1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sweet-ann [11.9K]
3 years ago
5

Solve for the given variable

Mathematics
2 answers:
Natalija [7]3 years ago
7 0

Answer:

k = 30

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

120° is an exterior angle of the triangle, thus

k + 90 = 120 ( subtract 90 from both sides )

k = 30

Ne4ueva [31]3 years ago
3 0

Answer:

30

Step-by-step explanation:

Well we know the first angle is 90 degrees, which means we have 90 degrees left to work with. Then, the top angle would be 60 degrees, because there is a straight line (which of course has to equal 180), so 180-120 = 60. Now, 90-60=30!

You might be interested in
Construct a 95​% confidence interval to estimate the population mean using the data below. x overbarequals37 sigmaequals10 nequa
kap26 [50]

Answer:

With 95% confidence when n equals 44, the population mean is between a lower limit of 33.96 and an upper limit of 40.04

Step-by-step explanation:

Confidence Interval = mean + or - Error margin (E)

mean = 37

sd = 10

n = 44

degree of freedom = n - 1 = 44 - 1 = 43

t-value corresponding to 43 degrees of freedom and 95% confidence level is 2.0165

E = t × sd/√n = 2.0165×10/√44 = 3.04

Lower limit = mean - E = 37 - 3.04 = 33.96

Upper limit = mean + E = 37 + 3.04 = 40.04

95% confidence interval is between 33.96 and 40.04

7 0
3 years ago
For what values of θ on the polar curve r=θ, with 0≤θ≤2π , are the tangent lines horizontal? Vertical?
Bond [772]
Given that r=\theta, then r'=1

The slope of a tangent line in the polar coordinate is given by:

m= \frac{r'\sin\theta+r\cos\theta}{r'\cos\theta-r\sin\theta}

Thus, we have:

m= \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta}



Part A:

For horizontal tangent lines, m = 0.

Thus, we have:

\sin\theta+\theta\cos\theta=0 \\  \\ \theta\cos\theta=-\sin\theta \\  \\ \theta=- \frac{\sin\theta}{\cos\theta} =-\tan\theta

Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:

</span><span>θ = 0

</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488



Part B:

For vertical tangent lines, \frac{1}{m} =0

Thus, we have:

\cos\theta-\theta\sin\theta=0 \\  \\ \Rightarrow\theta\sin\theta=\cos\theta \\  \\ \Rightarrow\theta= \frac{\cos\theta}{\sin\theta} =\sec\theta

</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:

</span>θ = <span>4.91718592528713</span>
3 0
3 years ago
What is 36.5625 in fraction form
Romashka [77]
The answer is one hundred seventeen over three hundred twenty or 117/320

4 0
3 years ago
Suppose a casino invents a new game that you must pay $250 to play. The game works like this: The casino drawsrandom numbers bet
Ira Lisetskai [31]

Answer:

clc%clears screen

clear all%clears history

close all%closes all files

p=250;

M=[];

for i=1:100000

re=0;

S=0;

while(S<=1)

S=S+rand;

re=re+100;

end

M(i)=re;

end

disp('Expected received money is');

mean(M)

disp('Since expcted is greater than what we pay. So, we will play')

Step-by-step explanation:

6 0
3 years ago
X + 25/-8 = -6 Solve for x.<br> Simplify your answer as much as possible.
balandron [24]

Step-by-step explanation:

if there is nothing missing, we have

x + 25/-8 = -6

in order to compare or add or subtract fractions, we need to bring them all to the same denominator (bottom part).

remember, integer numbers are fractions too. like here

-6 = -6/1

25/-8 = -25/8

so, how can we bring -6/1 to .../8 ?

by multiplying 1 by 8.

but we cannot multiply only the denominator by 8. otherwise we would suddenly have

-6/8

and is -6/8 = -6/1 ? no, certainly not.

to keep the original value of the fraction we have to do the same multiplication also with the numerator (top part).

so, we actually do

-6/1 × 8/8 = -48/8

with this little trick we have now .../8 to operate with, and our transformed fraction has still the same value

-6/1 = -48/8 indeed.

so, we have

x + -25/8 = -48/8

x - 25/8 = -48/8

x = -48/8 + 25/8 = -23/8

3 0
2 years ago
Other questions:
  • Solve 2 log7 5 + log7 x= log7 100
    14·2 answers
  • Use the quadratic formula to solve x2 + 7x + 8 = 0. Estimate irrational solutions to the nearest tenth.
    7·1 answer
  • How do you factor 3x^2-7x-2
    9·1 answer
  • Need help please help on number 5 help/23 points
    9·1 answer
  • PLEASE HELP!!!!There is an 80% chance of rain. The tennis team has a 75% chance of winning if it doesn't rain and only a 35% cha
    12·1 answer
  • Write the missing family<br>fact<br>5 x 16 = 80<br>80 : 5 = 16<br>16 x 5 = 80​
    6·1 answer
  • What's the answer?? Please try to answer correctly I will mark you most Brainly and fast!!
    14·1 answer
  • 5/12+8/12 I need help
    14·2 answers
  • You want to make sugar cookies and chocolate chip cookies. You have only one dozen eggs and 20 cups of flour. For each batch of
    11·1 answer
  • Evaluate the expression 3.8 +0+ y for the given values of y value value of expression -4.3 -1.6 0 5.2 -0.5​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!