we know that θ is in the I Quadrant, namely that cosine as well as sine are both positive, well, we know that
[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{2}}{\underset{hypotenuse}{\sqrt{19}}}\qquad\qquad \textit{let's get the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{(\sqrt{19})^2-2^2}=b\implies \pm\sqrt{19-4}=b\implies \pm\sqrt{15}=b\implies \stackrel{I~Quadrant}{+\sqrt{15}=b} \\\\[-0.35em] ~\dotfill[/tex]
[tex]tan(\theta)=\cfrac{\stackrel{opposite}{\sqrt{15}}}{\underset{adjacent}{2}}~\hspace{10em} tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)} \\\\[-0.35em] ~\dotfill\\\\ tan(2\theta)=\cfrac{2\cdot \frac{\sqrt{15}}{2}}{1-\left( \frac{\sqrt{15}}{2} \right)^2}\implies tan(2\theta)=\cfrac{\sqrt{15}}{1-\frac{15}{4}}\implies tan(2\theta)=\cfrac{\sqrt{15}}{~~\frac{4-15}{4}~~} \\\\\\ tan(2\theta)=\cfrac{\sqrt{15}}{~~ \frac{-11}{4}~~}\implies tan(2\theta)=-\cfrac{4\sqrt{15}}{11}[/tex]
Hi Everyone! Please Help! I really need help! Please answer as any as you can and he ones I already answered please stop if thy are prefect and if not please at the correct answer. Thanks! I really appreciate all of your peoples help!!!!!!!!
Answer:
12. B
13. B
14. C
15. C
16. D
17. C
18. C
19. C
20. D
21. B
Step-by-step explanation:
12.
16/8 = 2
13.
12 - 4 = 8
12 - 6 = 6
(8 + 6)/2 = 7
15. 2000 x 1000 = 2,000,000
16. 999 + 9999 = 10,998
17.
24/4 = 6
6 x 5 = 30
18.
6 x 3 = 18
19. July 18th
20.
728 cannot divide evenly by 72
21.
1111 x 1111 = 1,234,321
biggest odd number is 3
The Drama Club can spend no more than $120 for costumes. They already spent $79. How much more can they spend for costumes? HELP PLEASE!
An$41 dollars left to spend
Step-by-step explanation:
Need help with #8 its solving logarithm
Answer:
The answer to the logarithm is 2 so inputting this into the equation it would now be 2 ( 4 + 6) - 2(4) = 4 now solving it would be 20 - 8 which is 12/3 which is 4 so the final answer will be 1/4.
Step-by-step explanation:
Determine whether the relation is a function. Explain why or why not.
{(3, 7), (3, 8), (3, –2), (3, 4), (3, 1)}
Answer:
the relation is a function ..this the domains are the 3s and the co-domain are (7, 8, –2, 4,1) so here it's a function it does not matter if the domain are the same but if the co-domain is the same them it's not a function but here they're different
What is 2 + 2. Express answer as a fraction
Answer:
well i search "what is 2 in a fraction" answer is 1/50
It would, i think 1/50 + 1/50 = 0.04
( i used the calculater) ;-;''
hope it helped ':^
I think it's the same answer but take out the zero and decimal point
= 4
I need help fast……………
Step-by-step explanation:
it is the area of the square minus 4 quarter circles (which means 1 full circle) with radius of 10 ft (the half of a side of the square).
we know how to calculate the area of a square "As"
As = side²
we know how to calculate the area of a circle "Ac"
Ac = pi×radius²
so, the shaded area "Ashade"
Ashade = side² - pi×radius² = 20² - pi×10² =
= 400 - pi×100 = 85.84073464... ft²
I don't know, if you need to round the answer in some way.
if it is to e.g. 2 digits after the decimal point (hundredths), then it would be
85.84 ft²
Please help asap!! (75 points)
Answer:
B, C, A
Step-by-step explanation:
These form a straight line.
Answer:
The sheet is backwards for some reason i dont know why 12
Step-by-step explanation:
I would answer it but i cant see it.
Find the equation of a line that passes through the points (-1,3) and (3,-5).
Leave your answer in the form y = mx + c
Answer: y = mx+cG = A100G = A100G = A100
Step-by-step explanation: Solve for c
c=y−mx
{
m=−
x
c−y
,
m∈R,
x
=0
y=c and x=0
Answer:
y= -2x+1
Step-by-step explanation:
The slope of the line is -4/2, which gets simplified to -2. Then, the line passes through y-intercept (0,1), which becomes +1 as the y-intercept in y=mx+b form. Therefore, the equation is y= -2x+1. I'm 100% sure this is right. Hope that helps :)
i bought 15 laptops for 150,000. if the selling price is the cost price divided by 2 and then multiplied 3.what is my selling price and my profit or loss
Answer:
225,000 (selling price) 75,000 (profit)
Step-by-step explanation:
x = (150,000 ÷ 2) x 3
x = 75,000 x 3
x = 225,000
225,000 (sell) - 150,000 (cost)
= 75,000 (profit)
Advertising A bank manager wants to encourage new customers to open accounts with principals of at least $3,000. He decides to make a poster advertising a simple interest rate of 3%. What must the principal be if the bank manager also wants to advertise that one can earn $10 the first month? Can the poster correctly say, "Open an account of $3,000 and earn at least $10 interest in 1 month!"?
Answer: I GOT YOU
Step-by-step explanation: The poster says, "Open an account of $3,500 and earn at least $10 interest in 1 month!" is correct
He decides to make a poster advertising a simple interest rate of 4.8%.
We have to find what must the principal be if the bank manager also wants to advertise that one can earn $10 the first month
So, the statement is correct.
Hence, the amount to be invested is $2500 and the poster says correctly.
Answer: 4,000
Step-by-step explanation: Dont feel like explaining, just trust me.
what are the roots of the equation x^2 +30x =1000?
Answer:
x=20 and x=-50
Step-by-step explanation:
To find the roots, we need to simply solve for x. We do this by first moving all of the terms to the left and setting the right side equal to 0.
-1000
x^2+30x-1000=0
Now, factor it.
What adds up to 30 but multiplies to get -1000?
-10 and 40? No, because they multiply to get -400.
-20 and 50? Yes, because they add up to 30 and multiply to get -1000.
(x-20)(x+50)
x-20=0
x=20
x+50=0
x=-50
So, the roots are x=20 and x=-50
Given :-
x² + 30x = 1000 .To Find :-
The roots of the equation .Solution :-
As we know that if the quadratic equation is in standard form which is ,
[tex] ax^2+bx + c =0[/tex]
Then its roots are given by ,
[tex] x =\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
So on converting the equation in standard form ,
[tex] x^2+30x -1000=0[/tex]
With respect to the standard form ,
a = 1b = 30c = -1000Substitute in the Quadratic formula ,
[tex] x =\dfrac{-30\pm \sqrt{(30)^2-4(1)(-1000)}}{2(1)}[/tex]
Simplify,
[tex] x =\dfrac{-30\pm\sqrt{900+4000}}{2}[/tex]
Add the numbers inside square root ,
[tex] x =\dfrac{-30\pm\sqrt{4900}}{2}[/tex]
Divide each term in numerator by 2,
[tex] x =\dfrac{-30}{2}\pm\dfrac{\sqrt{70^2}}{2}[/tex]
Simplify ,
[tex] x = -15 \pm 35 [/tex]
Separate the two solutions ,
[tex] x = -15 + 35 , -15 -35[/tex]
Simplify ,
[tex]x = 20 , -50 [/tex]
Hence the solution of the equation are 20 and -50 .
I hope this helps.
WILL CHOOSE BRAINLIEST as long as it LOOKS correct
Mai and Tyler work on the equation 2 5 b + 1 = - 11 together. Mai's solution is b = - 25 and Tyler's is b = - 28 . Here is their work:
Mai:
2 5 b + 1 = - 11
2 5 b = - 10
b = - 10 ⋅ 5 2
b = - 25
Tyler:
2 5 b + 1 = - 11
2 b + 1 = - 55
2 b = - 56
b = - 28
Do you agree with their solutions? Explain or show your reasoning.
Answer:
I do not agree with the solutions, b=-30, reasoning below.
Step-by-step explanation:
Mai made an error between the first and second line, she added one to the right when she should have subtracted one:
2/5b+1=-11
2/5b=-12
She then multiplied by 5/2 which was correct, however she multiplied it by -10 when it should have been -12:
b=-12*5/2
b=-30
Tyler made an error between the first and second line when he did not multiply the 1 on the left by 5 also:
2/5b+1=-11
2b+5=-55
He did the next steps correctly, however he had the incorrect value, it should look like this:
2b=-60
b=-30
Which expression is equivalent to
Answer: C is correct answer
Step-by-step explanation:
5. A girl walks north 750 m in 10 minutes. What is her velocity?
Explanation:
Divide the distance (750) over the time (10) to get the speed
750/10 = 75
The velocity is made up of the speed and the direction. Therefore, her velocity is 75 meters per minute north. For each minute, she moves another 75 meters north.
The design is rotated about the line x=1 to produce the shape of the urn. Finish the potter's design by drawing a picture
of what the urn looks like. In your picture, include a properly labeled coordinate plane and the line x= 1.
Upload your drawing below.
Sign out
When the urn is reflected over x = 1, the new urn becomes a mirror of the old diagram.
How to draw the new poster designFrom the question, we understand that the new poster design is to be drawn by reflecting the urn (i.e. the red figure) across the line x = 1
The line x = 1 is a vertical line that passes through the x-axis at x = 1.
To reflect the urn across x = 1, we simply flip the urn over the line.
See attachment for the diagram
Read more about reflection at:
https://brainly.com/question/4289712
When the urn is reflected over x = 1, the new urn becomes a mirror of the old diagram.
The new poster design is to be drawn by reflecting the urn (i.e. the red figure) across the line x = 1
The line x = 1 is a vertical line that passes through the x-axis at x = 1.
To reflect the urn across x = 1, we simply flip the urn over the line.
_______|________
\ | /
\ | /
/ | \
/______|_______\
|
(copy and paste for the people that have to "draw" this out on odyssey ware <3) p.p.s just copy the thing. it won't paste correctly.
Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
Can someone explain this to me please?
Answer:
123
Step-by-step explanation:
Squaring the given equation gives
[tex]t^2+(2\cdot t \cdot \frac{1}{t} )+ \frac{1}{t^2}=9.[/tex]
The [tex]t[/tex] and [tex]\frac{1}{t}[/tex] terms cancel out nicely, which is one of the reasons for squaring the equation.
Simplifying gives
[tex]t^2+2+\frac{1}{t^2}=9,[/tex]
[tex]t^2+\frac{1}{t^2}=7.[/tex]
The question asks for [tex]t^5+\frac{1}{t^5},[/tex] so we can square the equation again and simplify to get higher powers into the expression:
[tex](t^2+\frac{1}{t^2})^2=49,[/tex]
[tex]t^4+(2 \cdot t^2 \cdot \frac{1}{t^2}) + \frac{1}{t^4}=49,[/tex]
[tex]t^4+2+ \frac{1}{t^4}=49,[/tex]
[tex]t^4+\frac{1}{t^4}=47.[/tex]
Multiplying this expression by [tex]t+\frac{1}{t}[/tex] to try and get a fifth power gives
[tex](t^4+\frac{1}{t^4})(t+\frac{1}{t})=t^5+t^3+\frac{1}{t^3}+\frac{1}{t^5}.[/tex]
The only thing left we need is [tex]t^3+\frac{1}{t^3}[/tex] to subtract from this; we know everything else. Since [tex]t^3+\frac{1}{t^3}[/tex] can be written as [tex](t+\frac{1}{t})(t^2-1+\frac{1}{t^2}),[/tex] we can simply plug in the values we know for [tex]t+\frac{1}{t}[/tex] and [tex]t^2+\frac{1}{t^2}:[/tex]
[tex]t^3+\frac{1}{t^3}=(3)(7-1)=18.[/tex]
All that is left is to plug it in our equation here:
[tex](t^4+\frac{1}{t^4})(t+\frac{1}{t})=t^5+t^3+\frac{1}{t^3}+\frac{1}{t^5},[/tex]
[tex](47)(3)=t^5+\frac{1}{t^5}+18,[/tex]
Multiplying and rearranging gives:
[tex]t^5+\frac{1}{t^5}=123.[/tex]
5a - 12 What are the number of terms?
Answer:
2
Step-by-step explanation:
There are 2 terms
Hope this helps!
The Gomez family ordered $39.50 worth of
pizza and subs. They gave the delivery person
a 20% tip. What was the total cost of the food
and tip? Roun to the nearest cent?
Step-by-step explanation:
To find the cost of the tip, we need to find 120% of 39.50.
120% = 100% (order) + 20% (tip)
Let's use fractions. 39.50 can be put over 1, and 120 can be put over 100.
Equation:
[tex]\frac{39.50}{1} \times \frac{120}{100} =?[/tex]
Multiply:
[tex]\frac{39.50}{1} \times \frac{120}{100} =\frac{4740}{100}[/tex]
Divide 4740 and 100 by 100:
[tex]\frac{4740 \div 100}{100 \div 100} = \frac{47.4}{1}[/tex]
The total cost of the food is $47.40.
solve system of equations:
-2x + y = 5
-4x + 3y = 7
answer:
(x,y)=( -4, -3)
Answer:
{x,y}={-4,-3}
Step-by-step explanation:
// Solve equation [1] for the variable y
[1] y = 2x + 5
// Plug this in for variable y in equation [2]
[2] -4x + 3•(2x+5) = 7
[2] 2x = -8
// Solve equation [2] for the variable x
[2] 2x = - 8
[2] x = - 4
// By now we know this much :
x = -4
y = 2x+5
// Use the x value to solve for y
y = 2(-4)+5 = -3
Solution :
{x,y} = {-4,-3}
pls, mark me as brainiest!
10) The ratio of boys to girls in Mrs. Ronilo's math class is 3 to 1. What PERCENT of the class is girls
Answer:
25%
Step-by-step explanation:
ratio is 3B : 1G (this means, out of 4 sections, 3 are boys and 1 are girls)
this means that 3/4 of class is boys and 1/4 are girls
1/4 equals 25%
Suppose f(x) = x2 - 5. Find the graph of
f(4x).
1
2.
Click on the correct answer.
3
4
A
Click on each graph to enlarge it.
graph 1
graph 2
graph 3
graph 4
Answer:
I think its 4 because the y intercept should be at -5 and it looks like oits going t a slope of 2. SO i think 4 is correct
Step-by-step explanation:
help ill give 5 stars
Answer:
[tex]-1\frac{7}{9}[/tex]
Step-by-step explanation:
Rewriting our equation with parts separated
[tex]2+\frac{8}{9} -4+\frac{2}{3}[/tex]
Solving the whole number parts
[tex]2-4=-2[/tex]
Solving the fraction parts
[tex]\frac{8}{9} -\frac{2}{3} =?[/tex]
Find the LCD of 8/9 and 2/3 and rewrite to solve with the equivalent fractions.
LCD = 9
[tex]\frac{8}{9} -\frac{6}{9} =\frac{2}{9}[/tex]
Combining the whole and fraction parts
[tex]-2+\frac{2}{9} =-1\frac{7}{9}[/tex]
Hence, -1 7/9 is the correct Answer.
[RevyBreeze]
The area of a rectangular window is 7614 cm^2.
If the width of the window is 81 cm, what is its length?
Answer:
94cm
Step-by-step explanation:
length= area/width
= 7614/81
= 94cm
Someone please help offering 25 points
Answer:
Assuming those triangles are both right, the answer is 5.3
Find the slope of the line that passes through (-41, 87) and (-42, 41).
Answer:
slope is 46
Step-by-step explanation:
picture
4a to the power of 2 + 18 = 118?
SOLUTION:
=) (4a)² + 18 = 118
=) 16a + 18 = 118
=) 16a = 118 - 18
=) a = 100/16
=) a = 6.25
Answer:
2.5
Step-by-step explanation:
(4a)^2 + 18 = 118
16a^2 = 100
a^2 = 100/16
a^2 = 25/4
a = 5/2 = 2.5
200 people stand in a circle in order 1 to
200. No. 1 has a sword. He kills the next
person (i.e. No. 2) and gives the sword
to the next living person (i.e. No. 3). All
people do the same until only 1
survives, which number survives to the
end?
Answer:
Number 1
Step-by-step explanation:
We know line segment BD is parallel to line segment AE. Which of the following statements must also be true (select two choices)
The statement that must be true about the two similar triangles based on the triangle similarity theorem is: option 2 and option 3.
What is the Triangle Similarity Theorem?The triangle similarity theorem states when a segment intersects the other two sides of a triangle, and the segment is parallel to the third side, then the two triangles formed are similar, and the corresponding sides are proportional to each other.
Given that line segment BD is parallel to line segment AE, therefore, triangles CBD and CAE are similar triangles, their corresponding angles are congruent, while their corresponding sides are proportional.
Therefore, the statement that must be true about the two similar triangles based on the triangle similarity theorem is: option 2 and option 3.
Learn more about triangle similarity theorem on:
https://brainly.com/question/8242716
Wayne Gretzky holds the NHL record for the most points scored in a career. He scored 2857 points in 1487 games.
a) Calculate his average points per game.
b) At this rate, how many more points would he have scored if he had played 79 more games.
Answer:
1999 The most points scored in an NHL career is 2,857, achieved by Wayne Gretzky (Canada) while playing for the Edmonton Oilers (Canada), Los Angeles Kings, St Louis Blues and New York Rangers (all USA) from 1979 to 1999. The points total comprises 894 goals and 1,963 assists in 1,487 games.
Step-by-step explanation:
a) Wayne Gretzky's average points per game is approximately 1.9202.
b) Wayne Gretzky would have scored approximately 151.5438 more points if he had played 79 more games.
a) To calculate Wayne Gretzky's average points per game, we divide the total points scored (2857) by the total number of games played (1487):
Average points per game = Total points scored / Total games played
Average points per game = 2857 / 1487 ≈ 1.9202
Wayne Gretzky's average points per game is approximately 1.9202.
b) To find out how many more points Wayne Gretzky would have scored if he had played 79 more games, we can use the average points per game calculated in part (a).
We know that his average points per game is approximately 1.9202. So, to find the additional points in 79 games, we can multiply the average points per game by the number of additional games:
Additional points = Average points per game * Additional games
Additional points = 1.9202 * 79 ≈ 151.5438
Wayne Gretzky would have scored approximately 151.5438 more points if he had played 79 more games.
To know more about average points:
https://brainly.com/question/16699422
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