The value of the equation is A = ( 6x - 9y ) / ( 3 + 2y )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = ( 12x - 18y ) / ( 6 + 4y )
On simplifying the equation , we get
Taking the common factor as 6 in the numerator , we get
A = 6 ( 2x - 3y ) / ( 6 + 4y )
Taking the common factor as 2 in the denominator , we get
A = ( 6/2 ) ( 2x - 3y ) / ( 3 + 2y )
On further simplification , we get
A = 3 ( 2x - 3y ) / ( 3 + 2y )
A = ( 6x - 9y ) / ( 3 + 2y )
Hence , the equation is A = ( 6x - 9y ) / ( 3 + 2y )
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Question 2: Express each of the following numbers using exponential rotation
a. 343 b. 3145
there are seniors and juniors in a particular social organization. in how many ways can seniors and juniors be chosen to participate in a charity event?
Total ways can 4 seniors and 2 juniors be chosen to participate in a charity event is 1,91,100.
There are 16 seniors and 15 juniors in a particular social organization and
4 seniors and 2 juniors had to be chosen to participate in a charity event.
Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by [tex]^nC_r[/tex] and it is given by, [tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex] , where 0 ≤ r ≤ n.
Therefore the total ways that 4 seniors and 2 juniors be chosen to participate in a charity event = [tex]^{16}C_{4}.^{15}C_{2}[/tex]
= [tex]\frac{16!}{4!(16-4)!}$\times \frac{15!}{2!(15-2)!}[/tex]
= 1820 × 105
= 1,91,100
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The complete question is:
There are 16 seniors and 15 juniors in a particular social organization. In how many ways can 4 seniors and 2 juniors be chosen to participate in a charity event?
B = { x: 1≤ x ≤ 11 where x is a prime number} What is x?
Answer: x is anything from the set {2, 3, 5, 7, 11}
This is the list of primes between 1 and 11. The value 1 is not prime.
Simplify the following using the properties of exponents.
Answer:
Step-by-step explanation:
7/x^-8 = 7x^8
solve the equation x^3-x^2-18=0 given that x-3 is a factor of x^3-x^2-18
The solutions to the equation x³ - x² - 18 = 0 are given as follows:
x = 3, x = -1 ± 2.236i.
How to obtain the solutions to the equation?The equation for this problem is defined as follows:
x³ - x² - 18 = 0
x - 3 is a factor, hence one solution is given as follows:
x - 3 = 0
x = 3.
Also considering that x - 3 is a factor, and x - 3 is of the first degree while the equation is of the third degree, we have that:
(x - 3)(ax² + bx + c) = x³ - x² - 18
ax³ + (b - 3a)x² + (c - 3b)x - 3c = x³ - x² - 18
Hence the coefficients are given as follows:
a = 1.b - 3 = -1 -> b = 2.-3c = -18 -> c = 6.Hence the remaining solutions are given as follows:
x² + 2x + 6 = 0.
Using a quadratic function calculator:
x = -1 ± 2.236i.
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Danielle earns a 7.75% commission on everything she sells at the electronics store where she works. She also earns a base salary of $725 per week. What were her sales last week if her total earnings for the week were $1,058.25?
Danielle's sales last week were $
Danielle's sales last week were $. At her job at an electronics store, Danielle receives a $4,295.16 commission on every sale.
What is an electronics store?
Courses in calculus (single and multivariable), complex analysis, differential equations (both ordinary and partial), linear algebra, and probability are typically required for jobs in electronics engineering. Additionally, topics like Z-transforms and Fourier analysis are frequently covered in electrical engineering curricula.More mathematics is required for electronics and telecommunications technicians, such as complex numbers, trigonometry, basic geometry, fundamental statistics, and differential and integral calculus.Every subject wants their students to be able to examine mathematics using technology, such as spreadsheets.Let's start by first finding out how much commission Danielle earned last week. We know that her total earnings were $1,058.25 and her base salary was $725 per week. Therefore, her commission must have been:
$1,058.25 - $725 = $333.25
We also know that Danielle earns a 7.75% commission on everything she sells. Let's use "x" to represent her total sales last week. Then we can set up an equation to solve for x:
0.0775x = $333.25
Solving for x, we get:
x = $333.25 / 0.0775
x = $4,295.16
Therefore, Danielle's sales last week were $4,295.16.
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The distance between Dallas and Houston is about 364 kilometers. There are approximately 8 kilometers in 5 miles. Which measurement is closest to the number of miles between these two towns?
Answer: Approximately 226 miles
Step-by-step explanation:
Km. to Mi.
364 = 226
how many pattern block triangles would create 2 hexagons
To make two hexagons out of pattern blocks, you would need a total of 12 triangles. Six triangles are needed for each hexagon.
To make two hexagons out of pattern blocks, you would need a total of 12 triangles. Each hexagon requires six triangles to make it, so two hexagons would need double that amount. Since the pattern blocks come in the shapes of triangles, you can easily construct the hexagons by placing the triangles together. Each triangle has two sides that fit together and two sides that overlap, so the six triangles will create a complete hexagon when they are all put together. Once you have two hexagons constructed, they will fit together to make a larger shape, depending on how you place them. With this method, you can easily make two hexagons out of pattern blocks.
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Which ordered pair is a solution of the equation? y=4x-7
A only (2,1)
B only (4, 9)
C both ( 2,10) and (4,9)
D neither
Answer: To find the ordered pair that is a solution of the equation y = 4x - 7, we need to substitute the values of x and y into the equation and see if it is true.
If (x, y) is a solution, then y = 4x - 7 must be true for that particular x and y.
Option A: (2, 1)
Substituting x = 2 and y = 1 into the equation, we get:
1 = 4 * 2 - 7
1 = 8 - 7
1 = 1
Since the equation is true for x = 2 and y = 1, (2, 1) is not a solution of the equation.
Option B: (4, 9)
Substituting x = 4 and y = 9 into the equation, we get:
9 = 4 * 4 - 7
9 = 16 - 7
9 = 9
Since the equation is true for x = 4 and y = 9, (4, 9) is a solution of the equation.
Option C: Both (2, 10) and (4, 9)
Substituting x = 2 and y = 10 into the equation, we get:
10 = 4 * 2 - 7
10 = 8 - 7
10 = 3
Since the equation is not true for x = 2 and y = 10, (2, 10) is not a solution of the equation.
So, the only ordered pair that is a solution of the equation y = 4x - 7 is (4, 9). The answer is B) only (4, 9).
Step-by-step explanation:
5. Solve for x.
S
(14x-15)
139⁰
V
U
T
7. Mark starts out the week with $8. Every day he gives sister $2. Write an equation and
graph the situation. What is the meaning of the values when x is greater than 4?
Answer:
y = -2x + 8
When x = 4, Mark has no more money , so when x is greater than 4, Mark is in debt or is not able to give his sister any more money.
Step-by-step explanation:
Ata school
number of boys : number of girls = 11: 9
There are 124 more boys than girls.
Work out the total number of students at the school.
Answer:
Step-by-step explanation:
Let's call the number of boys "b" and the number of girls "g". From the ratio, we know that b/g = 11/9.
Also, we know that b = g + 124, so we can substitute the second equation into the first:
b/g = 11/9
b = g + 124
g + 124 / g = 11/9
Cross multiply:
9g + 1112 = 11g
Solve for g:
-2g = -1112
g = 556
So there are 556 girls and 556 + 124 = 680 boys at the school.
The total number of students at the school is 556 + 680 = 1236.
PLS SHOW FULL WORK AND FULL ANSWERS ONLY OR WILL BE REPORTED
The rationalized form of the surd is;
1) 25/13
2) 144/3
3) 36
How do you rationalize a surd?We have to note that the term surd would have to refer to an irrational number as we know it.
1) The conjugate of the surd is;
5/4 + √3
Rationalizing we have;
5/4 - √3 * 5/4 + √3
25/16 + 4√3 - 4√3 -3
25/13
2) The conjugate is √7 - 2
Rationalizing we have;
12/√7 + 2 * 12/√7 - 2
144/7 -2√7 + 2√7 -4
144/3
3) The conjugate of the surd is √2 + √3
Rationalizing we have;
6/ √2 - √3 * 6/ √2 + √3
36/4 +√6 - √6 - 3
36/1 = 36
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What is the perimeter of a square if the area is 49cm^2
Answer:
Step-by-step explanation:
take length as x,
perimeter= 28cm
Answer:
28cm
Step-by-step explanation:
7+7+7+7
1) At a fund-raising event, 60% of the people were males and the rest were females. 20% of the females left the event in the afternoon. In the evening, after 33 males and 35 females left the event, 75% of the people at the event were males. (a) What percentage of the people left the event in the afternoon? (b) How many people were there at the start of the fund-raising event?
(a) The percentage of people that left the event in the afternoon is 8%
(b) The total number of people that were there at the start of the fund-raising event were 68.
How did we get these values?Let x be the number of people at the start of the event. Then, 0.6x were males and 0.4x were females.
In the afternoon, 0.2 * 0.4x = 0.08x females left the event.
So, there were 0.4x - 0.08x = 0.32x females left at the event.
In the evening, 33 + 35 = 68 people left the event, and x - 68 people were left.
Out of the x - 68 people, 0.6(x - 68) were males.
So, we have 0.75 * (x - 68) = 0.6 * (x - 68).
We can now solve for x:
0.75 * (x - 68) = 0.6 * (x - 68)
0.15 * (x - 68) = 0
x - 68 = 0
x = 68
Thus, there were 68 people at the start of the fund-raising event.
(a) The percentage of people who left the event in the afternoon was 0.08x / x * 100% = 0.08 * 100% = 8%.
(b) There were 68 people at the start of the fund-raising event.
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Trigonometry question
The value of sin (θ/2) in the trigonometry is π/9
How to find sin (theta / 2)Information given in the problem
tan θ = 7/8,
where
0 < θ < π/2
solving for θ, from tan θ = 7/8
tan θ = 7/8
θ = arc tan (7/8)
θ = 0.7188 radians
soling for sin (θ/2)
= sin (θ/2)
= sin (0.7188/2)
= 0.3517 approximately π / 9
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Multiply and simplify. Show work to earn full credit. (2 − 3)(7 2 − + 8
We can make advantage of the distributive property of multiplication over addition, which says that a(b + c) = ab + ac. As a result, -55 is the simplified expression.
What is distributive property, and what are some examples?When you multiply a value by a sum, the distributive property of multiplication over addition is put to use. For instance, you wish to multiply 5 by the product of 10 plus 3. Since the numbers are similar terms, we typically add the numbers first and then multiply by 5=> 5(10 + 3) = 65.
What is distributive property class 7?An algebraic principle known as the distributive property indicates that it is necessary to multiply each of the two integers by the factor being multiplied by the sum or difference of two terms.
Using this property, we can expand the expression as follows:
(2 − 3)(7 2 − + 8) = 2(7 2 − + 8) − 3(7 2 − + 8)
Now we can simplify each term separately:
2(7 2 − + 8) = 2(49 − 2 + 8) = 2(55) = 110
and
−3(7 2 − + 8) = −3(49 − 2 + 8) = −3(55) = −165
Therefore, putting the results together, we have:
(2 − 3)(7 2 − + 8) = 110 − 165 = -55
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While racking a circuit breaker in energized gear, what means could be used to reduce the arc flash hazard to 0 incident energy exposure to a worker?
The only way to completely eliminate the risk of arc flash is to de-energize the equipment before performing any maintenance or testing.
Racking a circuit breaker in energized gear poses a significant arc flash hazard to workers due to the potential for electrical energy to be released and cause an arc flash.
If it is not possible to de-energize the equipment, the following means could be used to reduce the arc flash hazard to 0 incident energy exposure to a worker:
Use remote racking: Remote racking systems allow workers to rack circuit breakers from a safe distance, reducing the risk of exposure to the arc flash hazard.Wear personal protective equipment (PPE): Workers should wear appropriate PPE.Implement an energy control program: An energy control program should be in place to ensure that workers are properly trained.Use a remote video camera: A remote video camera can be used to monitor the racking process from a safe distance, allowing workers to rack circuit breakers without being in the line of fire.Learn more about circuit breaker here:
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Please help me by determine the value of the missing angle using the inverse trig function
By applying the Pythagorean theorem to the provided question, we can say that in this triangle =>
AC =[tex]\sqrt{115}[/tex]
What exactly is a triangle?Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.
Pythagorean theorem applies here, in this triangle
AC = [tex]A^2 + B^2[/tex]
AC = [tex]\sqrt{14^2 -9^2}[/tex]
AC = [tex]\sqrt{115}[/tex]
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Calculate the volume of the solid generated by rotating the figure below around the vertical axis. Express
answer in terms of pi or m. For example, if your answer is 10 x , write answer as 10m or 10pi.
The volume of the solid of revolution is equal to 21π cubic units.
How to determine the volume of a solid of revolution
In this problem we find the representation of a figure, whose area is also shown and whose solid of revolution is can be defined by following formula:
V = π · A
Where:
V - Volume of the revolution, in cubic units.A - Area of the representation, in square units.First, the area of the representation is found by summing the areas of two compounding rectangles:
A = 5 · 3 + 2 · 3
A = 21
Second, compute the volume of the solid of revolution:
V = 21π
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Use the net to find the surface area of the prism.
5 in.
12 in.
13 in.
8 in.
Step-by-step explanation:
Rather than give you the full answer, let me point out the things that you need to know to work this out for yourself.
The surface area of the solid is the sum of all of the areas of its faces.
The area of a right triangle is a well-known formula. You should already know this.
Pls solve 3,4,5!!! Tyyy (I will mark brainliest!)
Answer:
Step-by-step explanation:
4 = d
5=1/5
3 the first one is 4x1/12 and 2x3/12
pls hurry! Write the equation for the line in slope-intercept form: y=mx+b.
how many such strings are if 2 of the ones are to be next to each other and the third is not next to the other two?
The number of strings where exactly two of the ones are next to each other, while the third one is not next to the other two, is (n-1) x (n-2).
In combinatorics, one of the fundamental concepts is counting the number of strings or sequences of symbols that satisfy certain conditions.
Let us first consider the case where the two ones that are next to each other are at the beginning of the string. In this case, we can place the third one in any of the remaining positions, which are n-2, where n is the total length of the string. Therefore, the number of such strings is (n-2).
Similarly, if the two ones are at the end of the string, we can place the third one in any of the n-2 remaining positions, and the number of such strings is again (n-2).
Now let us consider the case where the two ones are in the middle of the string. In this case, we can place the two adjacent ones in (n-2) ways, and the third one can be placed in any of the remaining n-3 positions, since it cannot be adjacent to the other two ones. Therefore, the number of such strings is (n-2) x (n-3).
To get the total number of strings that satisfy the given condition, we need to add up the number of strings in each of the three cases:
Total number of strings = (n-2) + (n-2) + (n-2) x (n-3)
Simplifying this expression, we get:
Total number of strings = (n-1) x (n-2)
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AHHHHHHHHHHHHHHHHHHH
Answer: look at the image for the answer and solution
Step-by-step explanation:
Answer: x = 365
Step-by-step explanation:
find the angle bisector and divide and multiply it
please help !!!! i will mark brainliest if correct
Answer:
Step-by-step explanation:
is this a bot or girl
Harvey has some 1 bills and some 5 in all he has 6 bills worth 22 let x be the number of 1 bills and let y be the number of 5 bills write a system of equations to represent the information and use substitution
can someone help please
Answer: x=3, y=-1
Step-by-step explanation:
2x+y=5
2y=2x-8
In equation 1, y=5-2x.
Substitute this value in equation 2.
2(5-2x)=2x-8
10-4x=2x-8
Thus,
4x+2x=10+8 (collecting terms)
6x=18
x=3
Now, we said earlier that y=5-2x.
Therefore, y=5-2(3) [because x=3]
y=5-6
y=-1
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which of the following is an example of a statistic? a.) average number of all high school graduates who will attend college b.) standard deviation of tuition costs for all private universities c.) 25 random students are asked how much they spent on books d.) summary value of a population
25 random students are asked how much they spent on books is an example of a statistic.
The primary areas of study in statistics include data collection, organization, organization, analysis, interpretation, and presentation. It is customary to begin with a statistical population or a statistical model that will be examined when applying statistics to a scientific, industrial, or social problem. There are many different groups of people or things that can be referred to as populations, such as "each person living in a country" or "each atom making up a crystal." Every aspect of data is covered by statistics, including the planning of data collection in terms of survey and experiment design. Statisticians gather data using custom experiment designs and survey samples in the absence of census data.
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What are some fast animals you can think of? What are some slow wins? How can fast can you run? Think about how you can predict who would win this race. Research the speed of at least four different animals. Then time how long it takes you to run 1/4 mile. If you and these four types of animals ran a marathon at those speed to win? How far into the race with the four other racers be when the winner cross the finish line? Would a sport article or research or record a sports new cast to predict the outcome of this race. Use the information you learned in this topic to justify your predictions. PLEASE HURRY!!!!
The answers include the following:
Some fast animals are cheetah, falcon.Some slow animals are snail, slug etc.Speed of cheetah is 114 km/hr, speed of lion is 81 km/hr. speed of snail is 0.048km/hr and speed of deer is 48.2km/hr.The time it will take me to run 1/4 mile is 2 minutes.Yes, a sport article or research or record a sports new cast to predict the outcome of this race.What is Speed?This is referred to as the ratio of distance to the time in which the distance was covered and it is a scalar quantity.
Sport article or research or record a sports new cast will be able to predict the outcome of this race due to the data being gathered which will provide more information about the race.
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