Prove that sin²α + cos²α = 1 and [tex]\frac{1}{cos^{2}\alpha }[/tex] = 1 + tan²α
Answer:
See Explanation
Step-by-step explanation:
[tex] { \sin}^{2} \alpha + { \cos}^{2} \alpha = 1 \\ \\ LHS = { \sin}^{2} \alpha + { \cos}^{2} \alpha \\ \\ = \cancel {\sin}^{2} \alpha + { 1 -\cancel{ \sin}}^{2} \alpha \\ \\ = 1 \\ \\ = RHS \\ \\ \\ \frac{1}{ { \cos}^{2} \alpha } = 1 + { \tan}^{2} \alpha \\ \\ LHS = \frac{1}{ { \cos}^{2} \alpha } \\ \\ = { \sec}^{2} \alpha \\ \\ = 1 + { \tan}^{2} \alpha \\ \\ = RHS[/tex]
Cos(0.5)+cos(0.5+2(3.14159265))+cos(0.5+4(3.14159265))
Answer:
2.63274768567
Step-by-step explanation:
First, note that 3.1415... is p, so 2(3.1415...) is 2pi and 4(3.1415...) is 4pi.
2pi and 4pi are full rotations, which will lead to the same cosine (i.e. cos(x) = cos (x+2pi) = cos(x+4pi) = ... = cos (x+2k*pi)).
So, the expression equals cos0.5 + cos 0.5 + cos0.5 = 3cos0.5 = 3(0.87758256189) = 2.63274768567
I hope this helps! :)
What is the population density of the US if the area of the United States is 4,000 square miles?
Answer:
82050 people/mi^2
Step-by-step explanation:
The population of the US is 328.2 million people and the area of the US is 4000 mi^2 as given. The population density is found by (population)/(area), so we input our values in:
Population density = 328, 200, 000/4000 = 82050 people/mi^2
I hope this helps! :)
what is the simplest form of this ratio?
100:40:20
Answer:
52
Step-by-step explanation:
this is my third time asking brainly for this question. Find the perimeter and in standard form.
What is the slope of the line that passes through the points
Answer:
The slope is -2
Step-by-step explanation:
(−4,7);(2,−5)
(x1,y1)=(−4,7)
(x2,y2)=(2,−5)
m= y2−y1 /x2−x1
−5−7 /2−4
−12 /6
−2
help fast please it's timed
Answer:
2x= 3x-7
-x=-7
x=7
so, the first option
Step-by-step explanation:
Debbie went to the store and bought 4¼ pounds of apples for $6.00. What is the cost per pound per pound of apples? Round your answer to the nearest CENT, if necessary.( im in middle school so pls keep it simple)
Ava' s cell phone plan allows her to send up to 125 text messages per month if she sent 90 text so far what percent of her monthly message limit has she used
Answer:
90/125*100=9000/125
9000/125=72
72%
Solve the system of equations by using the substitution method.
2x - 3y = 11
y=x-4
Pamela's age is three times Jiri's age. The sum of their ages is 68. What is Jiri's age?
Answer:
17
Step-by-step explanation:
x + 3x = 68
4x = 68
x = 17
Julie is drawing a map of the town. She knows that City Hall is 3 miles
down Main St. from the fire station. If the scale for the map is 0.25 in.:
0.5 miles, how long should Main St. be between City Hall and the fire
station on the map?
2. What is a positive coterminal angle to -123° that is between 500° and 750° and a negative coterminal angle to -123° that is between −300° and −500°?
Answer:
The two angles are 597° and -483°
Step-by-step explanation:
A coterminal angle to a random angle A, is an angle that has the same terminal side as A.
If we know the angle A, all the coterminal angles to A can be written as:
A + n*360°
Where n is an integer number.
In this case, we know that:
A = -123°
And we want to find a coterminal angle that is between 500° and 750°
Then we can do:
X = -123° + n*360°
And find the value of n such that X is between the desired values.
if we use n = 1 we get:
X = -123° + 1*360° = 237°
This is not enough, we can discard it.
If we use n = 2, we get:
X = -123° + 2*360° = 597°
This is a coterminal angle to -123°, and is in between 500° and 750°.
Now we want to find a coterminal angle to -123° that is in between -300° and -500°, we can do the same thing as before, but now we can try with negative values of n.
We can start with n = -1, then:
X = -123° - 1*360° = -483°
This is a coterminal angle to -123°, and is in between -300° and -500°.
Then the two angles are:
597° and -483°
3) Is this relationship a function? Why or why not?
Answer:
The relationship is not a function
Step-by-step explanation:
A function may NOT have two y-values assigned to the same x-value.
Nicholas started a canned-food drive at school. The equation representing this is y = 235x + 15, where x is the number of days, and y is the number of cans collected. Explain how to determine how many days it would take to collect 2600 cans.WILL GIVE BRAINLIEST
Answer:
well, 11 days
Step-by-step explanation:
if you were to put take out the y and put 2600 in the y place (2600=235x+15)
you solve that, and will come to 11 days
further explaining:
2600-15 = 2585
2585 / 235 = 11
( I'm not sure if this is right, the question is worded weird and almost doesn't make sense)
but I think it is looking for substitution
Hope this helps!
Answer:
I am given a number of cans, which is y, and I need to find the number of days, which is x. To do this, I would substitute 2600 for y, to get 2600 = 235x + 15. Solving for x, I would get x = 11. Thus, it would take 11 days to collect 2600 cans.
This is the Sample Answer on Edge.
how much would it cost for one cookie at the price of 2.49
Answer:
$2.49
Step-by-step explanation:
What do you mean?
What is 33 percent of 73?
Answer:
24.09
Step-by-step explanation:
Answer:
33% of 73 =24.09
Step-by-step explanation:
Rewrite in simplest terms: (x+10y)-(x+5y)(x+10y)−(x+5y)
Answer:
-x^2-15xy-50y^2+14y
Step-by-step explanation:
Drag and drop the answer into the box to match each point to its coordinates.
Please answer fast, thank you. :)
Answer:
A. 2, 1/2
B. -2, 1/2
C. -1.5, 1/4
Step-by-step explanation:
just solve
Answer:
point a: (2, 1 1/2)
point b: (-2,1 1/2)
point c: (-1 1/2, 1/4)
Step-by-step explanation:
can someone help me please?
Answer:
yesirr let me know!
Step-by-step explanation:
For the following function, state which variable is being transformed. (Will pick brainliest for right answer)
Answer:
dependant brainliest pls
Step-by-step explanation:
The owner of a small store buys coats for $40.00 each. Answer parts a and b. a. He sells the coats for $72.00 each. What percent of the purchase price is the sale price?
Answer:
180%
Step-by-step explanation:
Answer:
180%
Step-by-step explanation:
b. 3 ice cream cones cost $3.75.
At this rate, how much do 2 ice cream cones cost?
Answer:
2.50
Step-by-step explanation:
Lets find the unit rate first! 3.75/3 because that is the problem. Now once we divide that we get 1.25. With 1.25 we multiply by 2 to get your answer of 2.50!
Have a good day!
Answer:
The answer am almost postive is 2.5
Step-by-step explanation:
2) Michelle deposits $250 into a savings account, The account pays 1.5% simple
interest on an annual basis. If he does not add or withdraw money from the account,
how much interest will she earn after 6 months? Round to the nearest cent.
* annual means yearly
to of 2% ner year. How much simple interest will he
Answer:
um michelles broke that couldnt happen
Step-by-step explanation:
help ya girl out?:(
Answer:
Fourth choice, -2
Step-by-step explanation:
If you look at the t-chart at your right, when f(x) is -6, x is -2
la medida del vector se llama:
Step-by-step explanation:
suususisissiaisisjsjx
Five friends go to the movies. They each pay $9 to get in and $8 for a popcorn and drink combo.
a) Write two different expressions to find the total cost of the outing.
b) Evaluate each expression. Which expression was easier to evaluate? Justify your choice.
Answer:
x=5(9+8)
add 9+8 to get 17
multiply 17 by 5
answer: $85
(5x9)+(5x8)=x
multiply 5x9 to get 45
multiply 5x8 to get 40
add 45 and 40
answer: $85
The first expression was easier to evaluate because it required less steps.
Hope this helps :)
5 The backyard at Selena's new house is in the shape of a square and has an area of 250 square feet. What is
the approximate side length of her yard? (Between which two whole numbers?
A) 15 and 16
C) 16 and 17
B) 17 and 18
D) 18 and 19
In order to graph a line your equation must be set equal to y. If I gave you the following equation would you be able to graph it in the form it is given? If not, rewrite the equation so that you could graph it. - 6x + 12y = 9
Answer:
Step-by-step explanation:
Graphing the equation in the form it is given is eventually hard so we always rewrite the equation in the form of y. Lets rewrite the equation in the form of y.
[tex]-6x+12y=9\\12y=6x+9\\\\y=\frac{6x+9}{12} \\\\y=\frac{6x}{12}+\frac{9}{12} \\\\y=\frac{1}{2}x+\frac{3}{4}[/tex]
now if we compare it to our slope-intercept form which is
[tex]y=mx+b[/tex]
m is the slope which is 1/2 which tells us that if the slope is positive the graph is a positive slope means that two variables are positively related that is, when x increases so does y, and when x decreases y also decreases. Graphically, a positive slope means that as a line on the line graph moves from left to right, the line rises, and b is the y-intercept which is 3/4.
Intercept means where the line intersects the specific axis. In this case b is y-intercept which is 3/4 which means the line intersects the y-axis at 3/4
so we have our first point (0 , 3/4)
now in order to graph the line we need one more point that is the x-intercept which means where the line would intersect the x-axis the coordinate would be (x , 0) so lets insert this coordinate into our equation that we rewrote above.
[tex]y=\frac{1}{2}x+\frac{3}{4} \\\\0=\frac{1}{2}x+ \frac{3}{4}\\\\-\frac{3}{4}=\frac{1}{2} x\\\\-6=4x\\\\\frac{-6}{4}=x \\\\x=\frac{-3}{2}[/tex]
so our x-intercept is (-3/2 , 0)
Below I have attached the graph file you check it out for better understanding
What is the scale factor in the dilation?
Answer: 6
Step-by-step explanation:
