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°}
what is trigonometry ?
no explanation required !
Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.
please help me to do this question
Answer:
firdt method is
Length x breath
is equal to ½
Which of the following correctly uses exponents to write "6 factors of 2"?
26
6.2
12
62
Answer:
A. 26
Step-by-step explanation:
The base number (the first number) is what will be multiplied and the exponent is how many times you're multiplying the number, so for this it would be
2 x 2 x 2 x 2 x 2 x 2
The graph of y = Vx is translated 3 units to the left and 4 unitsdown.
What is the equation of the graph that results from this translation?
The equation of the graph after translation is y'' = √ ( x + 3 ) - 4
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.
Given data ,
Let the equation of graph be represented as y
Now , the value of y is
y = √x
And , after a translation of graph by 3 units to the left , we get
y' = √ ( x + 3 )
Now , the translation of 4 units down is given by
y'' = y' - 4
y'' = √ ( x + 3 ) - 4
Hence , the translated equation is y'' = √ ( x + 3 ) - 4
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Find the area of the triangle.
A. 75 km²
B. 107.3 km²
C. 84.3 km²
D. 71.8 km²
Answer:
A. 75 km²
Step-by-step explanation:
The area of a triangle
A =1/2 ab sin C where a and b are the lengths of the sides and C is the included angle
A = 1/2 (14)(11) sin (77)
A = 75.0264949885
A number divided by 4 plus 3 is 8
Answer:
[tex]number = x \\ \frac{x}{4} + 3 = 8 \\ \frac{x}{4} = 5 \\ x = 20 \\ thank \: you[/tex]
Answer:
[tex]let \: the \: number \: be \: x \: \\ then \: \\ \frac{x}{4} + 3 = 8 \\ \frac{x}{4} = 8 - 3 \\ \frac{x}{4} = 5 \\ x = 5 \times 4 \\ x = 20 \\ \: hence \: 20 \: is \: your \: answer \:hope \: it \: helped[/tex]
Plz help me with this
9514 1404 393
Answer:
see attached
Step-by-step explanation:
a) A table and graph are attached.
__
b) The relationship is NOT PROPORTIONAL. The line does not go through the origin (0, 0).
i’m genuinely confused, please help
Answer:
2x + 3 + 3x +12 + 90 = 180 (degree )
5x +105=180 (degree )
5x= 180-105 (degree )
5x = 75 (degree )
x = 75/5 (degree )
x = 15 #
therefore, 2x + 3= 2*15 + 3
=30+3
= 33#
3x + 12 = 3*15+12
= 45 +12
= 57#
What is the arc length of arc cd in the circle below. The circle has a radius of 6ft and an angle measure of 30
9514 1404 393
Answer:
π ft ≈ 3.14 ft
Step-by-step explanation:
The angle is 1/12 of the number of degrees in a circle, so the arc length will be 1/12 of the circumference of the circle.
C = 2πr
1/12C = 2/12π(6 ft) = π ft ≈ 3.14 ft
The arc length is about 3.14 feet.
Translate the sentence into an equation.
The sum of 5 times a number and 6 is equal to 7
Jungwon has $15. Notepads cost $2.50 each. How many notepads can Jungwon buy?
The midpoint of AB is (1, 2). The coordinates of A are (-3,6).Find the coordinates of B.
Midpoint has coordinates [tex](x_m,y_m)[/tex] which equal to,
[tex]x_m=\frac{x_1+x_2}{2}[/tex]
[tex]y_m=\frac{y_1+y_2}{2}[/tex]
We know the coordinates of a midpoint as well as the coordinates of [tex]A(x_1,y_1)[/tex] so we should be able to find coordinates of [tex]B(x_2,y_2)[/tex].
First solve both equations for [tex]x_2[/tex] and [tex]y_2[/tex] respectively,
[tex]x_2=2x_m-x_1[/tex]
[tex]y_2=2y_m-y_1[/tex]
Now insert the data,
[tex]x_2=2\cdot1-(-3)=\boxed{5}[/tex]
[tex]y_2=2\cdot2-6=\boxed{-2}[/tex]
The coordinates of B are therefore [tex](5,-2)[/tex].
Hope this helps :)
The midpoint of AB is (1, 2) the coordinates of A are (-3,6) coordinates of B coordinates of point B are (5, -2).
To find the coordinates of point B given that the midpoint of AB is (1, 2) and the coordinates of A are (-3, 6), use the midpoint formula:
Midpoint formula: M(x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Given that M is the midpoint (1, 2) and A is (-3, 6), we have:
(1, 2) = ((-3 + x2) / 2, (6 + y2) / 2)
Solve for x2 and y2:
For x-coordinate:
1 = (-3 + x2) / 2
2 = -3 + x2
x2 = 2 + 3
x2 = 5
For y-coordinate:
2 = (6 + y2) / 2
4 = 6 + y2
y2 = 4 - 6
y2 = -2
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A number is multiplied by 9 , and that product is added 3. The sum is equal to the product of 3 and 7 . Find the number.
Answer:
The unknown number is 2.
Step-by-step explanation:
Let x represent the unknown number.
It is multiplied by 9 then added to 3. Hence, it can be represented by the expression:
[tex]9x + 3[/tex]
The sum is equal to the product of 3 and 7, or 21. Therefore:
[tex]9x + 3 = 21[/tex]
Solve for x. Subtract 3 from both sides:
[tex]9x = 18[/tex]
And divide both sides by 2. Hence:
[tex]x = 2[/tex]
In conclusion, the unknown number is 2.
The pie chart below shows the Estrada family’s distribution of the monthly expenses for the last month. The Estrada family spent $366 on clothing last month.
What were the total expenses of the Estrada family last month?
Pie charts are used to show the relationship between data in a circle. The total expenses of the Estrada family last month are: $2287.5
Given that:
[tex]Clothing = \$366[/tex]
From the Pie chart, 13% of the total expenses were spent on clothing.
This means that
[tex]13\% \times Total = Clothing[/tex]
So, we have:
[tex]13\% \times Total = \$366[/tex]
Divide both sides by 13%
[tex]Total = \$366 \div 16\%[/tex]
[tex]Total = \$2287.5[/tex]
Hence, the total expenses are: $2287.5
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Write down a multiple of 4 between 29 and 37 ?
Answer:
8 or 9
Step-by-step explanation:
4 times 8 equals 32, and 4 times 9 equals 36
Help me with math please really need it
Answer:
Not too sure about this one, but I hope this helps.
Step-by-step explanation:
basically I just used the formula y=mx+b
m is the slope
and b is the y intercept
Will give brainly est
Find the difference. Enter your answer in simplest form.
3 1/3 minus 2 5/12 The First 3 and the first two are whole numbers btw
options
1 4/9 A
11/12 B
7/12 C
1 1/2 D
[tex]\\ \sf\longmapsto 3\dfrac{1}{3}-2\dfrac{5}{12}[/tex]
[tex]\\ \sf\longmapsto \dfrac{10}{3}-\dfrac{29}{12}[/tex]
[tex]\\ \sf\longmapsto \dfrac{40-29}{12}[/tex]
[tex]\\ \sf\longmapsto \dfrac{11}{12}[/tex]
Going into the final exam, which will count as two tests, has test scores of 77 , 82, 72 , 63 and 92 What score does need on the final in order to have an average score of 80?
Answer:
you either need to score a perfect on one exam and get a 80 on the second or get two 90s on both exams.
Step-by-step explanation:
Sam opened a restaurant. On the first day he had 100 customers. On the fourth day he had 160 customers. If the number of customers per day grew linearly, what was the number of customers on the second day?
Answer:
120 customers on the 2nd day
Step-by-step explanation:
100/1ST DAY
120/2nd day
140/3rd day
160/ 4TH DAY
Please help
Find the equation to the line below.
1 1
y = [? ]x +
[ ]
What type of relationship is expressed below?
f(x) = 7x +3
Answer:
Linear Function
Step-by-step explanation:
This is a linear function. A linear function is a function with the degree of 1, where the line increases continuously the whole graph. The growth of the graph is constant, making a straight line. This function is written in slope-intercept form, f(x) = mx+b. Where m is the slope and b is the y-intercept. The function will have 1 solution.
Find the value of x 3(4x+3)
3(4x+3)=12x+9
i don't know what do you need,
if roots, let 12x+9=0
the root is x=-3/4
Can someone help me solve these 3 trig identity problems? I am stuck on these last 3... I will give brainliest!
(calculators are allowed)
Answer:
1. 1,246
2. 0,545
3. 0,9539
Step-by-step explanation:
semoga membantu :)
pls help! I need the answer quickly!
Step-by-step explanation:
The correct answer is 4 (option B)
Think About the Process The length of a rectangle is twice the width. The area of the rectangle is
54 square units. Notice that you can divide the rectangle into two squares with equal area. How
can you estimate the side length of each square? Estimate the length and width of the rectangle.
+
27
B. Estimate
4
C. Estimate 27.
D. Estimate 54
The rectangle is
(Round to the nearest tenth as needed.)
units long and units wide.
0
vo
(10
More
Enter your answer in the edit fields and then click Check Answer.
Answer:
27
Step-by-step explanation:
- (x^2 - 3x + 2) - x(x - 4)
Answer:
[tex] - (x^{2} - 3x + 2) - x(x - 4) \\ = ( - x^{2} + 3x - 2) + ( - x ^{2} + 4x) \\ = - 2 {x}^{2} + 7x - 2[/tex]
I hope I helped you^_^
Answer:
[tex] = - 2 {x}^{2} + 7x - 2[/tex]
Step-by-step explanation:
[tex] - ( {x}^{2} - 3x + 2) - x(x - 4)[/tex]
[tex] - {x}^{2} + 3x - 2 - x(x - 4)[/tex]
[tex] - {x}^{2} + 3x - 2 - {x}^{2} + 4x[/tex]
[tex] - {2x}^{2} + 3x - 2 + 4x[/tex]
[tex] \boxed{\green{ = - 2 {x}^{2} + 7x - 2}}[/tex]
[tex]stan \: \: Dreamcatcher \\ and \: \: stream \: \: BEcause \\answered \: \: by \: \: a \: \: fellow \: \: InSomnia[/tex]
One positive number is 5 more than twice another. If their product is 1827, find the numbers.
smaller number =
larger number =
9514 1404 393
Answer:
smaller: 29larger: 63Step-by-step explanation:
If we let x and y represent "one number" and "another", respectively, then the given relations are ...
x = 5 +2y
xy = 1827
Substituting for x gives a quadratic in y:
(5 +2y)(y) = 1827
2y^2 +5y -1827 = 0 . . . . . written in standard form
We can use the quadratic formula to find the positive value of y that satisfies this:
y = (-5 +√(5² -4(2)(-1827)))/(2(2)) = (-5 +√14641)/4 = 116/4 = 29
x = 5 +2(29) = 63 . . . . using the above expression for x
The smaller number is 29; the larger number is 63.
Which of the h values are solutions to the following equation?
h^2=0.36
Choose all answers that apply:
A: h= square root of 0.6
B: h = square root of -0.6
C: h = 0.18
D:h = -0.18
E: None of the above
Answer:
a:h=square root of 0.6
Step-by-step explanation:
thank you for your time today
Answer:
none of the above
Step-by-step explanation:
KHAN
13. State the restrictions
and then simplify
8x2 +14x-49 /
2x²+x-21
Answer:
Whenever the denom is 0, that's where it's undefined -- or in your case "restrictions"
So factoring 2x^2 + x - 21 gets you (x-3)(2x+7). That means 3 and -7/2 are the restricted values.
To simplify, I'm going to factor it. (Assuming what you wrote is 8x^2 for the numerator)
[(4x-7)(2x+7)] / (x-3)(2x+7)
You can cancel 2x+7 out,
so you get 4x-7/x-3
P- 24000 R-10% T-2 years find the sum
Answer:
here
I =p×t×r/100
= 24000×2×10/100
= 4800
again,
sum = p+I
= 24000+4800
= 28800
