The value of the trignometric expression sin(a+b) is 0.3.
Given the trignometric equations sin a + cos b = -0.2 and sin b + cos a = 1.6
So, squaring both equations and adding them
we have
[tex](sin a + cos b)^2 = -0.2^2\\(sin a + cos b)^2 = 0.04\\sin^2a+cos^2b + 2 sina cos b= 0.04\\(sin b + cos a)^2 = 1.6^2\\sin^2b+cos^2a + 2 sinb cos a= 2.56\\\\[/tex]
adding both equations
[tex]sin^2a+cos^2b + 2 sina cos b + sin^2b+cos^2a + 2 sinb cos a= 0.04+2.56\\[/tex]
1+1+2( sina cos b + cos a sin b)= 2.6
2( sina cos b + cos a sin b) = 0.6
( sina cos b + cos a sin b) = 0.3
We know that sin(a+b)= ( sina cos b + cos a sin b)
So,
sin(a+b)=0.3
Therefore, the value of sin(a+b) = 0.3
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I WILL GIVE BRAINLIEST TO THE ONE WITH THE CORRECT ANSWER.
Solve for x. Assume that lines which appear to be diameters are actual diameters.
The value of x is 4 , the correct option is (C)4 .
In the question ,
it is given that AD and BE are diameters , hence they are straight lines .
From the figure shown below , we can see that
∠AOE and ∠BOD are vertically opposite angles ,
the property of vertically opposite angle states that " the vertically opposite angles are equal in measure ."
So,
substituting the values of ∠AOE and ∠BOD from the figure , we get
36x-4 = 92+(11x+4)
36x-11x = 92+4+4
25x = 100
x=4
Therefore , the value of x = 4, the correct option is (C)4 .
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A scientist needs 0.25 kilograms of a substance to conduct some experiments. The substance can only be purchased in milligrams. Which of the following amounts of the substance should the scientist order? 250,000 milligram 0.00025 milligrams 0.00000025 milligrams 250 milligrams
There are thing we must already know:
[tex]\begin{gathered} 1\text{kilogram}=1,000\text{gram} \\ 1\text{gram}=1,000milligram \end{gathered}[/tex]From this, we must know that:
[tex]1\text{kilogram}=1,000,000\text{milligram}[/tex]The scientis needs 0.25kilograms. From this we calculate:
[tex]0.25\text{kilograms}=0.25\times1000000milligrams=250,000milligrams[/tex]( Please help I'll mark brainliest )
Answer the question in the photo.
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
If QR = 6x, RS = 10, and QS = 5x + 13, what is QS?
If QR = 6x, RS = 10 and QS = 5x+13, then the length of the line QS is 28 units.
The length of the line QR = 6x
The length of the line RS = 10
The length of the line QS = 5x+13
We know
The length of the line QS = The length of the line QR + The length of the line RS
Substitute the values in the equation
5x+13 = 6x + 10
Move the 6x to the left hand side of the equation and move 13 to the right hand side of the equation
5x-6x = 10-13
Subtract the terms
(5-6)x = 10-13
-1x = -3
x = 3
Then the length of the QS = 5x+13
Substitute the value of x in the equation
The length of the line QS = 5×3+13
= 15+13
= 28 units
Hence, if QR = 6x, RS = 10 and QS = 5x+13, then the length of the line QS is 28 units
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In the given figure, AD is adjacent to BC.
if AB = 13 cm, BD = 5 cm and DC = 16 cm,
find the values of :
(I) sin B
(II) sec B
(III) cot B
(iv) cos C
(v) cosec C
(vi) tan C
By using the method of trigonometry,
(1)sin B=P/H=AD/AB=12/13
(2)sec B=H/B=AB/BD=13/5
(3)cot B=B/P=BD/AD=5/12
(4)cos C=B/H=CD/AC=16/20=4/5
(5)cosec C=H/P=AC/AD=20/12=5/3
(6)tan C =P/B=AD/DC=12/16=3/4
What is trigonometry?Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are the trigonometric functions (sometimes known as the circle functions) that make up trigonometry. The unit circle is the most straight forward way to define the trigonometric functions. Let theta represent an angle that is calculated along a circle's arc counterclockwise from the x-axis.
Given that,
[tex]AD^{2}= AB^{2}- BD^{2}= 13^{2}- 5^{2}= 169-25= 144[/tex]
=>AD=12cm
(1)sin B=P/H=AD/AB=12/13
(2)sec B=H/B=AB/BD=13/5
(3)cot B=B/P=BD/AD=5/12
[tex]AC^{2}= AD^{2}+ DC^{2}= 12^{2}+ 16^{2}= 144+ 256= 400[/tex]
=>AC=20cm
(4)cos C=B/H=CD/AC=16/20=4/5
(5)cosec C=H/P=AC/AD=20/12=5/3
(6)tan C =P/B=AD/DC=12/16=3/4
note: P=perpendicular
B=base
H=hypotenuse
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100 points, please answer and take time on the answer
1) The relationship between ∠2 and ∠6 is that they are alternate angles.
2) The relationship between ∠1 and ∠3 is that they are corresponding angles.
How to find the congruent angles?Corresponding angles are defined as the angles that are formed in corresponding corners with the transversal when two parallel lines are intersected by any other line.
Alternate angles are defined as the angles that are formed by the intersection of a transversal and two parallel lines.
This alternate angle could either be interior alternate or exterior alternate.
1) Since we are told that Line 1 is parallel to Line 2, then it means that from definition of alternate angles that ∠2 and ∠6 are alternate angles.
2) Since we are told that Line 1 is parallel to Line 2, then it means that from definition of corresponding angles that ∠1 and ∠3 are corresponding angles.
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Apply Laws of Exponents to write an equivalent expression.
d6df0
Answer: move the base and exponent to the other side of the fraction line and change the exponent to positive: 1/(24)
Choose the expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed.
The expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed is [tex]\frac{3^{6} }{9^{15} }[/tex]
Nine raised to the negative third power = [tex]9^{-3}[/tex]
Three raised to the negative second power times nine squared = [tex](3x^{-2})(9^{2} )[/tex]
The expression is [tex](\frac{9^{-3} }{(3^{-2})(9^{2} ) } )^{3}[/tex]
=[tex]\frac{9^{(-3)(3)} }{(3^{(-2)(3)})(9^{(2)(3)} }[/tex]
=[tex]\frac{9^{-9} }{(3^{-6})(9^{6}) }[/tex]
= [tex]\frac{3^{6} }{(9^{9})(9^{6}) }[/tex]
= [tex]\frac{3^{6} }{9^{15} }[/tex]
Hence, the expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed is [tex]\frac{3^{6} }{9^{15} }[/tex]
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The ratio of men to women working for a company is 4 to 7. If there is 253 employees total, how many men work at the company
Answer:
92 men
Step-by-step explanation:
First, since they give you the total employees, you need to add the ratios together to get a total.
4 + 7 = 11
Next, setup a proportion using men to total employees.
[tex]\frac{4}{11}=\frac{m}{253}[/tex]
The left side is the ratio and the right side is the actual. m will represent the total number of men employed.
Cross multiply then divide.
4 x 253 = 1012
11 x m = 11m
11m = 1012
11m/11 = 1012/11
m = 92
A
(3x+8)°
B=
(6x-2)
C =
69°
x=?
CAB=?
ACB=
ABC=
The value of x is 11.7.
The angles CAB, ACB, and ABC are 43.1°, 69°, and 68.2° respectively.
What is the Angle Sum Property?According to the triangle's "angle sum property," a triangle's three inner angles can never add up to more than 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180°, regardless of whether it is acute, obtuse, or right.Given angles are:
A = (3x+8)°
B= (6x-2)°
C = 69°
Using the Angle sum property we get,
(3x+8)° + (6x-2)° + 69° = 180°
9x + 75° = 180°
9x = 180°- 75°
x = 11.7
CAB = (3 × 11.7 + 8)° = 43.1°
ACB = 69°
ABC = (6 ×11.7 - 2) = 68.2°
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Can anyone tell me if what i put is correct? Thank you!
Find the equation of the line that contains the point P(−4, 6) and has slope 4. (Let y be the dependent variable and let x be the independent variable.)
The equation of the line that contains the point P(-4,6) and has slope 4 is y=4x+22 .
The equation of line passing through the point (x₁,y₁) with slope (m) is given by the formula
(y-y₁)=m(x-x₁)
In the question ,
it is given that
the required line passes through the point P(-4,6) and has slope 4
So, x₁= -4 , y₁=6 and m = 4
Substituting the values of x₁, y₁ and m in the equation of line formula , we get
y-6=4(x-(-4))
y-6=4(x+4)
y-6=4x+16
y=4x+16+6
y=4x+22
Therefore , the equation of the line that contains the point P(-4,6) and has slope 4 is y=4x+22 .
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Explain why the descriptions "right 5 up 2", "right 10 up 4", "left 5 down 2", "right 5/2 up 1", and "left 1 down 2/5" all describe the same inclination for a straight line.
All of the translations describes the same inclination for a straight line because the they all have a pitch (slope) of 2/5.
How to determine the pitch (slope) of a straight line?Mathematically, the pitch (slope) of a geometric figure or straight line can be calculated by using this formula:
Pitch (slope) = V/H
Where:
V represents the rising vertical distance of an object.H represents the horizontal distance an object runs through.Based on the information provided, the pitch (slope) of this line is given by:
Pitch (slope) = Up 2/Right 5 = 2/5
Pitch (slope) = Up 4/Right 10 = 2/5
Pitch (slope) = Down 42/Left 5 = 2/5
Pitch (slope) = Up 1/Right 5/2 = 2/5
Pitch (slope) = Down 2/5/Left 1 = 2/5
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A magazine subscription has a cover price of $35. Amanda received an offer for 67% off the cover price. What is the sale price of the magazine subscription?
The sale price of the magazine subscription is $11.55
How to calculate the sale price of the magazine subscription?From the question, the given parameters are:
Subscription = $35
Discount = 67% off
The sale price of the magazine subscription is then calculated as
Sales price = Subscription x (1 - Discount)
Substitute the known values in the above equation
So, we have the following equation
Sales price = 35 x (1 - 67%)
Evaluate the product
Sales price = 11.55
Hence, the sales price is $11.55
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What is the special angle pair relationship between the two?
Answer: Corresponding angles
Step-by-step explanation:
True by the definition of corresponding angles.
10
4. The English language consists of vowels and consonants totaling 26 letters. A,
E, I, O, U, and Y are the English vowels and the rest are consonants.
A. What is the ratio of consonants to vowels in the English language? (3
points)
B. What fraction of the letters of the English language are vowels? (3 points)
The ratio of consonants to vowels is 21:5.
What is ratio?
A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4), while the ratio of oranges to overall fruit is 8:14. (or 4:7).
No. of consonants = 21
No. of vowels = 5
(A) Ratio of consonant to vowels = 21/5 = 21:5
(B) Fraction of vowels = 5/26
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express the mix number as the sum of an integer and a fraction.
-1 2/3 = + (2/3)
We will add 1 to 2/3 to make sum of [tex]1\frac{2}{3}\\[/tex] of an integer and a fraction.
What is integer?
An integer, often known as a "round number" or "whole number," is any positive or negative number that does not contain fractional or decimal parts. Examples are 3, -10, and 1,025 which are all integers, but 2.76 (decimal), 1.5 (decimal), and 3 12 (fraction) which are not.Three categories of integers exist: Negative integers with a value of 0 (Natural numbers) Integer Negatives (Additive inverse of Natural Numbers).What is fraction?
An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.- [tex]1\frac{2}{3}[/tex] = _ + (2/3)
we will add 1 to 2/3 to make sum of [tex]1\frac{2}{3}\\[/tex] of an integer and a fraction.
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anyone have a clue on how to do this?
If CA and CE are opposite rays, CH bisects ∠ GCD, and GC bisects ∠ BGD. If m ∠ BGC = (7x - 2)° and m ∠ CGF = (8x - 8)°, then the value of m ∠ BGF exists 80°.
What is meant by angles?An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The two rays are called the sides of an angle, and the common endpoint is called the vertex.
If CA and CE are opposite rays, CH bisects ∠ GCD, and GC bisects ∠ BGD.
Given: m ∠ BGC = (7x - 2)° and m ∠ CGF = (8x - 8)°,
m ∠ BGC = m ∠ CGF
7x - 8 = 8x - 8
substracting 2 from both sides of the equation, we get
7x - 8 = 8x - 8 - 8
7x - 8 = 8x
simplifying the above equation, we get
x = 6
Therefore, the value of x = 6.
⇒ m ∠ BGC = m ∠ C G F = 40°
Therefore, the value of m ∠ BGF = 2(40)° = 80°
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There is a proportional relationship between the number of months a person has had a streaming movie subscription and the total amount of money they have paid for the subscription. The cost for 6 months is $47.94. The point (6,47.94) is shown on the graph below.
What is the constant of proportionality in this relationship?
$7.99 is the constant of proportionality in this relationship.
What is proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.
Given Data
The cost for 6 months is $47.94.
x = number of months
x = 6
y = total amount of money they have paid for the subscription
y = 47.94
Constant of proportionality = [tex]\frac{47.94}{6}[/tex]
Constant of proportionality = 7.99
$7.99 is the constant of proportionality in this relationship.
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The Distributive Property Use the Distributive Property to rewrite each expression without parenthesis. 1. 6(x + 3) 2. 5( y - 4 ) 3. -7( m - 1 )
Answer:
1. 6x+18 2. 5y-20 3. -7m+7
Step-by-step explanation:
1. 6(x+3) 2. 5(y-4) 3. -7(m-1)
6x+24. 5y-20. -7m+7 <--- - times - = +
how many non-empty subsets of consist entirely of prime numbers? (we form a subset of the group of numbers by choosing some number of them, without regard to order. so, is the same as .)
The question is testing knowledge on subsets. The application of combinations is used to sum up. Consider prime factors between 1 and 11. They are{1,2,3,4,5,6,7,8,9,10,11}.
The prime factors in the set are {2,3,5,7,11}. This set has 5 elements.
Apply combinations to obtain the total subsets.
The subsets with 1 element is 5C1 = 5 subsets
The subsets with 2 elements is 5C2= 10 subsets
The subsets with 3 elements is 5C3= 10 subsets
The subsets with 4 elements is 5C4= 5 subsets
The subsets with 5 elements is 5C5= 1 subset
The total non-empty subsets are 5+10+10+5+1 = 31 subsets.
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The Cookie Booth started with
148 cookies. They sold 66 cookies
by noon. What is the ratio of sold
cookies to non-sold cookies?
Answer:If 104 items were sold and 32 if these are cookies, to get number of brownies sold subtract 32 from 104. This gives 72 brownies sold.
A ratio is a fraction. If we want the ratio of brownies to cookies it would look like
brownies 72
________ = _____
cookies 32
This ratio could be reduced by dividing both parts of the fraction by the greatest common factor of 8.
This gives a reduced ratio of 9
_____
4
Step-by-step explanation:
Answer:I think 82 or 56
Step-by-step explanation:
An object in real life is 55 feet long. How many inches long should it be in the scale drawing?
When a scale factor of 1 inch to 6 feet is used, the length is 9 inches.
How to illustrate the information?From the information illustrated, a scale factor of 1 inch to 6 feet is used. In this situation, an object in real life is 55 feet long.
The number of inches that should be in the scale drawing will be:
= Number of feet / Scale used
= 55 / 6
= 9.17 inches
The length that should be in the scale is 9 inches.
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A scale factor of 1 inch to 6 feet is used. An object in real life is 55 feet long. How many inches long should it be in the scale drawing?
Write an equation that represents the line.
Use exact numbers.
Answer:
y=4/3-5
Step-by-step explanation:
Y=mx+c
mx=gradient which is 4/3
c is y intercept which is -5
Write a simplified equation in point-slope form.
Line 1: m = -3, passes through (-4, 10)
Answer:
y=-3x-2
Step-by-step explanation:
y=mx+b; adjust b value --> y=-3x-2
Find the distance from point A (-1, 7) to the line y = 3r. Round your answer to the nearest tenth.
The distance is about
units.
Answer:
We will get that the distance is 3.22.
Find the sum of APS 2+5+8+........ as far as the 18th term
Sum of APs 2+5+8+........ as far as the 18th term is 495.
Sum of n terms of A.P.
[tex]S_{n} = \frac{n}{2}[2a+(n-1)d][/tex]
where,
[tex]S_{n}[/tex] = sum of n terms of A.P.
a = first term of A.P.
d = Common difference.
Given,
d=5−2=3
a=2
[tex]S_{11}[/tex]=[tex]\frac{18}{2}[/tex][4+(18-1)×3]
=[tex]\frac{18}{2}\\[/tex][4+51]
=[tex]\frac{18}{2}[/tex]×55
=495
An arithmetic progression, or arithmetic sequence, is a sequence of numbers in which the difference between successive members is constant. Here is the AP formula for AP a, a + d, a + 2d, a + 3d, . . . a + (n - 1) d. The formula for finding the nth term is [tex]a_{n}[/tex] = a + (n – 1) × d.
Then the formula for finding the sum of the arithmetic progressions is:[tex]S_{n} = \frac{n}{2}[2a+(n-1)d][/tex] where a = first term in arithmetic progression, n = number of terms in arithmetic progression, and d = total difference.
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uh?????????????????????????
Answer:
I'm sure it's 1.2506407mm
Step-by-step explanation:
There are 10 students in a class. 6 of them wear glasses. If a student is chosen at random from the class, what is the probability that they do not wear glasses? Give your answer as a decimal.
There are 10 students in a class, 6 of them wear glasses. If a student is chosen at random from the class, then the probability that they do not wear glass is 2/5
Total number of Students = 10
Students who wear glasses = 6
Students who don't wear glasses = 4
Probability is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,
P(E) = (Number of favorable outcomes) ÷ (Total favorable outcomes).
The probability of a student not wearing glasses is,
Probability = Students who don't wear glasses/Total number of Students
Probability = 4/10 i.e., 2/5
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During 712months of hibernation, a black bear experienced a weight loss of 64.5 pounds.
On average, what was the bear’s weight change per month?
On average, the bear's weight change per month was 8.6 pounds.
What is the average?The average is the mean value in a data set.
We compute the average by adding the data values and dividing by the number of items in the data set.
In this scenario, the average weight loss per month offers an idea of the weight change the bear experienced during the 7¹/₂ months.
The number of months during hibernation = 7¹/₂ or 7.5 months
The total weight loss = 64.5 pounds
The average weight change per month = 8.6 pounds (64.5/7.5)
Thus, we can conclude that, on average, the bear experienced a weight loss of 8.6 pounds per month and reduced by a total of 64.5 pounds in 7¹/₂ months.
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Question Completion:During 7 1/2months of hibernation, a black bear experienced a weight loss of 64.5 pounds.