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Andrews [41]
3 years ago
13

If θ is an angle in standard position and its terminal side passes through the point (-4,-5), find the exact value of

Mathematics
1 answer:
NARA [144]3 years ago
7 0

9514 1404 393

Answer:

  cot(θ) = 4/5

Step-by-step explanation:

In the polar/rectangular coordinate representation (x, y) ⇔ (r; θ), we know that ...

  (x, y) = (r·cos(θ), r·sin(θ))

From the various trig definitions and identities, we also know that ...

  cot(θ) = cos(θ)/sin(θ) = (x/r)/(y/r) = x/y

For the given (x, y) = (-4, -5), the cotangent is ...

  cot(θ) = -4/-5 = 4/5

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Find the coordinates of the midpoint of the segment whose endpoints are H(5, 13) and K(7, 5). (12, 18)
gtnhenbr [62]

\text{The formula of the midpoint of segment AB:}\\\\\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right).\\\\\text{We have the points}\ H(5,\ 13)\ \text{and}\ K(7,\ 5).\ \text{Substitute:}\\\\x=\dfrac{5+7}{2}=\dfrac{12}{2}=6\\\\y=\dfrac{13+5}{2}=\dfrac{18}{2}=9\\\\Answer:\ \boxed{(6,\ 9)}

5 0
2 years ago
5/8 -0.5 evaluate each expression. Write answer as a decimal
gregori [183]

Answer:

0.125

Step-by-step explanation:

0.5 =1/2

Now

5/8 - 1/2

5/8 - 1*4/2*4

5/8-4/8

(5-4)/8

1/8

0.125

6 0
2 years ago
Nolan has some nickels and some dimes. He has no more than 19 coins worth no less than $1.30 combined. If Nolan has 5 nickels, d
Allushta [10]

Answer:

number of dimes 11 to 14

Step-by-step explanation:

given data

coin = 19

worth no less = $1.30

Nolan nickles = 5

solution

we convert 5 cent to dollars, it will be

5÷100 = $0.05

and

dime is worth 10 cents

so it will be 10 ÷ 100 = $0.1

so we consider here x as the number when nickels.

and we consider y as the number of dimes.

so here we can say

x + y ≤ 19      ..........................1

as here no less than $1.30 combined.

so

0.05 x + 0.1 y ≥ 1.3       ......................2

and

when Nolan has 5 nickels

put x = 5 in eq 1

5 + y ≤ 19  

y ≤ 19 - 5

y ≤ 14

and

now we put x = 5 in eq 2

0.05 × 5 + 0.1y ≥ 1.3

0.25 + 0.1y ≥ 1.3

0.1y ≥ 1.3 - 0.25

0.1y ≥ 1.05

y ≥ 10.5

so all possible values for the number of dimes 11 to 14

7 0
3 years ago
I need help<br><br><br><br> Thx guys
Evgesh-ka [11]
Plugging in the numbers 7x - 2y = 39 fitted and made sense
8 0
2 years ago
Read 2 more answers
I really need help please help me
hram777 [196]

Answer:

i11, i26, i20, i21

Step-by-step explanation:

Alright, so there's an order to imaginary numbers. At the 1st power, it's i. At the second, it's -1. At the 3rd, it's -i. At the 4th, it's 1. And at the 5th, it restarts.

5 0
3 years ago
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