Answer:
Using Descartes' Rule of Signs, we observe whether each consecutive term has a + or - sign:
f(x) = 3x4 − 5x3 − x2 − 8x + 4
Signs are: + - - - +
There are 2 sign changes (from +3 to -5, then from -8 to +4). This means that there are either 2 or 0 positive roots. (We take the number of sign changes, which is 2, and subtract by 2s to get all possible numbers of positive roots.)
For negative roots, we first invert all the odd-powered terms in f(x):
3x4 + 5x3 − x2 + 8x + 4
Signs are: + + - + +
There are 2 sign changes, from +5 to -1, and from -1 to +8. Therefore, there are either 2 or 0 negative roots.
Since the overall degree of f(x) is 4, the total number of roots must sum up to 4. There are either 2 or 0 positive roots, and 2 or 0 negative roots, and everything that remains will be a complex root. The possibilities are:
2 positive, 2 negative, 0 complex
2 positive, 0 negative, 2 complex
0 positive, 2 negative, 2 complex
0 positive, 0 negative, 4 complex.
Therefore we can have either 0, 2, or 4 complex roots.
The correct answer is the last choice.
Rachael is placing a protective cover on a glass case. The case is a cube, and the perimeter of one cube face is 56 inches.
How many square inches of the protective covering does she need for the case?
Answer:
336
Step-by-step explanation:
We know that a cube has 6 faces which means we can use this equation:
56 x 6 = 336
336 square inches is the answer.
Perimeter=56in
Side=56)4=14inSo area of one side=
(side)^2=(14)^2=196in^2Cube has 6sides
So total protection:-
6(196)1176in^2The following graph shows a proportional relationship.
What is the constant of proportionality between yyy and xxx in the graph?
Answer:
The constant of proportionality is thus 1
Step-by-step explanation:
Note that the green line passes through (6, 6) and has a y-intercept of 0. Thus, the equation of the line is y = (6/6)x + 0, or y = x, or y = 1x.
The constant of proportionality is thus 1, which is also the slope of this line.
Mr. Glenn is making 30 school supply baskets. notepads come in packs of 5. Erasers come in packs of 15 and markers come in packs of 3. what is the least number of each package she should buy to have 1 item in each basket and no supplies left over
Noah is making grilled cheese sandwiches for friends. He has 24 ounces of cheese. He plans to split the
cheese evenly between 6 sandwiches.
Write an equation to determine how many ounces of cheese, c, Noah can use on each sandwich
How many ounces of cheese can Noah use on each sandwich?
Answer:
4 ounces
Step-by-step explanation:
6c = 24
c = 4
Answer: Noah can use 4 ounces per sandwich
an equation is c=24/6
Step-by-step explanation:
PLEASE HELP FAST!!!
3
11
2
Which ordered pair is a solution to the system of linear equations 3 x- y- fo and x+By-to-
10?
O
12
o 5.3
21
o 35
21
3:5
Based on the Rational Zero Test, which of the following is
NOT a possible zero of f(x) given below after the reciprocal
of LCD is factored out?
f(x)=x^3 -5x + (2/5)
(A) 1/2
(B) 1/5
(C) 1
(D) -1
The rational zero test is also known as the rational root test, and it is used to determine the potential root of a function.
(a) 1/2 is not a possible zero of the function
The function is given as:
[tex]f(x) =x^3 - 5x + \frac 25[/tex]
For a function,
[tex]f(x) = px^n +......q[/tex]
The list of possible roots is:
[tex]Roots = \pm\frac{Factors\ of\ q}{Factors\ of\ p}[/tex]
Multiply both sides of [tex]f(x) =x^3 - 5x + \frac 25[/tex] by 5
[tex]5f(x) = 5x^3 - 25x + 2[/tex]
So, we have:
[tex]p= 5[/tex]
[tex]q = 2[/tex]
The factors are:
[tex]p =\pm 1, \pm 5[/tex]
[tex]q =\pm 1, \pm 2[/tex]
So, the possible roots are:
[tex]Roots = \pm\frac{1,2}{1,5}[/tex]
Split
[tex]Roots = \pm1, \pm \frac 15, \pm 2, \pm \frac 25}[/tex]
Hence, 1/2 is not a possible zero of the function
Read more about rational zero test at:
https://brainly.com/question/12860313
A line L is parallel to the line 2x-5y-8=0. What is the gradient of the line
Answer:
2/5
Step-by-step explanation:
1) rearrange the equation in the form y=mx+c where m is the gradient and y is the y intercept
2x-5y-8=0
add 5y to both sides
2x-8=5y
divide 5 on both sides
2/5x - 8/5 = y
overall equation is y=2/5x-8/5
the gradient is 2/5
Dose any one know the answers for geometry A: A semester exam
PLZ I NEED HELP FAST!!
Answer:
Step-by-step explanation:
82 +9=5000 thank me later
do the values in this table represent a proportional relationship? x 2/4 6 8 y 1 2 3 4 yes, and the constant of proportionality is 12. yes, and the constant of proportionality is 2. no. i don't know.
Answer: No
Step-by-step explanation:
Can somebody help me :
Answer:
A
Step-by-step explanation:
Negative numbers are smaller than positive numbers.
Answer:
Your correct 6.55 is a positive number while -6.5 is negitive and positive numbers are always larger then negitive ones
Hope This Helps!!!
Gatorade comes in two different sizes A 16 ounce costs $2.10 and a 20nounce bottle costs $3.15 which is a better deal to explain your thinking.
How much do you save per ounce by buying the better one?
Based on the cost of each bottle, the better deal is the 16 ounce size and the amount saved per ounce is $0.03
The first step is to find the cost per ounce of each bottle.
For the 16 ounce bottle:
= 2.10 / 16
= $0.13 per ounce
For the 20 ounce bottle:
= 3.15 / 20
= $0.16
The 16 ounce size is therefore better and the amount saved per ounce is:
= 0.16 - 0.13
= $0.03
In conclusion, the 16 ounce is better as it saves $0.03 per ounce.
Find out more at https://brainly.com/question/16805756.
A certain stock sold for $56.12 on Monday. On Tuesday it sold for $60.19. Find the increase in the price of the stock from Monday to Tuesday
Answer:
$ 4.07
Step-by-step explanation:
The problem is asking for the Increase in the stock price from Monday to Tuesday, meaning they want to know the difference between the stock price on Monday and Tuesday.
So we subtract Monday's price from Tuesday's price.
$60.19- 56.12 = $4.07
Express the perimeter of the following
rectangle in terms of n.
3n-7
n + 5
1. O 4n - 2
2. O 8n - 14
3. O 8n - 4
4. O 6n - 14
I need a fast answer because I’m about to get on a plane
Answer:
C
Step-by-step explanation:
-6 is less than 7
can someone plz help me I need the answer asap
Answer:
no. c is the correct answer
read what on the image then answer
Fraction 10/12 would be greater than 3/4
Share 120 in the ratio 3:5:7
Answer:
24:40:56
Step-by-step explanation:
3+5+7=15
120/15=8 1 Ratio is 8
3x8=24
5x8=40
7X8=56
i dont know if its the easiest method
Which mixed number is equivalent to the improper fraction 4 2/5?
4 2/5
7 4/5
8 2/5
9 3/5
the answer is 4 2/5, and I don't think others are equivalent to it
How many Match sticks will be In Image 6?
Answer:
19
Step-by-step explanation:
On a certain hot summer's day, 421 people used the public swimming pool. The daily prices are $1.75 for children and $2.00 for adults. The receipts for admission totaled $788.50. How many children and how many adults swam at the public pool that day?
There were _ children at the public pool.
There were _ adult at the public pool
Answer:
214 children and 207 adults
Step-by-step explanation:
214 x 1.75=374.5
207 x 2 = 414
414 + 374.5 = 788.5
Will mark brainly!
What is the inverse of [tex]f(x)=\frac{2}{x-1} +6?[/tex]
[tex]f^{-1} (x)=\frac{2}{x-1} +6[/tex]
[tex]f^{-1} (x)=\frac{2}{x} +7[/tex]
[tex]f^{-1} (x)=\frac{2}{y-6} +1[/tex]
[tex]f^{-1} (x)=\frac{2}{x-6} +1[/tex]
Answer:
[tex] {f}^{ - 1} (x) = \frac{2}{x - 6} + 1[/tex]
Step-by-step explanation:
we will subistitute f(x) by y and solve the equation in order to get the value of x,
then we subistitute x by y and y by x and y=f^-1(x)
What is m<6
A.80
B. 100
C.70
D.110
Step-by-step explanation:
to fully answer we would need to see at least one specific size (segment lengths, angle sizes).
but there is not one in the whole visible picture. so, everything just stays relative.
just be the presentation in the picture, angle 6 is larger than 90 degrees. so, B or D would be right.
if it helps you, it is clear that 6 = 1 = 9 = 14 = 180-2 = 180-5 = 180-10 = 180-13.
the original price of a jacket was $74.00 .A store manager marked the price down by
25 1/2% . By how much was the price reduced?
NEED HELP NOW!!!
Properties of Perpendicular Bisectors Properties of Both Perpendicular Bisectors and Angle Bisectors Properties of Angle Bisectors
The bisector passes through the midpoint of a segment
The bisector is equidistant from the endpoints of the segment
The bisector can only exist if the original figure is a line segment.
The bisector cuts the original figure into two congruent parts.
The bisector is equidistant from portions of the figure.
Only one of each type of bisector exists in a plane.
The bisector passes through the interior of an angle.
The bisector creates a right angle with the figure.
The bisector is equidistant from the sides of the angle.
Which piece of information is incorrectly placed in the table?
A. The bisector cuts the figure into two congruent parts.
B. The bisector is equidistant from portions of the figure.
C. The bisector passes through the midpoint of a segment.
D. The bisector creates a right angle with the figure.
D.
Explanation:
a landscape of farmland bisected by long straight roads"
divide into two parts.
hope I help you ☺️❤️
:) :>
Why does demand for a product or service play a significant role in starting a new business?
Answer:
Basic economics like demand should important to you whether you run a seasonal business, buy a vacation property for passive income, or run a more traditional firm.
CAN SOMEONE HELP ME PLEASE ASAP!?
Answer:
$8.00
Step-by-step explanation:
20% of 44.85=8.97
thats the closest to 8.00
Answer:
the answer is 9 dollars cuz the real answer is $8.97 and round to the nearest whole the answer is 9
Step-by-step explanation:
In order to join a yoga club you have to pay an annual fee and a fee per class. At Yoga For Us the annual fee is $30 and $5 per class. At Stretch Land the annual fee is $60 and
$2 per class. After how many classes would the fees be the same?
After 10
classes the feels the same.
It will take 10 classes for YOGA FOR US & STRETCH LAND to have the same amount of money spent on yoga classes.
For Yoga For Us after 10 classes . You would have spent 50 dollars for the classes,plus our $30 fee is (50+30) which is $80
For Stretch Land after 10 classes. You would have spent 20 dollars for the classes,plus our $60 fee is (60+20) which is $80.
Each yoga studio will have gathered $80 after 10 classes.
Hope this helps <3 & don't forget to drink water!!
2. What is the x-intercept for the equation -2x + 5y = -10?
Answer:
Step-by-step explanation:
X intercept occurs when y = 0
-2x + 5(0) = -10
x = -10/-2
x = 5
Write the quadratic equation whose roots are 1 and -2, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)
I = 0
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5
?
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Check
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Answer:
See belowStep-by-step explanation:
The quadratic equation in factored form:
a(x - α)(x - β), where a- leading coefficient, α and β - rootsWe have:
a = 3, α = 1, β = -2Substitute them to get:
3(x - 1)(x + 2)Converting this into standard form:
3(x - 1)(x + 2) =3(x² + x - 2) =3x² + 3x - 6Given that f(x)=x-5 g(x)=5x and h(x)=-f(x+1)-3g(x-1), then what is the value of h(3)?
please show step by step answer.
Answer:
Step-by-step explanation:
f(x) = x - 5 and g(x) = 5x
- f(x + 1) = - ( x + 1 - 5 ) = 4 - x
- 3g(x - 1 ) = - 3 [ 5 (x - 1)] = 15 - 15x
h(x) = 4 - x + 15 - 15x = 19 - 16x
h(3) = 19 - 16(3) = - 29