Answer:
[tex]sin 2 \theta = \frac{4 \sqrt5}{9}[/tex]
Step-by-step explanation:
Identities used :
[tex]1. sin^2 \theta = 1 - cos^2\theta\\\\2. tan^2 \theta + 1 = sec^2 \theta\\\\3.cos \theta = \frac{1}{sec \theta} \\\\4. sin 2 \theta = 2 sin\theta cos\theta[/tex]
[tex]Given \ tan \theta = -\frac{2 \sqrt5}{5}\\[/tex]
[tex]we \ know \ tan ^2 \theta + 1 = sec^2\theta[/tex]
[tex](-\frac{2 \sqrt 5}{5})^2 + 1 = sec^2 \theta\\\\\frac{4 \times 5}{25 } + 1 = sec^2 \theta \\\\\frac{20 + 25}{ 25} = sec^2 \theta \\\\\frac{45}{25} = sec^2 \theta \\\\sec \theta = \sqrt{ \frac{45}{25}}\\\\sec \theta = \sqrt{ \frac{9 \times 5}{5 \times 5}} \\\\sec \theta = \frac{3 \sqrt {5}}{5}\\\\[/tex]
[tex]We \ know \ cos \theta = \frac{1}{ sec \theta}[/tex]
[tex]So , \cos \theta = \frac{5}{3 \sqrt5}[/tex]
[tex]Next \ sin^2 \theta = 1 - cos^2 \theta[/tex]
[tex]= 1 - (\frac{5}{3 \sqrt5})^2\\\\=1 - \frac{25}{9 \times 5}\\\\=1 - \frac{25}{45}\\\\=\frac{45 - 25}{45}\\\\=\frac{20}{45}\\\\=\frac{4}{9}[/tex]
[tex]sin \theta = \sqrt{ \frac{4}{9}} = \frac{2}{3}[/tex]
[tex]Find \ sin 2 \theta[/tex]
[tex]sin 2 \theta = 2 (sin \theta \times cos \theta)[/tex]
[tex]= 2 \times \frac{2}{3} \times \frac{5}{3\sqrt5}\\\\= \frac{4 \times \sqrt5 \times \sqrt5}{9 \times \sqrt 5}\\\\=\frac{4 \sqrt5}{9}[/tex]
Part A: Estindlate the solution from the graph. -
Part B: What is the equation of each line in the system? blue line: _ and red line:
Answer:
Part A
The estimated solution of the graph is (37/29, -30/29)
Part B
The equation of the blue line is y = 0.6·x - 1.8
The equation of the red line is y = (-4/3)·x + 2/3
Step-by-step explanation:
Part A
From the given graph, we have two lines, one red and one blue line, intersecting in Quadrant IV
Given that the equation of the lines are also required, we find the solution of the graph, through the equation of the lines as follows;
The points through which the blue line passes are (-2, -3), and (3, 0)
The slope of the blue line, [tex]m_b[/tex] = (0 - (-3))/(3 - (-2)) = 0.6
Therefore, we have;
y - 0 = 0.6·(x - 3)
∴ The equation of the blue line is y = 0.6·x - 1.8
The approximate points through which the red line passes are (-1, 2) and (-2.5, 4)
The slope of the red line, [tex]m_r[/tex] = (4 - 2)/((-2.5) - (-1)) = -4/3
Therefore, we have;
y - 2 = (-4/3)·(x - (-1)) = (-4/3)·x - 4/3
∴ The equation of the red line is y = (-4/3)·x - 4/3 + 2 = (-4/3)·x + 2/3
y = (-4/3)·x + 2/3
The solution for the graph is the point where the y-values are equal
Therefore, wat the solution point, y = y, and 0.6·x - 1.8 = (-4/3)·x + 2/3
0.6·x + 4/3·x = 1.8 + 2/3
x = (1.8 + 2/3)/(0.6 + (4/3)) = 37/29 ≈ 1.28
At the solution of the graph, y = 0.6 × (37/29) - 1.8 = -30/29
Therefore, the estimated solution of the graph is (37/29, -30/29)
Part B
From the above solution of the graph, we have;
The equation of the blue line: y = 0.6·x - 1.8
The equation of the red line: y = (-4/3)·x + 2/3
A bank account starts with $3.00. The amount in the account doubles every year .
Answer:
Step-by-step explana
multiply it by 2 or sdd itself to it
The account will have $1536.007 after 9 years.
Part A:
To express the total amount of money A(t) in the account after 7 years, we can use the formula:
A(t) = P[tex](2^t)[/tex]
where:
A(t) is the total amount in the account after t years,
P is the initial amount in the account (starting with $3.00 in this case),
t is the number of years.
Substituting the values into the formula, we get:
A(t) = 3 ([tex]2^7[/tex])
A(t) = 3 x 128
A(t) = 384
Therefore, the total amount of money in the account after 7 years is $384.
B) To find out after how many years the account will have $1536.007, we need to solve the equation:
1536.007 = 3 [tex](2^t)[/tex]
Dividing both sides of the equation by 3, we get:
512.0023333333 = [tex]2^t[/tex]
Taking the logarithm (base 2) of both sides, we have:
log2(512.0023333333) = t
t = 9.000317.
Therefore, the account will have $1536.007 after 9 years.
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Y’all know the answer?
9514 1404 393
Answer:
(b) 36 in²
Step-by-step explanation:
The right triangle at lower right has a vertical leg of 3 and a hypotenuse of 5. Then the horizontal leg is ...
√(5² -3²) = √16 = 4
Then the horizontal diagonal is 4+4 = 8. The vertical diagonal is 6+3 = 9. The area is half the product of the diagonals, so is ...
A = 1/2(d1)(d2) = 1/2(8 in)(9 in) = 36 in²
__
You could figure the areas of the triangles separately, but you would come to the same result. This formula is good for a rhombus or a kite (or a square, which is also a rhombus), because the diagonals are perpendicular to each other.
0.202 round to the hundredth
Answer:
0.20
Step-by-step explanation:
A teacher is buying supplies for two art classes. For class 1, the teacher buys 24 tubes of paint, 12 brushes, and 17 canvasses. For class 2, the teacher buys 20 tubes of paint, 14 brushes, and 15 canvasses. Each tube of paint costs $3.35, each brush costs $1.75, and each canvas costs $4.50. Compute the following matrix multiplication to determine how much the teacher spent on each class.
if a/4=2/3, then (a-4)/4 would equal
a. -2/3
b. -1/3
c. 0
d. 1/3
Answer:
b. -1/3
Step-by-step explanation:
a/4=2/3
a=8/3
(a-4)/4
(8-12)/12
=-4/12
=-1/3
Answer:
-1/3
Step-by-step explanation:
a/4=2/3
Multiply each side by 4
a/4 *4=2/3 *4
a = 8/3
(a-4)/4
(8/3 - 4) /4
Getting a common denominator
(8/4 - 12/3) /4
(-4/3)/4
-1/3
find (a) the perimeter and (b) the area of the figure. use 3.13 or 22/7 for n. round your answer to the nearest hundredth, if necessary
Answer:
;)))
Step-by-step explanation:
SOMEONE PLEASE HELP THIS IS DUE TOMROROW EZ WORK
PLEASE ANSWER THEM PROPERY FULL SENTENCES
Answer:
1.) At times, designing a good structure with a specific function may often be difficult. If the structure is not well-designed or strong enough for the function it will not properly work. So in order for the design to be well-built, both the structure and function must cooperate.
2.) Symmetry is a balanced arrangement on the opposite sides of a structure. In order for for a structure to be stable and properly work without complications, it most commonly needs to be symmetrical. This is a very important part of designing a structure.
3.) If the structure cannot withstand the function nor the possible forces that it may encounter. It is likely that it will break or even be completely destroyed.
4.) Shape, line, color, texture, movement, space. The designer may have taken into consideration whom the desk may be used by for the shape and space. Color, texture, and line may have been based on the environment (ex. A carpenter, student, computer desk) it would be in. Although the designer may not have an exact knowledge of where the desk would be, he still could consider what the desk could "possibly" be used for. Once again, the designer could take into consideration the user, for the movement of the desk. If the desk was to be moved around on wheels, or possibly could even fold. The designer must take into consideration EVERY detail.
6.) When people design something, often times you do not know how well that design is going to work without testing it with a prototype. Yes, prototypes are expensive. Yet, if they were to build something without testing their design, something may be wrong with it. So as a result, you will spend more money manufacturing something with a defect than testing it with a prototype.
For question 5, I think it might be best if you answer that one. It is based on YOUR opinion and what YOU use. If you are asked about it, they will know it's from you and your opinion. Lol! But I hope I helped you out with the other questions! ;)
Please help fast!! What is the range of the scores shown in the stem and leaf plot
95
40
58
37
Answer:
37
Step-by-step explanation:
Highest take the lowest
95-58=37
Holly cuts 2 ribbons into tenths for a craft project how many 1/10 size ribbons does she have
Answer:
Holly would have 20 1/10 sized ribbons.
Step-by-step explanation:
One whole ribbon would equal out to 10, this number multiplied by 2 would be 20. Therefore meaning she should have 20 1/10 sized pieces of ribbon.
a bookcase is 500mm wide how many of these bookcase will fill a
space 2m wide
I think 4 but I could be wrong
Stuck on this one. I can’t remember the process to get the answer
Find the volume of a regular square pyramid with base edge 10 ft. and height 12 ft.
120 ft
75ft?
400 ft
D 300 ft?
Answer:
V = 400 ft^3
Step-by-step explanation:
The area of the base of this regular square pyramid is (10 ft)^2, or 100 ft^2.
Recalling that the area of a pyramid is V = (1/3)(base area)(height), in this case we get V = (1/3)(100 ft^2)(12 ft) = 400 ft^3
what is the equation, in point-slope form, of the ljne that is perpendicular to the given line and passes through the point (-4,-3)?
Answer:y+3=1/4(x+4)
Step-by-step explanation:
First find the slope of the line with the points -1,1 and 0,-3
1-(-3)/-1-0 = -4
perpendicular is negative reciprocal which is 1/4
now we have the slope, and a point so we can put it in point slope form
y+3=1/4(x+4)
point slope form is y-y1 = m(x-x1)
with x1,y1 being the point and m being the slope
Malik wanted to give away \frac{1}{5} 5 1 of his bag of balloons to his 3 friends. What fraction of balloons will he give away?
Answer:
The answer is 3/5
Step-by-step explanation:
The amount of balloon to be given away= 1/5
The number of friends to
receive the balloon = 3
Therefore the total fraction of balloons that he gave away = 1/5 × 3
=3/5
could u help me last part :)
Answer: 288pi in cubed
Step-by-step explanation: because area of a circle is pir^2 so 36*8=288
can you help me find the code
link/picture in the comments
Answer:
????? sus
Step-by-step explanation:
sussy baka????
among sus
WILL GIVE BRANLIEST!!! pls help tysm!!!
Approximately how long will it take $200 to double to $400 when the annual interest rate is 8 1/2?
Answer:
200/17 years
Step-by-step explanation:
Simple interest = (principle * time * rate) / 100i
A company has designed its new packaging for products to be shaped liked the prism shown. If the cost of packaging is $0.03 per square inch, find the total cost of the package shown. (10 inches horizontally, 4 inches vertically, and 4 inches on the side)
Answer:
$5.76
Step-by-step explanation:
We solve using the formula of the area of a rectangular prism
A = 2(LW + LH + WH)
The dimensions of the package are given as: 10 inches horizontally, 4 inches vertically, and 4 inches on the side
=2 × (4 × 10 + 4 × 10 + 4 ×4)
=192 square inches
If the cost of packaging is $0.03 per square inch, the total cost of the package is calculated as:
1 square inch = $0.03
192 square inches = x
Cross Multiply
= 192 × $0.03
= $5.76
i’m horrible at math, can anyone help?
Answer: no I'm actually horrible at math too sorry
Solve for x in the equation
Answer:
its the first one
Step-by-step explanation:
Which is the degree measure of an angle whose tangent is 1.19? Round the answer to the nearest whole number. A. 48° B. –48° C. 50° D. –50°
9514 1404 393
Answer:
C. 50°
Step-by-step explanation:
The angle whose tangent is 1.19 is ...
arctan(1.19) ≈ 49.9585° ≈ 50°
The 50° measure of an angle whose tangent is 1.19.
What is tangent?Tangent in geometry, is defined as "a line or plane that touches a curve or curved surface exactly at one point" .
According to the question,
The degree measure of an angle whose tangent in 1.19.
In order to an angle only if arctan(119) = 49.9585 ≈ 50.
Hence, the 50° measure of an angle whose tangent is 1.19.
Learn more about Tangent here
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which pairs of angles in the figure below are vertical angles select all that apply
Answer:the left one
Step-by-step explanation:
How does the range of g(x)=6/x compare with the range of the parent function f(x)=1/x?
Answer:
The range of both [tex]f(x)[/tex] and [tex]g(x)[/tex] is all nonzero real numbers.
Step-by-step explanation:
The range of the function is the set of real number for [tex]y[/tex]. The rational function of the form [tex]y = \frac{a}{x}[/tex], where [tex]a[/tex] is a constant, has a range represented by the subset of nonzero real numbers. This is: [tex]Ran\{f(x)\} = \mathbb{R}-\{0\}[/tex]
Hence, the correct answer is: The range of both [tex]f(x)[/tex] and [tex]g(x)[/tex] is all nonzero real numbers.
The bars of a histogram should be shown in increasing order. true or false
Answer:
false it can be in any order but must be according to the set of data
Which polynomial below could produce this graph?
Answer:
f(x) = (x + 20)(x - 24)(x + 10)(x + 12)
Step-by-step explanation:
This is an equation of degree 4 and as the beginning of the graph descends from negative x the polynomial will have a positive leading coefficient. The graph is roughly W shaped.
It also has zeroes at x = -20,-12 ,-10 and x = 24.
So it is the first option.
Please help. I am very confused about this problem.
jzgsgßiqhwgwgah I don't know
Answers:
number of sides = 15regular polygon name = regular 15-gon=======================================================
Explanation:
If 156 degrees is the interior angle measure, then 180-156 = 24 is the exterior angle measure.
Divide 360 over this to find that 360/24 = 15
This means the regular polygon has 15 sides.
I'm using the idea that if n is the number of sides, then 360/n is the exterior angle measure. So 180 - (360/n) is the interior measure.
Enter the value of x so that the expression (1.8a−5.7)+(xa+3.2) is equivalent to −1.6a+2.5.
Answer:
Step-by-step explanation:
ax+1.8a−2.5
Which equation represents a line which is perpendicular to the line 6x+y=-4
Answer:
y = 1/6x - 4
Step-by-step explanation:
y = -6x - 4
current slope is -6 so the slope of a line perpendicular would be 1/6
y = 1/6x - 4
