Step-by-step explanation:
Recall that
[tex]\cos{2\theta} = 1 -2\sin^2\theta[/tex]
so we can write our original equation as
[tex]3 - 6\sin^2{\theta} + \sin{\theta} = 1[/tex] or
[tex]6\sin^2{\theta} - \sin{\theta} - 2 =0[/tex]
Let [tex]x = \sin{\theta}[/tex] so our equation becomes
[tex]6x^2 - x - 2= 0[/tex]
which gives us two roots: [tex]x = -\frac{1}{2}[/tex] and [tex]x = \frac{2}{3}[/tex].
This is equivalent to [tex]\theta = 150°[/tex] and [tex]\theta = 41.8°[/tex]
what number is represented by 6 hundreds 14 tens and 12 ones?
Answer:
6 * 100 = 600
14 * 10 = 140
12 * 1 = 12
------------------------
752
you are solving an equation with a variable on each side. does the side on which you choose to isolate the variable affect the solution? why might you choose one side over the other?
Answer:
Does the side on which you choose to isolate the variable affect the solution?
No, because at the end you get an equation with a variable on one side only.Why might you choose one side over the other?
To simplify or minimize the number of operations you need. Moving part of the terms from one side to another adds at least one extra operation and it may also bring some complications.Is 1 3/4 closer to 1 or 2 ? Explain your answer
Answer:
it's closer to 2
Step-by-step explanation:
In order to get to 1 from that number, you have to subtract 3/4. In order to get to 2 from that number, you only have to add 1/4. Clearly, the jump in adding is smaller than the jump to subtracting, which means it's closer to 2.
The number is closer to 2
What is fraction?A fraction shows part of a whole. This whole can be a region or a collection. The word fraction is derived from the Latin word "fractio" which means 'to break'. The Egyptians, being the earliest civilization to study fractions, used fractions to resolve their mathematical problems, which included the division of food, supplies, and the absence of a bullion currency.
All fractions consist of a numerator and a denominator and they are separated by a horizontal bar known as the fractional bar.
The denominator indicates the number of parts in which the whole has been divided into. It is placed in the lower part of the fraction below the fractional bar.The numerator indicates how many sections of the fraction are represented or selected. It is placed in the upper part of the fraction above the fractional bar.Given number:
1 3/4 = 7/4
On dividing
7/4 = 1.75
Hence, the number is closer to 2.
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What is an equation of the line that passes through the point (-1, 4) and is perpendicular to the line x-6у = 12?
Answer:
y=-6x-2
Step-by-step explanation:
x-6y=12
y=x/6-2
y=mx+c
since theyre perpendicular, 1/6 * m = - 1
m = -6
y=-6x+c
sub x=-1,y=4
4=-6(-1)+c
c = -2
y=-6x-2
y+5=3/2(x-7) write in y=mx+b form
Answer:
[tex]y=\displaystyle \frac{3}{2}x-\frac{31}{2}[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
Notice how y is isolated in slope-intercept form.
[tex]y+5=\displaystyle \frac{3}{2} (x-7)[/tex]
To change this into slope-intercept form, isolate y.
Use the distributive property on the parentheses:
[tex]y+5=\displaystyle \frac{3}{2}x-\frac{21}{2}[/tex]
Subtract 5 from both sides:
[tex]y=\displaystyle \frac{3}{2}x-\frac{21}{2}-5\\\\y=\displaystyle \frac{3}{2}x-\frac{31}{2}[/tex]
I hope this helps!
Solve for K
20-6 + 4K =2-2k
Answer:
K = -2Step-by-step explanation:
20-6 + 4K =2-2k
=> 14 + 4k = 2 - 2k
=> 4k + 2k = 2 - 14
=> 6k = -12
[tex] = > k = \frac{ - 12}{6} [/tex]
=> K = -2 (Ans)
Arrange the decimal numbers from largest to smallest.
Answer:
0.845, 0.839, 0.748, 0.712, 0.643
Answer:
0.845, 0.839,0.748,0.712,0.643
Multply 7/8 to 2-1/3
Answer:
17/12
Step-by-step explanation:
7/8 x 2-1/3
7/4-1/3
17/12
I am a prime number. I am two digits.
The sum of my digits is 8.
My tens digit is 6 less than my ones digit.
Answer:
17
Step-by-step explanation:
17 is a prime number17 has two digitsThe digits in 17, 1 and 7, add up to 8The tens digit is 6 less than the ones digit place.Answer: 17
Step-by-step explanation:
1+7=8
The ten digit is (1) 6 less than the one digit (7)
Find (fog)(x) when f (x) =
=-2 and 3(A)= = (I point)
2x
O Gog)(x) =
1+ 6x
1
O Gog)(x) =
2+3x
O Gog(x) =
x+3
4
1
Otog)(x)=
x+3
Finish
Cance
Answer:
A
Step-by-step explanation:
fog(x) = f(g(x) = f(1/2x) = 4x/(1+6x)
a right triangle has a hypotenuse of length 2 inches. if one angle is 38°, find the length of each leg
Answer:
21
Step-by-step explanation:
Simplify the following expression and show your work in details please .
Answer:
9-2b
Step-by-step explanation:
Set up equation:
[tex]9 - 8b + 6b[/tex]
Add like terms
[tex]9 - 2b[/tex]
Can someone help me with this please?
PLEASE HELP
write and solve an equation to find the value of X. please explain in details and show your work!
Answer:45 degrees
Step-by-step explanation:
5x+8=3(x+2) anyone know the answer?
Step-by-step explanation
work out the question in bracket first then separate numericals and variables to make it easier.
Answer:
distribute
5 + 8 = 3 ( + 2 )
expand to
5 + 8 = 3 + 6
subtract 8 from both sides
5 + 8 = 3 + 6
5 + 8 − 8 = 3 + 6 − 8
simplify
5 = 3 − 2
subtract 3 from both sides
5 − 3 = 3 − 2 − 3
simplify
2 = − 2
then divide both sides by 2
2 / 2 = − 2/ 2
= − 2/ 2
answer is
= −1
Step-by-step explanation:
Hope that helps>3
A reviewer decides to interview patrons to see how they would rate a particular restaurant. The following table lists the responses from
twenty-five patrons. What is the level of measurement for the data? Are the data qualitative or quantitative?
Restaurant Ratings
One Star Two Stars Three Stars
Five Stars
Four Stars
Three Stars
Four Stars
Four Stars
Five Stars
Three Stars
Five Stars
Four Stars
Five Stars
Four Stars Three Stars
Three Stars Five Stars
One Star
One Star
Two Stars
Five Stars
Two Stars
Four Stars
One Star
Five Stars
The level of measurement of the data is ORDINAL and the data is QUALITATIVE.
An Ordinal level of measurement is one whereby measurement follows a natural order, however, the difference or distance between each category cannot be measured. Ordinal data level are applicable to categorical variables.
In the scenario given,
The different categories available are :
One star, two stars, three stars, four stars and five stars.
The categories are ordered with the number of stars depicting better quality however, the difference between the quality offered isn't measurable.
Qualitative data groups variables into different categories and are used for non - numeric variables.
Quantitative data on the other hand are used for numeric data.
Hence, the level of measurement is Ordinal and the data is QUALITATIVE
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Answer:one star
Step-by-step explanation:
A student rotated figure A 270° clockwise about the origin to create figure D. Evaluate whether the student performed the rotation correctly.
Step-by-step explanation:
The student incorrectly performed a rotation of 90° clockwise.
Answer:
C, the student incorrectly preformed a rotation of 90 degrees clockwise.
Step-by-step explanation:
The product of 4x and 0 is:
a- 4x
b- 4
c- 0
d- none of these
2. STEM A circuit board manufacturer rejects a 100-ohm resistor if its measured resistance is 0.15 ohm more than or less than 100 ohms. Resistors A and B are rejected. Resistor A's resistance differs from 100 ohms by 0.15 ohm. Resistor B's resistance differs from 100 ohms by -0.78 ohm. How do the resistances of these two resistors compare? Explain.
The comparison of both resistors is defined by an inequality. Resistor A has a higher resistance than resistor B because [tex]100.15\Omega > 99.22\Omega[/tex]
Given that:
[tex]R = 100 \Omega[/tex] ---- the reference resistor
First, we calculate the resistance of both resistors
Resistor A differs by [tex]0.15\Omega[/tex] means that:
[tex]R_A = 100\Omega + 0.15\Omega[/tex]
[tex]R_A = 100.15\Omega[/tex]
Resistor A has a resistance of [tex]100.15\Omega[/tex]
Resistor B differs by [tex]-0.78\Omega[/tex] means that:
[tex]R_B = 100\Omega -0.78\Omega[/tex]
[tex]R_B = 99.22\Omega[/tex]
Resistor B has a resistance of [tex]99.22\Omega[/tex]
By comparing the calculated values, we can conclude that:
Resistor A has a higher resistance than resistor B because [tex]100.15\Omega > 99.22\Omega[/tex]
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If you invested $7000 for 10 years at an annual interest rate of 3% how much is the accrued interest?
please help me this is for tomorrow and i have to sleep
Answer:
The answer is C
Step-by-step explanation:
The line graph shows the line going right so it greater than or >. The circle is not colored in so there is no line under the greater than sign > so answer is C
How do i solve this?
Answer:
1.-4
2.7
3.-11
4.18
5.13
Step-by-step explanation:
0-4=-4
-2+9=7
-2-9=-11
5+13=18
-10+23=13
I need help explaining, this homeschool work so hard!!
Answer:
61
Step-by-step explanation:
(7 + 5) + 4 * 13 - 2
~Simplify using PEMDAS
12 + 4 * 13 - 2
12 + 52 - 3
64 - 3
61
Best of Luck~
Please help due tomorrow
Answer:
just observe its like corresponding soo..
CAB = DEF
ABC = EFD
ACB = EDF
EMJOY ;)
Formula to find perimeter of rectangle
Hey there!
The formula to find the perimeter of a rectangle is "P=2(l+w)".
Hope this helps!
Have a great day! :)
Answer:
formula to find the perimeter of rectangle is
2(l+b)hope it helps
stay safe healthy and happy.
5 thousand is ———————- times as many as 5 hundred
Answer:
Ten
Step-by-step explanation:
5000/500 = 10
Answer: 10 times as many 5 hundreds
Step-by-step explanation: five times five hundreds equals 5,000
power set of MIRACLE
Answer:
The Kathryn Kuhlman Miracle Box Set is a captivating collection of 3 truly heart-warming essentials that will rejuvenate your faith; giving you a sense of hope that you may have never felt before. The three wonderful books are titled I Believe in Miracles, Nothing Is Impossible with God and God Can Do It Again. This collection of books allows you to experience the magnificent power of Kathryn's miracle services. Through the power of God Kathryn helped to heal people all over the world in what seemed hopeless situations, inspiring readers to believe that you too can be healed by the almighty power of God.
What are the opposite rays
Answer:
ab and ed are opposite rays
Step-by-step explanation:
PLEASE MARK AS BRAINLIRST
Answer:
A pair of opposite rays are two rays that have the 'same endpoint and extend in opposite directions. So, together a pair of opposite rays always forms a straight line
given that 3x+2=4 and 2y+6=5 what is x+y?
Really need help on this one!
The value of x+y using given equations is 3x+2y=1.
The given equation are 3x+2=4 and 2y+6=5.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
To find x+y:
3x+2+2y+6=4+5
⇒ 3x+2y+8=9
⇒ 3x+2y=1
Hence, the value of x+y using given equations is 3x+2y=1.
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Use the Perfect Square Trinomial and provide the first step to calculating 32^2 without a calculator.
(30 − 2)2
(30 + 2)2
(28 − 4)2
(28 + 4)2
Answer:
64
Step-by-step explanation:
(30+2)2
30*2+2*2
60+4
64
Answer:
B. (30+2)^2
Step-by-step explanation:
(30+2)^2=30^2+2(30)(2)+2^2=900+120+4=1024
32^2=1024. The way to solve without calculator is above.
Hope this helps!
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