When solving a linear system of equations, what you obtain are the roots of the equation.
What is a linear equation?A linear equation is the type of equation in which he highest power of the variable is one. In some cases, we would have a system of linear equations and we have to solve the system.
When we are solving the system of equations, there are various methods that we could use such as;
Substitution methodElimination methodCramer's ruleGraphical methodThe solutions that we obtain from the equation are the root of that equation.
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the equation of a line is y equals 4 over 3 x minus 5 over 3. what would be the slope of a line perpendicular to this line?
The slope of the line perpendicular to the given line is calculated by taking the negative reciprocal of the given slope.The slope of the given line is 4/3. The slope of the line perpendicular to the given line is -3/4.
To find the slope of a line perpendicular to the given line, we need to take the negative reciprocal of the slope of the given line. The equation of the given line is y = 4/3x - 5/3. To calculate the slope, we need to rearrange the equation to the form y = mx + b, where m is the slope and b is the y-intercept. Rearranging the equation to the form y = mx + b, we get y = 4/3x - 5/3 which can be written as 4/3x - y = 5/3. The slope of the given line is 4/3. To find the slope of the line perpendicular to the given line, we take the negative reciprocal of 4/3 which is -3/4. Therefore, the slope of the line perpendicular to the given line is -3/4.
y = 4/3x - 5/3
4/3x - y = 5/3.
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please show how to simplify 3x +7x −28+31−8x for x =2043 and show how to solve
Answer:
4091
Step-by-step explanation:
Given the equation;
3x + 7x − 28 + 31 − 8x
First, we would collect like terms;
3x + 7x − 8x − 28 + 31
Simplifying, we have;
For x = 2043;
2(2043) + 5 = 4086 + 5 = 4091.
what is the partial-fraction expansion of the rational function f(s)=7s2+30s+27s3+9s?
The partial fraction expansion of the rational function
f(s) = 7s²+30s+27s/3+9s is 7s/9 - 164/81s + 27 + 164/27
In math the term partial fraction is defined as a method that is used to split the complicated fraction into a simpler form.
Here we have given the rational function f(s) = 7s²+30s+27s/3+9s.
And we have to find the partial fraction expansion for the function.
While we looking into the given rational function, for the given function we have to perform the partial fraction decomposition of
=> f(s) = 7s²+30s+27s/3+9s.
And it can be simplified as,
=> f(s) = 7s²+57s/3+9s.
Take s as common on the numerator, then we get
=> f(s) = s(7s + 57) / 3 + 9s
Since the degree of the numerator is not less than degree of the denominator, perform synthetic division, then we get the result as
=> f(s) = 7s/9 + 164/27 + [-164/9]/9s + 3
When we further simplify this expression, then we get,
=> f(s) = 7s/9 + 164/27 - 164/81s + 27
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What is the value of the following expression 20 19 − 5 7?
The value of the expression after simplification is found as 415.
What is meant by the term simplification?To simplify simple means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler.
Calculations and problem-solving techniques simplify the issue.
We can —
By eliminating all common elements from the numerator and denominator and putting the fraction through its simplest/lowest form, fractions can be made simpler.By combining and grouping like terms, mathematical expressions can be made simpler. This makes the phrase simple to comprehend and to solve.The given expression is-
= 20 x 19 + 5 x 7
Applying the BODMAS, multiply the numbers.
= 380 + 35
Add the values,
= 415
Thus, the value of the expression after simplification is found as 415.
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The correct question is-
What is the value of the following expression 20 x 19 + 5 x 7?
the ratio of milk to water in a mixture is 12:5.if there is 144liters of waterinth mixture. find d amount of milk
The ratio of milk to water in the mixture is 12:5, which means that for every 12 parts of milk, there are 5 parts of water. We can set up a proportion to solve for the amount of milk in the mixture. Let's call the amount of milk x.Then the proportion is:(12 parts milk) / (5 parts water) = (x liters milk) / (144 liters water)To solve for x, we can cross-multiply and simplify:12x = 5 * 144
x = (5 * 144) / 12
x = 60 litersThus, the amount of milk in the mixture is 60 liters.
According to the question,
ratio amount of water : milk is 5:12
given amount of water in the mixture is 144 litre,
then we have to find the value of x,
as given, 12x=144
x=144/12
x=12
or, 5(12) = 60litre.
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The area of a right triangle is 44 m². Find the lengths of its legs if one of the legs is 3 m longer than the other.
Answer:
[tex]Lengths:8m and 11m[/tex]
Step-by-step explanation:
Area of a triangle is [tex]\frac{1}{2}bh[/tex]
[tex]44=\frac{1}{2} (x+3)(x)\\[/tex]
[tex]44=\frac{1}{2} (x_{2 +3x)[/tex]
[tex]88=x^{2} +3x[/tex]
[tex]x^{2} +3x-88=0[/tex]
[tex](x+11)(x-8)=0[/tex]
[tex]x=8[/tex]
[tex]Lengths:8m and 11m[/tex]
What is the median of the sample 5 5 11 9 8 5 8?
The median for the next batch of observations is 8.
What is median?The median is the value in the middle of a data set, which indicates that 50% of the data points have a value less than or equal to the median, and 50% have a value greater than or equal to the median. The median is the number in the middle of a set of numbers. The median represents the 50th percentile of the set of numbers. In other words, the median is the value in the center of a set of numbers where half are less than the median and half are more than the median.
Here,
given set of observation,
= 5,5,5,8,8,9,11
n=7
median=(7+1)/2
=4th term
=8
The median for following set of observation is 8.
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endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hr. and a standard deviation of 40 hr. what is the probability that an endure all battery selected at random will last more than 550 hours? a) exam image b) exam image c) exam image d) exam image e) exam image f) none of the above.
Therefore , the probability that an endure all battery selected at random will last more than 550 hours is 0.0301.
What is the process of probability?Probabilities can be expressed as proportions with a 0–1 range or as percentages with a 0%–100% range. If an event has a probability of 1, it is very certain to occur; if it has a probability of 0, it has no chance of occurring. There are 45 chances out of 100 that an event will occur when its probability is 0.45 (45%).
Here,
let say this variable is X.
so we have to find P(X>575)
=> P((X-500)/40 > 1.88)
=> P(Z>1.88)
=> 1 - P(Z<1.88) = 0.0301
Therefore , the probability that an endure all battery selected at random will last more than 550 hours is 0.0301.
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Is there a calculator that solves algebra?
Answer:
yes
Step-by-step explanation:
do you want names for online ones
Are AAA triangles solvable?
Yes, they are solvable.
In geometry, a triangle is considered to be an "AAA" triangle (or "AAA similarity") if all three of its angles are equal. Such a triangle is also known as an equilateral triangle.
An equilateral triangle is a type of triangle that has all three sides of equal length and all three angles of equal measure (60 degrees). It is a regular polygon, and it is one of the few geometric shapes that has this property.
Because all three angles in an equilateral triangle are equal, it is relatively easy to solve for various properties of the triangle. For example, the length of each side can be found if the measure of one angle and the length of one side are known. Similarly, the measure of an angle can be found if the length of one side and the measure of one angle are known.
In summary, AAA triangles are solvable because they have a consistent and predictable structure, with all sides and angles being equal.
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Alexa is trying to pick out an outfit for the first day of school. She can choose from 8 pairs of pants, 6 t-shirts, 6 sweaters or hoodies, and 2 pairs of shoes. How many different outfits does Alexa have to choose from?
The number of different outfits is 576
How to determine the number of different outfits?From the question, we have the following parameters that can be used in our computation:
8 pairs of pants, 6 t-shirts, 6 sweaters or hoodies, and 2 pairs of shoes
The number of different outfits is the products of the count of each apparel
This is represented as
Different outfits = Pants * T-shirts * Sweaters or hoodies * Pairs of shoes
Substitute the known values in the above equation
Different outfits = 8 * 6 * 6 * 2
Evaluate
Different outfits = 576
Hence, there are 576 different outfits
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How do you find the duplicate number on a given integer array in Python?
The duplicate number on a given integer array in Python can be found through two loops.
How do you find the duplicate number on a given integer array in Python?We need to print the duplicate elements present in the array. This can be done through two loops. The first loop will select an element and the second loop will iteration through the array by comparing the selected element with other elements. If a match is found, print the duplicate element.
ALGORITHM:
STEP 1: Declare and initialize an array.
STEP 2: Duplicate elements can be found using two loops. The outer loop will iterate through the array from 0 to length of the array. The outer loop will select an element. The inner loop will be used to compare the selected element with the rest of the elements of the array.
STEP 3: If a match is found which means the duplicate element is found then, display the element.
PYTHON PROGRAM:
#Initialize array
arr = [ ];
print("Duplicate elements in given array: ");
#Searches for duplicate element
for i in range(0, len(arr)):
for j in range(i+1, len(arr)):
if(arr[i] == arr[j]):
print(arr[j]);
The duplicate number on a given integer array in Python can be found through two loops.
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Find (x^4 − 5x^3 + 17x + 3) divided
by (x − 3).
Answer:
the division of (x^4 − 5x^3 + 17x + 3) by (x − 3) is equal to x^3 - 3x^2 + 4x - 3, with a remainder of 0.
Step-by-step explanation:
To divide (x^4 − 5x^3 + 17x + 3) by (x − 3), we can use polynomial long division. This involves dividing the polynomial by the divisor (x - 3) and expressing the result as a quotient plus a remainder. The remainder will be a polynomial of degree less than the degree of the divisor.
Here is how the division would look:
x -3 x^4 -5x^3 17x 3
--- ----- ---- ----- --- ---
x -3 x^3 -5x^2 17 0
x^3 -3x^2 -2x^2 3
0 -2x^2 -2x^2 0
0 0 -4x^2 3
0 0 -4x^2 -9
0 0 0 -9
0 0 0 0
From this division, we can see that the quotient is x^3 - 3x^2 + 4x - 3, and the remainder is 0. Therefore, we can express the division as:
(x^4 − 5x^3 + 17x + 3) / (x − 3) = (x^3 - 3x^2 + 4x - 3) + 0
This means that the division of (x^4 − 5x^3 + 17x + 3) by (x − 3) is equal to x^3 - 3x^2 + 4x - 3, with a remainder of 0.
Given equation= (x^4 - 5 x^3 + 17 x + 3)/(x - 3)
alternate form-x^3 - 2 x^2 - 6 x - 1 (for x!=3)
expanded form-x ((x - 2) x - 6) - 1 (for x!=3)
x^4/(x - 3) - (5 x^3)/(x - 3) + (17 x)/(x - 3) + 3/(x - 3)
quotient form and reminder-x^4 - 5 x^3 + 17 x + 3 = (x^3 - 2 x^2 - 6 x - 1)(x - 3) + 0.
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Where is the domain and range of a function?
On solving the provided question we can say that - The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,∞)
What is Domain?The range of values that may be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. Let y = f(x) be a function where x and y are the independent and dependent variables. If a function f offers a means of successfully generating a single value y while employing a value for x to that end, then the selected x-value is said to belong to the domain of f.
f(x)= -3x-2 x <4
3/4x-1 x [tex]\geq[/tex] 4
Domain =
The range of f(x) is a subset of this range, which is the range of -3x-2 (-14,∞).
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pls help me due asap
Answer:
iam think that y=2x cause curve y have two curve x
find the limit of the points specified
Which of the following is equal to (x^4 + 4x^3 − 3x^2 − 12x) divided by (x + 4)?
F x^3 − 3x G x3 + 3x
H x^3 − 2x^2 − 3x
G x^3 + 3x
J x^3 + 2x^2 − 3x
Answer:
F
Step-by-step explanation:
[tex]x^4+4x^3-3x^2-12x=x^3(x+4)-3x(x+4)=(x^3-3x)(x+4) \\ \\ \therefore \frac{x^4+4x^3-3x^2-12x}{x+4}=x^3-3x[/tex]
Juan Vance Weekly salary: $231.67
Not self-employed
Find the annual amount of FICA at 7.51% by computing his annual salary
The annual income of Juan Vance is $12,955.17.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
In order to pay for Social Security and Medicare, the Federal Insurance Contributions Act(FICA) mandates payroll deductions from both employers and employees.
Given, Juan Vance's Weekly salary is $231.67.
∴ Annually Juan earns $(52×231.67) = $12,046.84.
FICA deducts 7.51% from it and then combines another 7.51% with the employee,
∴ The net annual income of Juan Vence is
= [{12046.84 - (7.51/100)×12046.84 + {(7.51 + 7.51)/100}×12046.84}]
= (12046.84 - 904.71 + 1813.04}.
= $12,955.17
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What is the solution to the system of equations?
x-y+2z=9
3x+y=z=2
2x-y+z=8
Answer:
x=8/7, y=-25/7, z=15/7
Step-by-step explanation:
x-y+2z=9 ==> equation 1
3x+y=z=2 ==> equation 2
2x-y+z=8 ==> equation 3
3x+y+z=2
+ (2x-y+z=8)
3x+2x + y+(-y) + z+z = 2+8 ==> add equation 2 and 3 to eliminate y
5x + 2z = 10 ==> equation 4
x-y+2z=9
- (2x-y+z=8)
x - 2x + (-y)-(-y) + 2z-z = 9-8 ==> subtract equation 1 and 3 to eliminate y
-x + 0 + z = 1 ==> Let's say -y=a. (-y)-(-y) = a-a = 0.
(-x + z = 1)*2 ==> multiply by 2 to get z to become 2z
-2x + 2z = 2 ==> equation 5
5x + 2z = 10
- (-2x + 2z = 2)
5x-(-2x) + 2z-2z = 10-2 ==> subtract equation 4 and 5 to solve for x
5x+2x = 8
7x = 8 ==> divide both sides by 7 to isolate x
x = 8/7
-2(8/7) + 2z = 2 ==> plugin x into equation 5 to solve for z
-16/7 + 2z = 2 ==> simplify
(-16/7 + 2z = 2)*7 ==> multiply the equation by 7 to eliminate fractions
-16 + 14z = 14
14z = 30 ==> add 16 on both sides to isolate z
z = 30/14 ==> divide each side by 14
z = 15/7 ==> simplify
2(8/7)-y+(15/7)=8 ==> plugin x = 8/7 and z = 15/7 into equation 3
16/7 - y + 15/7 = 8
(16/7 + 15/7 - y = 8)*7 ==> multiply the equation by 7 to remove fractions
16 + 15 - 7y = 56
31 - 7y = 56
-7y = 25 ==> subtract 31 on both sides to isolate y
7y = -25
y = -25/7
Answer: (x=8/7, y=15/7, z=-25/7)
How do you remember commutative and associative property?
The commutative property of addition states that a + b = b + a and the commutative property of multiplication states that a × b = b × a and the associative property of addition states that (a + b) + c = a + (b + c) and the associative property of multiplication states that: (a × b) × c = a × (b × c).
Commutative Property - The Commutative Property is derived from the word commute, which means to move. It states that the product or sum of two numbers do not change even if the places of numbers are changed or if the numbers move from one place to another. The commutative property of addition states that a + b = b + a and the commutative property of multiplication states that a × b = b × a.
Associative Property - It is related with the grouping of numbers. It states that the product or sum of three numbers do not change even if the grouping of numbers are changed. The associative property of addition states that (a + b) + c = a + (b + c) and the associative property of multiplication states that: (a × b) × c = a × (b × c).
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Benjamin bought two pounds of strawberries for 12.80. What is the price, in dollars per ounce of strawberries?
Answer: 6.4
Step-by-step explanation:
divide in half
N
A city has a population of 360,000 people. Suppose that each year the population grows by 3%. What will the population be after 13 years?
Use the calculator provided and round your answer to the nearest whole number.
Answer:
528,672
Step-by-step explanation:
A=P(1+r)^t
360,000(1+.03)^13 = 528,672.1368
Rounded: 528,672
is the integer r divisible by 3 ? (1) r is the product of 4 consecutive positive integers. (2) r < 25
Yes, the integer is divisible by 3.
To determine if r is divisible by 3, we must first determine the value of r. According to statement 1, r is the product of 4 consecutive positive integers.
This means that the 4 integers must be increasing by 1 each time. The smallest integer must be 1, and the 4th integer must be 4 higher than the first, making it 5.
The product of these 4 integers is 1 x 2 x 3 x 4 = 24, which is less than 25.
Since 24 is divisible by 3, r is also divisible by 3.
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After you both have bought some items you decide its time for some candy at the candy store. you decide to buy 5 and 1/2 pounds of jelly beans your friend suggests that you share your jelly beans with your other friends tomorrow. you decide to give each friend 1/4 of a pound. how many friends can you share your jelly beans with? set up an expression to find the number of friends you can share it with____.
5 and 1/2 pounds of jelly beans can be shared with 22 friends.
The process of converting phrases into equations and then solving those equations is known as solving algebraic word problems. Simple arithmetic procedures will be all that is required to write the equations. a single variable, and. In a real-world situation, the variable often stands for an unknowable quantity.
Given that,
Total pounds of jelly beans = five and a half pounds
Jelly beans to be given to each friend = 1/4 of a pound
Let x be the number of friends,
x = 5 and 1/2 pounds / 1/4 of a pound
Since 1 pound = 1/4 * 4
then, 5 and 1/2 pounds = 4*5 + 2 = 22
Therefore, 5 and 1/2 pounds of jelly beans can be shared with 22 friends.
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Given that,
Total pounds of jelly beans = five and a half pounds
Jelly beans to be given to each friend = 1/4 of a pound
Let x be the number of friends,
x = 5 and 1/2 pounds / 1/4 of a pound
Since 1 pound = 1/4 * 4
then, 5 and 1/2 pounds = 4*5 + 2 = 22
Therefore, 5 and 1/2 pounds of jelly beans can be shared with 22 friends.
if I bought a $40 basket and it was on sale for 50% off but added 10% sales tax how much is it
Answer:
$24
Step-by-step explanation:
50% of 40 = 20
10% of 40 = 4
20+4=$24
What are the roots of quadratic equation x 5 )( x 2 )= 0 *?
The roots of the quadratic equation x^5 - x^2 = 0 are x = 0 and x = ±√2, which can be found by factoring and setting each factor equal to 0. The quadratic can be factored into (x^2)(x^3 - 1) = 0 and then the factors can be set equal to 0, resulting in x = 0 and x = ±√2.
To find the roots of the quadratic equation x^5 - x^2 = 0, first we must factor the equation. To do this, we can recognize that there are two terms, x^5 and x^2, and that the exponents are both greater than 1, so we can factor out an x^2 from both terms. When we do this, we get (x^2)(x^3 - 1) = 0. Now we can set each factor equal to 0, so that x^2 = 0 and x^3 - 1 = 0. Solving for x in the first equation, we get x = 0. To solve for x in the second equation, we can add 1 to both sides, so that x^3 = 1. Taking the cube root of both sides, we get x = ±√2. Therefore, the roots of the quadratic equation x^5 - x^2 = 0 are x = 0 and x = ±√2.
x^5 - x^2 = 0
x^2(x^3 - 1) = 0
x^2 = 0 → x = 0
x^3 - 1 = 0 → x^3 = 1 → x = ±√2
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What are the actual parameters in C++ Mcq?
Actual parameters are those that are supplied into a function when it is called or those that are used to make a function call.
Using parameters, subprograms pass information. The variables or expressions listed in a subprogram call's parameter list are the real parameters.
For instance, the procedure call that follows lists the two real parameters amount and emp num:
raise_salary(emp_num, amount);
The parameters that are used when calling a function at any point in the code are the actual parameters. It is the real value that a caller has given the process. When a subroutine like Functions is invited, the parameters are what you decide.
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I think of a number, double it, then subtract 7. The result is 10.
Find the number.
Answer:
17/2
Step-by-step explanation:
Work backwards. you have 10, then opposite of subtract 7 is add 7 which gives you 17. then opposite of double is half getting you 8.5 or 17/2
Answer:
Your number is 8.5 or 17/2
Step-by-step explanation:
Let's say your number is equal to the variable n.
Then we can set up an equation for this scenario: 2n - 7 = 10
Now, we need to use algebra to solve:
2n - 7 = 10 → add 7 to both sides
2n = 17 → divide both sides by 2
n = 17/2 = 8.5
Thus, the number you were thinking of was 8.5, or 17/2
lins family had completed 60% of a trip. they have traveled 30 miles. how many miles is the trip
Lin's family make a trip of length 50 miles.
What is a trip?
People move between far-off geographic regions when they travel. Travel can be done with or without luggage, on foot, by bicycle, car, rail, boat, airline, ship, or by another mode of transportation. It can also be one way or round trip.
Given that Lin's family had completed 60% of a trip.
Thus they have to travel (100 - 60)% = 40% of the trip.
Also given that, they have traveled 30 miles..
Therefore,
60% of the trip is equal to 30 miles.
1% of the trip is equal to 30/60% miles.
100% the trip is equal to (30× 100%)/60% miles.
= 50 miles.
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What is division example?
Answer:
42 divided by 2
Step-by-step explanation:
42 divided by 2 equals 21 and how to find if it is correct is to add it together 21+21 or multiply it by what it was divided by 21x2
What are the median of 5 7 10 12 11?
The Median of the following observation set 5 7 10 12 11 will be 10.
One measure of central tendency is the median. The median is the number that lies in the middle of the specified range of integers. It separates the higher half from the lower half of a particular data sample. At least half of the observations are above or equal to the median, and at least half of the observations are below the median.
The median can be calculated as follows when there are odd numbers of observations in a data collection:
First, arrange the data in ascending or descending order.
Step 2: If the number of observations (let's say n) is odd, the middle observation is the median of the given data.
Median = [tex](\frac{n+1}{2} )^{th}[/tex] Observation.
Here n = 5, So median will be 3rd term that is 10.
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