The simplest form of the value of the trigonometric identity cos(A-B) is
1508/1517.
What is are the trigonometric identities?
Trigonometric Identities are equality conditions that apply to all values of the equation's variables and which require trigonometry functions.
There are numerous unique trigonometric identities that involve both the side length and angle of a triangle. Only the right-angle triangle is valid for the trigonometric identities to work.
cos(A-B) = cosA cosB + sinA sinB
Given,
tan A = 12 / 35
So sin A = 12 / [tex]\sqrt{12^2 + 35^2}[/tex] = 12 / 37
cos A = 35 / 37
Now,
sin B = 9/41
cos B = [tex]\sqrt{1 - sin^{2} B }[/tex] = [tex]\sqrt{1 - (\frac{9}{41} )^{2} }[/tex] = 40/41
Now substituting the above values in the cosine formula
cos(A-B) = cosA cosB + sinA sinB
= (35/37) (40/41) + (12/37) (9/41)
= 1508/1517 = 0.994
Therefore the simplest form of cos(A-B) is 1508/1517.
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ADEF has coordinates D(2, 0), E(3, 3), and F(4, 1). What are the coordinates of AD E F if the original triangle is dilated by a scale factor of 4?
Option C is correct. The coordinates of ADE'F' after dilation by a scale factor of 4 are A'(8,0), D'(8,0), E'(12,12), and F'(16,4).
What are coordinates?Using one or more numbers, or coordinates, a coordinate system in geometry establishes a unique way to locate points or other geometrical objects on a manifold, such Euclidean space. The order of the coordinates is important, and they can sometimes be distinguished by their place in an ordered tuple or by a letter, such as "the x-coordinate." In simple mathematics, the coordinates are assumed to be real numbers, while they could also be complex numbers or components of a more abstract structure, such a commutative ring. Analytic geometry is based on the usage of coordinate systems, which make it possible to convert geometry-related problems into numerical problems and vice versa.
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-1=1/3v
show work
∨=
⇄
Answer:
v = 1/-3
Step-by-step explanation:
cross multiply
-3v = 1
then:
divide through by the coefficient of v which is -3
-3v/-3 = 1/-3
[tex]-1=\dfrac{1}{3} v[/tex]
Flip:
[tex]\dfrac{1}{3} v=-1[/tex]
Multiply both sides by 3:
[tex]3\times(\dfrac{1}{3} v)=3\times(-1)[/tex]
[tex]\fbox{v = -3}[/tex]
5
Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.
What are the missing segment lengths shown in the image?
20
10 10√3
20√3 10 2 20√2
45° 45°
4
45°
20
00
45°
The missing segment lengths are CD = 10√2, AC = 10√2, BC = 10 and AB = 10.
Drag each length to the correct location accordingly
How to find the missing segment lengths?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
In ΔACD,
sin 45° = CD/20 (sin = opp/hyp)
(√2)/2 = CD/20
CD = (√2)/2 × 20
CD = 10√2
cos 45° = AC/20 (cos = adj/hyp)
(√2)/2 = AC/20
AC = (√2)/2 × 20
AC = 10√2
In ΔABC,
sin 45° = BC/10√2 (sin = opp/hyp)
(√2)/2 = BC/10√2
BC = (√2)/2 × 10√2
BC = (10 × 2)/2
BC = 10
cos 45° = AB/10√2 (cos = adj/hyp)
(√2)/2 = AB/10√2
AB = (√2)/2 × 10√2
AB = 10
Drag each length of the missing segment to the correct location
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If the two solids have the same volume and height, find the area of one of the cross sections. A. 18 cm B. 36 cm C. 48 cm? D. 72 cm
A. 18
Step-by-step explanation:
If the two solids have the same height and same cross-sectional area at every level, this means that the radius of the oblique cylinder is the same as the radius of the right cylinder.
Since the radius of the right cylinder is 16/2=8, this means that the radius of the oblique cylinder must also be 8.
Answer:
18
Step-by-step explanation:
A water sample must be taken from water at least 20 feet deep. Find the depth of the water feet from shore
The depth of water from the shore is 15 feet.
What is a proportion?
A proportion is an equation that states that two ratios are equal. It can be written in the form of a/b = c/d. The two ratios, a/b and c/d, are called the terms of the proportion.
The cross-products of a proportion are also equal, so ad = bc.
To solve for d in the equation 5/1.5 = 50/d, you can start by multiplying both sides of the equation by 1.5 to cancel out the denominator on the left side. This gives:
5 = 50/d * 1.5
Next, you can simplify the right side of the equation by multiplying 50 and 1.5, which gives:
5 = 75/d
To solve for d, you can now cross-multiply to get:
75 = 5d
Finally, you can divide both sides of the equation by 5 to get:
d = 75/5
d = 15
the value of d is 15.
Hence, the depth of water from the shore is 15 feet.
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The depth of water from the shore is 15 feet.
What is a proportion?
A proportion is an equation that states that two ratios are equal. It can be written in the form of a/b = c/d. The two ratios, a/b and c/d, are called the terms of the proportion.
The cross-products of a proportion are also equal, so ad = bc.
To solve for d in the equation 5/1.5 = 50/d, you can start by multiplying both sides of the equation by 1.5 to cancel out the denominator on the left side. This gives:
5 = 50/d * 1.5
Next, you can simplify the right side of the equation by multiplying 50 and 1.5, which gives:
5 = 75/d
To solve for d, you can now cross-multiply to get:
75 = 5d
Finally, you can divide both sides of the equation by 5 to get:
d = 75/5
d = 15
the value of d is 15.
Hence, the depth of water from the shore is 15 feet.
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What is the experimental probability of NOT landing on green
22%
25%
75%
78%
ILL BRAINLIEST YOU PLEASE HELP ME
How do you write 125 in scientific notation?
Answer:
1.25 x [tex]10^2[/tex]
Step-by-step explanation:
Move the decimal point to make 125.0 a new number between 1 and 10. Because our number is greater than 10, we move the decimal point to the left. Drop any trailing zeroes. Keep track of how many times we move the decimal point. 125.0 -> 1.25. Our new number is 1.25. We moved the decimal point 2 times.
Question down below :)
Answer: 16 it right i hope or 6
Step-by-step explanation:
solve this please (quick)
Answer:
4x10^12, or the 4th one
Step-by-step explanation:
C. It will
make 18 more parts.
5
Which number line shows the solution set to 1< -49 - 13/9 x <55/3?
The inequality is x 26 and asks for the values of x where the perimeter of the rectangle is smaller than 112.
The definition of inequalityIn mathematics, a link between two terms or values that isn't comparable is referred to as an inequality. As a result, imbalance leads to inequality. A mathematical inequality is a relationship between two non-equal expression . Egality is distinct from inequality. The not common basic is frequently used to denote that two values aren't actually equal (). Various inequalities are used to contrast the values, no matter how small or large. Many simple inequalities can be resolved by switching the two aspects until the variables are the only thing remaining. But a number of things encourage inequality: Values that are negative are divided or added along either side.
Here,
given
A rectangle's perimeter is determined by its length, width, and height.
rectangle's perimeter is calculated as length + length + width + width.
(x +4) + (x+4) + x + x < 112
x + 4 + x + 4 + x + x < 112
4x + 8 < 112
4x < 104
x < 26
In order to find the x value that occur when the rectangle's boundary is less than 112, the inequality is x 26.
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0.6. Divided by 01.518
Answer:
0.4
Step-by-step explanation:
0.6÷1.518=0.395256917
On a number line -1 2/3 (negative one and two-thirds) would be placed between what 2 integers? *
70%of $10=$
Comlelete the folling statements
Answer:
$7
....
....
....
....
....
11c+ 8) (-9c - 1)
Help plssss
Answer:
Step-by-step explanation: (11c + 8) (-9c - 1)
Then expand
which would be 11c ( -9c - 1) + 8 ( -9c - 1)
-99c^2 -11c - 72c - 8
It becomes -99c^2 - 83c -8
I hope this was helpful
last year marina earned 35000 from one job and 25000 from a another job. she puts 3600 in her saving account. what percent of her total income did she put into saving
Answer:
The answer 5.83
Step-by-step explanation:
Answer:
0.06 or 6%
Step-by-step explanation:
35000+25000=60000
3600/60000=0.06
Si se tiene cierta cantidad de alimento para mantener por 14 días a 40 cerdos; la cantidad de días que puedo mantener a los cerdos si se aumentan en un 40% es.
Answer:
La cantidad de días para mantener una población de cerdos mayor en 40 % es de 10 días.
Step-by-step explanation:
Para una misma cantidad de alimentos, el tiempo de duración de los alimentos ([tex]t[/tex]) es inversamente proporcional a la cantidad de cerdos ([tex]c[/tex]), es decir:
[tex]t \propto \frac{1}{c}[/tex]
[tex]t = \frac{k}{c}[/tex] (1)
Donde [tex]k[/tex] es la constante de proporcionalidad, en días.
Podemos eliminar esa constante mediante la siguiente relación:
[tex]\frac{t_{1}}{t_{2}} = \frac{c_{2}}{c_{1}}[/tex] (2)
Si sabemos que [tex]t_{1} = 14\,dias[/tex], [tex]c_{1} = 40[/tex] and [tex]c_{2} = 56[/tex], entonces la cantidad de días asociada una población de cerdos mayor en 40 % es:
[tex]t_{2} = t_{1}\times \frac{c_{1}}{c_{2}}[/tex]
[tex]t_{2} = 14\,dias \times \frac{40}{56}[/tex]
[tex]t_{2} = 10\,dias[/tex]
La cantidad de días para mantener una población de cerdos mayor en 40 % es de 10 días.
Tell whether the rate form a proportion. 4. 8 lap every 8 minute; 3. 6 lap every 6 minute
Yes, the rate 4.8 laps every 8 minutes; 3.6 laps every 6-minute form a proportion.
A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:
1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)
4.8 lap every 8 minutes will be equal to (4.8/8) = 0.6 lap a minute.
3.6 lap every 6 minutes will be equal to (3.6/6) = 0.6 lap in a minute.
Here, as the value of the ratio of both the quantities are same so the given values are said to be in Proportion.
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A commuter wants to determine the average price of gas in the area. Which is the best method of collecting a population sample so that the commuter can answer this question? Responses: A. Check gas prices at several gas stations near the commuter’s house. B. Find the gas prices over the past several years at a single particular gas station in the area. C. Look up a number of randomly selected gas stations in the area to find out gas prices. D. Survey friends on social media to see how much people are paying for gas.
The best method of collecting a population sample so that the commuter can answer this question is C. Look up a number of randomly selected gas stations in the area to find out gas prices.
What is the population?The entire group about which you want to draw conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the total population size.
A sample is characterized as a more manageable and compact version of a larger group. a smaller population that possesses the traits of a larger population. When the population size is too large to include all participants or observations in the test, a sample is used in statistical analysis.
This method would be the most representative of the entire population of gas stations in the area, and therefore the most likely to produce an accurate average price.
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A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number less than 2.
35 over 60
25 over 60
13 over 60
12 over 60
Experimental probablity will be - 12 over 30
Answer: D: 12/60 (12 over 60)
Step-by-step explanation:
a rectangular prism has dimensions of 8cm by 9cm by 10cm what is its volume?
A rectangular prism has dimensions of 8cm by 9cm by 10cm therefore the volume is 720cm³.
What is Volume?This is referred to as the measure of the space occupied within the boundaries of any three-dimensional solid.
Volume of rectangular prism = l × w × h where l is length, w is width and h is height.
Volume = 8cm × 9cm × 10cm = 720cm³.
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Solve each equation. State any extraneous solutions.
11/2x + 2/4x = 1/4
Can someone please help me with this?
Answer:
Choice C
Step-by-step explanation:
Rational numbers are any number that can be written as a quotient or fraction.
4. BK has endpoints B(1, 4) and K(4, -3). Rotate BK clockwise 270 degrees about the
origin.
Part AWrite an algebraic description of the transformation of BK.
Part B: What are the endpoints of the new line segment?
The algebraic description of the transformation of B(x, y) = B'(y + 0, 0 - x)
The algebraic description of the transformation of K(x, y) = K'(y + 0, 0 - x)
The endpoints of the new line segment are B'(4, -1) and K'(-3, -4).
As per the given data BK has endpoints B(1, 4) and K(4, -3).
Rotate BK clockwise 270 degrees about the origin.
Every point of a source image is transformed in a plane via a rotation that rotates it around a fixed point at a specific angle and direction. The fixed point is referred to as the rotational center.
The term "angle of rotation" refers to the rotation's amount and is expressed in degrees.
Rotating a figure 270 degrees clockwise is the same as rotating a figure 90 degrees anticlockwise.
Now, it would be (x, y) = (-y, x)
We have;
R (x, y) to R' (y, -x)
The algebraic description is simply written as;
R (x, y) = R'(y + 0, 0 - x)
B (x, y) = B'(y + 0, 0 - x)
K (x, y) = K'(y + 0, 0 - x)
To get the new endpoints, we simply write the transformation as shown;
B(1, 4) becomes B'(4, -1)
K(4, -3) becomes K'(-3, -4)
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plzzzz help, it’s on khan academy
Which expression is equivalent to
Answer:
4 ^ -8
Step-by-step explanation:
Cooper is a shoe sillesman, and he works on commission. This week, there is a special incentive to sell shoes and boots by a certain company. Yesterday, Cooper sold 2 pairs of shoes and 10 pairs of boots, earning $160 in commission. Today, he sold 4 pairs of shoes and 10 pairs of boots, earning a total commission of $170. How much does Cooper earn for the sale of each type of footwear?
The commission from selling each pair of shoe is $5 while that from selling each boot is $15
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Let x represent the commission earned from selling each pair of shoe and y represent the commission from selling each pair of boot.
Cooper sold 2 pairs of shoes and 10 pairs of boots, earning $160 in commission. Hence:
2x + 10y = 160 (1)
Also, he sold 4 pairs of shoes and 10 pairs of boots, earning a total commission of $170, hence:
4x + 10y = 170 (2)
From both equations:
x = 5, y = 15
The commission from selling each pair of shoe is $5
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The vertices of DEF are D(-2, 5), E(5, 1), F(-4, -5). Find the coordinates of the orthocenter of DEF
Using a graph, the orthocenter for this triangle has a coordinate at (x, y) are (-0.46, 0.2)
What is an OrthocenterThe intersection of a triangle's three elevations is called the orthocenter. It is the intersection of the three lines that run perpendicular to the triangle's three sides. Due to its several intriguing characteristics, the orthocenter is a crucial place in the study of triangles..
In this problem, we need to use a graphing calculator and plot each of the coordinates and then find the orthocenter which is an equidistant position from all the coordinates.
In this particular problem, the orthocenter for this triangle is (-0.46, 0.2)
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Tamicca bought a Computer for $1200 and made 12 monthly payments of $115.
What was the finance charge that she paid? Round your answer to the nearest cent.
Answer:
Tamicca made 12 monthly payments of $115, for a total payment of 12*$115 = $<<12*115=1380>>1380.
She bought a computer for $1200, so the finance charge that she paid is $1380-$1200 = $<<1380-1200=180>>180.
Therefore, the finance charge that Tamicca paid was $180, rounded to the nearest cent.
Step-by-step explanation:
In the arrangement below, each number is the non-negative difference of the two numbers above it. What is the sum of the four greatest distinct possible values for $z$
The numbers in the arrangement can be represented by x, y, z, a, b, c and d, where x is at the top and d is at the bottom. The relationship between the numbers is as follows:
x = y - z
y = a - b
z = c - d
We can use this information to find the values of z, c, and d in terms of x, y, and a:
z = y - x
c = z + d
d = z - c
Since we are looking for the four greatest distinct possible values for z, we can assume that x, y, and a are as small as possible (i.e. 0) and c and d are as large as possible.
Thus, the four greatest distinct possible values for z are:
z = y - x = 0 - 0 = 0
z = a - y = 0 - 0 = 0
z = c - d = c
z = c - d = d
The sum of these four values is 0 + 0 + c + d = c+d.
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