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]
Help thank you ………….
Answer:
The answer is option 1
Step-by-step explanation:
For the linear inequality on the top line of the system, it's saying that the y-value must be greater than or equal to 1. This is verified by the graph because all y-values that fit the criteria of the linear inequality are shaded. The graph is also showing for the dotted line that the area is shading all points where, if you subtract an x-value from a y-value, the difference will always be greater than 0. Note that this does not apply for points ON the line, as it cannot be equal to 0. This matches with the linear inequality on the bottom line of option 1.
Ella buys eggs and apples at the store.
She pays a total of $44.35.
• She pays a total of $2.95 for the eggs.
• She buys 6 bags of apples that each cost the same amount.
Write and solve an equation which can be used to determine x, how much each bag
of apples costs.
Equation:
Answer: X =
Submit Answer
Subtract. Write your answer in simplest form.
5/- 10/5
Answer:
-1/10
Step-by-step explanation:
(5/(-10))/5 = -(5/10)/5 = 1/10
(Hopefully this helped you out!)
what are the coefficients of the equation y=x^2+5x+6
Answer:
1, 5
Step-by-step explanation:
a numerical or constant quantity placed before and the variable in an algebraic expression (e.g. 4 in 4x y).
Answer: 1 and 5
Step-by-step explanation:
what is 15 times 7/5 compared to 15 equal?
Answer:
I do not know
Step-by-step explanation:
A recipe calls for 3 cups of pecans for every 5 cups of walnuts. How many cups of pecans should be added to 8 cups of walnuts?
Answer:
4.8
Step-by-step explanation:
3:5
3/5 : 1
8(3/5):1(8)
4.8:8
John's bank account was overdrawn. The status of his account was -$112. He did not realize the problem and wrote another check for $22. The bank charged him a $21 fee for being overdrawn.
What was the new status of John's account at this point?
Answer:
-155
Step-by-step explanation:add them all up together
The new status of John's account at this point is -$155
Using this formula
New status=(-Account status-Cheque amount)-Bank charges
Let plug in the formula
New status= (-$112-$22)-$21-
New status=-$134-$21
New status=-$155
Inconclusion The new status of John's account at this point is -$155
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Helpp
Ok I don’t know how they got 3y-24
Answer:
y = -5/3x + 3
Step-by-step explanation:
First lets turn the equation from standard form to slope intercept form.
3x - 5y = 1
~Subtract 3x to both sides
-5y = 1 - 3x
~Divide -5 to everything
y = -1/5 + 3/5x
~Reorder
y = 3/5x - 1/5
Now that we have the equation in slope intercept form, we can find the new equation. A perpendicular line will have the opposite reciprocal of the original slope.
3/5x -> -5/3x
Now that we have the slope, we can use the given point to find the y-intercept.
y = -5/3x + b
8 = -5/3(-3) + b
8 = 5 + b
3 = b
Put all the information we solved for into a final equation.
y = -5/3x + 3
Best of Luck!
In Evan's math class, there are 7 boys and 10 girls. Which of the following is the ratio of boys to girls in Evan's math class?
Answer:
7/17
Step-by-step explanation:
prove that 1³+2³+....n³=n²(n+1)²/4. principle of mathematics induction
[tex]\sf 1^3+2^3\dots n^3=\dfrac{n^2(n+1)^2}{2}[/tex]
[tex]\\ \sf\longmapsto 1^3+2^3+\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2[/tex]
Solution:-Let
[tex]\\ \sf\longmapsto P(n)=1^3+2^3\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2[/tex]
For n=1
[tex]\\ \sf\longmapsto P(1)=\left(\dfrac{1(1+1)}{2}\right)^2[/tex]
[tex]\\ \sf\longmapsto P(1)=\left(\dfrac{1(2)}{2}\right)^2[/tex]
[tex]\\ \sf\longmapsto P(1)=\left(\dfrac{2}{2}\right)^2[/tex]
[tex]\\ \sf\longmapsto P(1)=(1)^2[/tex]
[tex]\\ \bf\longmapsto P(1)=1=1^3[/tex]
Let k be any positive integer.
[tex]\\ \sf\longmapsto P(k)= 1^3+2^3\dots k^3=\left(\dfrac{k(k+1)}{2}\right)^2[/tex]
We have to prove that p(k+1) is true.
consider
[tex]\sf 1^3+2^3\dots k^3+(k+1)^3[/tex]
[tex]\\ \sf\longmapsto \left(\dfrac{k(k+1)}{2}\right)^2+(k+1)^3[/tex]
[tex]\\ \sf\longmapsto \dfrac{k^2(k+1)^2}{4}+(k+1)^3[/tex]
[tex]\\ \sf\longmapsto \dfrac{k^2(k+1)^2+4(k+1)^3}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{k+1)^2\left\{k^2+4k+4\right\}}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{(k+1)^2(k+2)^2}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{(k+1)^2(k+1+1)^2}{4}[/tex]
[tex]\\ \sf\longmapsto \left(\dfrac{(k+1)(k+1+1)}{2}\right)^2[/tex]
[tex]\\ \sf\longmapsto (1^3+2^3+3^3\dots k^3)+(k+1)^3[/tex]
Thus P(k+1) is true whenever P(k) is true.
Hence by the Principal of mathematical induction statement P(n) is true for [tex]\bf n\epsilon N.[/tex]
Note:-
We can solve without simplifying the Question .I did it for clear steps and understanding .
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Answer:
Step-by-step explanation:
[tex]1^3=1=\dfrac{1^2*(1+1)^2}{4} =\dfrac{4}{4} =1\\\\\\\displaystyle \sum_{i=1}^{n+1}\ i^3=(\sum_{i=1}^{n}\ i^3) + (n+1)^3\\\\\\=\dfrac{n^2*(n+1)^2}{4} +(n+1)^3\\\\\\=(n+1)^2*(\frac{n^2}{4} +n+1)\\\\\\=(n+1)^2*\dfrac{n^2+4n+4}{4} \\\\\\=\dfrac{(n+1)^2*(n+2)^2}{4}[/tex]
Amanda was given three numbers: 8,
5, and 1. She needs to use two of
these numbers to make a fraction.
Can she make a fraction that is
greater than four-fifths?
Answer:
Yeah, She can.
Step-by-step explanation:
Simply using 8/5
(65x - 12) angle a
(43x+10) angle b
it’s a vertical angle I just don’t understand.
Answer:
x = 1
Step-by-step explanation:
Vertical angles are opposite angles formed by two lines.
Both the angles are equivalent
65x - 12 = 43x + 10
Subtract 43x from both sides
22x - 12 = 10
add 12 from both sides
22x = 22
Divide each side by 22
x = 22/22
x = 1
If my answer is incorrect, pls correct me!
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-Chetan K
<3 help mi i’m down bad
Sol Levin sold 22 pairs of shoes each day.
Monday through Wednesday, 28 pairs on Thursday,
and 31 on Friday. How many shoes must he sell on
Saturday to average 29 pairs sold for the 6 days
he worked during the week?
Answer:
Sol Levin needs to sell 49 pairs shoes on Saturday.
Step-by-step explanation:
29 x 6 = 174
(22 x 3) + 28 + 31 + x = 174
66 + 28 + 31 + x = 174
94 + 31 + x = 174
125 + x = 174
(125 - 125) + x = (174 - 125)
x = 49
-15 + 8x = x + 3
STEP BY STEP
[tex] - 15 + 8x = x + 3 \\ 8x - x = 3 + 15 \\ 7x = 18 \\ \\ x = \frac{18}{7} \\ \\ x = 2.571[/tex]
We put the unknown on one side, and the other end is empty of the unknown , When it turns to the other side, its sign changes.
As for the number with the unknown, it becomes the denominator with the number without the unknown.
I hope I helped you^_^
Let x = 0.99999....Do you think that x < 1 or x = 1?
Answer:
x<1
Step-by-step explanation:
why? because is still 0....
In a football game, what is the probability that one team will tie and lose?
Answer:
1/3
Step-by-step explanation:
The set of even natural numbers greater than or equal to 6
Answer:
{6, 8, 10, 12, 14, 16, 18, 20, ...}
Step-by-step explanation:
even natural numbers >/= 6.
Thus this has no upper limit and the set is thus infinite.
The set of even natural numbers greater than or equal to 6 is
What are the natural numbers?" The natural numbers are those numbers used for counting and ordering. Numbers used for counting are called cardinal numbers."
We know the natural numbers are:
{1, 2, 3, 4, 5, 6, 7,..........}
Now, the set of even natural numbers are:
{2, 4, 6, 8, 10...........}
Therefore, the set of even natural numbers greater than or equal to 6 is
{6, 8, 10, 12,..............}
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Please help it’s due tomorrow!!
Answer:
-5/3
Step-by-step explanation:
Answer:
13 + 7/9-5-16
answer : -5/3
use BODMAS to solve this question
Triangle ABC is similar to triangle DEF with a ratio of 3/5 If the difference of their
perimeters is 40 inches, find the perimeter of each triangle.
9514 1404 393
Answer:
ΔABC -- 60 inchesΔDEF -- 100 inchesStep-by-step explanation:
If P is the perimeter of the larger triangle, then 3/5P will be the perimeter of the smaller one. The difference in perimeters is ...
P -3/5P = 40 in
2/5P = 40 in
P = (5/2)(40 in) = 100 in
3/5P = 3/5(100 in) = 60 in
The smaller triangle perimeter is 60 in; the larger is 100 in.
In the coordinate plane, plot AB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯ given by the points A(−4, 5), B(−4, 8), C(2, −3), D(2, 0)
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The x-coordinate is the same in each pair of points, so the line segment will be a vertical line segment 3 units long.
Greyson will get a discount on his health insurance if he participates in their weekly step-challenge program and logs 50,000 steps a week. If his monitor calculates each step to be 2 feet, how many miles is he supposed to walk each week?
Greyson will need to walk "18.94 miles" each week. A complete solution is provided below.
According to the question,
One step's length,
= 2 feet
Total number of steps,
= 50,000
then,
→ The total distance travelled will be:
= [tex]50000\times 2[/tex]
= [tex]100000 \ feet[/tex]
We can say that the relation between feet and miles will be 5280 ft,
= 1 mile
hence,
→ [tex]100000 \ feet = \frac{100000}{5280}[/tex]
[tex]=18.94 \ miles[/tex]
Thus the above is the correct answer.
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F(x) = (x-2)(x + 1)
X+1
Which statements describe the end behavior of the graph of the function shown? Check all that apply.
As x,
y1.
As x,y".
As x,y -—-.
As x,y 1.
As x,y.
As x + y -0.
Answer:
the second and the last one
Step-by-step explanation:
answer was revealed on edg after i took quiz
The option (2) As x → ∞, y → ∞, and option (6) As x → –∞, y → –∞ are correct if the function f(x) = (x - 2)(x + 2)/(x + 1).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function shown in the picture.
f(x) = (x - 2)(x + 2)/(x + 1)
The above function is a fractional function:
The denominator of the function cannot be zero:
x + 1 ≠ 0
x ≠ -1
From the graph of a function:
If x → ∞, y → ∞
If x → –∞, y → –∞
Thus, the option (2) As x → ∞, y → ∞, and option (6) As x → –∞, y → –∞ are correct if the function f(x) = (x - 2)(x + 2)/(x + 1).
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What is the differentiation of 2cos2x
2cos2x=y
dy/dx(2cos2x)=-4sin2x
d/du cosu= u'×cos'u=-u'×sinu
d/du sinu= u'×sin'u= u'×cosu
d/du tanu = u'×(1+tan²u)
d/du cotu = u'×-(1+cot²u)
proof for cosu :
cos2x= 1-2sin²x
or 2cosx²-1
or cos²x-sin²x
we will one of this fro example let's take the first one
d/dx 1-2sin²x=0-2×2(sinx)×cosx=-2sin2x
and we have 2 in the begining so its -4sin2x
MATH
NATION
An art museum has a pentagon-shaped room. When drawn to scale on a coordinate grid, the corners of the room are points A(15,21);
B(8,21); C(8,10); D(13,8); E(19,14.5), shown in feet. The walls are 11 feet high.
The museum is going to paint four of the walls: AB, BC DE, and AE. Assume one gallon of paint is enough to cover 147
square feet
How many gallons of paint should the museum purchase? Enter your answer as a whole number.
12
1
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Answer:
3 gallons
Step-by-step explanation:
When calculations are repetitive, I find it convenient to use a spreadsheet to do them. The formulas used are ...
distance between points (x1, y1) and (x2, y2) = √((x2-x1)² +(y2-y1)²)
length of walls to be painted: AB +BC +DE +EA = 34.5 ft
area of walls to be painted: (length)(11 ft) = 379.3 ft²
gallons of paint needed: area/(147 ft²/gallon) = 2.6 gal
About 3 gallons of paint are needed to paint 4 walls of the room.
If , then the ordered pair of f -1(10) = (10, 31) (10, 3) (3, 10)
help asap
Answer:
B
Step-by-step explanation:
f^(-1) (x) = (x-1)/3
f^(-1) (10) = (10-1)/3 = 3.
i’ll give brainliest pls
i need to finish this quickly, i need part a b and c
What is the solution to the equation below? Round your answer to two decimal places.
4e^2x + 16 = 36
A. X = 3.22
B. x = 0.80
C. x = 1.61
D. x = 1.39
9514 1404 393
Answer:
B. x = 0.80
Step-by-step explanation:
We suspect you want the solution to the exponential equation ...
4e^(2x) +16 = 36
e^(2x) +4 = 9 . . . . . . . . . . . divide by 4 (because we can)
e^(2x) = 5 . . . . . . . . . . . . . . subtract 4
2x = ln(5) . . . . . . . . . . . . . . . take natural logs
x = ln(5)/2 ≈ 0.804719 . . . . .divide by the coefficient of x
x ≈ 0.80
(2x-5)3 =Alguien sabe cual es el resultado de esta operación
Answer:
6x - 15
Step-by-step explanation:
(2x - 5)3
3(2x) - 3(5)
6x - 15
Candice recorded outdoor temperatures as -5°C, 2°C and 1°C. Which of the following correctly compares the three temperatures?
Answer:
2°C
Step-by-step explanation:
outdoor temperature
Jessica made 2 pounds of fudge. How many -pound servings are in the 2 pounds of fudge?
Answer:
2
Step-by-step explanation:
2 pounds of fudge ÷ 1 pounds servings = 2 servings
If my answer is incorrect, pls correct me!
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Answer: 8
Step-by-step explanation: