The answers to the equation x2 – 6x = 16 are x = -2 and x = 8.
What is the answer of x2 6x 16?Two approaches to the equation x2 - 6x = 16 will be examined. First, factoring is used; second, the quadratic formula.
We shall employ the subsequent steps when factoring a solution:
Put all of the terms that are not zero on one side of the equation and zero on the other.
Add the non-zero component of the equation.
Solve the equation by setting each factor to 0.
Getting all non-zero terms on one side of the equation is the first thing want to do.
They are 8x and -2x, respectively. Therefore, (x+8) are the factors of x2 + 6x - 16 = 0. (x-2).
Therefore, the answers to the equation is x2 – 6x = 16 are x = -2 and x = 8.
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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 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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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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What are the 4 types of values?
Thousands, hundreds, tens and ones are four types of values and there are many more.
What is value?Value in mathematics is a number that represents the outcome of a computation or function. In the aforementioned example, you may inform your teacher that 5 + 6 Equals 30 or that x + y = 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.
What is the value of 4?The number 4 is in this case in the tens column. As a result, the place value of the number four is tens or tens.
Thousands, hundreds ,tens and ones are four types of values and there are many more like ones etc. Moreover after solving any problem for unknown variable the resulting numerical solution can also be termed as value.
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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.
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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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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If x² + 6x = 40, what are the values of x-6?
Answer:
-2
Step-by-step explanation:
x² + 6x = 40
This equation has the value of x as 4
Let's test
(4)^2 + 6(4) = 40
16 + 24 = 40
So, x is 4 in this equation
Now for the question, what is the value of x-6
We know x is 4
4 - 6 = -2
What is the formula for finding the circumcenter of a triangle?
Answer:
P(X, Y) = [(x1 sin 2A + x2 sin 2B + x3 sin 2C)/ (sin 2A + sin 2B + sin 2C), (y1 sin 2A + y2 sin 2B + y3 sin 2C)/ (sin 2A + sin 2B + sin 2C)]
Step-by-step explanation:
How to Construct Circumcenter of a Triangle?
The circumcenter of any triangle can be constructed by drawing the perpendicular bisector of any of the two sides of that triangle. The steps to construct the circumcenter are:
Step 1: Draw the perpendicular bisector of any two sides of the given triangle.
Step 2: Using a ruler, extend the perpendicular bisectors until they intersect each other.
Step 3: Mark the intersecting point as P which will be the circumcenter of the triangle. It should be noted that, even the bisector of the third side will also intersect at P.
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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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 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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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
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
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
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]
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?
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 there a calculator that solves algebra?
Answer:
yes
Step-by-step explanation:
do you want names for online ones
5. For each scenario, fill in numbers in the blanks to create a scenario that
can be solved using a system of equations. Make sure the scenario that you
provide has ONE solution. Then, answer the questions that follow.
Scenario 1
There are
some are cows. There are
total animals in the barn. Some of the animals are chickens and
legs in all.
a. What is the system of equations that represents the scenario you created?
B. Prove your solution is correct.
The scenario in this problem is described as follows:
There are 50 total animals in the barn, and there are 160 legs in total.
The system of equations that describes this situation is given as follows:
x + y = 50.4x + 2y = 160.What is the system of equations that describes this scenario?The variables that describe the system of equations are given as follows;
Variable x: number of cows in the barn.Variable y: number of chickens in the barn.There are 50 total animals in the barn, hence:
x + y = 50.
There are 160 legs in total. Considering that each cow has four legs, while each chicken has two legs, we have that:
4x + 2y = 160.
The system of equations is composed by these two equations and can be solved using any method to identify the amounts of each animal.
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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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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)
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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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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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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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
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
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.
How do you solve inverse ratios and proportions?
Assuming that x and y be inversely proportionate, we can denote their relationship as x ∝1/y. It follows that as the value of x rises, the value of y falls, and vice versa.
Define the term inverse ratios and proportions?When the product of two values, x and y, is a constant, they remain inversely proportional to one another (always remains the same). Accordingly, as x rises, y falls, and conversely, by a certain amount so that x and y remain constant.Making an equation to determine the value of a new variable is also made possible by understanding that product does not change.We must first establish the connection between the two variables in order to calculate the value of the variable that's also inversely proportionate to the other.We need to figure out the proportionality constant k, which is similar to the a directly proportional connection.
Thus, x ∝1/y
x = k/y
k = xy.
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