The elimination method is used to solve a system of equations with multiple variables. Repeat this process until all of the variables have been eliminated, then simplify the equations to solve for the remaining variable.
Once a variable has been isolated, it can then be eliminated from the other equations by either adding or subtracting the equations from each other. This process should be repeated until all of the variables have been eliminated from all of the equations.
For example, let's solve the following system of equations with 3 variables a, b, and c:
a + b + c = 8
2a + b + 2c = 12
3a + 2b + 3c = 18
First, isolate the variable c in equation 1 by subtracting b and a from both sides:
c = 8 - a - b
Substitute this expression for c in equation 2 and 3 to eliminate c:
2a + b + 2(8 - a - b) = 12
3a + 2b + 3(8 - a - b) = 18
Then simplify the equations to solve for the remaining variables:
2a + 3b = -4
9a + 6b = 36
Next, isolate the variable a in equation 2 by subtracting 3b from both sides:
a = -4/2 - 3b/2
Substitute this expression for a in equation 1 and 3 to eliminate a:
-4/2 - 3b/2 + b + 8 - b = 8
9(-4/2 - 3b/2) + 6b + 3(8 - b) = 36
Then simplify the equations to solve for the remaining variable:
15b = -12
b = -12/15
Finally, substitute b back into equation 1 or 2 to solve for a:
a + (-12/15) + 8 = 8
a = 8 - (-12/15) - 8
a = 24/15
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Calculate the percentage by which the orangutan population has changed from 1900 when there were 85,000 orangutans to the present day when there are about 6,600 orangutans. Give your answer to 2 decimal places.
The percentage by which the orangutan population has changed is 92.23%
We know that the formula for the relative change.
R = |x2 - x1| ÷ x1
where x2 is the final value
and x1 is the initial value
R is the relative change
Here, the orangutan population has changed from 1900 when there were 85,000 orangutans to the present day when there are about 6,600 orangutans.
This means, x1 = 85000 and x2 = 6600
So, the relative change would be,
R = |6600 - 85000| ÷ 85000
R = 78400 / 85000
R = 0.9223
and the percentage change would be,
P = R × 100
P = 0.9223 × 100
P = 92.23%
Therefore, the percentage change = 92.23%
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Jeremy borrowed money from his dad for a car repair. The graph represents the amount
remaining that Jeremy owes his dad.
a. Write an equation to represent the situation.
b. What does the slope mean in the context of
the situation?
c. What does the y-intercept mean in the context
of the situation?
a. The linear equation is -75x+700 which represents the situation.
b. The slope represents the rate of change in the amount owed.
c. The y-intercept represents the amount that Jeremy borrowed from his dad.
What is a linear equation?
Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. The general form is y=ax+b, where a is the slope and b is the y-intercept.
a. We know that general form of an equation is y=ax+b.
So, after substituting (0,700) and (8, 100) into y=ax+b, we get,
700= 0+b
b=700
100=8a+700
a=-75
Hence, the linear equation is -75x+700 which represents the situation.
b. The slope represents the rate of change in the amount owed.
c. The y-intercept represents the amount that Jeremy borrowed from his dad.
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Find the slope of the line
Answer: -4
Step-by-step explanation: Start where the y-intercept is and go from there to the next point.
You go down by 4 to go to the point and then to the left one.
-4/1 = rise/run
-4= rise/run
What is the length of the children shoes?
Answer:
60mm
Step-by-step explanation:
240*1/4=60mm
Answer:
40 mm
Step-by-step explanation:
Given information:
The average adult shoe is 240 mm in length.The children's shoes are smaller than the adult shoesTo find the length of the children's shoes, multiply the length of the adult shoes by the scale factor:
[tex]\begin{aligned}\implies 240 \times \dfrac{1}{6}&=\dfrac{240 \times 1}{6}\\\\&=\dfrac{240}{6}\\\\&=\dfrac{40 \times 6}{6}\\\\&=40\; \sf mm\end{aligned}[/tex]
Therefore, the length of the children's shoes is 40 mm.
TRUE/FALSE. When algebraic, or numerical fractions are added or subtracted, the result is a single fraction.'
The statement that when algebraic or numerical fractions are added or subtracted, the result is a single fraction is True.
For addition or subtraction of algebraic or numerical fractions, the denominator has to be the same for all terms in the equation.
For common denominator,
Suppose 2 numerical fractions are being added which have a common denominator: 3/5 + 1/5
The resultant fraction will be 4/5, which is a single fraction
For algebraic fractions, considering the denominators are common, such as 3x/5 + 4x/5 = 7x/5
The result is also a single fraction.
For different denominators,
Suppose 2 numerical fractions are being subtracted which have different denominators such as, 5/9 – 3/7
In this case, the least common multiple for the denominators are calculated: 9*7= 63, and the opposite numerators are multiplied to the opposite denominators
Therefore, (5*7 – 3*9)/63 = (35 – 27)/63 = 8/63, which gives us a single fraction.
The process is same for algebraic fractions, for example,
4x/7 – 3x/5 = (4x*5 – 3x*7)/35 = (20x – 21x)/35 = -x/35, which is also a single fraction.
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Can absolute value be less than zero?
The absolute value of a number can never be less than zero, because the graph has a minimum value of 0 and is never negative, never below the x-axis.
If the absolute value is less than zero, there is no solution.
If the absolute value is less than or equal to zero, there is one solution.
If the absolute value is greater than zero, the solution is all real numbers
except for the value which makes it equal to zero, this will be written as a union.
The absolute value is always a positive value and not a negative number. so those numbers are called absolute values.
It is represented as |a|, which defines the magnitude of any integer ‘a’.
Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin of a number line or coordinate system.
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Communication Explain how to use algebra to find two numbers whose difference is 8 and whose product is a minimum.
The two numbers are 4 and -4, and their product is 4 * -4 = -16, which is the minimum value.
What is algebra?Generally, To find two numbers whose difference is 8 and whose product is a minimum, we can use algebra. Let's call the two numbers x and y. We know that:
x - y = 8 (the difference between the two numbers is 8)
To find the product of the two numbers, we can multiply x and y:
xy = x(x - 8) = x^2 - 8x
To find the minimum value of the product, we can take the derivative of this expression with respect to x and set it equal to 0:
d(xy)/dx = 2x - 8 = 0
Solving for x, we find that x = 4.
Therefore, one of the numbers is 4. We can use the equation x - y = 8 to find the other number:
4 - y = 8
y = -4
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What's the percentage of 6 by 5 ?
Answer:
0.3
Step-by-step explanation:
Were you asking for 5% of 6? Because then you would just multiply 6 by 0.05 (because percents are always out of 100%, so converted to decimal it is out of 1) and then get 0.3
Answer: The percentage of 6 by 5 (i.e. 6:5) is 120
Step-by-step explanation:
Given: 6 by 5 i.e. 6/5
Solution: (value/ total value)* 100
hence, (6/5)*100
=1.2*100
=120.
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I need this done in 20 minutes please
Answer:
Step-by-step explanation:
12. all angles are the same size.
all ik sry
how many gallons of water should be packed for two people for three days in the case of an emergency?
According to the Federal Emergency Management Agency (F.E.M.A.) , In case of emergency for two people , three days , number of gallons that should be packed is 6 gallons .
During Emergency Situations as we stock food, we need to take into account the family’s unique needs and tastes.
We try to include foods that require no refrigeration, water, special preparation, or cooking are best in case of emergency .
So , by FEMA , it states that we need to store at least one gallon per person per day .
Since there are two people , so , we need 2 gallons per day ;
and for three days , it would requires [tex]2 \times 3 = 6[/tex] gallons per day .
Therefore , 6 gallons of water should be packed .
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Three types of beverage were served at a wedding dinner. 2 persons shared a can of beer. 3 persons shared a jar of fruit punch. 4 persons shared a bottle of wine. 78 cans of beverange were served altogether. How many guests were at the dinner?
Therefore , the solution of fraction problem is number of guests in the dinner were 72.
What is fraction with an example from real life?A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.
Here,
Given :
Let the number of guests be x,
2 persons shared a can of beer. 3 persons shared a jar of fruit punch. 4 persons shared a bottle of wine ++78
12+8x+6x 24
26x = 1872
x = 72
= 78
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On the $xy$-plane, the origin is labeled with an $M$. The points $(1,0)$, $(-1,0)$, $(0,1)$, and $(0,-1)$ are labeled with $A$'s. The points $(2,0)$, $(1,1)$, $(0,2)$, $(-1, 1)$, $(-2, 0)$, $(-1, -1)$, $(0, -2)$, and $(1, -1)$ are labeled with $T$'s. The points $(3,0)$, $(2,1)$, $(1,2)$, $(0, 3)$, $(-1, 2)$, $(-2, 1)$, $(-3, 0)$, $(-2,-1)$, $(-1,-2)$, $(0, -3)$, $(1, -2)$, and $(2, -1)$ are labeled with $H$'s. If you are only allowed to move up, down, left, or right by one unit at each step, starting from the origin, how many distinct paths can be followed to spell the word MATH
On solving the provided question, we can say that there are 66 ways , on counting .
What is counting?Calculating the number of components in a limited collection of objects is the process of counting. H. Calculate the set's size. Calculating the quantity or overall number of items in a collection or group is the definition of counting in mathematics. In other words, counting something entails reciting the number in order and individually valuing each item in the group. To count objects, use the count number. 1, 2, 3, 4, 5, and so forth are examples of counting numbers. In daily life, people employ the numbers required to count items, items, money, etc. Because of this, count numbers cannot be fractions, integers, negative numbers, or decimals.
here in question,
there are 66 ways.
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a bag contains red marbles and blue marbles. zuri randomly removes marbles from the bag, one at a time and without replacement, and stops when she has removed all the red marbles from the bag. what is the expected value of the number of marbles zuri removes from the bag?
The expected value of the number of marbles Zuri removes from the bag is the sum of the number of red marbles plus the number of blue marbles.
The expected value of the number of marbles Zuri removes from the bag is the sum of the number of red and blue marbles. This is because the expected value of an event is the sum of the probability of each outcome multiplied by the associated outcome. Since Zuri is randomly removing marbles from the bag, one at a time and without replacement, the probability of each outcome (red or blue) is equal. Therefore, the expected value of the number of marbles Zuri removes from the bag is the sum of the number of red marbles plus the number of blue marbles. This is because each marble has an equal chance of being removed and, therefore, each marble has the same expected value.
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what is the solution to the system of equations graphed below answers
Answer:
(4,2)
Step-by-step explanation:
the solution to the system of equations is the point where the 2 lines intersect: (4,2)
ben participates in a prize draw. he receives one prize that is equally likely to be worth $5, $10 or $20. jamie participates in a different prize draw. she receives one prize that is equally likely to be worth $30 or $40. what is the probability that the total value of their prizes is exactly $50?
The probability of getting a total value of $50 is 1/6.
There are three possible outcomes for Ben's prize: $5, $10, or $20.
There are two possible outcomes for Jamie's prize: $30 or $40.
Therefore, there are 3 x 2 = 6 total possible outcomes for the combined value of their prizes.
To find the probability that the total value of their prizes is exactly $50, we need to find the number of outcomes that result in a total value of $50, and divide that by the total number of possible outcomes.
The only way to get a total value of exactly $50 is that Ben wins $20 and Jamie wins $30. This is only one combination out of 6 possible combinations. So the probability of getting a total value of $50 is 1/6 or approximately 0.166.
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Scale is 1' =1mm What is the circle's actual diameter
The circle's actual diameter is given as follows:
90 inches.
How to obtain the actual diameter of the circle?The radius of a circle represents the distance between the circle of the center to any point on the circumference of the circle.
The diameter of a circle represents the distance between two points on the circumference of the circle, passing through the center.
Hence the diameter length is twice the radius length.
From the image given at the end of the answer, the radius of the circle is given as follows:
r = 45 mm.
Hence the diameter is given as follows:
d = 2r
d = 90 mm.
The scale is that each mm on the drawing represents one inch of actual distance, hence the actual diameter is given as follows:
90 inches.
Missing Information
The circle is given by the image presented at the end of the answer.
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Solve the given differential equation by separation of variables. csc(y) dx + sec2(x) dy = 0
The given differential equation with variable separation will be cosy = -1/2 sin2x + C.
What is a differential equation?A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.
Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.
Due to the prevalence of these relationships, differential equations are widely used in many fields, including engineering, physics, economics, and biology.
So, we have the differential equation:
csc(y) dx + sec2(x) dy = 0
We, are aware that:
csc(y) = 1/ siny
sec(x) = 1/ cosx
We can also write it:
dx/siny = dy/cos2x
Cross multiplication with variable separation:
siny dy = cos2x dx
Differentiate:
cosy = -1/2 sin2x + C
As a result, the given differential equation with variable separation will be
cosy = -1/2 sin2x + C.
Therefore, the given differential equation with variable separation will be cosy = -1/2 sin2x + C.
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A sports marketing company is interested in how many hours teenagers in a town spend watching sports. They randomly select 40 teenagers in this town and ask how many hours per week they spend watching sports. The mean amount is 6.25 hours with a standard deviation of 4.33 hours. Which of the following is the 90% confidence interval for the true mean amount of time teenagers from this town watch sports
(5.097, 7.404) is the 90% confidence interval for the true mean amount of time teenagers from this town watch sports. This can be solved using the concept of standard deviation.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered. The deviation of each observed value from the mean is measured using this metric. The majority of data in any distribution will fall within a 2 standard deviation range of the mean.
Thus, (5.097, 7.404) is the 90% confidence interval for the true mean amount of time teenagers from this town watch sports.
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The complete question is as follows:
A sports marketing company is interested in how many hours teenagers in a town spend watching sports. They randomly select 40 teenagers in this town and ask how many hours per week they spend watching sports. The mean amount is 6.25 hours with a standard deviation of 4.33 hours. Which of the following is the 90% confidence interval for the true mean amount of time teenagers from this town watch sports?
Find the t-table here.
(4.396, 8.104)
(4.865, 7.635)
(5.097, 7.404)
(5.245, 7.256)
6. 21 and 22 form a linear pair. If m/1 = (5x + 9) and m/2 = (3x + 11), find the measure of
each angle.
7. 21 and 22 are vertical angles. If mZ1 = (17x + 1) and m/2 = (20x-14), find m22.
8. ZK and ZL are complementary angles. If mZK = (3x + 3) and mL = (10x-4), find the
measure of each angle.
Answer:
Since 21 and 22 are vertical angles, they are congruent. Therefore, m/1 = m22.
Using the equation m/1 = (17x + 1) we can find the measure of the angle m22.
m22 = (17x + 1)
Since ZK and ZL are complementary angles, the sum of their measures is 90 degrees.
mZK + mL = 90
Using the equations mZK = (3x + 3) and mL = (10x-4) and substituting them in the equation, we can find the measure of each angle.
3x + 3 + 10x - 4 = 90
13x - 1 = 90
13x = 91
x = 7
Therefore, mZK = (3x + 3) = (3(7) + 3) = 24 and mL = (10x-4) = (10(7) - 4) = 66
Step-by-step explanation:
I WILL CHOOSE YOUR ANSWER BRAINLIEST HELPP
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{3}{4}[/tex] x - 1 ← is in slope- intercept form
with slope m = [tex]\frac{3}{4}[/tex]
• Parallel lines have equal slopes , then
y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the parallel line
to find c substitute (8, 4 ) into the partial equation
4 = [tex]\frac{3}{4}[/tex] (8) + c = 6 + c ( subtract 6 from both sides )
- 2 = c
y = [tex]\frac{3}{4}[/tex] x - 2 ← equation of parallel line
---------------------------------------------------------------
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] , then
y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (8, 4 ) into the partial equation
4 = - [tex]\frac{4}{3}[/tex] (8) + c = - [tex]\frac{32}{3}[/tex] + c ( add [tex]\frac{32}{3}[/tex] to both sides )
4 + [tex]\frac{32}{3}[/tex] = c , then
c = [tex]\frac{44}{3}[/tex]
y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{44}{3}[/tex] ← equation of perpendicular line
Plan V: $10.00/day + $40.00/month; 100 texts (extra cost $.50 each), 100 minutes of talk roverage is $.99/minute), 100 MB of data (overage is $2.05/MB)
Plan V is a mobile phone plan that costs $10.00 per day, or $40.00 per month. The plan includes 100 texts. If the customer goes over the 100 included texts, they will be charged $0.50 for each additional text. The plan also includes 100 minutes of talk coverage, but if the customer goes over the 100 minutes, they will be charged $0.99 per additional minute. Additionally, the plan includes 100 MB of data, but if the customer goes over the 100 MB, they will be charged $2.05 per additional MB.
Find the value of x, if it has a value:-
[tex]\tt 33-5(x-4)=3[/tex]
Step-by-step explanation:
[tex]\tt 33-5(x-4)=3[/tex]
[tex]\tt 33-5x+20=3[/tex]
[tex]\tt 53-5x=3[/tex]
[tex]\tt -5x=3-53[/tex]
[tex]\tt 5x=50[/tex]
[tex]\tt x=10[/tex]
I hope it's helpful
2. A flagpole stands in the center of a square, and the distance from the base of the
pole to each corner of the square is 8 feet. How tall is the flagpole?
This is the answer above mentioned
please help with 4, 5 and 6 pleasee someone
The volume of the ice cream cone is 100.48 in³.
The volume of the basketball is 267.95 in³.
The volume of the can of corn is 169.56 in³
How to find the volume of the ice cream cone?To find the volume of the ice cream cone, use the formula for the volume of cone, which is given by:
V = (1/3)πr²h
r = 4 in and h = 6 in
V = 1/3 × 3.14 × 4² × 6 = 100.48 in³
To find the volume of the basketball, use the formula for the volume of sphere, which is given by:
V = (4/3)πr³, where r = 4 inches
V = (4/3) × 3.14 × 4³ = 267.95 in³
To find the volume of the can of corn, use the formula for the volume of cylinder, which is given by:
V = πr²h, where r = 3 in and h = 6 in
V = 3.14 × 3² × 6 = 169.56 in³
code: HG DA CF
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(1) tyler ate x fruit snacks, and han ate 3/4 less than that. write an expression for the number of fruit snacks han ate. (2) mai skated x miles, and clare skated 3/5 farther than that. write an expression for the distance clare skated
(1) Han ate: x(1 - 3/4) = x/4. (2) Clare skated: x(1 + 3/5) = 8/5x.
What is algebraic expression ?
An algebraic expression is a mathematical phrase that can include numbers, variables, and operations. It represents a value or a set of values, but it does not provide a specific numerical result until the variables are replaced with specific numbers.
(1) Let's say x is the number of fruit snacks Tyler ate.
Han ate 3/4 less than that, so the expression for the number of fruit snacks Han ate would be x - (3/4)x = x(1 - 3/4) = x/4.
(2) Let's say x is the number of miles Mai skated.
Clare skated 3/5 farther than that, so the expression for the distance Clare skated would be x + (3/5)x = x(1 + 3/5) = 8/5x.
(1) Han ate: x(1 - 3/4) = x/4. (2) Clare skated: x(1 + 3/5) = 8/5x.
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A salesperson earns 25% commission. If they sell $1,750.00 how much do they earn on commission?
The earned commission would be $437.50.
What is a commission?
A commission is a payment made to an employee, typically in sales or finance, for services rendered in the form of a percentage of the revenue generated by the employee's efforts. It is a way for companies to incentivize employees to sell more products or services, as the employee's income is directly tied to the success of their sales efforts.
The salesperson earns $437.50 on commission. This can be calculated by multiplying $1,750.00 by 25% (0.25).
$1,750.00 * 0.25 = $437.50
Hence, the earned commission would be $437.50.
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how many extraneous solutions does the equation below have?startfraction 9 over n squared 1 endfraction
The equation has one extraneous solution which is n is approximately 2.38
Here we have the following equation
=> 9/n²+1 = n+3/4
Now, we have to find the value of n by simplifying the given equation,
In order to so the simplification we have to do the cross multiplication on then, then we get the resulting expression as,
=> n²+1(n + 3) = 36
When we expand it then we get,
=> n²+1(n) + n²+1(3) = 36
=> n³ + n + 3n² +3 - 36 = 0
=> n³ + 3n² + n - 33 = 0
Here we have to find the roots are the x values where the graph intersects the x-axis.
And then we have to find the roots replace y with 0 and solve for x.
Then the value of n is obtained as
=> n ≈ 2.38
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The ratio of the measures of the three angles in a triangle is 14:5:11. Find the measures of the angles.
The measures of the angles.
14x6 = 84 (angle 1) 5x6 = 30 (angle 2) 11x6 = 66 (angle 3)What are the angles in a triangle?Generally, In a space defined by Euclidean geometry, the sum of the angles of a triangle is equal to the angle that is straight.
A triangle is characterized by the presence of three angles, one at each vertex, and is defined by a set of sides that are next to one another. For a very long time, it was not known for certain whether or not there are alternative geometries for which this sum is different.
The measures of the angles in a triangle add up to 180 degrees. So, to find the measure of each angle in the triangle, we can set up the equation:
14x + 5x + 11x = 180
where
x represents the number of degrees in each angle.
Simplifying this equation, we get:
30x = 180
Dividing both sides by 30, we get:
x = 6
So, each angle in the triangle measures 6 degrees. To find the measure of each angle, we can simply multiply the ratio by 6.
14x6 = 84 (angle 1)
5x6 = 30 (angle 2)
11x6 = 66 (angle 3)
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A cruie hip ha 2,400 regular paenger. Children make up 120 of them, 23 are teenager and the ret are adult paenger. What fractional part of the regular paenger are the adult paenger?
So, the fractional part of the regular passengers that are adult is 0.9404 or 94.04%.
We know that the cruise ship has 2,400 regular passengers, and that 120 of them are children and 23 are teenagers. To find the fractional part of the regular passengers that are adults, we need to subtract the number of children and teenagers from the total number of regular passengers.
First, add the number of children and teenagers: 120 + 23 = 143
Then, subtract this number from the total number of regular passengers: 2,400 - 143 = 2,257
This is the number of adult passengers. To find the fraction of adult passengers, divide the number of adult passengers by the total number of regular passengers and convert the result to a fraction.
2,257/2,400 = 0.9404
So, the fractional part of the regular passengers that are adult is 0.9404 or 94.04%.
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(PLS HELP!!!)
Divide.
(6x²+19x+10) ÷ (3x+2)
Your answer should give the quotient and the remainder.
Quotient:
Remainder:
