac{y2 - y1}{x2 - x1}$ . Remember, 'm' represents the slope of the line.

We can use the point (12, 10) as (x1, y1) and the point (12, 5) as (y1, y2):

$m = \frac{5 - 10}{12 - 12}$

$m = \frac{-5}{0}$

$m = 0$

So, the answer is 0, which means the slope is undefined.

cestrela7 [59]3 years ago

5 0

5/0 UNDEFINED... The answer is a vertical line.

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How is this solved using trig identities (sum/difference)?

GenaCL600 [577]

FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

$cos \beta = -\frac{1}{2} \sqrt{3}$

$tan \beta= \frac{1}{3} \sqrt{3}$

SECOND PART
Solve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
$sin( \alpha + \beta )=(- \frac{12}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{5}{13} )( -\frac{1}{2} )$
$sin( \alpha + \beta )=(\frac{12}{26}\sqrt{3})+( \frac{5}{26} )$
$sin( \alpha + \beta )=(\frac{5+12\sqrt{3}}{26})$

Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
$cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )$
$cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )$
$cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )$

Find tan (α - β)
$tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha tan \beta }$
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}$

Simplify the denominator
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{1+(\frac{5\sqrt{3}}{24})}$
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }$

Simplify the numerator
$tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }$
$tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }$

Simplify the fraction
$tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})$
$tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}$

7 0

3 years ago

Kim needs 10 cups of apple juice for a recipe. How many quarts does she need?

sergey [27]

She will need 2.5 quarts.

5 0

2 years ago

PLEASE HELPPPPPPPPP!!!!?????

natta225 [31]

Answers:

Mean = 69
Median = 69
Mode = {68, 70}

===============================================

Explanations:

To get the mean, you add up all of the values and then you divide by N, where N is the number of values in the list. In this case, you'll divide by N = 8.

Adding up all the values gets you 70+68+70+72+68+66+65+73 = 552. Dividing that over 8 then leads to the arithmetic mean of 552/8 = 69

-------

To find the median, you'll first sort the values from smallest to largest. You should have this set {65, 66, 68, 68, 70, 70, 72, 73} after sorting. Next, cross off the smallest and largest values to end up with this smaller set {66, 68, 68, 70, 70, 72}. We do this so we can locate the middle-most item.

Repeat the process of crossing off the smallest and largest items to get {68, 68, 70, 70}. Do so one more time and we get {68,70}.

The midpoint of those two values is (68+70)/2 = 138/2 = 69. The median is 69. The mean and median may not always be the same value.

--------

The mode is the most frequent value. In this case, we have 68 and 70 show up exactly twice for each unique value. This is the most compared to the other unique values that only show up exactly once.

It is possible to have more than one mode, as long those values are more frequent than the rest. We denote the mode as a set, so the mode is {68, 70}

8 0

2 years ago

Find the circumference of a circle whose area is 247 ft2.

LuckyWell [14K]

Answer:

55.71 ft.

Step-by-step explanation:

hope this helps have a good day!

8 0

3 years ago

Find the volume for the regular pyramid.<br><br><br><br> V =

mylen [45]

The volume is given by:
V = L * Apb * h
Where,
L: side of the base
Apb: apothema of the base
h: height
Substituting we have:
V = (4) * ((root (3) / 2) * 4) * (6)
Rewriting we have:
V = (4) * ((root (3) / 2) * 4) * (6)
V = 96 * (root (3) / 2)
V = 48 * root (3)
Answer:
V = 48 * root (3)

7 0

3 years ago

Read 2 more answers