9514 1404 393
Answer:
arcsin(2/3) ≈ 41.81°, 138.19°Step-by-step explanation:
Rewrite as a quadratic in sin(θ) and solve that in the usual way.
3cos(2θ) +sin(θ) = 1
3(1 -2sin²(θ)) +sin(θ) = 1 . . . . use an identity for cos(2θ)
6sin²(θ) -sin(θ) -2 = 0 . . . . . rearrange to standard form
(3sin(θ) -2)(2sin(θ) +1) = 0 . . . . factor
The values of sin(θ) that make this true are ...
sin(θ) = 2/3, sin(θ) = -1/2
In the range 0 < θ < 180°, we're only interested in ...
sin(θ) = 2/3
θ = arcsin(2/3) or 180° -arcsin(2/3)
θ ≈ {41.81°, 138.19°}
A line segment on a number line has its endpoints at -9 and 6. Find the coordinate of the midpoint of the segment.
A. 1.5
B. -1.5
C. 2
D. -3
Answer:
B -1.5
Step-by-step explanation:
please give brainliest if you can, have a good day<3 :)
Answer:
-1.5
Step-by-step explanation:
4. (k? - 4k+7)+(k? +9k – 3)
ON SA
Answer:
7k + 4
Step-by-step explanation:
I don't know what ON SA means, but here's how I solved it:
(k - 4k + 7) + (k + 9k – 3)
(-3k + 7) + (10k - 3)
(-3k + 10k) + (7 - 3)
7k + 4
Write the equation of a line that passes through ( 4, 6), and has a slope of 1/3
Answer:
y = 1/3x + 14/3
Step-by-step explanation:
y = mx + b
we know the slope, so the equation would be --> y = 1/3x + b
Now we plug in the coordinates of the given point (4, 6) the line goes through, and solve for b:
y = 1/3x + b
6 = 1/3(4) + b
6 = 4/3 + b
-4/3 -4/3
----------------
14/3 = b
Find the linear function f if f^-1(2)=-1 and f^-1 (-9)=3
Answer:
[tex]\displaystyle f(x) = -\frac{11}{4}(x + 1) + 2[/tex]
Step-by-step explanation:
We want to find the linear function given that:
[tex]f^{-1}(2) = -1\text{ and } f^{-1} (-9) = 3[/tex]
Recall that by the definition of inverse functions:
[tex]\displaystyle \text{If } f(a) = b\text{ then } f^{-1}(b) = a[/tex]
In other words, f(-1) = 2 and f(3) = -9.
This yields two points: (-1, 2) and (3, -9).
Find the slope of the linear function:
[tex]\displaystyle m = \frac{\Delta y}{\Delta x} = \frac{(-9) - (2)}{(3) -(-1)} = -\frac{11}{4}[/tex]
From point-slope form:
[tex]\displaystyle y - (2) = -\frac{11}{4}( x- (-1))[/tex]
Hence:
[tex]\displaystyle f(x) = -\frac{11}{4}(x + 1) + 2[/tex]
We can simplify if desired:
[tex]\displaystyle f(x) = -\frac{11}{4}x -\frac{3}{4}[/tex]
the set of all natural numbers less than 15 write set build notation
Answer:
{x : x Σ N, x<15}
Step-by-step explanation:
Set of all natural number less than 14 = {x : x Σ N, x<15}
-4b+3(6-7b)=93 please help with the asnswr
Answer:
b = -3
Step-by-step explanation:
-4b + 3(6 - 7b) = 93
-4b + 18 - 21b = 93
-4b - 21b = 93 - 18
-25b = 75
[tex]\sf{b = \frac{75}{ - 25} }[/tex]
b = -3
b = - 3
Step-by-step explanation:
-4b + 3(6-7b) = 93
-4b + 18 - 21b = 93
-25b + 18 = 93
-25b = 93 - 18
-25b = 75
b = 75 : - 25
b = - 3
What method would you choose to solve the
equation 2x2 - 7 = 9? Explain why you chose this
method.
Answer:
» ◻ Add and divide to isolate x²
[tex]2 {x}^{2} - 7 = 9 \\ 2 {x}^{2} = 9 + 7 \\ 2 {x}^{2} = 16 \\ {x}^{2} = \frac{16}{2} \\ \\ {x}^{2} = 8[/tex]
» ◻ use the square root property of equality
[tex] {x}^{2} = 8 \\ x = \sqrt{8} [/tex]
The point A(1,4) has been transformed using the composition T(-1,2) D2. Where is A at?
Answer:
(6, 6)
Step-by-step explanation:
T (-1, 2) = move down 1, right 2
(1, 4) turns into (3, 3)
Dilation scale factor = 2
Multiply x and y value by 2
(3, 3) = (6, 6)
Point O is the centroid of triangle ABC. If OD=3x -2 and OC= 5x, find x.
At centroid medians bisect each other in the ratio 2:1
[tex]\\ \sf\longmapsto OC=2(OD)[/tex]
[tex]\\ \sf\longmapsto 2(3x-2)=5x[/tex]
[tex]\\ \sf\longmapsto 6x-4=5x[/tex]
[tex]\\ \sf\longmapsto 6x-5x=4[/tex]
[tex]\\ \sf\longmapsto x=4[/tex]
The value of x is 4, when we are given O is the centroid of the triangle ABC, OD = 3x - 2, and OC = 5x.
What is the centroid of a triangle?The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians connect. The junction of all three medians is another definition for it. The median is a line that connects the middle of a side to the triangle's opposite vertex. The median is divided by the centroid of the triangle in a ratio of 2:1.
How to solve the question?In the question, we are given that O is the centroid of triangle ABC, and are asked to find the value of x, for which OD = 3x - 2, and OC = 5x.
We know that the median is divided by the centroid of the triangle in a ratio of 2:1.
Thus, the median CD is divided by the ratio of 2:1 as,
2/1 = OC/OD,
or, 2/1 = (5x)/(3x - 2),
or, 2(3x - 2) = 1(5x) {Cross-multiplying},
or, 6x - 4 = 5x,
or, 6x - 5x = 4,
or, x = 4.
Thus, the value of x is 4, when we are given O is the centroid of the triangle ABC, OD = 3x - 2, and OC = 5x.
Learn more about the centroid of a triangle at
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can a math god help me out?
Answer:
[tex]f(1)=70[/tex]
[tex]f(n)=f(n-1)+6[/tex]
Step-by-step explanation:
One is given the following function:
[tex]f(n)=64+6n[/tex]
One is asked to evaluate the function for [tex](f(1))[/tex], substitute [tex](1)[/tex] in place of [tex](n)[/tex], and simplify to evaluate:
[tex]f(1)=64+6(1)[/tex]
[tex]f(1)=64+6[/tex]
[tex]f(1)=70[/tex]
A recursive formula is another method used to represent the formula of a sequence such that each term is expressed as a function of the last term in the sequence. In this case, one is asked to find the recursive formula of an arithmetic sequence: that is, a sequence of numbers where the difference between any two consecutive terms is constant. The following general formula is used to represent the recursive formula of an arithmetic sequence:
[tex]a_n=a_(_n_-_1_)+d[/tex]
Where ([tex]a_n[/tex]) is the evaluator term ([tex]a_(_n_-_1_)[/tex]) represents the term before the evaluator term, and (d) represents the common difference (the result attained from subtracting two consecutive terms). In this case (and in the case for most arithmetic sequences), the common difference can be found in the standard formula of the function. It is the coefficient of the variable (n) or the input variable. Substitute this into the recursive formula, then rewrite the recursive formula such that it suits the needs of the given problem,
[tex]a_n=a_(_n_-_1_)+d[/tex]
[tex]a_n=a_(_n_-_1_)+6[/tex]
[tex]f(n)=f(n-1)+6[/tex]
Aim: I can solve two-step word problems involving per
1. A supermarket stocks 300kg of potatoes. 25% of the potatoes are
are sold in 1.5kg bags. What mass of potatoes are sold in 1.5kg b
Answer:
75 kg
Step-by-step explanation:
300*25/100
3*25
75 Kg
Answer:
75kg
Step-by-step explanation:
potatoes are stocked =300kg
25% of potatoes in kg= 25% * 300kg
=75kg
75kg potatoes are sold in 1.5kg bags.
PLSSS NEED HELP WILL GIVE CROWN
Add :
-1.25 + 2.5 = 1.25
For plotting the first one we first need to see the integer as here is 1 we will move to 1. Now, here it is given 0.25. Each line between 1 and 2 has 10 numbers gap so, as it 25 > 20 and 25 < 30. So, we should plot it between the 2nd and the 3rd line. As it is 5 it should be in between the line.
Refer the plotting for better identification
Add :
4.2 + (-0.4)
4.2 - 0.4
3.8
For plotting this one we will move to 3 than it has 8 < 10 so it should be plotted within the first dot.
Refer the attachment for better identification
please help with the screenshot
Answer:
7.5
Step-by-step explanation:
Triangles: RST and RPQ are similar so
Triangle RST has 12.5 and x
Triangle RPQ has 20 (comes from 12.5+7.5) and x+4.5
Therefore you divide
x/x+4.5 = 12.5/20
20x= 12.5x+56.25
7.5x=56.25
x=7.5
Which of the following is equal to 4 and 1 over 2 divided by 2 and 2 over 3?
Answer:
4.91666666667
Step-by-step explanation:
this is what i got
either 9/2 x 8/3 or 9/2 x 3/8
I am still stuck on this basic math question. Rosa has 3 3/4 pounds of dough. She uses 1/8 of a pound for one roll. How many rolls could be made from Rosa's dough? I was told 30. But how did they get this answer?
Step-by-step explanation:
First convert the amount of dough into an improper fraction:
[tex]3\frac{3}{4}\:\text{lbs} = \dfrac{15}{4}\:\text{lbs}[/tex]
Each roll is 1/8 lb so divide the amount of dough by this amount:
[tex]\dfrac{\left(\dfrac{15}{4}\:\text{lbs}\right)}{\left(\frac{1}{8}\:\text{lb/roll}\right)} = \left(\dfrac{15}{4}\:\text{lbs}\right)\cdot \left(8\:\dfrac{\text{roll}}{\text{lb}}\right) = 30\:\text{rolls}[/tex]
what’s the solution for
-108pi=6pij
Answer:
j is -18
Step-by-step explanation:
[tex] - 108pi = 6pij \\ - 108 = 6j \\ j = - 18[/tex]
The solution is j = -18 for the expression -108π = 6πj
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operations is called the arithmetic operator.
Operators who let do basic mathematical calculations.
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
Given that the expression
⇒ -108π = 6πj
Divided by 6π both sides
⇒ -108π/6π = 6πj/6π
⇒ -18 = j
⇒ j = -18
Thus, the solution is j = -18 for the expression -108π = 6πj
Learn more about Arithmetic operations here:
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Which symbol correctly compares the two fractions? Use >, <, or =. Select the correct choice from the drop down. 2/4 Choose... 3/8
Answer:
3/8
Step-by-step explanation:
How many sentences does 2 paragraphs have?
Answer ASAP
Answer: depends how much you type
Step-by-step explanation:
X^2 -24x-108=0 factorize
Answer:
(x-27)(x+4) = 0
Step-by-step explanation:
I think you have a typo, and meant
x^2 -23x-108
what are two factors of 108 that differ by 23?
x^2 -24x-108 does not factor with rational coefficients.
Evaluate the expression
Step-by-step explanation:
this is correct answer thank you
let me see mathematics genius help me answer this question.
Step-by-step explanation: Answer is
(i). 19% or 14/75
(ii) 28% or 7/25
We are asked to find multiple probabilities.
We got to find the number of combinations posible,
Use the combinations formula
[tex]c {}^{n} _r{?} = \frac{(r + n - 1) \: fractorial).}{r \: fractorial(n - 1)fractorial} [/tex]
For math this is read as,
if n choose r,( r+n-1)!/r!(n-1)!.
Where r is how many things we need from and n is the number of things we choose from.
We need 2 things and we have 24 objects to pick from.
So r=2 N equal=24
Which equal
25!/2!(23)!
Which equals
[tex]300[/tex]
So there are 300 possible combinations.
Using
For the 1st question, Since we are given two independent events, we can just multiply the number of good articles by major.
[tex]14 \times 4 = 56[/tex]
So this means the probability is
[tex] \frac{56}{300} = \frac{14}{75} [/tex]
Which is 19%
For the 2nd question, the can multiply the number of minor articles by major articles.
[tex]6 \times 4 = 24[/tex]
So the probability
is
[tex] \frac{24}{300} = \frac{8}{100} = \frac{2}{25} [/tex]
Which is equal to 8%
Find the mean and standard deviation for the set of data. {27, 21, 8, 17, 23,6, 22, 26, 30}
solve this equation and show work.
5(c-8)-3(2c+12)=-84
John ate 1/6 of a cake. Mike ate 1/12 of it. How much of the cake did the two boys eat?
Answer:
1/4
Step-by-step explanation:
1/6 + 1/12 = 1/4
Answer:
3/3
Step-by-step explanation:
1/6= to 2/12 and 1 /12 = 2 /6
Solve.
6*7-3^2*9+4^3
Every time I did this, I got -103, and my teacher kept saying it's wrong. Please solve and show your work so I can see what I did wrong .
Answer:
25
Step-by-step explanation:
6*7-3^2*9+4^3
Exponents first
6*7-9*9+64
Multiply and divide from left to right
42 -9*9+64
42 - 81 +64
Add and subtract from left to right
-39 +64
25
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{6\times7-3^2\times9+4^3 }}\\\huge\boxed{\mathsf{= 42 - (9)(9) + 4^3}}\\\huge\boxed{\mathsf{= 42 - 81 + 64}}\\\huge\boxed{\mathsf{= -39 + 64}}\\\huge\boxed{\mathsf{= 25}}}}\\\huge\boxed{\mathsf{Therefore, your\ answer\ is: 25}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
When solving the given equation, what is the first step?
(a)
Given: -3 + 2 = 4
А
Add 3 to both sides
B
Subtract 3 from both sides
с
Multiply -3 to both sides
D
Divide -3 from both sides
(b)
What is the solution to the give equation?
Given: -3 + x = 4
x = "write the answer (number only) in the answer box"
Answer:
(a) A
(b) x = 7
Step-by-step explanation:
(a) Given : -3 + 2x = 4
Step 1: Isolate the x to one side. To do so, we get rid of -3 by adding 3 to both sides. (-3 + 3 =0)
2x = 4 + 3
(b) -3 + x = 4
x = 4 + 3
= 7
Last one for the night
Answer:
C. 2/3, 0.66, 66 2/3%
Step-by-step explanation:
There are 36 inches in a yard.
24/36 (simplify) = 2/3
Trình bày khái niệm và cách giải phương trình bậc nhất 1 ẩn, hệ phương trình bậc nhất 2 ẩn
178X718DIVIDED BY 20x12+478-289divided by 12
Answer:
77136.3166667
Step-by-step explanation:
Hope it helps
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)