What are the possible numbers of positive real, negative real, and complex zeros of f(x) = 6x3 − 3x2 + 5x + 9?
Answer:
Positive Roots: 2 or 0
Negative Roots: 1
Step-by-step explanation:
f (x) = 6x3 − 3x2 + 5x + 9
To find the possible number of positive roots, look at the signs on the coefficients and count the number of times the signs on the coefficients change from positive to negative or negative to positive.
f (x) = 6x3 − 3x2 + 5x + 9
Since there are 2 sign changes from the highest order term to the lowest, there are at most 2 positive roots (Descartes' Rule of Signs). The other possible numbers of positive roots are found by subtracting off pairs of roots (2 − 2).
Positive Roots: 2 or 0
To find the possible number of negative r oots, replace x with −x and repeat the sign comparison.
f (−x) = 6(−x)3 − 3(−x)2 + 5 (−x) + 9
Simplify each term.
Apply the product rule to −x.
f (−x) = 6 ((−1)3x^3) − 3(−x)^2 + 5 (−x) + 9
Raise −1 to the power of 3.
f (−x) = 6 (−x^3) − 3(−x)^2 + 5 (−x) + 9
Multiply −1 by 6.
f (−x) = −6x^3 − 3(−x)^2 + 5 (−x) + 9
Apply the product rule to −x.
f (−x) = −6x^3 − 3 ((−1)^2(x^2)) + 5 (−x) + 9
Raise −1 to the power of 2.
f (−x) = −6x^3 − 3 (1x^2) + 5 (−x) + 9
Since there is 1 sign change from the highest order t erm to the lowest, there is at most 1 negative
root (Descartes' Rule of Signs). Negative Roots: 1
The possible number of positive roots is 2 or 0, and the possible number of negative roots is 1. Positive Roots: 2 or 0
Negative Roots: 1
Jayla paints a book case. She uses 1 5/6 cups of paint on the outside of the book case and 3/8 cup of paint on the inside. How many cups of paint does Jayla use altogether
Answer:
Answer: Kayla used 2&5/24 cups of paint all together.
Step-by-step explanation:
Kayla paints a bookcase by using
1 5/6 cups of paint on the outside of the bookcase. Converting 1 5/6 cups to improper fraction, it becomes 11/6 cups of paint.
She also used 3/8 cup of paint on the inside.
Therefore, the total number of cups of paint that Kayla used all together would be cups of paint:
[tex]11/6 + 3/8 = (44 + 9)/24 = 53/24[/tex]
Converting to mixed fraction, it becomes
2 and 5/24 cups of paint
can someone help me please im struggling and can’t figure these 2 problems out :(
9514 1404 393
Answer:
2. G 10.72 units
3. B 3.6, 6, 4.8
Step-by-step explanation:
2. The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the sides.
14^2 = 9^2 + CB^2
196 = 81 + CB^2 . . . . find the square values
115 = CB^2 . . . . . . . . subtract 81
√115 = CB ≈ 10.72 . . . . . matches G
__
3. You know that lengths 3, 4, 5 form a right triangle. This is a special triple for several reasons. One of them is that it is the smallest integer Pythagorean triple. Another is that it is the only Pythagorean triple that is an arithmetic sequence (has constant differences between lengths).
You can use this as a reference to look at the choices offered.
A. The lengths 3.2, 4.1 and 5.0 have constant differences of 0.9. The shortest length is not 3 times this value, so this is not a right triangle.
B. The lengths 3.6, 4.8, 6 have constant differences of 1.2. These numbers are 3, 4, and 5 times that difference, so these segments will form a right triangle.
C, D. The longest length is an integer. The sums of the squares of the decimal values will not be integers, so these are not right triangles.
4.5^2 +6.7^2 = 65.14 not 8^2
5.2^2 +8.5^2 = 99.29 not 10^2
Solve the question below, please
Answer:
4.621
Step-by-step explanation:
You'll use the sine rue
Answer:75
Step-by-step explanation:
C=180 - (68 + 37)
=180 - 105
=75
A bowl holds the 10 pieces of fruit shown below.
If Jasmine writes the fraction of fruit that are apples and does not reduce the fraction, which of the following would be the numerator of the fraction?
Answer: 10
Step-by-step explanation: 10 is the total number of all the fruits so that is what you are dividing by
Answer:
Step-by-step explanation:
Solve x2 − 7x = −12. (6 points) Question 8 options:
1) x = 2 and x = 6
2) x = 6 and x = −2
3) x = −4 and x = −3
4) x = 4 and x = 3
please look at the question, I uploaded it!
Answer:
angle JKL is 21
Step-by-step explanation:
the angle of the two triangles are the same, so (2x + 1) = (3x - 9)
You would then find the x, which equals to 10.
Then replace x with ten with the equation.
If 200 of the 550 reptiles in as you are on display what percent of the reptiles are on display
Answer:
200/550×100%
=20000/550
=36.37%
Find the area of each triangle?
Line m has a slope of 10. Another line n is parallel to line m. What is the slope of line n ?
Answer:
We conclude that the slope of line 'n' is: m₂ = 10
Step-by-step explanation:
Given
The slope of line m is: m₁ = 10
It is stated that another line is parallel to line m.Let m₂ be the slope of the 'n' line.
We know that when two lines are parallel, they have equal slopes.
i.e. m₁ = m₂
as
The slope of line m is: m₁ = 10
and
The lines are parallel
so
The slope of line 'n' is: m₂ = 10
Therefore, we conclude that the slope of line 'n' is: m₂ = 10
the equation of a circle whose center is (-5, 3) and whose radius is 6?
Answer:
Center:(-5,3)
The center of a circle is a point from which all points on a circle are the same distance.
Radius:6
The radius of a circle is the length of a line segment from its center to its perimeter.
The radius is typically denoted as "r" or "R".
Diameter:12
The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle.
Circumference or (or Permieter) = 2*π*R = 2*3.14*6 = 37.6991118430775
The circumference of a circle is the distance around it.
Area:113.097335529233
Area of a Circle is the amount of space occupied by the circle.The area of a circle is p times the radius squared, which is written: A = π*R2.
An item is regularly priced at $33. It
now priced at a discount of 55% off the regular price.
Use the ALEKS calculator to find the price now.
Answer
$14.85
Step-by-step explanation:
calculate 33.00 x .55= 18.155 (thats the discount) subtract it from the cost
33.00 -18.15 +$14.85
-3x+5y=2x+3y−3x+5y=2x+3y Which ordered pair is a solution of the equation?
Answer:
the answer is neither
Step-by-step explanation:
A line passes through the points (6,-6) and (9,-5). What is it’s equation in point slope form?
Answer:
[tex]y=\frac{1}{3}x-8[/tex]
Step-by-step explanation:
Slope-intercept form of an equation is written as [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
The slope of a line that passes through the points [tex](x_1,\: y_1)[/tex] and [tex](x_2, \: y_2)[/tex] is [tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]. Using the coordinates [tex](6,-6)[/tex] and [tex](9,-5)[/tex] as given in the problem, we have slope of this line to be:
[tex]m=\frac{-5-(-6)}{9-6}=\frac{1}{3}[/tex].
Now using this slope we've found and any point the line passes through, we can find the y-intercept of this equation:
[tex]-6=\frac{1}{3}(6)+b, \\ b=-8[/tex]
Therefore, the equation of this line in slope-intercept form is [tex]\fbox{$y=\frac{1}{3}x-8$}[/tex].
Which number line best shows how to solve this? please help quickly thank you!
Answer:
Step-by-step explanation:
I attached the work and answer below, take a look!
Points!
( you cant respond from the last 2 i did)
have a nice day :)
Answer:
Thank youuuu!!
7. How many terms are in the expression?
7q+6q + 2 .
(1 Point)
Answer:
3 terms
Step-by-step explanation:
Hi there!
Terms are constants or variables in an algebraic expression separated by plus and minus signs.
With this information, that means that 7q is a term, 6q is a term, and 2 is a term.
Without simplifying the expression, there are 3 terms.
I hope this helped!
Simplify using order of operations.
7(6 + 3) - 4 x 5
Answer:
7 × 9 - 4 × 5
63-20= 43
Step-by-step explanation:
we start with () then multiplication then subtract we use the BEDMAS method in order.
B: brackets
E: exponents (powers)
D: divide
M: multiply
A:addition
S: subtract
Which statement about 4(x-3) is true?
O A. 4(x-3) has three terms.
OB. 4(x-3) is a sum.
O C. 4(x - 3) is a product.
O D. 4(x-3) has two variables.
Think about all the ways in which a line and a parabola can intersect select all the numbers of ways in which a line in a parabola can intersect 01234 infinitely many
Answer:
0, 1, 2
Step-by-step explanation:
There is a way for them to intersect at 0 points, for example y=x^2 and y = -1
The way to intersect at 1 point is for the linear function to be tangent to the parabola, like y = x^2 and y = 0
The way to intersect 2 points is just for the linear function to be a secant to the parabola, like y = x^2 and y = 1
PLEASE ANSWER ASASP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!!!!
Mei runs 93.24 miles in 3 weeks. If she runs 6 days each week, what is the average distance she runs each day?
Answer:
5.18 miles each day
Step-by-step explanation:
3 weeks × 6 days = 18 days
93.24 miles in 18 days gives an average of 93.24 ÷ 18 = 5.18 miles per day
The population of a community of foxes is observed to fluctuate on a 10-year cycle due to variations in the availability of prey. When population measurements began (t=0, the population was 35 foxes. The growth rate in units of foxes>>year was observed to be P′(t)=5+10sinπt/5
a. What is the population 15 years later? 35 years later?
b. Find the population P(t) at any time t≥0.
Answer:
Population 15 years later P(15) = 100 + 50/π
Population 35 years later P(35) = 200 + 50/π
Population any t ≥ 0 P(t) = 35 + 50 /π + 5*t + 10*cos(π*t/5)
Step-by-step explanation:
P´(t) = 5 + 10*sinπt/5 ⇒ dP/dt = 5 + 10*sinπt/5
dP = ( 5 + 10*sinπt/5 ) *dt
P(t) = ∫ ( 5 + 10*sinπt/5 ) dt
P(t) = 5*t + 10 * ∫ sinπ*t/5* dt
P(t) = 5*t - 10*5/π *cos πt/5 + k
To determine k t = 0 P(t) = 35
P(0) = 5*0 - 50/π (1) + k
35 = - 50/π + k
k = 35 + 50/π and
P(t) = 5*t + 10*cos(π*t/5) + 35 + 50/π
b)P(t) = 35 + 50 /π + 5*t + 10*cos(π*t/5) (1)
a) Population 15 years later
P(15) = 35 + 50/π + 5*15 - 10
P(15) = 100 + 50/π
Again from equation (1)
P(35) = 35 + 50 /π + 5*35 + 10*cos(35*π/5)
P(35) = 35 + 50/π + 175 + 10*cos (7*π )
P(35) = 210 + 50/π - 10
P(35) = 200 + 50/π
Which best describes a difference between SALT I and SALT II?
SALT I limited weapons, while SALT II limited launchers.
SALT I expanded the production of arms, while SALT II limited production.
SALT I allowed the sides to trade weapons, while SALT II expanded this practice.
SALT I limited military forces of each country, while SALT II allowed their growth.
The difference between SALT I and SALT II is SALT I limited weapons, while SALT II limited launchers. So, correct option is A.
The Strategic Arms Limitation Talks (SALT) were a series of negotiations between the United States and the Soviet Union to limit and reduce the number of nuclear weapons and delivery systems.
SALT I was signed in 1972 and focused on limiting the number of ballistic missiles and bombers each side could possess. It also established a system for verifying compliance with the treaty.
SALT II was signed in 1979 but was never ratified by the U.S. Senate due to increased tensions between the two countries. SALT II aimed to further reduce the number of strategic nuclear weapons and delivery systems, but unlike SALT I, it focused on limiting the number of launchers rather than weapons themselves.
Therefore, the correct answer is A.
To learn more about SALT click on,
https://brainly.com/question/29569705
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Answer:
I just took the test and I can confirm that the answer is A
Step-by-step explanation:
The length of a rectangle is 2 meters less than 3 times the width. The perimeter is 44
meters. Find the width
Answer:
Width of rectangle = 6 meters
Step-by-step explanation:
Let
Width of rectangle = x
Length of rectangle = 3x-2
Perimeter of rectangle = 44 meters
We need to find:
The Width of rectangle.
The formula used is:
[tex]Perimeter\:of\:rectangle=2(Length\times Width)[/tex]
Putting values and finding value of x
[tex]Perimeter\:of\:rectangle=2(Length\times Width)\\44=2(3x-2+x)\\44=2(4x-2)\\44=8x-4\\8x=44+4\\8x=48\\x=\frac{48}{8}\\x=6[/tex]
So, we get the value of x = 6.
We know that Width of rectangle = x = 6
So, Width of rectangle = 6 meters
Given 1 inch = 2.54 centimeters, enter the value that will complete this expression for converting 3.5 feet to centimeters. (What value goes where the ♣ is?)
[tex](\frac{3.5 feet}{1} )(\frac{♣inches}{1 foot})(\frac{2.54}{1 inch})\\[/tex]
Answer: the answer is 12
Step-by-step explanation: the answer is 12 because there are 12 inches in a foot.
Please help this is worth 30 points
Gareth 30 students in a class and the ratio of boys to girls in the class is 2:3 calculate the number of goals
Answer:
There are 12 boys and 18 girls
Step-by-step explanation:
Equations
There are 30 students in a class. Let's call:
x = number of boys
Since the sum of boys and girls is 30:
30 - x = number of girls
The ratio of boys to girls is 2:3, thus:
[tex]\displaystyle \frac{x}{30-x}=\frac{2}{3}[/tex]
Crossing denominators:
3x = 2(30 - x)
Operating the parentheses:
3x = 60 - 2x
Adding 2x:
5x = 60
Dividing by 5:
x = 60/5 = 12
x = 12
There are 12 boys and 30-12=18 girls
A deck of cards contains RED cards numbered 1,2,3,4,5,6 and BLUE cards numbered 1,2,3. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card. Drawing the Blue 2 is one of the outcomes in which of the following events?
a. R OR O
b. B AND O
c. R OR E
d. R AND O
e. R′
f. E
Answer: c. R OR E
e. R′
f. E
Step-by-step explanation:
Outcomes for Red card ={1,2,3,4,5,6} = 6
Outcomes of Blue card = {1,2,3} =3
R = event of drawing a red card, B = event of drawing a blue card, E=event of drawing an even numbered card, and O = event of drawing an odd card.
Then, R= {1R,2R,3R,4R,5R,6R} , B= {1B,2B,3B}
E={2R, 4R, 6R , 2B}
O = {1R, 3R, 5R, 3B}
R or O = { 1R,2R,3R,4R,5R,6R ,3B} [all elements of R and O]
B and O = {3B} [all elements common in B and O]
R or E = {1R,2R,3R,4R,5R,6R,2B }
R and O = {1R, 3R, 5R} [all elements common in R and O]
R' = B= {1B,2B,3B} [all elements except R]
Blue 2 = 2B belongs to B, R or E, R' and E.
Correct options are c. e. f.
Answer:
Blue 3
E'
B AND O
Step-by-step explanation:
Help me pls pls pls
Answer:
omg I'm doing the same thing