$0, He earned $8798 in net taxable income the previous year. He has a negative amount of taxable income since the exemption and the allowed deduction are larger than his annual gross income.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest.
In finance and economics, compound interest is common.
In contrast to simple interest, which does not compound since past interest is not added to the principal for the current period, compound interest allows interest to build over time.
The interest per period multiplied by the number of periods in a year yields the simple annual interest rate.
According to our question-
Last year, a part-time housekeeper earned $8798.
He claimed he was exempt, costing $365.
$570.00 is the standard deduction.
Gross income less the standard deduction and all exemptions equals taxable income.
= 8798 - 3650 - 5700 = $-552
There is a negative number, which indicates that he owes no taxes.
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what are the domain and range of the function f(x)=2^x+1
Answer: The domain is all values of x that make the expression defined. The range is the set of all valid y values
Step-by-step explanation:
Therefore , the solution of the given problem of function comes out to be Domain: (-∞, ∞) and Range: (0,∞).
What is function?Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.
Here,
Given : f(x)=[tex]2^{x}[/tex]+1
If a value has not been added, an exponential function's curve normally approaches a horizontal asymptote at y=0 or the x-axis. The curve changes if it has.
The asymptote is unaffected by this function's addition on the exponent because it does not apply to the entire function.
The values of its y-axis remain between 0 and. This is the set of y values, or the range.
However, depending on the leading coefficient, the range of exponentials can vary. If the value is negative, the graph turns inside-out and the range reaches -. It's also lacking in this.
The exponent's addition to 1 moves the function to the left without changing the range.
The x values in exponential functions are often unaffected and all are taken into account in the function. The domain stays the same even while it changes. Its range is (0,∞)
Range: (0,∞)
Therefore , the solution of the given problem of function comes out to be
Domain: (-∞, ∞) and Range: (0,∞).
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Don and Ana are driving to their vacation destination. Upon entering the freeway they began driving at a constant rate of 60 miles an hour. Don noticed that 3 hours into the trip they were 650 miles from the destination.
How far from their destination will they be 3. 7 hours since entering the freeway?
How far from their destination were they 2. 3 hours since entering the freeway?
Please help quick
Distance between them and their destination after 3.7 hours since entering the freeway is 608 miles and the distance between them and their destination after 2.3 hours since entering the freeway is 692 miles.
We know that the relationship between speed, distance, and time is given as,
Speed = distance/time
Speed = 60 miles an hour
Time = 3 hours
We know that Don and Ana are travelling at a constant speed and they are travelling for 3 hours.
Distance = speed × time
Distance = 60 × 3
Distance = 180 miles
Thus, the distance travelled by them in 3 hours is 180 miles.
We know that Don and Ana are travelling on the freeway for the past 3 hours and they are still 650 miles away, therefore,
Total Distance from their destination
= Distance travelled by them in 3 hours + 650 miles
= 180 miles + 650 miles
= 830 miles
Thus, the distance travelled by then is 830 miles.
Now, the distance between them and their destination after 3.7 hours since entering the freeway,
Distance travelled by them = speed x 3.7 = 60 x 3.7 = 222 miles
Distance between them and the destination
= Total Distance from their destination - Distance travelled by them
= 830 miles - 222 miles
= 608 miles
Therefore, they are 608 miles far from their destination.
And, Distance between them and their destination after 2.3 hours since entering the freeway,
Distance travelled by them = speed x 2.3 = 60 x 2.3 = 138 miles
Distance between them and the destination
= Total Distance from their destination - Distance travelled by them
= 830 miles - 138 miles
= 692 miles
Therefore, they are 692 miles far from their destination.
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I don't know HOW TO DO THIS
Answer:
sorry, I forget how to do the other ones and I'm just as confused but for 4. AD is 20 and 5. GJ is 17
Step-by-step explanation:
4. side AD is equal to side CD so therefore its 20.
5. side are equal again so make
4x+5 = 2x+11
-5 -5
4x = 2x+6
-2x -2x
2x = 6
/3 /3
x = 3
2(3)+11
6+11
17
F39) if x## is defined as x## = x² - x for all values of x, and A## = ( A - 2 )##, then what is the value of A?
The value of A in A## = ( A - 2 )## if x## = x² - x is 2 Or 3.
What are coding and decoding?Topics in the reasoning part include coding, decoding, and reasoning. One of the most frequently occurring portions in all of the important competitive exams specifically created for employment procedures and higher education is this one. Because Coding-Decoding and Reasoning problems can be difficult for some applicants to complete, they avoid them and lose some quick and simple marks.
Given, x## is defined as x## = x² - x.
Therefore,
A## = (A - 2)##
= (A - 2)² - (A - 2).
= A² - 4A + 4 - A + 2.
= A² - 5A + 6.
Let, A² - 5A + 6 = 0.
A² - 3A - 2A + 6 = 0.
A(A - 3) - 2 (A - 3) = 0.
(A - 3)(A - 2) = 0.
A = 3 Or A = 2.
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HELP ASAP PLEASE!! The table shows the numbers of cars manufactured in thousands by a company for selected years. Use a calculator to write a quartic model for the number of cars manufactured in a given year since 2000. Then use the model to estimate the number of cars manufactured in 2007
In algebra, a symbol is used to denote an unknown numerical value in an equation or algebraic expression.
What is meant by variables?A variable in mathematics is a letter that is substituted for an unknown integer in equations, expressions, and formulas.
An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed.
The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.
A.) (x) ≈ 0.572[tex]$$x^4[/tex] − 15.63x³ + 146.273x² − 523.325x + 687.334
Approximately 203 automobiles were produced in 2007, according to estimates.
B.) f(x) ≈ 0.423x³ − 12.463x2 + 123.485x − 223.309
Approximately 178 automobiles were produced in 2007, according to estimates.
C.) f(x) ≈ 0.572[tex]$$x^4[/tex] + 15.63x³ − 146.273x² − 523.325x + 687.334
Approximately 203 automobiles were produced in 2007, according to estimates.
D.) f(x) ≈ 0.423x³ + 12.463x² − 123.485x + 223.309
Approximately 178 automobiles were produced in 2007, according to estimates.
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Number of cars manufactured in 2007 will be equal to 178 or 203 based on quartic model.
What is meant by variables?A variable in mathematics is a letter that is substituted for an unknown integer in equations, expressions, and formulas.
An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed.
The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.
A.) (x) ≈ 0.572 − 15.63x³ + 146.273x² − 523.325x + 687.334
Approximately 203 automobiles were produced in 2007, according to estimates.
B.) f(x) ≈ 0.423x³ − 12.463x2 + 123.485x − 223.309
Approximately 178 automobiles were produced in 2007, according to estimates.
C.) f(x) ≈ 0.572 + 15.63x³ − 146.273x² − 523.325x + 687.334
Approximately 203 automobiles were produced in 2007, according to estimates.
D.) f(x) ≈ 0.423x³ + 12.463x² − 123.485x + 223.309
Approximately 178 automobiles were produced in 2007, according to estimates.
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Blake has $17.00 to spend at the grocery store. She is going to buy bags of fruit that cost $4.50 each and one box of crackers that costs $3.50
The point (14, –3) and (–10, –3) fall on a particular line. What i it equation in lope-intercept form?
Its equation in the slope-intercept form will be y = -3 because the y coordinates of both points are equal.
Given points in terms of coordinates so let's try to understand what are coordinates.
Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x-axis (horizontal) and y-axis(vertical) are the two axes that make up a coordinate plane. (Telling children that the x-axis crosses because "x" is a cross helps them remember which of these is which.)
We have total 4 coordinates
First Coordinate both x and y are positive.
Second Coordinate x is negative and y is positive.
Third Coordinate both x and y are negative.
Fourth Coordinate x is positive and y is negative.
Point A is (14, -3)
Point B is (-10, -3) both have the same y coordinate.
So line AB is parallel to the x-axis.
The formula for the equation in the slope-intercept formula is
y = mx + c.
m is the slope of the line and c is the intercept on the y-axis.
Line AB is parallel to the x-axis the equation is y = -3.
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Each shape is 1 whole. For numbers 13a–13e, choose Yes or No to show whether the number names the parts that are shaded
In each shape there are 4 wholes hence the answer is yes.
What are fractions?A fraction is referred to as the portion of a whole in mathematics. There are two components to a fraction: a numerator and a denominator. The numerator is the number at the top, and the denominator is the number at the bottom.
13a. There are 4 wholes, hence the answer is yes.
13b. Every whole is divided into 2 parts hence the total number of equal parts is 4 *2 = 8. Hence the answer is yes.
13c. The answer is yes.
13d. No
13e. No
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how do i anser this question
The graph that is not a straight line does not represent a direct variation.
What is direct variation?Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -
y = Kx
K = y/x
where -
{K} is scale factor.
Given are the graphs representing direct variation.
Direct variation is represented by the equation -
y = kx
The graphs representing the direct variation are straight lines. Since all the graphs are not given, any graph that is not a straight line does not represent a direct variation.
Therefore, the graph that is not a straight line does not represent a direct variation.
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Graph the line with 1 passing through the point (3, -4)
Answer:y=1x-7
Step-by-step explanation:
How do you tell if a log function is increasing or decreasing?
If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x) = log_b(x),[/tex] where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of [tex]f(x) = log_b(x)[/tex] is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
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If the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x)=log_b(x)[/tex]. where b is the base of the logarithm.
To determine whether a logarithmic function is increasing or decreasing, you can look at the sign of the derivative of the function. If the derivative is positive, the function is increasing; if the derivative is negative, the function is decreasing.
In the case of logarithmic functions, the derivative of [tex]f(x)=log_b(x)[/tex]. is f'(x) = 1/x*ln(b), which is always positive for x > 0, so the logarithmic function is increasing for any base b.
Hence, if the derivative of the function is positive, the function is increasing; if the derivative is negative, the function is decreasing.
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Fill in the missing information in the table.
Note: The cylinder and cone in each row have the same dimensions.
(I already solved some of them just give me the answers to the parts where I put the zeros, and please hurry)
The missing information, considering the volume of the cone and the cylinder, is given as follows:
Second row: height = 13.3, volume of cylinder = 120π.Third row: Diameter = 12, radius = 6, height = 4, volume of cylinder = 144π.How to obtain the volume of a cone and of a cylinder?The volume of a cylinder of radius r and height h is given as follows:
Vcy = πr²h.
The volume of a cone is one third that of the cylinder, hence:
Vco = πr²h/3.
At the second row, the volume of the cylinder is three times that of the cone, hence:
40π x 3 = 120π.
Considering the volume of the cylinder and the radius, the height is obtained as follows:
πr²h = 120π
9h = 120
h = 120/9
h = 13.3.
For the third row, we have that the base area is of 36π squared units, hence the radius is obtained as follows:
πr² = 36π
r = 6. (as the base is circular).
Hence the diameter is of 12 units, as the length of the diameter is twice that of the radius.
The volume of the cylinder is three times that of the radius, hence:
3 x 48π = 144π
Meaning that the height is then calculated as follows:
πr²h = 144π
36h = 144
h = 144/36
h = 4.
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pls help with this question its due today the picture is under
Using PEDMAS to solve the mathematical expression given, the value is 2
What is PEMDASPEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It is an acronym used to remember the order of operations in math problems. It is also sometimes referred to as Order of Operations.
In this problem, we will need to use and apply the rules of PEMDAS.
We will need to break this into different components and then bring them together afterwards.
[(3/5 + 0.425 - 0.005) ÷ 0.1] / [30.5 + 1/6 + 3(1/3)] + [6(3/4) + 5(1/2)] / [(26 ÷ 3(5/7)] - 0.05
This becomes ;
[10.2 / 34] + [12.25 / 7] - 0.005
We can further resolve this into
2.05 - 0.005
And then we just subtract the values from one another
2.05 - 0.005 = 2
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Can you help me with this
Answer: 1/4
Step-by-step explanation:
Method 1
this method only works when there is a visual graph, but you can oick 2 points. then go to the point farthest to the left ide of the graph. then count up to be on the same y coordinate as the other point. then count over to be on the same x point, hence 1/4 (up 1 over 4)
Method 2
You can also pick 2 points, and put them into this formula to find slope ([tex]\frac{x2-x1}{y2-y1} }[/tex] then you plug in so the point farthest left would be x1 and y1 and the other point would be y1 and y2 so when you plug in and solve you get 1/4
Answer:
Step-by-step explanation:
rise/run
=1/4
normally distributed with a mean of 5 days and a standard deviation of 4 days. What is the probability that the product has a shelf life of at least 1 week and at most 2 weeks
The probability that the product has a shelf life of at least 1 week and at most 2 weeks is 0.30.
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability is a concept in mathematics that helps predict the likelihood of certain events. Probability generally refers to the degree to which something is likely to occur.
A standard normal variable with a mean of 0 and a variance of 1 can be created from a normally distributed random variable with a defined mean and variance.
Thus, The probability that the product has a shelf life of at least 1 week and at most 2 weeks is 0.30.
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Additive Relationships
What is the value of y when x=100y=?
The value of y in the equation is y = x / 100.
How to make a variable the subject of the formula?Subject of the formula is a variable which is expressed in terms of other variables involved in the formula.
Therefore, let's make y the subject of the formula in the equation x = 100y.
Hence, we will find y in terms of x.
Therefore,
x = 100y
divide both sides of the equation by 100
100y / 100 = x / 100
y = x / 100
Therefore,
y = x / 100
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What is the equation for the linear model in the scatter plot obtained by choosing the two points closest to the line?
A)Y = -3 x+ 56
B)Y = -2 x +46
C)Y = -2 x +56
D)Y = 2 x + 56
The equation for the linear model in the scatter plot is Y = -2x + 56.
To calculate this equation, we need to find the slope (m) and the y-intercept (b). The slope is calculated with the formula m = (y2 - y1) / (x2 - x1), where x and y represent the coordinates of two points on the graph.
The two points closest to the line in the scatter plot are (2, 48) and (4, 52). Substituting these values into the formula gives us m = (52 - 48) / (4 - 2) = 4/2 = 2.
The y-intercept is the point where the line crosses the y-axis. To find it, we need to substitute the slope and one point's coordinates into the equation y = mx + b. For our equation, we will use the coordinates (2, 48). Substituting these values into the equation gives us 48 = 2x + b, and solving for b gives us b = 48 - 2(2) = 44.
Therefore, the equation for the linear model in the scatter plot is Y = -2x + 56.
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100 students were surveyed about which subject they liked best. 41 students said they like math, and 25 students said they liked Science. Of those students surveyed, 19 said they liked both.
How many students is the complement of math?
In 100 students, Science was rated favorably by 25 students, while math received ratings from 41 students. 19 of the students polled indicated that they approved of both. 16 students are the complement of math.
What is complement of a number?The phrase "complement" is typically used to describe a subset of a set that does not include another subset. The entire original set is obtained by adding the complement and its taking. The complement of a set is typically represented by the notations. The complement of a set is the set that includes all the elements of the universal set that are not present in the given set.
The Total number of students were 100
Students who like maths were 41
Students who like science were 25
Students who like both maths and science were 19
Students who does not like maths are 41-25 = 16.
So the students who are the complement of math are 16.
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Evie practices her violin for exactly
310 minutes each week. On Monday, she
practices twice as long as she does on
Tuesday. On Thursday, she practices the
same number of minutes as Tuesday. On
Saturday, she practices 5 fewer minutes
than three times her Tuesday practice.
How many minutes does Evie practice on
Monday?
On Monday, Evie practices 2T = 2*45 = 90 minutes.
Define percentage.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Define Fraction.Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Let's call the amount of time Evie practices on Tuesday T.
On Monday, she practices twice as long as she does on Tuesday, so she practices 2T minutes.
On Thursday, she practices the same number of minutes as Tuesday, so she practices T minutes.
On Saturday, she practices 5 fewer minutes than three times her Tuesday practice, so she practices 3T-5 minutes.
We know that Evie practices 310 minutes in total in a week.
So we can set up an equation:
T + 2T + T + 3T-5 = 310
7T-5 = 310
7T = 315
T = 45
On Monday, Evie practices 2T = 2*45 = 90 minutes.
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How do you find the sides of an acute triangle?
To find the missing side length of the acute angled triangle apply the cosine law as follow:
a² = b² + c² - 2bccosA
b² = a² + c² - 2accosB
c² = b² + a² - 2abcosC
As given in the question,
Given triangle is acute angled triangle.
Let us consider the measure of two sides and its included angle of the acute angled triangle is given.
Let the triangle be ABC,
Side opposite to ∠A, ∠B , and ∠C are a , b, and c respectively.
Apply cosine law to find the measure of the missing side in the acute angled triangle:
a² = b² + c² - 2bccosA
b² = a² + c² - 2accosB
c² = b² + a² - 2abcosC
Therefore, to get the measure of the missing side length in the acute angled triangle apply cosine law.
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26. Six oranges in a bag of 30 oranges are bad. Express the number of bad oranges as a fraction in its lowest terms.
Answer:
The fraction representing the number of bad oranges can be written as 6/30. This fraction can be simplified by dividing both the numerator and the denominator by 2, which gives us 3/15. This fraction is already in its lowest terms, so 3/15 is the final answer.
Step-by-step explanation:
Solve the problem as directed. The volume of a right circular cone varies jointly as the altitude and the square of the radius of the base. If the volume of the cone is 154 cubic inches when its altitude is 12 inches and the radius of the base is 3 1 2 312 inches, find the altitude when the volume of the cone is 77 cubic inches and the radius of the base is 2 1 3 213 inches. (Put your response in decimal form.) Altitude
The altitude of the right circular cone is 13.5 inches.
What is volume?
Volume is a term used in mathematics to describe the volume of three-dimensional space occupied by an object or a closed surface. The measurement of volume is done in cubic units, like m3, cm3, in3, etc. Volume is also referred to as capacity on occasion.
Here, the volume of a right circular cone varies jointly as the altitude and the square of the radius of the base
So our equation for volume becomes
V = c*h*r^2
where 'h' is altitude and
'r' is radius of base and
'c' is constant
Putting the values of V, h, r, in the volume equation.
we get,
154 = c*12*3.5*3.5
c = 22/21
Now we have volume = 77 cu and radius of the base =7/3, so putting the values we get,
77 = 22/21*h*7/3*7/3
or, h = 13.5 inches
Hence, the altitude of the right circular cone is 13.5 inches.
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At the beginning of the year, a blogger has 150 subscribers. Since then, the number of subscribers to her blog has been doubling every 6 months, thanks to some successful appearances on television.
1) by what factor is the number of subscribers increasing every month?
2) write an equation that represents the number of subscribers (s) in terms of m months since the beginning of the year( when she had 150 subscribers)
The number of subscriber is increasing by factor 1,12 every month. The number of subscribers m months since the beginning of the year can expressed by the growth model equation S(m) = 150 . e^(0.12m)
The problem can be solved using exponential growth model.
1) The relation between growth rate and doubling time is given by:
doubling time = 70 / growth rate
In this case, doubling time = 6 months.
Hence,
growth rate = 70/6 = 11.67% = 0.1167 ≈ 0.12
Growth factor is defined as:
Growth factor = 1 + growth rate
= 1 + 0.12 = 1,12
2) The growth model of the number of subscribers is given by:
S(m) = So . e^(r.m)
Where:
S(m) = number of subscriber after m months
So= initial number of subscriber
r = growth rate
t = time period
Substitute So = 150 and r = 0.12
S(m) = 150 . e^(0.12m)
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What is an equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35?
Answer: To find an equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35, we can use the fact that two lines are parallel if and only if they have the same slope.
The slope of the line 4x−5y=35 is -4/5. Therefore, we can find an equation of the line that passes through (-5,-6) and is parallel to 4x−5y=35 by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
Substituting the values into the slope-intercept form, we get:
y = (-4/5)x + b
To find the value of b, we can substitute the coordinates of the point (-5,-6) into the equation:
-6 = (-4/5)(-5) + b
-6 = 8/5 + b
-6 - 8/5 = b
-24/5 = b
Therefore, the equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35 is:
y = (-4/5)x - 24/5
This can also be written as:
y = -4/5x - 24/5
Step-by-step explanation:
What does a 30 60 90 triangle look like?
The 30-60-90 triangle is shaped like half of an equilateral triangle.
A special right triangle with angles 30°, 60°, and 90° is called a 30-60-90 triangle. Since 30° is the smallest angle in the triangle, the side opposite to the 30° angle is always the smallest.
The side opposite to the 60° angle is the longer leg, and finally, the side opposite to the 90° angle is the largest side of the right triangle, also known as the hypotenuse.
30°-60°-90° Triangle Rule:
In a 30-60-90 triangle, we can find the measure of any of the three sides by knowing the measure of at least one side in the triangle. This is known as the 30-60-90 triangle rule.
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x^2+6x+8=0 complete the square method
Answer:
x = - 2 or x = - 4
Step-by-step explanation:
Via completing the square:
x^2 + 6x + 8 = x^2 + 6x + (6/2)^2 - (6/2)^2 + 8
= (x + 3)^2 - 3^2 + 8
= (x + 3)^2 - 9 + 8
= (x + 3)^2 - 1
Since x^2+6x+8=0,
(x + 3)^2 - 1 = 0
(x + 3)^2 = 1
x + 3 = +- sqrt(1)
x + 3 = +- 1
x + 3 = 1 or x + 3 = -1
x = -2 or x = -4
The coefficient b and c in the equation x^2bxc=0 are alo the root of that equation (c≠0)
[tex]x^2[/tex] - (b+c)x +bc=0 is the quadratic equation whose roots are b,c.
If the roots of a quadratic equation are given, the equation can be written by factoring the equation using the roots.
Given the roots, let's say r1 and r2, the quadratic equation can be written as (x - r1)(x - r2) = 0.
Expanding the above equation x^2 - (r1 + r2)x + r1r2 = 0
Therefore, if the roots of a quadratic equation are given as r1 and r2, the quadratic equation can be written as:
x^2 - (r1 + r2)x + r1r2 = 0
since we are given that the root of the equation are b,c;
so r1=b,r2=c;
putting the value in the above equation we get the equation with b and c as root:
[tex]x^2[/tex] - (b+c)x +bc=0
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Complete question :
The coefficient b and c in the equation [tex]x^2+bx+c[/tex] is also root of another equation where c≠0 .
please write the equation
What are the zeroes of the polynomial 4x2 4x 3?
The zeroes of this polynomial equation is [tex]$4 x^2-4 x-3$[/tex] are [tex]\frac{3}{2}$[/tex] and [tex]$-\frac{1}{2}$[/tex].
First form the equation
As per the given data the given polynomial equation is [tex]$4 x^2-4 x-3$[/tex].
Here we have to determine the zeroes of a polynomial equation is [tex]$4 x^2-4 x-3$[/tex].
We know that the zeroes of a polynomial are evaluated by equating them with zero.
Therefore p(x)=0
[tex]& \Rightarrow 4 x^2-4 x-3=0[/tex]
Then solve to find the zeroes
[tex]& 4 x^2-4 x-3=0 \\[/tex]
[tex]& \Rightarrow 4 x^2-6 x+2 x-3=0 \\[/tex]
2x(2x - 3) + 1(2x - 3) = 0
(2x - 3) (2x + 1) = 0
[tex]& \Rightarrow x=\frac{3}{2},-\frac{1}{2}[/tex]
Then do verification
We know that for a given polynomial [tex]$a x^2+b x+c$[/tex]
Sum of the zeroes [tex]$=-\frac{b}{a}$[/tex] and product of the roots [tex]$=\frac{c}{a}$[/tex]
Sum of the zeroes [tex]$=\frac{3}{2}-\frac{1}{2}=1$[/tex]
Again, [tex]$-\frac{b}{a}=\frac{4}{4}=1$[/tex]
Product of the zeroes [tex]$=\frac{3}{2} \times-\frac{1}{2}=-\frac{3}{4}$[/tex]
Again, [tex]$\frac{c}{a}=-\frac{3}{4}$[/tex]
Thus, the relationship between the zeroes and the coefficients of the polynomial is verified.
Hence, the zeroes of this polynomial are [tex]\frac{3}{2}$[/tex] and [tex]$-\frac{1}{2}$[/tex].
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Which proportion is solved correctly using cross products?
4/6 = 12/18 = 4x12=9x18
or
4/6 = 12/18 = 4x12=9x12
The proportion that is solved correct using cross products is given as follows:
4/6 = 12/18 = 4x18 = 6x12
How to solve a proportion applying cross product?A proportion represents a fraction of a total amount, hence it is written as follows:
p = x/y.
In which the terms are given as follows:
x is the numerator of the fraction.y is the denominator of the fraction.For cross products, we have two proportions that are equal, hence the numerator of the first fraction multiplies the denominator of the second fraction, while the denominator of the first fraction multiples the numerator of the second fraction.
The proportion in this problem is given as follows:
4/6 = 12/18.
Hence the cross product is applied as follows:
4 x 18 = 6 x 12
72 = 72 (which is a true statement).
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Finding the slope ?identify the slope
the slope of the given straight line will be -3
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
We know that formula two find the slope of the line joining two points which is
Slope is = y2-y1/x2-x1
=9-0/0-3
=-3
Hence the slope of the given straight line will be -3
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