The amount borrowed is $84,000. The annual interest rate is 6%. There are 12 payments per year for 21 years at a monthly payment amount of $587.
Explanation:The question pertains to the fundamentals of loan calculation. Let us identify the components asked:
The amount borrowed, as clearly stated, is $84,000.The annual interest rate, also known as the APR (Annual Percentage Rate), is 6%Since it was mentioned that payments are set to be monthly, the number of payments per year is 12.The loan term, the length of time given to repay the loan, is indicated as 21 years.The payment amount, which is the monthly payment the borrower must make, is $587.Learn more about Loan Calculation here:https://brainly.com/question/28244942
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In the loan scenario, the person borrowed $84,000 at an annual interest rate of 6%. They will make 12 payments of $587 each year for a term of 21 years.
Explanation:In the provided loan scenario, the following key components can be identified:
The amount borrowed - This is the initial amount that is provided to the individual. In this case, it is $84,000.The annual interest rate - This is the percentage of the loan amount that is charged as interest each year. Here, it is 6%.The number of payments per year - As the payments are made monthly, there are 12 payments in a year.The loan term - This is the period over which the loan will be repaid. In this scenario, it is 21 years.The payment amount - This is the amount that is paid each month towards the loan. It amounts to $587 per month in the given context.Learn more about Loan Terms here:https://brainly.com/question/29755394
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Write the expression as a difference of a monomial and a trinomial: 2a^4+5a^3-2a^2+4
(2a^4+5a^3+4) -2a^2
Step-by-step explanation:There are 4 terms. Your trinomial could consist of any three of them. Here, we've chosen to use the one with the negative sign as the monomial, because the question asks for a difference.
Use your classmates to write 5 or more ratios. For example, you could compare boys to girls or people with glasses to people without glasses.
Answer:
1/3 3/1 5/6 6/5 8/9 9/8
Step-by-step explanation:
What transformations change the graph of f(x) to the graph of g(x)? f(x) = 3x2 g(x) = 9x2 - 4
Question 2 options:
The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/3 and translated up 4 units.
The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/3 and translated down 4 units
. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated up 4 units.
The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated down 4 units.
Answer:
D.
Step-by-step explanation:
The coefficient of the leading term tells you how "stretchy" a graph is. Since g(x)'s leading coefficient is 3, and f(x)'s leading coefficient is 9, and they're both [tex]x^{2}[/tex], g is just 3 times f. Then g's constant term is -4, and f's constant term is 0, then g is just f but translated 4 down.
Answer:
Option 4
Step-by-step explanation:
The 3 changing to the 9 stretches the graph vertically by a factor of 3. The - 4
translates the graph 4 units down .
Its Option 4
Whose beaker has the least amount of liquid in it.
Jay 0.8
Alana 1.05
Evan 1.2
Stacey 0.75
Jim needs to rent a car. A rental company charges $21.00 per day to rent a car and $0.10 driven. for every mile . He will travel 250 miles. . He has $115.00 to spend. Write an inequality that can be used to determine d, the maximum number of days that Jim can re ays that Jim can rent a car
Answer:
21d +25 ≤ 115
Step-by-step explanation:
Jim's cost will be ...
... 21.00·d + 0.10·250 = 21d +25
He wants his cost not to exceed his budget, so ...
... 21d +25 ≤ 115
_____
The solution is ...
... 21d ≤ 90 . . . . subtract 25
... d ≤ 90/21 ≈ 4.3
so Jim can rent the car a maximum of 4 days.
The inequality that can be used to express this scenario is
115 ≤ 21*d+ 25
Given data
Charges = $21 per day
Cost per driven distance = $0.10
Distance he will travel = 250 miles
Amount her has to spend = $115
Let the maximum number of days Jim can rent a car with $115 be "m"
Hence
Total amount = 21*d+ 0.1*250
Substituting and Simplifying we have
115 ≤ 21*d+ 25
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Derek established his own retirement account 10 years ago. He has discovered that he can obtain a better rate for the next 10 years at 12 percent interest compounded semiannually. Consequently, Derek established a new ordinary annuity account (beginning amount $0.00) and he will contribute $7,000.00 semiannually into the account for the next 10 years. What will be the value of this account at the end of the 10-year period?
$83,652.59 $244,707.61 $257,502.00 $264,501.86
Answer:
https://brainly.com/question/10687203
Step-by-step explanation:
Solve the inequality) 3a - 4 < 5 (line under greater or less then) As you solve the problem, do it with numbers instead of the word form, for example, 1+1=2 instead of one plus one equals two.
a ≤ 3
Step-by-step explanation:Undo what is done to the variable. The variable is multiplied by 3 and 4 is subtracted from that result. To undo these operations, you add 4, then divide by 3.
... 3a ≤ 9 . . . . 4 is added to both sides of the inequality
... a ≤ 3 . . . . . both sides of the inequality are divided by 3
_____
Comment on solving inequalities
These are the same steps you would use to solve the 2-step equation ...
... 3a -4 = 5
The only difference between solving equations and solving inequalities is that when you multiply or divide by a negative number, you reverse the sense of the comparison (> becomes <, and vice versa; ≥ becomes ≤, and vice versa). You can see this if you consider numbers: 2 > 1. Multiplying by -1 gives -2 < -1.
In a trapezoid the lengths of bases are 11 and 18. The lengths of legs are 3 and 7. The extensions of the legs meet at some point. Find the length of segments between this point and the vertices of the greater base.
Answer:
[tex]AS=18\ units,\ DS=\dfrac{54}{7}\ units.[/tex]
Step-by-step explanation:
Consider trapezoid ABCD with bases BC=11 units and AD=18 units. The lengths of legs are AB=7 units and CD=3 units. Point S is the point of intersection of the extensions of the legs AB and CD.
Let BS=x units and CS=y units.
Consider triangles BSC and ASD. By AAA theorem these triangles are similar (because ∠SAD≅∠SBC, ∠ADS≅∠BCS and ∠S is common).
Then
[tex]\dfrac{BS}{AS}=\dfrac{CS}{DS}=\dfrac{BC}{AD},\\ \\\dfrac{x}{x+7}=\dfrac{y}{y+3}=\dfrac{11}{18}.[/tex]
Therefore,
[tex]\dfrac{x}{x+7}=\dfrac{11}{18},\\ \\18x=11(x+7),\\ \\18x=11x+77,\\ \\7x=77,\\ \\x=11\ units.[/tex]
[tex]\dfrac{y}{y+3}=\dfrac{11}{18},\\ \\18y=11(y+3),\\ \\18y=11y+33,\\ \\7y=33,\\ \\y=\dfrac{33}{7}\ units.[/tex]
The lengths of segments between point S and the vertices of the greater base are
[tex]AS=AB+BS=7+11=18\ units,\ DS=DC+CS=3+\dfrac{33}{7}=\dfrac{54}{7}\ units.[/tex]
Evaluate f(3) x(5x-9)
I think I have the answer just now sure thanks if you can help
18
Step-by-step explanation:Put 3 where x is, then do the arithmetic.
... f(x) = x(5x -9)
... f(3) = 3(5·3 -9) = 3(15 -9) = 3·6
... f(3) = 18
_____
Your calculator can do this, too.
A farmer wants to build a fence enclosing a rectangular region bordering a river. If the farmer has 500 feet of fencing, find the maximum area that can be enclosed.
Answer:
31,250 ft²
Step-by-step explanation:
Let x represent the length of fence parallel to the river. Then the ends of the rectangle will have dimesion (500-x)/2, and the total area will be ...
... A = x(500-x)/2
This function describes a parabola with zeros at x=0 and x=500. The vertex (maximum) will be located halfway between these, at x=250.
The maximum size pen has area ...
... A = 250(500 -250)/2 = 31,250 . . . . sq ft
A cardboard box has a square base and an open top. the four sides are made of wood that costs 2 dollars per square foot, while the base is made of aluminum that costs 25 dollars per square foot. if the volume of the box is to be 50 cubic feet, what is its minimum possible cost?
Answer:
$300
Step-by-step explanation:
Let x represent the side length of the square base in feet. Then the height of each side is ...
... h = (50 ft³)/(x ft)² = (50/x²) ft
The cost of the sides of the box is then ...
... (4 sides) × (x ft)(50/x² ft)/side × $2/ft² = $400/x
The cost of the bottom is ...
... (x ft)² × $25/ft² = $25x²
So, the total dollar cost is
... C = 400/x + 25x²
This will be a minimum where its derivative with respect to x is zero.
... 0 = -400/x² +50x
... 400/50 = 8 = x³ . . . . . add 400/x²; multiply by x²/50
... x = ∛8 = 2
For this value of x, the minimum cost is ...
... C = 400/2 + 25·2² = 300
The minimum possible cost is $300.
_____
Comments on the problem
1) Cardboard boxes are usually made of cardboard. They are rarely made of wood and alumninum.
2) The cost of the bottom is half the cost of the sides. When the dimensions are unconstrained, you will find (as here) the cost is shared equally between the bottom and pairs of opposite sides—each being 1/3 the total cost.
how many tables will be needed to seat 65 people if each table seats 7 people
Answer:
10 tables are needed to seat 65 people.
Step-by-step explanation:
Given :
There are total 65 people.
7 people can be seated on each table .
To Find : No. of tables required to seat 65 people.
Solution :
Since 7 people can sit on no. of tables = 1
1 people sit on no. of tables = 1/7
65 people sit on no. of tables
= [tex]\frac{1}{7} *65[/tex]
⇒ [tex]9.28[/tex]
⇒ 9.28 ≈ 10 tables are needed to seat 65 people.
Thus 10 tables are needed to seat 65 people.
f(x) = (x+2)(x-1)(2x+3)
Which statements are true? (Graph is pictured)
Select ALL that apply
A)The end behavior of functions f(x) and g(x) are exactly the same.
B)Both functions have exactly three x-intercepts.
C)The function f(x) is an odd degree function.
D)The function g(x) has a positive leading coefficient.
E)The x intercepts for g(x) are (1, 0); (2, 0) and (-3/2, 0)
Answer:
B) Both functions have exactly three x-intercepts.
C) The function f(x) is an odd degree function.
E) The x intercepts for g(x) are (1, 0); (2, 0) and (-3/2, 0)
Step-by-step explanation:
The function f is a function of degree 3 (there are 3 x-terms in the product contributing to the highest-degree term), so is of odd degree. The leading coefficient in f(x) is the product of the coefficients of x: 1·1·2 = 2, a positive number.
For a polynomial function of odd degree, the general shape of the graph will be "/" if the leading coefficient is positive, and "\" if the leading coefficient is negative. That is, end behaviors will be opposites of each other. Function f has a positive leading coefficient, so its end behavior will be (-∞, -∞) and (+∞, +∞). Function g has end behavior that is (-∞, +∞) and (+∞, -∞), so is not the same. Apparently, g(x) has a negative leading coefficient.
The graph of g(x) shows it to have 3 x-intercepts. They can be read from the graph as (-3/2, 0), (1, 0) and (2, 0). The factoring of f(x) shows it to have 3 x-intercepts, the same number. There is an x-intercept of f(x) for each factor. (The x-intercept value is the value of x that makes the factor zero.)
The function f(x) is of odd degree and has three x-intercepts at -2, 1, and -3/2. The statements regarding the function g(x) cannot be confirmed without further information.
Explanation:The function given is f(x) = (x+2)(x-1)(2x+3). The degree of the function is 3 as there are three terms multiplied together. Therefore, f(x) is an odd degree function, which makes option C correct.
The x-intercepts of the function occur where y = 0, i.e. where f(x) = 0. Solving this will give the roots or intercepts for x which are -2, 1, and -3/2. This means that the function f(x) has three x-intercepts, which makes option B correct.
Without information or a graph of function g(x), we cannot accurately answer options A, D and E. We cannot know the end behavior, the leading coefficient or the x intercepts for g(x). Therefore, only options B and C are true statements.
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In one year, a bird farm sold 375 total chickens. of these, there were 37 more Cornish hens than turkeys. How many Cornish hens and how many turkeys were sold?
Answer:
206 Cornish hens
169 turkeys
Step-by-step explanation:
Let c represent the number of Cornish hens sold. Then c-37 is the number of turkeys sold. The total sales would be ...
... c + (c-37) = 375
... 2c = 412 . . . . collect terms, add 37
... c = 206 . . . . Cornish hens sold
... (c-37) = 169 . . . turkeys sold
_____
Comment on this type of problem
Note that the solution to this problem is that the larger number (number of cornish hens) is half the sum of the total and the difference: (375+37)/2 = 206. This is the general solution for this type of "sum and difference" problem.
The larger contributor is half the total plus half the difference; the smaller contributor is half the total minus half the difference.
Cornish hens = (1/2)(375 +37) = 206
Turkeys = (1/2)(375 -37) = 169
(7x^3y^2)(4x^3y^2)
^=exponents
solve in scientific Notation
(2.8×10¹)x⁶y⁴
Step-by-step explanation:Multiplication can be done in the usual way, then the number converted to scientific notation. Scientific notation does not apply to the variables.
[tex](7x^3y^2)(4x^3y^2)=(7\cdot 4)x^{3+3}y^{2+2}=28x^6y^4\\\\=2.8\cdot 10^1x^6y^4[/tex]
_____
If you write the numbers in scientific notation to start, then do the multiplication, the effect is virtually the same: an adjustment is needed in the product to get it back to scientific notation.
(7)(4) = (7×10⁰)(4×10⁰) = 7·4×10⁰⁺⁰ = 28×10⁰ = 2.8×10¹
Lisa completed the table to describe the product of a mystery one-digit factor and each number.
× 1 2 3 4 5
? even even even even even
Part A Give all of the possible numbers that could be Lisa’s mystery one-digit factor.
Part B Explain how you know that you have selected all of the correct possibilities.
Part A.
We're only told that the product of the mystery factor and the number shown is even. This is true when the number shown is odd as well as even, hence the mystery factor is even.
There are no other conditions on the product that might limit the value of the mystery factor (non-zero, or < 10, for example).
Hence, the mystery factor could be any single-digit even number. In our base-10 number system, there are 5 of them: {0, 2, 4, 6, 8}.
___
Part B.
There are only 5 even single-digit numbers in our base-10 number system, so by choosing 5, I know I have all of them.
(I WILL GIVE YOU BRAINLIEST AND ANSWER ALL YOU CAN IDC) a market researcher tracks the number of people who visits a company's web site each month. the tables shows the data from the last five months of the year.
month web site visitors (thousands)
8 5.74
9 12.00
10 25.07
11 52.40
12 109.42
Part A: which type of function (linear or exponential) best models this situation. EXPLAIN
Part B: describes the approximate monthly growth demonstrated in the table USING WORDS.
Part C: assuming that the growth rate was the same for the entire year, give me an estimate of the number of visitors to the website for month 7. SHOW WORK OR EXPLAIN
Part A: The exponential function is the best model for the given data. The data shows that every month the number of visitor approximately doubles from previous month. In other words the number is some base value (2, in this case) with the number of month (t) being in the exponent. This the a key characteristic of an exponential growth.
Part B: (also explained above). Every month the number of visitors approximately doubles. Starting with 5.74 at month 8, the numbers goes up by about the same amount to 12.0 at month 9. At month 10, a similar increase occurs (doubling would be 24, and the data shows 25, so this is all "aproximate"). This trend continues throughout the table.
Part C:
Month 7 will be estimated as half of month 8 (going backward):
Month 7: 5.74/2=2.87
Estimate for month 7 = 2.87 thousand visitors.
I need help answering this question
21 miles
Step-by-step explanation:Big Bird's nest is halfway between Bert's place and Ernie's place, so the distance from the nest to either apartment is the same. Equating those distances, we have ...
... 5x +4 = 15x -30
... 34 = 10x . . . . . . add 30-5x
... 3.4 = x . . . . . . . .divide by 10
The value of x is not the distance. The distance is given by either of the two expressions
5x+415x-30Using the first of these, the distance from either apartment to Big Bird's nest is ...
... 5·3.4 +4 = 17 +4 = 21 . . . . miles
Of course, using the second gives the same answer:
... 15·3.4 -30 = 51 -30 = 21
300 bears were out of hibernation. after 2 years, the population grew to 381 bears. if the population continues to grow how many bears will there be in 10 years?
Answer:
561 because if you multiple 300 /8 times the number of the before populaiton u got it right Step-by-step explanation:
tomas wrote an equation 4/5x-8=. Finish the equation so that the equation will have no solution. Explain how you know.
Answer:
Right part: [tex]\dfrac{4}{5}x+a,[/tex] where [tex]a\neq -8.[/tex]
Step-by-step explanation:
Linear equation have no solution if it is impossible for the equation to be true no matter what value we assign to the variable x.
The left part of the equation Tomas wrote is
[tex]\dfrac{4}{5}x-8.[/tex]
The right part of the equation should be of the form
[tex]\dfrac{4}{5}x+a,[/tex]
where [tex]a\neq -8.[/tex]
In this case, the equation will take look
[tex]\dfrac{4}{5}x-8=\dfrac{4}{5}x+a,\\ \\-8=a.[/tex]
Since [tex]a\neq -8,[/tex] this equality is always false.
Remark: 1) If a=8, the equation [tex]\dfrac{4}{5}x-8=\dfrac{4}{5}x+a[/tex] is equivalent to the equation
[tex]\dfrac{4}{5}x-8=\dfrac{4}{5}x-8,\\ \\0=0[/tex]
and the lest equation has infinitely many solutions.
2) When coefficient at x differs from [tex]\dfrac{4}{5},[/tex] the equation has unique solution.
A geometric sequence is shown below 2,-6,18,-54,162,... part A: what a recursive relationship for this sequence. Explain how you determined your answer part B: write an explicit formula for this sequence
A) The problem statement tells you it is a geometric sequence, so you know each term is some multiple of the one before. The first terms of the sequence are given, so you know the first term. The common ratio (the multiplier of interest) is the ratio of the second term to the first (or any term to the one before), -6/2 = -3.
So, the recursive definition is ...
... a_1 = 2
... a_n = -3·a_(n-1)
B) The explicit formula is, in general, ...
... a_n = a_1 · r^(n -1)
where r is the common ratio and a_1 is the first term. Filling in the known values, this is ...
... a_n = 2·(-3)^(n-1)
Answer:
a1=2
an=(an-1)(-3)
Step-by-step explanation:
Hope it helps. :)
Kohls is offering a special discount promotion. A merchandise order totaling less than $25 will receive a 25% discount, and an order totaling $25 or more will receive a 50% discount. Which of these correctly describes purchases made at the store during this promotion? Select all that apply.
A A purchase of 3 pairs of socks selling for $4 a pair will be charged as $9 after the promotion is applied.
C A purchase of 3 pairs of skirts selling for $8 each will be charged as $6 after the promotion is applied.
D A purchase of 3 video games selling for $32.45 each will be charged as $48.68 after the promotion is applied.
B A purchase of 1 pair of shoes selling for $78 will be charged as $58.50 after the promotion is applied.
A customer placed an order with a bakery for cupcakes. the Baker has completed 37.5% of the order after being 81 cupcakes how many cupcakes with a customer order
Answer:
216 cupcakes
Step-by-step explanation:
81 = 0.375 × order
81/0.375 = order = 216 . . . . . divide by the coefficient of the variable
_____
About percentages
% means /100
37.5% = 37.5/100 = 375/1000 = 0.375
Which line shows the first error in the solution?
A number divided by 3 is four more than -11. What is the number?
x/ + 4 = -11 (1)
x/3 + 4 -4 = -11 -4 (2)
x/3 = -15 (3)
x/3 x 3 = -15 x 3 (4)
x = -45 (5)
A. Line
B. Line 3
C. Line 4
D. Line 2
The first line.
Step-by-step explanation:If we let x represent "a number", then "a number divided by 3" is x/3. The denominator is missing on the first line.
Further, this "is 4 more than -11", so is = 4 + (-11). The constant 4 is on the wrong side of the equal sign in line 1.
_____
The solution should be ...
... x/3 = 4 + (-11)
... x = 3·(-7)
... x = -21
___
Check
-21 divided by 3 is -7. That is 4 more than -11.
could the triangle be classified as a right triangle?
as you recall from the pythagorean theorem, which applies only to right-triangles, c² = a² + b².
so, a = 6, b = 8, c = 9...... if that triangle is indeed a right triangle, then 9² = 6² + 8², let's check if that's true.
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{9}\\ a=\stackrel{adjacent}{6}\\ b=\stackrel{opposite}{8}\\ \end{cases} \\\\\\ 9=\sqrt{6^2+8^2}\implies 9=\sqrt{36+64}\implies 9=\sqrt{100}\implies 9\ne 10~~\bigotimes~~nope[/tex]
A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. A cylindrical hole cut out of the center has a radius of 6 millimeters.Which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? Check all that apply.
options:
21π(10)2 – 21π(6)2
π(20)2(21) – π(6)2
2,100π – 756π
7,644π
1,344
The volume of metal is the difference of the overall volume of the cylinder and the volume of the hole in it. The formula for the volume of a cylinder is ...
... V = π·r^2·h . . . . . radius r and height h
For the overall dimensions, the radius is half the diameter, so is 10 mm. The hole is said to have a radius of 6 mm. The overall "height" is 21 mm, so the volume in mm³ will be ...
... V_overall -V_hole = π(10)^2(21) -π(6)^2(21)
... = 21π·10^2 -21π·6^2 . . . . . . . matches the first selection
... = 2100π -756π . . . . . . . . . . . matches the third selection
... = 1344π . . . . . . . . . . . . . . . . doesnt' match any selection
The correct expressions for the volume of metal needed, in cubic millimeters, to make the pipe are,
⇒ 21π(10)² – 21π(6)²
⇒ 2,100π – 756π
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters.
And, A cylindrical hole cut out of the center has a radius of 6 millimeters.
Hence, The formula for the volume of a cylinder is,
V = π·r²·h
Where, radius r and height h.
Now, For the overall dimensions, the radius is half the diameter, so is 10 mm. The hole is said to have a radius of 6 mm. The overall "height" is 21 mm,
so the volume in mm³ will be;
V (overall) -V (hole) = π(10)²(21) -π(6)²(21)
= 21π·10² -21π·6²
= 2100π -756π
= 1344π
Thus, The correct expressions for the volume of metal needed, in cubic millimeters, to make the pipe are,
⇒ 21π(10)² – 21π(6)²
⇒ 2,100π – 756π
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jim leaves his house traveling at 200 feet per hour, he wants to travel 400 yards to get to 4:00pm. How many hours does he need to travel? Answer and explain your answer.
I'm giving brainliest for the best answer.
A. 2 hours
B. 4 hours
C. 5 hours
D. 6 hours
Answer:
D. 6 hours
Step-by-step explanation:
There are 3 ft in 1 yd, so 400 yd = 1200 ft.
At 200 ft/h, Jim's travel time for 1200 ft will be
... time = distance/speed = (1200 ft)/(200 ft/h) = (1200/200) · ft · (h/ft)
... time = 6 h
f(x)=log5 (2x+12)+2 yeah this ome threw me off
Answer:
See below for a graph
Step-by-step explanation:
Let's call the parent function g(x) = log₅(x), which has a vertical asymptote at x=0, and goes through the points (1, 0), (5, 1), (25, 2).
Then this function is
... f(x) = g(2(x+6)) +2
That is, the function is horizontally compressed by a factor of 2, shifted left 6 units, and shifted up 2 units. This moves the points listed above to ...
... (-5.5, 2), (-3.5, 3), (6.5, 4)
The graph shows the parent function and the listed points in blue, then the transformed function and the corresponding points in red.
Find all the zeros of the equation x^4-6x^2-7x-6=0 Explain please.
I like to look at a graph of the function to see where the zeros might be. Here, there are x-intercepts at x=-2 and x=3. These can be factored out using synthetic division to find the factorization to be ...
... (x +2)(x -3)(x² +x +1) = 0
By completing the square, using the quadratic formula, or by looking at the graph of it, the complex roots of the quadratic factor can be found to be ...
... x = (-1 ±i√3)/2
_____
The second attachment shows my synthetic division. The first division takes out the root x=3 to give a quotient of x³ +3x² +3x +2. The second division takes out the root -2 to give the quotient of x² +x +1. (You can see that I tried -1 as a root first.)
The graph shows both the quartic and the quadratic factor of it. The latter has a leading coefficient of 1 and a vertex at (-1/2, 3/4), so you know the complex roots are -1/2 ±i√(3/4).
_____
From the beginning
There is only a very complicated formula for the roots of a quartic equation, so these are usually solved by machine or by some form of trial and error (iteration). There are some helps, like Descarte's Rule of Signs, and the Rational Root theorem.
Here, the former looks at the one sign change in the coefficients to tell you there will be 1 positive real root. Changing the sign of the odd-degree terms makes there be 3 sign changes, so there will be 3 or 1 negative real roots. Thus, we're assured at least two real roots, one of each sign.
We can look at the constant term to find the y-intercept to be -6. We can add the coefficients to find the value of the function is -18 for x=1, so the positive real root is larger than 1.
The Rational Root theorem says any rational roots will be factors of 6, the constant term. Choices are 1, 2, 3, 6. We have already eliminated 1 as a possibility, and we consider it unlikely that 6 will be a root. (The 4th power overwhelms the other terms in the function.) We tried 2 and found it doesn't work (this was before we graphed the function). The attached division result shows that 3 is a root, as does the graph.
Once you get down to a quadratic, you can find the remaining roots in the usual way. Because it is so simple to read them from the graph, we decided to graph the quadratic factor.
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Comment on terminology
"root" and "zero" are essentially the same thing when the function is equated to zero, as here. The terms refer to the value(s) of x that make the polynomial function evaluate to zero.
To find the zeros of the equation x^4-6x^2-7x-6=0, we can apply the rational root theorem and synthetic division. By trying different factors of the constant term -6, we can determine that one of the roots is x = -2. After dividing the equation by (x + 2), we obtain a quadratic equation x^3 - 2x^2 - 11x + 3 = 0. We can then solve this equation by factoring or using a graphing calculator to find the remaining two roots.
Explanation:To find the zeros of the equation x^4-6x^2-7x-6=0, we can apply the rational root theorem and synthetic division. By trying different factors of the constant term -6, we can determine that one of the roots is x = -2. After dividing the equation by (x + 2), we obtain a quadratic equation x^3 - 2x^2 - 11x + 3 = 0. We can then solve this equation by factoring or using a graphing calculator to find the remaining two roots.
Learn more about Finding zeros of a polynomial equation here:https://brainly.com/question/33963189
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Mr. O'Brien is paid $7.30 per hour for the first 40 hours he works in a week. he is paid 1.5 times that rate for each hour after that.
Last week, Mr O'Brien work 44 hours he says he earned $321.20 last week do you agree?