a) The degree of the polynomial function is 4
b) The positive real zeros does the function have are 3
a. The degree of the polynomial is equal to the sum of the real and complex zeros. There are four total zeros in the sum (1 negative real) + 3 positive real/complex). The polynomial has a degree of 4.
The solution to part b and the end-behavior, which tends to - for |x|, both support the even degree.
b. The intermediate value theorem informs you that, given the numbers in the table, there will be zeros in the intervals (0, 1), (1, 2), and (2, 3). Within certain time periods, the function's sign changes. Thus, there are three genuine positive zeros.
By examining the table of function values, Stanley is unable to infer anything about Descartes' rule of signs.
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Complete question -Stanley analyzes the table of values for a polynomial function. He has determined through applying Descartes’ rule of sign that there is 1 negative real zero, and either 1 or 3 positive real zeros. He has also determined that the upper bound of the function is 3.
X , f(x)
-2, -105
-1, 0
0, 5
1, -2
2, 3
3, -20
4, -175
a. What is the degree of the polynomial function? How can you tell?
b. How many positive real zeros does the function have? How can you tell?
To manufacture an automobile requires painting, drying, and polishing. Epsilon Motor Company produces three types of cars, the Delta, the Beta, and the Sigma. Each Delta requires 11 hours for painting, 5 hours for drying, and 3 hours for polishing. A Beta requires 17 hours for painting, 8 hours for drying, and 4 hours for polishing, and a Sigma requires 4 hours for painting, 5 hours for drying, and 1 hour for polishing. If the company has 253 hours for painting, 149 hours for drying, and 63 hours for polishing per month, how many of each type of car are produced?
Step-by-step explanation:
d = number of Delta cars
b = number of Beta cars
s = number of Sigma cars
253 = 11d + 17b + 4s
149 = 5d + 8b + 5s
63 = 3d + 4b + 1s
s = 63 - 3d - 4b
149 = 5d + 8b + 5(63 - 3d - 4b) =
= 5d + 8b + 315 - 15d - 20b = -10d - 12b + 315
-166 = -10d - 12b
-83 = -5d - 6b
83 = 5d + 6b
5d = 83 - 6b
d = (83 - 6b)/5
with these 2 "identities" we are going into the 3rd equation and solve for the third variable (b), followed by solving the first 2 identities :
253 = 11((83 - 6b)/5) + 17b + 4(63 - 3((83 - 6b)/5) - 4b)
1265 = 11(83 - 6b) + 85b + 20×63 - 12(83 - 6b) - 80b
1265 = -(83 - 6b) + 5b + 1260
5 = -83 + 6b + 5b
88 = 11b
b = 8
d = (83 - 6b)/5 = (83 - 48)/5 = 35/5 = 7
s = 63 - 3d - 4b = 63 - 3×7 - 4×8 = 63 - 21 - 32 = 10
7 Delta cars
8 Beta cars
10 Sigma cars
were produced.
A+1/6=1/6 solve the equation
Answer:
Step-by-step explanation:
A + 1/6 = 1/6
subtract 1/6 from both sides
A = 0
Find the measurement of the angle indicated for each trapezoid.
*
Answer: m∠B=53°
Step-by-step explanation:
A property that is inherent in a trapezoid of any kind: the sum of the angles adjoining a side is equal to 180°
Hence,
(32x-1)+(14x-3)=180
32x-1+14x-3=180
46x-4=180
46x-4+4=180+4
46x=184
Divide both parts of the equation by 46:
x=4
m∠B=14x-3
m∠B=14(4)-3
m∠B=56-3
m∠B=53°
2x + = x + 5
Solve using a mental strategy
The required solution of the given equation is 5.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The given equation is
2x + = x + 5
According to given question we have
Mental Math is an exercise where we solve mathematical equations mentally without the help of a calculator.
To do the bigger or important quantities first. This gives an estimate of the value expected. Such an approach is front end or left to right multiplication.
2x = x + 5
Substract x from both sides we get,
x=5
Therefore, the required solution of the given equation is 5.
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7 is a factor of which number?
Are these ratios equivalent?
17 1
33 3
Answer:
no
Step-by-step explanation:
Joshua Vermier of Sacramento, California, received a raise after his first year on the job to $45,400 from his initial salary of $42,800. What was Joshua’s raise stated as a percentage? Inflation averaged 2.4 percent for the year. Round your answer to one decimal place.
1. Joshua's raise stated as a percentage is 6.1%.
2. When inflation is factored in, Joshua's raise reduces to 3.7%
What is a percentage?A percentage is the ratio of a variable when compared to the whole.
Percentages are expressed over 100, like ratios, probabilities, and proportions.
Data and Calculations:Initial salary on the job = $42,800
New salary after the raise = $45,400
The salary increase in dollars = $2,600 ($45,400 - $42,800)
The salary increase in percentage = 6.1% ($2,600/$42,800 x 100)
Inflation rate = 2.4%
The real increase in salary = 3.7% (6.1 - 2.4%).
Thus, Joshua’s raise stated as a percentage is 6.1%.
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what is the image of the point (4, 0) after a rotation of 90 degrees counterclockwise about the origin
When point is rotated 90 degrees counterclockwise about the origin, point (x,y) becomes (-y,x).
Solving the QuestionWe're given
(4,0) rotated 90 degrees counterclockwise about the originMake the y-coordinate negative:
(4,0)
Switch around the coordinates:
(0,4)
Answer(0,4)
The perimeter of a baseball diamond is 360 ft. If you take 12 laps around the diamond, what is the total distance you run.
Answer:6-lane, 200-meter rubberized track (8 laps = 1 mile)
Step-by-step explanation:
X °
52°
230°
38°
Find the value of X.
Answer:
Step-by-step explanation:
all of the angles complete a circle so they must add up to 360 degrees.
230 + 38 + 52 + x = 360
320 + x = 360
x = 40 degrees
On a day when the speed of sound is 343 m/s you drop a rock into a well and hear it hit the bottom 3s later. How deep is the well?
Answer:
1029
Step-by-step explanation:
d=s*t
s=343m/s
t=3s
=343m/s*3s
= 1029
Find the value of k the diagram is not to scale
○ 80
○ 36
○ 100
○112
Find the value of k the diagram is not to scale
○ 80
○ 36
○ 100
○112
100 is your answer
Help me pleasseeee lelelelelele
PVIF8%,5 means that the rate is[blank]
and the time is[blank]
years?
Answer:
Step-by-step explanation:
it means the rate is 8% and the time is 5 years
The difference of 3 times a number and 5 is 13. Write and solve an equation to
find the number.
Answer:
n=8/3
Step-by-step explanation:
3n-5=13
3n=8
n=8/3
Suppose that 650lb of coffee are sold when the price is $4 per pound
Money earned = $162.50
Explanation:
650 / 4 – You make $4 for every pound sold
= 162.5
Which is $162.50
please help!
given f(x)=3(4-x), what is the value of f(-2)?
Answer:
18
Step-by-step explanation:
f(-2) = 3(4-x)
=3(4+2)
=3*6=
=18
What is the conjugate?
a √a-1
Step-by-step explanation:
In maths, Conjugates are defined as a pair of binomials with identical terms but parting opposite arithmetic operators in the middle of these similar terms. For example, p – q is the conjugate of p + q.
complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, the complex conjugate of {\displaystyle a+bi} is equal to {\displaystyle a-bi.}
The math conjugate of a number is a number that when multiplied or added to the given number results in a rational number. For example,
The conjugate of a surd 6 + √2 is 6 - √2.
The conjugate of a complex number 5 - 3i is 5 + 3i.
If p=7 and q=1, what is 4pq squared + (-7)pq squared +5p?
For the exponents, I don’t know how to distribute the squared/power of two within each term.
Answer:
14
Step-by-step explanation:
q² = 1
and 1² = 1 * 1 = 1
4pq² + (-7)pq² +5p
Evaluate for p=7,q=1
(4)(7)(1²)+((−7)(7))(1²)+(5)(7)
(4)(7)(1²)+((−7)(7))(1²)+(5)(7)
=14
Given the lease terms below from a local car dealership, what is the total cash due at
signing if the dealership requires down payment, security deposit, first month's
payment and the acquisition fee at signing?
Length of lease = 24 months
MSRP of the car = $22, 750
Purchase value of the car after lease = $16, 900
Down payment = $1,800
Monthly payment = $425
Security deposit = $375
Acquisition fee = $300
The total cash due at signing if the dealership requires down payment, security deposit, first month's payment and the acquisition fee at signing is 2400 + 375 + 500 = 3275
When you buy a car, you don't make monthly payments at the beginning. Plus, you don't care how much the buyout costs when you close the lease, that's after you've had it for two years.
You must take care of the deposit, this is your good faith commitment to the rental car. In addition, you may have to pay a deposit based on your credit, and the acquisition fee is what you would pay a broker or dealer to get the car to you if you wanted it from somewhere else.
Therefore,
2400 + 375 + 500 = 3275
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Given (x,7) and (−1,y) find x and y such that the midpoint between these two points is (3,5)
The solution to the system of linear equations is (x, y) = (7, 3).
How to find the missing coordinates of the two ends of a line segmentHerein we find that the coordinates of the midpoint and part of the coordinates of the ends of the line segment are known. We must determine the values of the missing coordinates by the midpoint formula:
0.5 · (x, 7) + 0.5 · (-1, y) = (3, 5)
Which is equivalent to the system of linear equations:
0.5 · x - 0.5 = 3 (1)
3.5 + 0.5 · y = 5 (2)
The solution to the system of linear equations is (x, y) = (7, 3).
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What is the least common denominator of 1/6 and 2/3
Answer:
It is 6 since the denominator 3 can be moved to 6 by only multiplying it by 2
if the midpoint of line AB is (4,4) and the coordinates of A is (2,1) what is the coordinates if B
The required coordinate of b is given as (6, 7 ).
To find out the coordinate of b if M is the midpoint of AB. A(1, -4) and M(-3 ,0).
What is the midpoint?
The midpoint is that point the line whose length from both the ends of the line is equal.
Here,
We have coordinates of two points i.e. A(1, -4) and M(-3, 0).
Definition of midpoint says,
x = [x₁ + x₂] / 2 ; y = [y₁ + y₂] / 2
x₁ = 2, x = 4 , y₁ = -1, y = 4
now,
4 = [2 + x₂] / 2 ; 4 = [1 + y₂] / 2
x₂ = 8 - 2 ; y₂ = 8 - 1
x₂ = 6 : y₂ = 7
Thus, the coordinate of b is given as (8, 7 ).
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Express the following inequality using interval notation.
1/2x−1>7
The inequality using interval notation is (18, ∝)
How to express the inequality using interval notation?The inequality is given as
1/2x − 1 > 7
Add 1 to both sides of the inequality
So, we have
1/2x − 1 + 1 > 7 + 1
Evaluate the like terms
So, we have
1/2x > 8
Multiply through by 2
So, we have
x > 16
Using interval notation, we have
(18, ∝)
Hence, the inequality using interval notation is (18, ∝)
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please help my geo grade is so low
As m ∠ COD = 90°, then the angle COD is a right angle.
What kind of angle is the measure seen in the protractor?
According to geometry, angles are generated by semirrays with a common point. There are different kinds of angles concerning its measure:
Acute angle - Its measure is between 0° and 90°.Right angle - Its measure is 90°.Obtuse angle - Its measure is between 90° and 180°. Straight angle - Its measure is 180°.Based on all the information given by the protractor, we find that the measure of the angle AOD is:
m ∠ COD = m ∠ AOD - m ∠ AOC
If we know that m ∠ AOD = 115 ° and m ∠ AOC = 25°, then the measure of the angle COD is:
m ∠ COD = 115° - 25°
m ∠ COD = 90°
As m ∠ COD = 90°, then the angle COD is a right angle.
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You are the owner of four Taco Bell restaurant locations. You have a business loan with Citizens Bank taken out 60 days ago that is due in 90 days. The amount of the loan is $50,000, and the rate is 9.5% using ordinary interest.
You currently have some excess cash: $35,000. Due to situations beyond your control, you, as the owner, must make an immediate business decision now to pursue only one of these two choices:
1) sending all of the $35,000 to Citizens Bank as a partial payment on your loan, or
2) using the $35,000 to purchase serving supplies such as food containers, cups, and plastic dinnerware for your inventory. This is the last day to take advantage of the opportunity to save some money due to a special discount price that is "10% off" the normal cost of $35,000 for these items.
Consider these calculations:
(a)
How much interest (in $) will you save on this loan if you make the partial payment and don't purchase the additional serving supplies? (Round your answer to two decimal places.)
$
(b)
How much money (in $) will you save if you purchase the serving supplies with the discount and don't make a partial payment on the loan? (Round your answer to two decimal places.)
$
(c)
How much (in $) will you save by purchasing the discounted serving supplies rather than making the partial payment? (Hint: Find the difference between the savings on the supplies found in part (b) and the savings on the loan interest found in part (a). Round your answer to two decimal places.)
$
(d)
What other factors should you consider before making this decision?
The amount saved by repaying the loan early is $831.25
The amount of discount received by purchasing supplies is $3,500
The net amount saved by purchasing supplies rather than repaying loan is $2,668.75
What is ordinary interest?
Ordinary interest is the interest computation that is based on 360-day a year count rather than 365-day year count, hence, in determining the amount saved by paying $35,000 out of the amount due to Citizens Bank, we time-apportion the interest for 90 days with respect to 360 days not 365 days.
Amount saved in interest=$35,000*9.5%*90/360
Amount saved in interest=$831.25
Using the $35,000 to purchase serving supplies, 10% discount is given off the normal cost of $35,000
Amount saved with discount=10%*$35,000
Amount saved with discount=$3,500
The difference between discount on supplies and interest saved=$3,500-$831.25
The difference between discount on supplies and interest saved=$2,668.75
The other factors to consider before making the final decisions include, the fact the loan is more important than the supplies because the loan relates to the firm's financing rather than operational needs of supplies
Secondly, the amount saved in interest may be more if another loan of $35,000 can be borrowed elsewhere with significant lower interest rates
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Question Which graph represents the inequality? 2x−3y<6
I think the answer is B, the one with a complete line and shaded to the bottom
Evaluate the expression when x= 6 and y= -4.
-x + 6y
Answer:
Step-by-step explanation:
substitute the value for x and y
-6 + 6(-4)
= -6 -24
= -30
Answer:
-30
Step-by-step explanation:
plug in variables
-6 + 6(-4)
-6+ -24
= -30
Ji-yoon started the week with a balance of -$90 in her checking
account. She then wrote a check for $130. Write an expression with
addition that can be used to find the new balance.
Answer:
-$90 + $130= $40
Step-by-step explanation:
Im not sure if this is what you were looking for
$953 is ________% of $1717
Select one:
A. 0.6
B. 55.5
C. 0.1
D. 180.2
