Mathematics High School
Answers
Answer 1
Answer:
[tex]\csc(\theta)=\sqrt{2}[/tex]
Step-by-step explanation:
Please refer to the attachment below.
We have:
[tex]5\cos^2(\theta)+6\sin^2(\theta)=11/2[/tex]
Remember that cosine is the ratio of the adjacent side to the hypotenuse. Therefore:
[tex]\cos(\theta)=\frac{b}{c}[/tex]
And sine is the ratio of the opposite side to the hypotenuse. Therefore:
[tex]\sin(\theta)=\frac{a}{c}[/tex]
Substitute into our original equation:
[tex]5(\frac{b}{c})^2+6(\frac{a}{c})^2=11/2[/tex]
Square:
[tex]\frac{5b^2}{c^2}+\frac{6a^2}{c^2}=\frac{11}{2}[/tex]
Multiply both sides by c squared:
[tex]5b^2+6a^2=\frac{11}{2}c^2[/tex]
Let’s also multiply both sides by 2 to eliminate the fraction:
[tex]10b^2+12a^2=11c^2[/tex]
Remember that according to the Pythagorean Theorem:
[tex]c^2=a^2+b^2[/tex]
Hence, we can make another substitution:
[tex]10b^2+12a^2=11(a^2+b^2)[/tex]
Distribute:
[tex]10b^2+12a^2=11a^2+11b^2[/tex]
Subtract 10b² from both sides:
[tex]12a^2=11a^2+b^2[/tex]
Subtract 11a² from both sides:
[tex]a^2=b^2[/tex]
Take the square root of both sides:
[tex]a=b[/tex]
Hence, a is equivalent to b.
Then, we must have a 45-45-90 Triangle.
Therefore, our angle θ is 45°.
We can substitute this back into our original equation to make sure. Remember that cos(45)=sin(45)=√2/2:
[tex]\begin{aligned} 5\cos^2(45)+6\sin^2(45)&=11/2 \\ 5(\frac{\sqrt{2}}{2}})^2+6(\frac{\sqrt{2}}{2})^2&=11/2 \\ 5(2/4)+6(2/4)&=11/2 \\ 5(1/2)+6(1/2)&=11/2 \\ 5/2+6/2&=11/2 \\ 11/2&=11/2 \;\checkmark \end{aligned} \\[/tex]
Hence:
[tex]\begin{aligned} \sin(45)&=\frac{1}{\sqrt{2}} \\ \Rightarrow \csc(\theta)&=\sqrt{2} \end{aligned}[/tex]
Related Questions
Which expression is equivalent to 4k+2k?
Answers
Answer:
it equals 6k but an equivalent expression could be 2k + 4k
Step-by-step explanation:
2k + 4k = 4k + 2k
Answer:
6k
Step-by-step explanation:
You can combine both of these terms because they both have the same variable (k). We know that 4+2=6, and the variable stays the same, 6k.
~theLocoCoco
Rewrite the equation in slope intercept form. 4x + 5y = 8
Answers
y = -4/5x + 8/5 (slope intercept form is y = mx + b)
Answer:
y=-4/5+8/5, or y= -.8+1.6
Step-by-step explanation:
Slope intercept form-
y=mx+b
y=-4/5+8/5
Does anybody like/play Slime Rancher
Answers
Answer:
yes but y do u ask?
Step-by-step explanation:
PLEASE HELP!!! ILL GIVE BRAINLIEST RIGHT ANSWERS ONLY
Answers
Answer:14
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
(x2-x1) = (6 - -4)
= 10
(y2-y1) = (2 - -2)
= 4
We square the numbers and add
10^2
= 100
4^2
= 16
100 + 16 = 116
Now we square root 116
[tex]\sqrt{116}[/tex]
= 2[tex]\sqrt{29}[/tex]
is the square route of 25 a integer
Answers
Answer:
Yes.
Step-by-step explanation:
The square root of 25 is an integer. 25 is a perfect square meaning Tyou can multiply an integer by itself and obtain 25. Hope this helps.
Answer:
Yes its 5
Step-by-step explanation:
ILL MARK BRAINLIEST PLS HELP
Select all of the descriptions
which describe a transformation of the graph of f(x)=x that could result in
the graph of g(x)=4x.
A
The graph is rotated about (0,0), becoming steeper.
B
The graph is vertically stretched.
The graph is translated 4 units up.
D
The graph is translated 4 units to the right.
E
The graph is vertically shrunk.
F
The graph is reflected across the x-axis.
Answers
Answer: A)
Step-by-step explanation:
4(3xy^4)^3/(2x^3y^5)^4
Answers
Answer:
[tex]\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=\frac{27}{4x^9y^8}[/tex]
Step-by-step explanation:
Given the expression
[tex]\:\:\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}[/tex]
solving the expression
[tex]\:\:\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=4\cdot \:\frac{\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}[/tex]
[tex]=4\:\frac{27x^3y^{12}}{16x^{12}y^{20}}[/tex]
[tex]=4\cdot \frac{3^3}{2^4x^9y^8}[/tex]
The multiply fractions are defined as
[tex]\:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
so the expression becomes
[tex]=\frac{3^3\cdot \:4}{2^4x^9y^8}[/tex]
[tex]=\frac{3^3\cdot \:2^2}{2^4x^9y^8}[/tex]
[tex]=\frac{3^3}{2^2x^9y^8}[/tex]
Refining
[tex]=\frac{27}{4x^9y^8}[/tex]
Therefore,
[tex]\frac{4\left(3xy^4\right)^3}{\left(2x^3y^5\right)^4}=\frac{27}{4x^9y^8}[/tex]
please please answer .
Answers
Answer:
1025
Step-by-step explanation:
At noon, the minute and hour hands overlap. In how many hours will they overlap again?
Answers
24 hours
Because 24 hours equals 1 day or one rotation of the clock
Answer:
1 hour 5 9/20 minutes
Step-by-step explanation:
what is 688*18471 answer?
Answers
Answer:
12,708,048
Step-by-step explanation:
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Answers
6.55
Have a great day!
Y =72/11 or in decimal form it is 6.54 repeating:)
Write the following numbers in order from smallest to largest.
0.02, 0.05, 0.025, 0.052, 0.005, 0.002
Enter the numbers separated by commas ( , ).
Answers
Answer:
0.002,0.005,0.02,0.025,0.05,0.052
Plz help me !!! I will cash app you !!! Plz help meeee ❤️
Answers
Answer:
9. A 10. D
Step-by-step explanation:
9. 99.60 divided by 8
$12.45/book
10. 288/80
3.6
3.6 times 10 cookies
36 grams
Answer:
1. (A) 12.45 2. (D) 36
Step-by-step explanation:
The value of a boat if depreciating at at a rate of 9% per year. In 2006 the boat was worth $17,800. Find the worth of the boat in 2013.
Answers
Answer:
The worth of boat in 2013 will be $9202.6
Step-by-step explanation:
Rate of depreciation = 9% = 0.09
Cost of Boat in 2006 =$ 17,800
Cost of Boat in 2013 = ?
Years = 2013-2006= 7 years
The formula used is: [tex]\mathbf{A=P(1+r)^{t}}[/tex]
Since the value of boat is depreciating the value of r will be r=-0.09
Here P = 17,800 , r=-0.09 and t = 7 years Finding A
[tex]A=P(1+r)^{t}\\A=17,800(1+(-0.09))^7\\A=17,800(0.91)^7\\A=17,800(0.517)\\A=9202.6[/tex]
So, the worth of boat in 2013 will be $9202.6
Mark bought an electronic tablet on sale for 1 fourth off the original price of $825.00. He also wanted to use a coupon for 1 fifth off the sales price. How much did Mark pay for the tablet?
Answers
Mark paid for $1 for the tablet
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
The triangle shown is a right triangle. Create the equation to be used to find the missing lengths. Format your answer in
the sequence: hypotenuse, unknown leg, known leg.
9
5
9
234567810/
72 xy a b
Answers
The length of the missing side of the triangle is 7.5 from the image attached.
What is the Pythagoras theorem?
A fundamental concept in geometry that has to do with right triangles is the Pythagorean theorem. After the Greek mathematician Pythagoras, it establishes a link between the lengths of the sides of a right triangle.
According to the theorem, the square of the hypotenuse's length (the side that faces the right angle) in a right triangle equals the sum of the squares of the lengths of the other two sides.
We know that;
[tex]x^2 = 9^5 - 5^2[/tex]
x = 7.5
Learn more about Pythagoras theorem:https://brainly.com/question/31658142
#SPJ1
if f(x) = 3x-1 and g(x)= x+2 find (f-g)(x)
Answers
Answer:
2x-3
Step-by-step explanation:
f(x) = 3x-1
g(x) = x+2
Find (f-g)(x), this means we need to subtract g from x.
(3x-1) - (x+2)
Subtract the like terms:
3x -x = 2x
-1 -2 = -3
Combine them to get 2x-3
I don’t know how to write this the way it’s supposed to be written but I hope U understand it Y^5/y^2
Answers
Answer:
is 14 sorry if i am wrong
Step-by-step explanation:
Pacos tacos sells three tacos for $1.32 Taco Bell sell five tacos for $4.20 which is a better deal
Answers
Answer:
$0.44
Step-by-step explanation:
We find the unit rate for each taco
$1.32/3 for Pacos tacos
$4.20/5 for Taco Bell
We will then get
$0.44 per taco for Pacos tacos
$0.84 per taco for Taco Bell
$0.44 < $0.84
Pacos tacos is the better deal
Answer:
Pacos tacos
Step-by-step explanation:
Evaluate the expression "12 - (-36) / -6"
Answers
Answer:
ah bbhgggvgujjbgg
hhhjj
One factor of this polynomial is (2x − 1).
2x^3 + 5x^2 - 27x +12
Use long division to determine which expression represents the other factor.
answer choices:
x2 − 3x + 12
x2 + 3x − 12
x2 − 12x + 3
x2 + 12x − 3
Answers
See attachment for answer:
Answer:
B: x^2+3x-12
Step-by-step explanation:
Can 7, 8 and 11 be the sides of a right
triangle? Justify your answer
Answers
It would make an obtuse scalene triangle. The area would be 27.928 and the perimeter would be 26.
Find the new price for the markdown given. Round to the nearest cent if necessary.
$14.99 marked down 20%
Answers
20% of 14.99 = 2.998 so you subtract 14.99- 2.998 which equals 11.992 which rounds to just 11.99
Answer:
$11.99
Step-by-step explanation:
Select all of the ratios that are equivalent to 6:3 *
2:1
12:6
3:6
30:15
6:6
12:9
Answers
Answer:
2 : 1
12 : 6
30 : 15
Step-by-step explanation:
Look at the ratios one by one. Starting with 6 : 3, we can see that it's of the form 2a : a.
2 : 1
12 : 6
30 : 15
These are all equivalent.
Help pwease :( will give brainliest.
Answers
Answer:
a. $7
b. $x
c. $20
d.$5y
e.$x + $5y
Divide the polynomials. Your answer should be in the form p(x)+\dfrac{k}{x+2}p(x)+ x+2 k p, left parenthesis, x, right parenthesis, plus, start fraction, k, divided by, x, plus, 2, end fraction where ppp is a polynomial and kkk is an integer. \dfrac{x^2+7x+12}{x+2}= x+2 x 2 +7x+12 =start fraction, x, squared, plus, 7, x, plus, 12, divided by, x, plus, 2, end fraction, equals
Answers
Answer:
[tex](x+5)+ \dfrac{2}{x+2}[/tex]
Step-by-step explanation:
Given
[tex]\dfrac{x^2+7x+12}{x+2}[/tex]
Required
Simplify and present your answer in
[tex]p(x)+\dfrac{k}{x+2}[/tex]
First, we need to expand and factorize the numerator:
[tex]\dfrac{x^2+7x+12}{x+2}[/tex]
Express 12 as 10 + 2
[tex]\dfrac{x^2+7x+10+2}{x+2}[/tex]
Split into two using brackets
[tex]\dfrac{(x^2+7x+10)+2}{x+2}[/tex]
Split to two fractions:
[tex]\dfrac{(x^2+7x+10)}{x+2}+\dfrac{2}{x+2}[/tex]
Factorize the numerator of the first fraction
[tex]\dfrac{(x^2+5x+2x+10)}{x+2}+\dfrac{2}{x+2}[/tex]
[tex]\dfrac{x(x+5)+2(x+5)}{x+2}+\dfrac{2}{x+2}[/tex]
[tex]\dfrac{(x+2)(x+5)}{x+2}+\dfrac{2}{x+2}[/tex]
The first fraction can be simplified to give:
[tex](x+5)+ \dfrac{2}{x+2}[/tex]
Hence, by comparison:
We have simplified the given expression to the required format of:
[tex]p(x)+\dfrac{k}{x+2}[/tex]
Which implies that:
[tex]p(x) = x + 5[/tex] and [tex]k = 2[/tex]
Answer:
Step-by-step explanation:
hope this helps
help me match these pleasee and explain!
Answers
3x=9 is C
4x+12 is A
X+1 is B
The Sarsen Circle at Stonehenge has a circumference of 304.7 feet. What is the radius in feet of the Sarsen Circle?
Answers
Answer: r≈48.49ft
Step-by-step explanation:
hoped that help if so plz mark me brainlest =)
who is correct science or religious
Answers
Answer:
it depends on what you believe, butttt i would say science
Answer: Science.
Step-by-step explanation: In my opinion science makes more sense than religion because it has proof, but I do not have anything against religious people.
answers please needed for school obviously
Answers
Answer:
y=6x+30
Step-by-step explanation:
y is the total temperature
6x is the increase of temperature by 6° per x hours
30 is the y-intercept, you start with this number
9514 1404 393
Answer:
y = 30 + 6xsee below for a graph
Step-by-step explanation:
The increase in temperature is the product of the increase per hour and the number of hours: 6x.
The temperature at any time is the sum of the initial temperature (30°) and the increase (6x).
y = 30 + 6x . . . . . temperature equation
__
This is graphed as a line with an initial value of 30 and a slope of 6. (Note the attached graph has different grid line spacing vertically than horizontally.)
