To simplify the complex fraction ((1)/(f^(3))-(1)/(a^(3)))/((1)/(f^(2))-(1)/(a^(2))), we can use the common denominator method.
Step 1: Find the common denominator for the numerator and denominator of the complex fraction. The common denominator for the numerator is (f^(3))(a^(3)) and the common denominator for the denominator is (f^(2))(a^(2)).
Step 2: Multiply each term in the numerator and denominator by the common denominator to get rid of the fractions.
Numerator: ((1)(a^(3))-(1)(f^(3)))/(f^(3))(a^(3))
Denominator: ((1)(a^(2))-(1)(f^(2)))/(f^(2))(a^(2))
Step 3: Simplify the numerator and denominator by combining like terms.
Numerator: (a^(3)-f^(3))/(f^(3))(a^(3))
Denominator: (a^(2)-f^(2))/(f^(2))(a^(2))
Step 4: Divide the numerator and denominator by the common factor (f^(2))(a^(2)).
Simplified fraction: (a-f)/(f^(1))(a^(1))
Step 5: Simplify the final fraction by canceling out the common factors.
Final answer: (a-f)/(fa)
Therefore, the simplified complex fraction is (a-f)/(fa).
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PLEASE HELP PLEASE DUE TOMORROW WILL MARK BRAINLIESY!(PICTURE ATTACHED)
Answer:(1)/(4)
Step-by-step explanation:n>1/4
What are the number in the number line and solve and graph?
A solution to the given compound inequality is m < 6 or m > 2.
What are the inequalities rules?In Mathematics, it is very important to note that you do not flip the inequality symbol (sign) when you are solving an inequality by multiplication or division with a positive numerical value (number).
In this context, we can logically deduce that you would flip the inequality symbol (sign) when you isolate the variable in an expression such as it's highlighted in the following steps:
4 - m < - 2
-m < -2 - 4
-m < -6
m < 6
For the second inequality, we have;
12 < -5m + 2
12 - 2 < -5m
10 < -5m
m > -10/5
m > 2.
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Find two numbers a and b such that the following system of linear equations is inconsistent. ax-3y=2 -4x+5y=b
The values of a and b that will result in an inconsistent system are a = 12/5 and b = 20x - 5y.
To find two numbers a and b such that the system of linear equations is inconsistent, we need to make sure that the two equations have the same slope but different y-intercepts. This will result in the two equations being parallel to each other and never intersecting, making the system inconsistent.
The first equation is: ax - 3y = 2. We can rearrange this equation to solve for y and find the slope:
3y = ax - 2
y = (a/3)x - (2/3)
The slope of this equation is a/3.
The second equation is: -4x + 5y = b. We can rearrange this equation to solve for y and find the slope:
5y = 4x + b
y = (4/5)x + (b/5)
The slope of this equation is 4/5.
For the system to be inconsistent, the slopes need to be equal. So we can set a/3 = 4/5 and solve for a:
a/3 = 4/5
a = 12/5
Now we need to find a value for b that will result in a different y-intercept. We can do this by plugging in the value of a into one of the equations and choosing a different value for the y-intercept:
y = (12/5)(1/3)x - (2/3)
y = 4x - (2/3)
If we choose a different value for the y-intercept, such as -1, we can solve for b:
y = 4x - 1
5y = 20x - 5
b = 20x - 5y
So the values of a and b that will result in an inconsistent system are a = 12/5 and b = 20x - 5y.
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PLEASE HELP
The expression (x-3)^2-16 is a difference of squares.
A. Identify a and b.
B. Factor and simplify.
Step-by-step explanation:
I think it might be A
I am not sure
Describe the translation that maps figure ABCD onto figure EFGH
The translation that maps figure ABCD onto figure EFGH is described as follows: Translate figure ABCD 7 units right to form figure EFGH..
What is a translation?Translation transformation is a type of geometric transformation that moves every point of an object or shape in a straight line without changing its orientation or size.
A translation happens when either a figure or a function are moved horizontally or vertically.
How to determine the translation ruleIf we look at the corresponding vertices on each figure, we have that:
7 was added to the x-coordinate of each vertex.The y-coordinate of each vertex remains constant.Hence: Translate figure ABCD 7 units right to form figure EFGH.
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what are the domain and range of the function f(x)=2^x+1
The domain of a function is the set of all possible input values (x) for which the function is defined.
The range of a function is the set of all possible output values (f(x)) that the function can produce.
For the given function f(x) = 2^(x+1), the domain includes all real numbers because we can substitute any real number for x and obtain a valid output.
To find the range, we can examine the behavior of the function as x approaches positive and negative infinity. As x approaches negative infinity, the exponent (x+1) becomes very large negative number, and 2^(x+1) approaches zero. As x approaches positive infinity, the exponent (x+1) becomes very large positive number, and 2^(x+1) approaches infinity. Therefore, the range of the function is (0, infinity).
So, the domain is (-infinity, infinity) and the range is (0, infinity).
converting feet and inches 8 and 4
Let A = and B a matrix of type (2,3). We assume that the second line of
B^tA^t is [1 − 2]. Calculate the second column of B. You must
justify your answer.
The second column of matrix B can be calculated by solving the equation where A and B are matrices of size (2,3). The second column of B is
[tex][b_21, b_22] = [(1 - a_11b_11 - a_13b_31)/a_12, (-2 - a_11b_12 - a_13b_32)/a_12][/tex]
First, we must transpose both A and B:
[tex]A^t[/tex]= [tex][a_11, a_12, a_13][a_21, a_22, a_23][/tex]
[tex]B^t[/tex] = [tex][b_11, b_21][b_12, b_22][b_13, b_23][/tex]
The second column of B.
[tex]B^tA^t[/tex] = [tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]
[1, -2] = [tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]
Since we have two equations and two unknowns, we can solve for the elements of the second column of B.
Solving for [tex]b_21[/tex]:
[tex][a_11b_11 + a_12b_21 + a_13b_31, a_11b_12 + a_12b_22 + a_13b_32][/tex]
Solving for [tex]b_22[/tex]:
[tex]-2 = a_11b_12 + a_12b_22 + a_13b_32b_22 = (-2 - a_11b_12 - a_13b_32)/a_12[/tex]
Therefore, the second column of B is:
[tex][b_21, b_22] = [(1 - a_11b_11 - a_13b_31)/a_12, (-2 - a_11b_12 - a_13b_32)/a_12][/tex]
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Identify the terms, the degree of each term and the degree of the polynomial. Then identify the leading term, th leading coefficient, and the constant term. -6r^(10)-11r^(3)+7r^(2)+3r-5
The leading term is -6r10; its coefficient is -6. The leading coefficient is -6. The constant term is -5.
What is leading term?Leading term is the term with the highest degree within an expression. It is the most important term and is used to determine the overall behaviour of a function.
The terms, degrees, and coefficients of the given polynomial are as follows:
-6r10: term, 10th degree, coefficient -6-11r3: term, 3rd degree, coefficient -117r2: term, 2nd degree, coefficient 73r: term, 1st degree, coefficient 3-5: term, 0th degree, coefficient -5To know more about leading term click on below link:
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When Mason goes to the gym, he spends one half of an hour lifting weights and one third of an hour on the treadmill. Which are correct descriptions of the relationship of time Mason spends lifting weights and on the treadmill.
Mason spends one half of an hour lifting weights and one third of an hour on the treadmill, so the ratio of time Mason spends lifting weights to time Mason spends on the treadmill is 1:2.
How Treadmill works?A treadmill is a machine used for walking or running while staying in one place. It usually has a belt and a platform to stand on, and the belt moves at a speed determined by the user. It is a great way to get a good cardio workout.
The question asks which are correct descriptions of the relationship of time Mason spends lifting weights and on the treadmill.
Mason spends one half of an hour lifting weights and one third of an hour on the treadmill, so the fraction of time Mason spends lifting weights is 2/3.
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I am needing some help with this
The volume of the rectangular pyramid is 1200 m³, the volume of the oblique cone is 5890 ft³ while the volume of the triangular prism is 321.75 ft³
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.
a) The volume of the rectangular pyramid is:
Volume = (1/3) * area of base * height
Substituting:
Volume = (1/3) * (15 m * 12 m) * 20 m = 1200 m³
b) The volume of the oblique cone is:
Volume = (1/3) * π * radius² * height
but radius = 30 ft / 2 = 15 ft,
Substituting:
Volume = (1/3) * π * 15² * 25 = 5890 ft³
The volume of the cone is 5890 ft³
c) The volume of the triangular prism is:
Volume = area of base * height
Substituting:
Volume = (1/2 * 9 ft * 5 ft) * 14.3 ft = 321.75 ft³
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1/2 + a = 1 3/4 = 7
1/2 + ? = 7
To solve the equation 1/2 + a = 1 3/4, we need to convert the mixed number 1 3/4 to an improper fraction:
1 3/4 = 4/4 + 3/4 = 7/4
Now we can rewrite the equation as:
1/2 + a = 7/4
To isolate the variable a, we need to subtract 1/2 from both sides:
a = 7/4 - 1/2
To add these two fractions, we need to find a common denominator, which is 4:
a = (7/4 - 2/4)
a = 5/4
Therefore, a = 5/4.
To solve the equation 1/2 + ? = 7, we can follow a similar approach. We need to isolate the variable on one side of the equation, so we need to subtract 1/2 from both sides:
? = 7 - 1/2
We need to find a common denominator to add these two fractions, which is 2:
? = (14/2 - 1/2)
? = 13/2
Therefore, the missing number is 13/2.
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If f(x) = 3x +7 and g(x) = x2 - 2x, what is g(f(1)) equal to? Answer: If f(x) = x + 4 and g(x) = 2x + 1, find (g o f)(x). Select one: a. 2x + 9 b. 2x^2 + 9x + 4 c. 2x^2 + 4 d. 2x + 5
Answer:
80 and 2x + 9
Step-by-step explanation:
to evaluate g(f(1)) , evaluate f(1) then substitute the value obtained into g(x)
f(1) = 3(1) + 7 = 3 + 7 = 10 , then
g(10) = 10² - 2(10) = 100 - 20 = 80
------------------------------------------------------
to calculate (g ￮ f)(x) , substitute x = f(x) into g(x)
(g ￮ f)(x)
= g(f(x))
= g(x + 4)
= 2(x + 4) + 1
= 2x + 8 + 1
= 2x + 9
Kaylee has a total of $30 in nickels, dimes, and quarters. There are twice as many nickels as dimes and 4 times as many quarters as dimes. How many nickels does Kaylee have?
a 25
b 50
c 75
d 100
By answering the above question, we may infer that The answer is yes, equation and Kaylee now has 26 nickels. Option B, or 50, is the correct response, therefore.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
Hence, she has twice as many nickels and quarters as normal.
The combined worth of Kaylee's coins is $30. This may be expressed as an equation:
[tex]0.05(2x) + 0.10x + 0.25(4x) = 30\\0.10x + 0.10x + 1.00x = 30\\2.20x = 30\sx = 13.64[/tex]
Kaylee has 2x = 28 nickels and 4x = 56 quarters if x = 14. These coins are worth 0.05(28), 0.10(14), and 0.25(56), for a total of $7.70.
This does not equal $30, hence the suggested solution is invalid.
Kaylee has 2x = 26 nickels and 4x = 52 quarters if x = 13. These coins are worth [tex]0.05(26) + 0.10(13) + 0.25(52) = $30.[/tex]
The answer is yes, and Kaylee now has 26 nickels.
Option B, or 50, is the correct response, therefore.
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A road map is drawn to a scale of 1mm : 50m calculate:
i) The distance on the map which represents 20km on the road
ii) The distance on the road which correspond to 228 on the map
The ratio used to depict the relationship between the dimensions of a model or scaled figure and the corresponding dimensions of the real figure or object is called the scale. On the other hand, a scale factor is a value that is used to multiply all of an object's parts in order to produce an expanded or decreased figure.
Given, A road map is drawn to a scale of 1mm: 50m
i) To find the distance on the map which represents 20 km on the road, we need to use the scale of the map.
Since 1 mm on the map represents 50 m on the road, we can set up a proportion:
1 mm / 50 m = x mm / 20,000 m
Cross-multiplying and solving for x, we get:
x = (1 mm / 50 m) * 20,000 m = 400 mm
Therefore, the distance on the map which represents 20 km on the road is 400 mm.
ii) To find the distance on the road which corresponds to 228 on the map, we can again use the scale of the map.
Since 1 mm on the map represents 50 m on the road, we can set up a proportion:
1 mm / 50 m = 228 mm / x m
Cross-multiplying and solving for x, we get:
x = (228 mm / 1) / (50 m / 1) = 4.56 km
Therefore, the distance on the road which corresponds to 228 on the map is 4.56 km.
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Find the length of the third side if necessary round to the nearest tenth 8 14
Answer:
Step-by-step explanation:
based on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest whole numberbased on the median of the samples, what is a reasonable estimate of the number of students that bike to school? Round to the nearest who
Does anyone know how to answer this?
Following surgery, a patient has been receiving a pain relief medication intravenously. The concentration C� (in milligrams per liter) of the medication in the patient's bloodstream t� hours after this process started is given by
C(t)=60t+12t+6,t≥0�(�)=60�+12�+6,�≥0
a) The patient will not receive pain relief unless the concentration of the medication is 1010 or more milligrams per liter. Use this function to determine the time interval for which the concentration of the medication, C� , will be greater than or equal to 1010 milligrams per liter.
The time interval for which the patient will receive pain relief is hours. (Express your answer in interval notation and round any decimals to the nearest tenth of an hour).
The time interval for which the patient will receive pain relief is [1.3, 8.3] hours.
To determine this, we can use the equation C(t) = 60t + 12t + 6, where t is the number of hours after the surgery. Setting C(t) = 1010 and solving for t, we get t = 13.3, so the patient will receive pain relief for t > 13.3 hours, or [1.3, 8.3] hours.
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Donny is combining two nut mixtures to create a new mixture. Both mixes are a combination
of peanuts and almonds. The first mixture is 40% almonds and the second is 25% almonds. How
much of each mixture should Donny combine to make 6 kg of a mixture of 33% almonds?
To find out how much of each mixture Donny should combine to make 6 kg of a mixture of 33% almonds, we need to use a system of equations. Let x be the amount of the first mixture and y be the amount of the second mixture.
The first equation represents the total amount of the mixtures:
x + y = 6
The second equation represents the amount of almonds in the mixtures:
0.40x + 0.25y = 0.33(6)
Solving the system of equations, we get:
0.40x + 0.25y = 1.98
0.40x + 0.25(6 - x) = 1.98
0.40x + 1.50 - 0.25x = 1.98
0.15x = 0.48
x = 3.2
Substituting the value of x back into the first equation:
3.2 + y = 6
y = 2.8
So Donny should combine 3.2 kg of the first mixture and 2.8 kg of the second mixture to make 6 kg of a mixture of 33% almonds.
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Triangle ABC has vertices A (-1, 2), B (5, 2), and C (5,-3) and triangle XYZ has vertices X(-0.5, 1), Y(2.5, 1), and 2(2.5, "-1.5)." What is the scale factor of the dilation that maps Triangle ABC onto triangle XYZ. ((PLS HELP ITS DUE TOMORROW))
The solution is, the scale factor of the dilation that maps Triangle ABC onto triangle XYZ is √2.
What is scale factor?A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.
here, we have,
given that,
Triangle ABC has vertices A (-1, 2), B (5, 2), and C (5,-3)
and triangle XYZ has vertices X(-0.5, 1), Y(2.5, 1), and 2(2.5, "-1.5)."
now, we now that,
distance formula:
d=√(x2−x1)^2+(y2−y1)^2
so, we get,
length of AB = 3√2
and, length of XY = 3
so, scale factor = AB/XY
=3√2/3
=√2
Hence, The solution is, the scale factor of the dilation that maps Triangle ABC onto triangle XYZ is √2.
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A ferry traveled
1
6
6
1
start fraction, 1, divided by, 6, end fraction of the distance between two ports in
3
7
7
3
start fraction, 3, divided by, 7, end fraction hour. The ferry travels at a constant rate.
At this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
The ferry travels at constant rate is 7/18 miles/hour
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
As per the data given in the question we have to find the ferry travels at a constant rate.
As per the question it is given that a ferry traveled 1/6 of the distance between two ports in 3/7 hour.
Now, Ferry travelled 1/6 miles of distance between two ports in 3/7 hours
Hence, Rate of Ferry is equal to distance travelled over time taken.
Rate of ferry = 1/6 ÷ 3/7
Now we calculate it.
Rate of ferry = 1/6 × 7 / 3 miles/hour
Rate of Ferry = 7/18 miles/hour
Hence, The ferry travels at constant rate is, 7/18 miles/hour.
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8x^2+18x+9
Box method
Answer:
144x^3+9
Step-by-step explanation:
First of all multiply 8x^2 and 18x then it is 144
Fill in the missing value. Input fractions as( a)/(b). (n^(2))^(2)=n Answer Check
The missing value in this equation is 4, or (4)/(1) in fraction form.
The missing value in this equation is the exponent of n in the final expression. To find this value, we can use the rule of exponents that states that when raising a power to another power, we multiply the exponents. In this case, we have (n^(2))^(2), so we multiply the exponents 2 and 2 to get a final exponent of 4. Therefore, the missing value is 4 and the equation can be written as (n^(2))^(2)=n^(4).
In fraction form, the missing value would be (4)/(1), since any whole number can be written as a fraction with a denominator of 1. So, the equation can also be written as (n^(2))^(2)=n^((4)/(1)).
Overall, the missing value in this equation is 4, or (4)/(1) in fraction form.
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What is the simplified form of [tex]\sqrt{400x ^{100}[/tex]
Answer:
[tex]20x^{50}[/tex]
Step-by-step explanation:
This is because you are simplifying the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
There is your answer!
solve equation . show or explain your method
5(y+2/5)=−13
Answer:
Step-by-step explanation:
You can use simple algebraic principles for this. First we distribute:
5(y + 2/5) = -13
5y + 10/5 = -13
5y + 2 = -13
Now we isolate the variable term:
5y + 2 = -13
5y = -15
Now we divide to isolate the variable itself:
5y = -15
y = -3
Hope this helps!
Find the y intercept and slope of the linear equation x+y=-6 1/2
The slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.
To find the y-intercept and slope of the linear equation x +y=-6 1/2, we
need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, let's isolate y by subtracting x from both sides of the equation:
x + y = -6 1/2
y = -x - 6 1/2
Now we can see that the equation is in slope-intercept form, where the slope (m) is -1 and the y-intercept (b) is -6 1/2.
Therefore, the slope of the equation x + y=-6 1/2 is -1, and the y-intercept is -6 1/2.
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The diagram shows two squares overlapping.
Work out the size of the angle marked z.
The measure of the angle ∠Z will be 88°.
What is geometry?Geometry is the study of two-dimensional and three-dimensional figures such as quadrilaterals, triangles, circles, their sides, and angles. Symmetry is defined as if the object is cut by its centre line the two cut parts should be the mirror image of each other so that we can call them symmetric to each other.
Given that the two angles are (9p + 20)° and (7p + 32 )°. The value of angle z is calculated as,
9p + 20 + 7p + 32 = 180
16p = 180 - 20 - 32
16p = 128
p = 8
The measure of the angle ∠Z will be,
9p + 20 + ∠Z= 180
72 + 20 + ∠Z= 180
∠Z = 180 - 72 - 20
∠Z = 88°
Therefore, the angle ∠Z is 88°.
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What is the total surface area of the rectangular prism shown?
Hence, the total surface area of the rectangular prism is 736 in².
Provide an example to help people understand what surface area is.A 3D object's surface area is calculated as the total of all of its faces. For instance, if we wanted to figure out how much paint we would need to paint a cube, we would use the cube's surface area.
To calculate the total surface area of the rectangular prism, we need to find the area of each of its six faces and add them together.
The area of the top and bottom faces, which are identical, is:
Length x Breadth = 16 in x 8 in = 128 in².
The area of the front and back faces, which are also identical, is:
Height x Breadth = 10 in x 8 in = 80 in².
The area of the left and right faces, which are also identical, is:
Height x Length = 10 in x 16 in = 160 in².
Therefore, the total surface area of the rectangular prism is:
2(Length x Breadth) + 2(Height x Breadth) + 2(Height x Length)
= 2(16 in x 8 in) + 2(10 in x 8 in) + 2(10 in x 16 in)
= 256 in² + 160 in² + 320 in²
= 736 in²
Hence, the total surface area of the rectangular prism is 736 in².
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"Use the Law of Sines to solve (if possible) the triangle. If two
solutions exist, find both. Round your answers to two decimal
places.
A = 21° , a = 9.5, b = 22
Case 1:
B=? C=? c=?
Case 2:
B=? C=? c=?"
The two possible solutions for the given triangle are:
Case 1: $B = 51.92°$, $C = 107.08°$, $c = 25.93$
Case 2: $B = 128.08°$, $C = 30.92°$, $c = 13.45$
Both solutions exist and are rounded to two decimal places.
The Law of Sines states that for any triangle ABC, the following equation holds:
$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
Using this equation, we can solve for the missing angles and side lengths in the given triangle.
Case 1:
To find angle B, we can rearrange the equation to get:
$\sin B = \frac{b \sin A}{a}$
Plugging in the given values:
$\sin B = \frac{22 \sin 21°}{9.5}$
$\sin B = 0.789$
Taking the inverse sine of both sides:
$B = \sin^{-1}(0.789)$
$B = 51.92°$
To find angle C, we can use the fact that the sum of the angles in a triangle is 180°:
$C = 180° - A - B$
$C = 180° - 21° - 51.92°$
$C = 107.08°$
Finally, to find side c, we can use the Law of Sines again:
$\frac{c}{\sin C} = \frac{a}{\sin A}$
Rearranging and plugging in the given values:
$c = \frac{a \sin C}{\sin A}$
$c = \frac{9.5 \sin 107.08°}{\sin 21°}$
$c = 25.93$
So the solution for Case 1 is:
$B = 51.92°$, $C = 107.08°$, $c = 25.93$
Case 2:
In this case, we need to consider the possibility of an obtuse angle B. To find this angle, we can use the fact that the sine of an obtuse angle is the same as the sine of its supplement:
$\sin B = \sin (180° - B)$
So we can find the supplement of the angle we found in Case 1:
$B = 180° - 51.92°$
$B = 128.08°$
Plugging this value back into the Law of Sines equation, we can find the other missing values:
$C = 180° - A - B$
$C = 180° - 21° - 128.08°$
$C = 30.92°$
$c = \frac{a \sin C}{\sin A}$
$c = \frac{9.5 \sin 30.92°}{\sin 21°}$
$c = 13.45$
So the solution for Case 2 is:
$B = 128.08°$, $C = 30.92°$, $c = 13.45$
Therefore, the two possible solutions for the given triangle are:
Case 1: $B = 51.92°$, $C = 107.08°$, $c = 25.93$
Case 2: $B = 128.08°$, $C = 30.92°$, $c = 13.45$
Both solutions exist and are rounded to two decimal places.
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cindy bought 7/8 yard of ribbon jacob bought 4/5 more than cindy how much did he buy
In linear equation, 7/10 did he buy .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
multiply the fractions by each other.
7/8*4/5
7*4=28
8*5=40
28/40
"B" would be the correct answer but, it the fraction should be reduced to 7/10.
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You bought water bottles to sell and spent a total of $50. You sell each bottle for $2. Which graph shows how many bottles you have to sell to earn back the money spent on water?
The graph that shows the number of bottles that need to be sold to earn back the money spent on water is Graph C.
How to find the graph ?The number of bottles that need to be sold to earn back the amount spent on water is :
= Total spent / profit per bottle
= 50 / 2
= 25 bottles
Graph C starts from - $ 50 to show that the amount you have is - $ 50 to show the amount spent on the bottles.
Graph C then ends at 25 bottles to show that this is where you would need to stop to have made back what you spent.
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