The correct value of answer is B. $9100.The interest on the loan is 5% of the principal. So, the interest amount is:= $350
To calculate the total amount Callie has to pay back at the end of the loan, we need to add the principal amount (the original loan amount) and the interest accrued over the six-year period.
The interest can be calculated using the formula: Interest = Principal * Rate * TimeHere, the principal amount is $7000, the interest rate is 5% (or 0.05 as a decimal), and the time is 6 years.
Interest = $7000 * 0.05 * 6 = $2100
Adding the interest to the principal, the total amount Callie has to pay back is:
Total amount = Principal + Interest = $7000 + $2100 = $9100
Therefore, the correct answer is B. $9100.
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What is the rate of change of the function y = \frac{5}{4}x+1y=
4
5
x+1?
Rate of change of y =[tex]\frac{5}{4}x +1[/tex] is 5/4.
What is rate of change?The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.
Given that the expression, y =[tex]\frac{5}{4}x +1[/tex] .
To find the rate of change,
first we make the equation in standard form.
Slope intercept form ;
(y₂ - y₁) =m (x₂ -x₁) + c
Comparing the expression to the standard form;
Here, x intercepts: ( -4/5 , 0) and y intercepts: (0,1)
Rate of change = (y₂ - y₁) / (x₂ -x₁)
Rate of change = 5/4
Therefore, rate of change of y = is 5/4.
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wendy has a monopoly in the retailing of motor homes. she can sell five per week at a price of $21,000 each. if she wants to sell six, she must charge $20,000 each. the marginal revenue of selling the sixth motor home is: -$5,000 -$1,000 $15,000 $20,000
She may sell five of them each week for $21,000. She needs to ask for $20,000 for each unit if she wants to sell six. The marginal revenue of selling the sixth motor home is -$5000. Here option A is the correct answer.
If demand is price inelastic, then raising the price will decrease income. If price increases elastic, lowering the price will boost earnings.
Demand is considered to be elastic if an increase in price results in a loss in overall income because the quantity required is significantly impacted by the price rise. Depending on whether they are requirements or wants, the marketplace. in other words, may have varying elasticities (accessories).
Thus, a fall in revenue because of a rise in price
= (20,000 - $21,000) × (5)
= -$5000
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8. Jim hopes a park will be built within 5 miles of his
house. If a park is built at the coordinates (3, 7),
does that meet Jim's criteria? Explain.
No, he wanted a park developed within 5 miles of his residence, yet this park is 8.30 miles away.
What is coordinate?The horizontal and vertical distances from the two reference axes are used to define the location of a point on a coordinate plane. The x-value and y-value are often denoted as (x,y). To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to determine the y-coordinate. The distance between two points is known as the x-coordinate, or abscissa, while the distance between two points is known as the y-coordinate, or ordinate.
Here,
let the house be (0,0).
coordinate of park=(3,7)
distance=√3²+7²
=√21+49
=√69
=8.30 miles.
No, He wanted a park to be built within 5 miles of his house while this park is 8.30 miles from his house.
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Ticket sales for Six Flags White Water totaled $94,520 this summer. Tickets for the water park cost $17 each. How many tickets were sold?
Answer:
5,560
Step-by-step explanation:
Answer:
Step-by-step answer should
be 5560 because if you divide 94,520 by 17 you can use calculator and the answere should be 5,560
10x-8y=4
20x-16y=8
Please help me solve this
If f(x) = - 3x ^ 2 + x - 9 and g(x) = x ^ 3 + 6x
what is (f + g)(- 4) ?
If the supplied functions are f(x) = - 3x 2 + x - 9 and g(x) = x 3 + 6x and the value of x is -4, the value of (f + g)(- 4) is -137.
What is function?A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable). Functions are typically categorized into four categories. Depending on the Element: One function to one function, many functions to one function, onto function, one function to one and onto function, into function A "vertical line test" can be used to identify whether a relation is a function when looking at a graph. If a vertical line can be drawn anywhere on the graph and cross the relation twice, the relationship is not a function.
Here,
(f+g)(x)=f(x)+g(x)
f(-4)=-3*(-4)²-4-9
f(-4)=-61
g(-4)=(-4)³-3*4
g(-4)=-76
(f+g)(-4)=f(-4)+g(-4)
=-61-76
(f+g)(-4)=-137
If the supplied functions are f(x) = - 3x 2 + x - 9 and g(x) = x 3 + 6x and x is -4, the value of (f + g)(- 4) is -137.
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i need help with this 2 answers
(Oops forgot pic)
The angle measures in this problem are given as follows:
7 - m < ADC = 82º.
8 - m < ADC = 44º.
How to obtain the angle measures?In item 7, the angle measure is found obtained the angle addition postulate, meaning that the measures are obtained as follows:
m<ADB = m < BDC + m < ADC.
Then the equation to find the value of x is obtained as follows:
144 = 7x + 34 + 9x + 46
16x = 64
x = 64/16
x = 4.
Then the angle ADC is obtained as follows:
m < ADC = 9(4) + 46 = 82º.
In item 8, the bisection means that the two angle measures are equal, hence the value of x is obtained as follows:
7x - 19 = 9x - 37
2x = 18
x = 18/2
x = 9.
m < ADC = 9(9) - 37 = 44º.
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Which of the following are true concerning this diagram? You may assume that the lines are parallel.
The solution is
a) ∠1 ≅ ∠5 by Corresponding Angles
b) m∠4 + m∠5 = 180° by Co-Interior Angles or same side Interior angles
c) ∠6 ≅ ∠4 by Alternate Interior Angles
d) ∠2 ≅ ∠8 by Alternate Exterior Angles
What are Parallel Lines Cut by Transversal?
Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
From the figure , we can see that
The Corresponding angles are
Angle 1 and Angle 5
Angle 2 and Angle 6
Angle 4 and Angle 8
Angle 3 and Angle 7
The Alternate Interior angles are
Angle 4 and Angle 6
Angle 3 and Angle 5
The Co-Interior angles are
Angle 4 and Angle 5
Angle 3 and Angle 6
The Alternate exterior angles are
Angle 1 and Angle 7
Angle 2 and Angle 8
Hence , the angles from the figure that are true are
a) ∠1 ≅ ∠5 by Corresponding Angles
b) m∠4 + m∠5 = 180° by Co-Interior Angles or same side Interior angles
c) ∠6 ≅ ∠4 by Alternate Interior Angles
d) ∠2 ≅ ∠8 by Alternate Exterior Angles
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Graham graphs the following system of equations to determine its solution.
2x + 4y = 12
2x - y = 2
What is the correct solution?
Please explain step by step to get marked as brainliest!
Answer:
x=2 and y=2
Step-by-step explanation:
2x=12-4y
x=12-4y/2
x=6-2y
substitute equation on in two
2(6-2y)-y=2
12-4y-y=2
12-5y=2
5y=12-2
5y=10
y=10/5
y=2
substitute in the equation 6-2(2)=2
y=2 and x=2
Determine whether the Mean Value theorem can be applied to fon the closed interval [a, b]. (Select all that apply.) f(x) = 9 sin x, [0, 1] a. Yes, the Mean Value Theorem can be applied. b. No, f is not continuous on [a, b]. c. No, f is not differentiable on (a, b). d. None of the above.
According to the Mean value theorem conditions. The answer will be (a) that is Mean Value Theorem can be applied.
What is Mean Value Theorem?The Mean Value Theorem says that there exists a point c in the interval (a, b) such that f'(c) equals the function's average rate of change throughout [a , b] if a function f is continuous on the closed interval [a , b] and differentiable on the open interval (a , b).
Why is it called mean value theorem?The name derives from the fact that an average rate of change during an interval may be considered as an average (or mean) of the instantaneous rates of change along the interval thanks to the fundamental theorem of calculus.
[tex]f(x) = 9\sin x[/tex] is continuous on [0,1] since every value for [tex]9\sin x[/tex] exist in that interval.
[tex]f(x) = 9\sin x[/tex] is differentiable on (0,1) since at every point the derivative exist that is [tex]9 \cos x[/tex] is valid in that interval.
The answer is (a) that is Yes, The Mean Value Theorem can be applied.
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Jane is having difficulty deciding whether to put her savings in the Mystic Bank or in the Four Rivers Bank. Mystic offers a 12% rate compounded quarterly, and Four Rivers offers 14% compounded semiannually. Jane has $40,000 to invest and expects to withdraw the money at the end of five years. The better deal is:
Multiple Choice
Four Rivers because she will earn about $6,442 more.
Four Rivers because she will earn about $6,523 more.
Four Rivers because she will earn about $4,000 more.
Four Rivers because she will earn about $20,000 more.
Jane must therefore deposit her savings in the four rivers bank.
What is compound interest?Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.
As per the data provided in the question,
Rate, r = 12%
After five years, the total amount, if Jane had saved at Mystic Bank,if Jane had saved at Mystic Bank would be:
[tex]A = P(1+\frac{r}{100} )^n[/tex]
For compounded quarterly,
n = 5 × 4
n = 20
A = 40000(1 + 12/(4 × 100))²⁰
A = 72244.44 (i)
If Jane placed her savings with the Four Rivers, then,
A = 40000(1 + 14/(2 × 100))¹⁰
A = 40000 × 1.9671
A = 78686.054 (ii)
Therefore, it is evident that case (ii) is higher than case (i). Jane must therefore deposit her savings in the four rivers bank.
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Notice
-4x plus what results in 5x?
Answer: 9x
Step-by-step explanation:
-4x+y=5x
solve for x
y=9x
What is - 8/15 - 3 4/5 mixed number in simplest form?
Answer:
–3 4/15
or
3 4/15
Step-by-step explanation:
What does the number in the bottom right hand corner of a two-way frequency table represent?; What is a 2 way frequency table?; What are the important parts of a two-way frequency table?
The solutions for all three questions regarding two-way frequency tables are given below.
A two-way frequency table is a method used to visually represent two sets of categorical data. Unlike one-way frequency tables which have only one categorical variable, these have two. The important parts of a two-way frequency table are the topmost rows that have the name of the category. The leftmost column also has the categories listed. The middle columns and rows contain the data (frequency).
The number in the bottom right-hand corner of a two-way frequency is used to denote the total number of data points that are there in the data set given. This is also equal to the sum of the total rows/columns.
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help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
344
Step-by-step explanation:
6 percent of 530 is 31.8
530-31.8=498.2 or 498
6 percent of 498=29.88
498-30=468
6 percent of 468=28.08
468-28=440
6 percent of 440=26
440-26=414
6 percent of 414=24.84
414-25=389
6 percent of 389=23.34
389-23=366
6 percent of 366=21.96
366-22=344
Thus, our answer is 344
Five subtracted from the product of 6 and a number is at most -25.
The value of the number from the equation 6A - 5 ≤ -25 is A = -3.33
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number be represented as A
Now , the value of A is calculated as
Five subtracted from the product of 6 and a number is at most -25
So , the inequality equation will be
And , substituting the values in the equation , we get
6A - 5 ≤ -25 be equation (1)
Now , adding 5 on both sides of the equation , we get
6A ≤ -25 + 5
6A ≤ -20
Divide by 6 on both sides of the equation , we get
A ≤ -3.33
Therefore , the value of A is -3.33
Hence ,
The value of the number from the equation 6A - 5 ≤ -25 is A = -3.33
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A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one half gallon of water is needed, and for every 5 scoops of mix, one and one fourth gallons of water are needed.
Part A: Find the constant of proportionality. Show every step of your work.
Part B: Write an equation that represents the relationship. Show every step of your work.
Part C: Describe how you would graph the relationship. Use complete sentences.
Part D: How many gallons of water are needed for 12 scoops of drink mix?
Answer:
A. 1/4 gal/scoop
B. w = 1/4s
C. line through the origin with slope 1/4; s-, w- axes labeled "scoops" and "gallons"
D. 3 gallons
Step-by-step explanation:
Given 2 scoops of powdered drink mix needs 1/2 gallon of water, you want (A) the constant of proportionality, (B) the equation for the relationship, (C) a description of the graph, (D) gallons for 12 scoops.
Proportional relationshipA proportional relationship between gallons of water (w) and scoops of drink mix (s) can be written as ...
w = ks
where k is the constant of proportionality.
A Proportionality constantSolving the equation for k, we get ...
k = w/s
Using the given values, we find k to be ...
k = (1/2 gal)/(2 scoops) = 1/4 gal/scoop
The constant of proportionality is 1/4 gallon per scoop.
B EquationWe show the equation in part A. Filling in the value of k gives ...
w = 1/4s . . . . . . . where s is number of scoops, and w is gallons of water
C GraphThe attached shows a graph. A line starts at the origin with slope 1/4; s-, w- axes are labeled "scoops" and "gallons". The practical domain is s ≥ 0, so no part of the graph is in the 3rd quadrant.
D 12 scoopsThe equation tells you that 12 scoops will require ...
w = 1/4·12 = 3 . . . . gallons
3 gallons of water are needed for 12 scoops of drink mix.
<95141404393>
Milo worked for 5 hours on Monday and 4 hours on Tuesday. he earned $14 per hour. How much money did milo earn on both days combined? show
your work
Answer:
$126
Step-by-step explanation:
Monday: 5HR X $14 = $70
Tuesday: 4HR X $14 = $56
$70+$56=$126
suppose an analysis of variance (anova) has determined that there is a difference between means and the following tukey's results are shown. determine which mean is different.
the difference between Group B and Group C (-0.3) is less than the other differences, we can conclude that Group B and Group C are the means that are different.
The ANOVA test has determined that there is a difference between the means, and the Tukey's results can help to determine which mean is different. In this case, Group B (4.0) and Group C (4.3) are significantly different, meaning that one of those means is different from the other groups.
An ANOVA test has been conducted and it has been determined that there is a difference between the means. The Tukey's results can be used to identify which mean is different. In this case, Group B (4.0) and Group C (4.3) are significantly different, meaning that one of those means is different from the means of the other groups (A: 2.2 and D: 4.5). Therefore, Group B and Group C are the means that are different.
Tukey's Test
Group A vs B: 2.2 - 4.0 = -1.8
Group B vs C: 4.0 - 4.3 = -0.3
Group C vs D: 4.3 - 4.5 = -0.2
Since the difference between Group B and Group C (-0.3) is less than the other differences, we can conclude that Group B and Group C are the means that are different.
The complete question is :
suppose an analysis of variance (anova) has determined that there is a difference between means and the following tukey's results are shown. determine which mean is different.
Group A: 2.2
Group B: 4.0
Group C: 4.3
Group D: 4.5
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Determine whether the following statement is sometimes, always, or
never true.
The range of an even function is (-∞o, max], where max is the
maximum of the function.
It is occasionally accurate to say that the range of an even function is (-∞o, max), where max is the function's maximum.
what is range ?the range of variation that is conceivable or the boundaries between it: pricing for various grades of steel; a variety of designs. a thing's operation or action's reach or extent: accessible to the eye. a projectile's range is how far a weapon can or will shoot it.
here the explanation
We can say that our range is any real number value between -infinity and infinity, or (,), if our range is any real number value. The range is all real numbers, but we can express this more succinctly by using the symbol R.
a position where the value of a function is highest. It is an absolute maximum if the value is larger than or equal to all other function values.
It is occasionally accurate to say that the range of an even function is (-∞o, max), where max is the function's maximum.
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CAN SOMEONE HELP ME WITH ALGEBRA 2?
The solution set is for the given inequality is (-∞, -2.25]
How to solve the inequality?Here we want to solve the following inequality:
-11 - 8k ≥ 23 - (7 - 4k)
To solve this, we need to isolate the variable k in one side of the equation.
First we can expand the right side so we get:
-11 - 8k ≥ 23 - (7 - 4k)
-11 - 8k ≥ 23 - 7 + 4k
Group like terms:
-11 - 23 + 7 ≥ 4k + 8k
-34 + 7 ≥ 12k
-27 ≥ 12k
-27/12 ≥ k
-2.25 ≥ k
Then the solution is the set of all values smaller than or equal to -2.25, then the solution set is (-∞, -2.25]
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sample of 16 students from a large university is taken. The average age in the sample was 22 years with a standard deviation of 6 years. Construct a 95% confidence interval for the average age of the population. Assume the population of student ages
The confidence interval for the average age of the population would be (18.8, 25.2).
What is the confidence interval?
In frequentist statistics, a confidence interval is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used.
Given that,
Point estimate = sample mean = [tex]\bar x[/tex] =22
sample standard deviation = s = 6
sample size = n = 16
Degrees of freedom = df = n - 1 = 16 - 1 = 15
At 95% confidence level
[tex]\alpha[/tex] = 1 - 95%
[tex]\alpha[/tex] =1 - 0.95 =0.05
[tex]\alpha/2[/tex] = 0.025
[tex]t_{\alpha/2},df[/tex] = t 0.025 , 15 = 2.131
Margin of error = E = [tex]t\alpha/2,df * \frac{s}{\sqrt n}[/tex]
=2.131 * (6 / √16)
Margin of error = E = 3.20
The 95% confidence interval estimate of the population mean is,
= [tex]\bar x \pm E[/tex]
= 22 ± 3.20
= (18.8, 25.2)
Hence, the confidence interval for the average age of the population would be (18.8, 25.2).
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based on the survey data and calculated expected values, what is the value of the chi-square (\chi^2) test statistic, using the following formula? \chi^{2}
The value of chi-square statistic is;
In the contingency table, "O" stands for the observed value, "E" for the predicted value, and "I" for the "ith" position.
Given,
Chi- Square test;-
A statistical technique called the chi-square test is used to compare actual outcomes with predictions. The goal of this test is to establish whether a discrepancy between observed and expected data is the result of chance or a correlation between the variables you are researching.
We have to find the value of chi- square statistic;
The chi-squared statistic is a single figure that indicates the degree to which the counts you saw deviate from the counts you would anticipate if there were no association at all in the population. If I is the "ith" position in the contingency table, "O" is the observed value, "E" is the anticipated value, and "O" is the observed value.
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You bought a car 3 years ago, taking out a $14,000.00 loan at a 5.8% interest rate for 4 years.
Your monthly payments are $327.51.
A. How much will still be owed after making payments for 3 years?
I will still owe ________
after making payments for 3 years.
B. If the car's value is now $7,500.00 then how much equity do you have after making payments for 3
years?
I will have ______ in equity after making payments for 3 years.
Enter the given values.
N: =
0
Number of Compounding Periods
1:%=
0
Annual Interest Rate as a Percent
PV: =
0
Present Value
PMT: = 0
Payment
FV: =
Future Value
P/Y:
Payments per Year
C/Y:
0
12 :
Solve
Solve
12 :
Compounding Periods per Year
PMT: = END Payments are made at the end of the period
Answer:
To answer these questions, we need to first calculate the total number of payments you have made over the past 3 years. We can do this by multiplying the number of payments per year (12) by the number of years (3). This gives us a total of 36 payments.
Next, we can use a financial calculator or spreadsheet program to solve for the remaining balance on your loan after making 36 payments of $327.51 each. In a financial calculator, we can enter the following values:
N: 36
I: 5.8
PV: -14000
PMT: 327.51
FV: 0
Solving for PV gives us a remaining balance of $4,819.56. Therefore, the answer to part A is $4,819.56.
To find your equity in the car, we can subtract the remaining balance on the loan from the value of the car. In this case, your equity would be $7,500.00 - $4,819.56 = $2,680.44. Therefore, the answer to part B is $2,680.44.
Step-by-step explanation:
Brainliest? :>
7. A five-person committee is to be selected from a group of 12 people. How many
different combinations are possible?
Answer: 792 Combinations
find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe−x2/32, [−2, 8]
The absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.
What is meant by absolute maximum and absolute minimum values?
A function's absolute maximum point is the point at which it can reach its highest value. A similar absolute minimum point is where the function's least possible value is obtained.
Given: [tex]f(x)=xe^{\frac{-x2}{32} }[/tex]
Differentiate the function,
[tex]f'(x)=e^{\frac{-x^{2} }{32} } -\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }[/tex]
[tex]e^{\frac{-x^{2} }{32} } -\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }=0[/tex]
[tex]\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }=e^{\frac{-x^{2} }{32} }[/tex]
[tex]\frac{x^{2} }{16} =1[/tex]
[tex]x^{2} =16[/tex]
[tex]x=[/tex] ±[tex]4[/tex]
The interval is given as: [-2,8]
This means that the value of x = -4, is out of the interval.
So, we have the following critical points:
x = (-2, 4, 8)
⇒ f(x) at x = -2
[tex]f(-2)=-2[/tex] × [tex]e^{\frac{-(-2)^{2} }{32} }[/tex]
[tex]f(-2)=-2[/tex] × [tex]e^{\frac{-4}{32} }[/tex]
[tex]f(-2)=-1.765[/tex]
⇒ f(x) at x = 4
[tex]f(4)=4[/tex] × [tex]e^{\frac{-(4)^{2} }{32} }[/tex]
[tex]f(4)=4[/tex] × [tex]e^{\frac{-16}{32} }[/tex]
[tex]f(4)=2.426[/tex]
⇒ f(x) at x = 8
[tex]f(8)=8[/tex] × [tex]e^{\frac{-(8)^{2} }{32} }[/tex]
[tex]f(8)=8[/tex] × [tex]e^{\frac{-64}{32} }[/tex]
[tex]f(8)=1.083[/tex]
Hence, by comparison, the absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.
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what’s 10.37304 rounded to the nearest hundredth?
Answer:
10.37
Step-by-step explanation:
3 in the thousandths place is lower than 5 therefore you have to turn the thousandths into a 0 and don't change the forenumber
How did you transform the given equation into it's Standard form?
The standard form of such an equation is Ax + By + C = 0 or Ax + By = C.
What is standard form of an equation ?
The standard form of such an equation is Ax + By + C = 0 or Ax + By = C.
If you rewrite this equation in a different way, you'll obtain y by itself on the left side, it then forms y = mx +b.
An assertion of equality between two expressions containing variables and/or numbers is called an equation.
In essence, equations are questions, and attempts to discover systematic answers to those questions have spurred the development of mathematics.
Linear equations can be written in three different ways: point-slope form, standard form, and slope-intercept form.
General Procedure:
Equation in slope intercept form has the basic structure
y = mx + b
y - mx = (mx - mx ) + b
y - mx = b
y - mx - b = b - b
y - mx - b = 0
-mx + y - b = 0−mx+y−b=0
If m is an integer, then B will equal 1.
-A/Bx + y - b = 0−
x+y−b=0
-Ax + By - Bb = 0−Ax+By−Bb=0
-Ax + By - C = 0−Ax+By−C=0
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Given f(x) = 3x - 5, find f(X - 2)
This question is about evaluating Functions.
Answers are
f(x- 2) = 3x - 7
f(x - 2) = x -7
f (x - 2) = 3x - 11
f(x - 2) = 3x² - 11x + 10
After evaluating f(x) = 3x - 5, the answer is f(x-2) = 3x - 11
What do you mean by functions?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). Expressions of well-known functions can be found in many frequently used mathematical formulas. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
The set X is called the domain of the function and the set Y is called the codomain of the function.
Given function:
f(x) = 3x - 5
For f(x-2) substitute x as (x-2) in given function
f(x-2) = 3(x - 2) - 5 = 3x - 6 - 5 = 3x - 11
therefore, f(x-2) = 3x - 11
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if a is an nxn diagonalizable matrix then each vector in rn can be written as a linear cobination of eigenvectors of a
the given statement if a is an n x n diagonalizable matrix then each vector in R^n can be written as a linear combination of eigenvectors of a is false.
What is Diagonalizable matrix?
If there is an invertible matrix P and a diagonal matrix D such that
P^-1AP=D, or alternatively A=PDP^-1, then the square matrix A is said to be diagonalizable or non-defective in linear algebra.
If and only if the algebraic multiplicity of each of A's eigenvalues is equal to the geometric multiplicity of each eigenvalue, then A is diagonalizable. The fact that the geometric sum of the eigenvalues of A is n is an equivalent description.
The given statement is false.
If A is diagonalizable, then A had n distinct eigenvalues. It could have repeated eigenvalues as long as the basis of each eigenspace is equal to the multiplicity of that eigenvalue.
Hence, the given statement is false.
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