QM Q2.) Find the multiplicities of the greatest zero, second greatest zero, and the smallest zero.
Answers
First check out the zeros (first box).
Step One.
Put brackets around terms 1 and 2 and another set around terms 3 and 4.
f(x) = (x^3 + 8x^2) - (4x + 32) Watch out that you change the sign on the 32. Minus signs can be devastating. The idea is that when the brackets are removed, the question will be exactly as it was before you put the brackets there.
Step Two
Pull out any common factors.
f(x) = x^2(x + 8) - 4(x + 8)
Step Three.
If there is a common binomial pull it out as well. This is the hardest part of the problem. The binomials have to be exactly alike (in this case they are).
f(x) = (x + 8) (x^2 - 4)
Step Four
Factor (x^2 - 4). This is an exact difference of squares. It factors into
x^2 - 4 = (x + 2)(x - 2)
Step five
Find the zeros.
f(x) = (x + 8)(x - 2)(x + 2)
x + 8 = 0
x = - 8
x + 2 = 0
x = - 2
x - 2 = 0
x = 2
I know you didn't ask for all of this, but when someone asks a question, it's always a good idea to check the work done. In your case it was all correct. That's a very good thing.
Definition
Multiplicity is the number of times a root appears in the solution of a polynomial.
For example, g(x) = (x - 5)^2 (x - 4)
The five would have a multiplicity of 2 because the equation is really
g(x) = (x - 5)(x - 5) ( x - 4). There are 2 roots that are the same (both are 5).
4 has a multiplicity of 1 in this example.
Answer
The largest root is 2. It has a multiplicity of 1
The second largest root is -2. It has a multiplicity of 1
The tiniest root is - 8 . It has a multiplicity of 1
Related Questions
Calculate the number of integers divisible by 4 between 50 and 500, inclusive.
Answers
500 = 4*125
There are 125 -12 = 113 numbers between 50 and 500 that are divisible by 4.
PLZ HELP ASAP FEATURES OF A CIRCLE FROM ITS EXPANDED EQUATION LAST ONE
Answers
x2 + y2 + 6y - 72 = 0
Rewriting we have:
x2 + y2 + 6y = 72
Complete squares we have:
x2 + y2 + 6y + (6/2) ^ 2 = 72 + (6/2) ^ 2
x2 + y2 + 6y + (3) ^ 2 = 72 + (3) ^ 2
x2 + y2 + 6y + 9 = 72 + 9
x2 + (y + 3) 2 = 81
So, the center is:
(0, -3)
The radio is:
r = 9
Answer:
(0, -3)
r = 9
A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 2 cm more than the shorter leg and the hypotenuse 2 cm more than the longer leg. How long should the sides of the triangle be?
Answers
6 cm, 8 cm, 10 cm
If Dr. Suzuki rides his bike to his office, he averages 9 miles per hour. If he drives his car, he averages 27 miles per hour. His time driving is one third hour less than his time bicycling. How far is his office?
Answers
Riding speed = 9 mph
Driving speed = 27 mph
Time
If x hours is the time taken when riding, (x - 1/3) hours is the time taken when driving.
Distance in both instances is the same, D= Speed * time
Therefore,
9*x = 27(x-1/3)
9x = 27x - 27/2
9x = 27x - 9
(9-27)x = -9
-18x = -9
x = 9/18 = 1/2 hours
Distance, D = 1/2 *9 = 4.5 miles
Express the given quantity as a single logarithm. ln x + a ln y − b ln z
Answers
• [tex]\ln(a)+\ln(b)=\ln(a \cdot b)[/tex]
• [tex]a \cdot \ln(b)=\ln(b^{a})[/tex]
[tex]\ln(x)+a \cdot \ln(y)-b \cdot \ln(z)=\ln\left( \dfrac{x \cdot y^{a}}{z^{b}} \right)[/tex]
To express ln x + a ln y - b ln z as a single logarithm, use the properties of logarithms.
Explanation:To express ln x + a ln y - b ln z as a single logarithm, we will use the properties of logarithms. The key properties we will use are:
ln xy = ln x + ln y: The logarithm of a product is the sum of the logarithms of the factors.ln (x/y) = ln x - ln y: The logarithm of a quotient is the difference of the logarithms of the numerator and denominator.Using these properties, we can simplify the expression:
ln x + a ln y - b ln z = ln x + ln(y^a) - ln(z^b)= ln (x(y^a)/(z^b))
So, the given quantity can be expressed as a single logarithm: ln (x(y^a)/(z^b))
Learn more about Express the given quantity as a single logarithm here:https://brainly.com/question/32612676
#SPJ11
Which ordered pair is a solution of y = x - 4?
( -3, -7 )
( 3, -7 )
( -3, 7 )
( 3, 7 )
Answers
an order pair follows the (x, y) pair, in which (in this case), x = -3, and y = -7
plug in to the respective places inside the equation.
y = x - 4
(-7) = (-3) - 4
-7 = -7 (true)
Therefore, (-3, -7) is your answer
hope this helps
Express using a negative exponent.
1/z^9
Answers
1/a^b=a^-b
thus using this rule, our value will be expressed as follows:
1/z^9=z^-9
Hence the answer is: z^-9
On a blueprint with a scale of 1cm = 2ft, the length of a wall is 12cm. If the scale of the blueprint were 1cm = 3ft, what will be the length of the wall?
(Please show work, I will mark brainliest)
Answers
The actual length of the wall is
12 cm * (2 ft / 1 cm) = 24 ft
On the new blueprint of 1 cm = 3 ft, the length on blueprint becomes
24 ft * (1 cm / 3 ft) = 8 cm
The length of the wall on the new blueprint is 8 cm.
im posting several questions i need help with in an image
Answers
(1) n = 4
(2) x = 30
(3) a = -4
(4) n =10
(5) n = -46.2
Explanation:
(1) Given
9n-8 = 28
9n = 28 + 8
9n = 36
n=4
(2) Given
-1-x = -31
-x = -31 + 1
x = +31 - 1
x = 30
(3) Given
9-4a = -5a + 5
-4a + 5a = 5 - 9
a = -4
(4) Given
n/2 = 5
n=5*2
n = 10
(5) Given
29.5 = -16.7 -n
n = -16.7 - 29.5
n = -46.2
9n = 28 + 89n = 36n=4
2.
-x = -31 + 1x = 31 - 1x = 30
3.
9-4a = -5a + 5-4a + 5a = 5 - 9
a = -4
4.
n/2 = 5n=5*2 n =10
5.
29.5 = -16.7 -nn = -16.7 - 29.5n = -46.2
A rectangular pyramid has a volume of 210 cubic centimeters. Find two possible sets of measurements for the base area and height of the pyramid.
Answers
V = 1/3Bh, where B is the area of the base.
210 = 1/3Bh
630 = Bh; this means the area of the B time the height must equal 630
Find 3 factors that will give you 630.
Ex #1: 10 cm (length) x 6 cm (width) x 9 cm (height)
Ex #2: 5 cm (length) x 9 cm(width) x 14 cm(height)
Answer:
630 cm 3 is the answer to the question
Marta jogged 7/10 of a mile Monday. On Tuesday, she jogged 5/10 of a mile. What is the total distance Marta jogged on Monday and Tuesday?
Answers
7/10 + 5/10 = 12/10
12/10 simplified = 1 2/10 = 1 1/5
Your answer is 1 1/5 miles
Hope this helps :)
When flying at an altitude of 5 miles, the lines of sight to the horizon looking north and south make about a 173.7 degree angle. how much of the longitude line directly under the plane is visible from 5 miles high?
Answers
To find the visible part of the longitude line from an altitude of 5 miles, we can use the Law of Sines in combination with the given angle of 173.7 degrees. The resulting arc length signifies what portion of the Earth is visible from this altitude.
Explanation:This question pertains to plane geometry and spherical geometry. Given that the angle formed by the lines of sight to the northern and southern horizons is 173.7 degrees when flying at an altitude of 5 miles, we can find the visible part of the longitude line using the Law of Sines.
Imagine a figure with a central angle of 173.7 degrees and a radius of 5 miles (the altitude of the airplane). Here, the radius of Earth is 3959 miles. Thus, from the center of the Earth to the airplane is a total of 3959+5 = 3964 miles.
Using the law of sines, we have: (sin(173.7 deg) / s) = (1 / 3964). Simplifying this gives us the arc length, s, which is the visible part of the longitude line. This visible part signifies the portion of the Earth you can see from the airplane's perspective.
Learn more about Visible Longitude from Altitude here:https://brainly.com/question/1407600
#SPJ12
Using the horizon line formula, D = 112.88 km x √h, where h is the height in kilometers, we can determine the length of the longitude line visible from 5 miles up. This calculation takes into account, but barely modifies for not looking at a perfect 180-degree angle.
Explanation:In order to find out how much of the longitude line directly under the plane is visible from 5 miles high, we need to apply some mathematical and geographical concepts. The key concept here is the idea of the horizon line, which is the furthest point you can see from a given point of elevation.
Using the formula D = 112.88 km x √h, where h is the height in kilometers (in this case, 5 miles or approximately 8.05 km), you would calculate D = 112.88 km x √8.05. This calculation gives you the distance to the horizon or how much of the line directly beneath the plane is visible.
However, the student's question also mentions an angle of 173.7 degrees - it represents nearly a complete observable circle from the airplane (as 180 degrees would be a complete straight line view). So, the observable part of longitude from the plane will also be correspondingly reduced by a very small amount, since we are not looking at a perfect 180 degrees.
Learn more about Visible Longitude Line Calculation here:https://brainly.com/question/13478781
#SPJ6
Which is the equation of a parabola with Vertex (0, 0) and directrix y = 4?
Answers
Vertex (0, 0) and directrix y = 4
is a vertical parabola------> open down (directrix above the vertex)
the equation is of the form
(y-k)=4p(x-h)²--------> y=4p*x²-------> vertex (0,0)
y=4
y=h-p-----> y=-p
p=-4
the equation of the parabola is
y=-16x²
the answer is
y=-16x²
see the attached figure
Answer:
D. x^2 = -16y
Step-by-step explanation:
got it right on edge
Find the value of x. If necessary, found your answer to the nearest tenth. The figure is not drawn to scale
Answers
The scores on an exam are normally distributed with a mean of 74 and a standard deviation of 7. What percent of the scores are greater than 81?
A. 50%
B. 13.5%
C. 84%
D. 16%
Answers
81 - 74 = 7
This is exactly the value of the standard deviation. You know that the "empirical rule" tells you 68% of all scores lie within 1 standard deviation of the mean. That tells you 32% of all scores lie beyond 1 standard deviation from the mean.
The normal distribution is symmetrical, so half of those (16%) lie above 1 standard deviation above the mean; the other half (16%) lie below 1 standard deviation below the mean. We're only concerned with the first group—those scores above 1 standard deviation above the mean.
The appropriate choice is
D. 16%
some help help help help help help help help help help help help help help help help help help help help me please please please some
Answers
Mission Control sends a signal to a Mars robot to travel to a mysterious rock 52.8 meters away. A return signal 59.0 minutes later tells scientists that the robot is at the rock. It took the signal 9.5 minutes to get from Earth to Mars, and the same time to get back. What was the robot’s average speed in meters per minute?
Answers
59 min = 2*(9.5 min) +travel time
59 min -2*(9.5 min) = travel time = 40 min
The speed is distance / travel time
speed = (52.8 m)/(40 min) = 1.32 m/min
The robot's average speed was 1.32 meters per minute.
Somebody helppppp pleassse
Answers
180-118=62,
Good luck!
WILL MARK BRAINLIEST IF RIGHT!!!
Meg described four triangles as shown below:
Triangle P: All sides have length 7 cm.
Triangle Q: Two angles measure 55°.
Triangle R: Two sides have length 8 cm, and the included angle measures 60°.
Triangle S: Base has length 8 cm, and base angles measure 55°.
Which triangle is not a unique triangle?
A) Triangle P
B) Triangle Q
C) Triangle R
D) Triangle S
Answers
Answer:
It is q i think
Step-by-step explanation:
what is the difference? (x+5)/(x+2)-(x+1)/(X^2+2x)
Answers
Answer:
[tex]\text{The difference is }\frac{x^2+4x-1}{x(x+2)}[/tex]
Step-by-step explanation:
Given two expression, we have to find the difference of these two.
[tex]\frac{x+5}{x+2}-\frac{x+1}{x^2+2x}[/tex]
[tex]=\frac{x+5}{x+2}-\frac{x+1}{x(x+2)}[/tex]
[tex]\text{Taking (x+2) common from the denominator }[/tex]
[tex]=\frac{1}{x+2}((x+5)-\frac{x+1}{x}[/tex]
[tex]=\frac{1}{x+2}(\frac{x(x+5)-(x+1)}{x})[/tex]
[tex]=\frac{1}{x+2}(\frac{x^2+5x-x-1}{x}[/tex]
[tex]=\frac{1}{x+2}(\frac{x^2+4x-1}{x})[/tex]
[tex]=\frac{x^2+4x-1}{x(x+2)}[/tex]
which is required difference.
a soccer ball has the same diameter as a lenght of a cube shaped box. if the diameter of the soccer ball is 12 inches what volume inside that is not filled by a soccer ball
Answers
volume of ball is (4/3) x pi x radius cubed =288 pi
then answer is 1728 - 288 pi
Please rate me don't just say thanks
The volume of box which is not used is (1728 - 288π) inch³.
What is Volume?Volume is a three-dimensional quantity used to calculate a solid shape's capacity. That means that the volume of a closed form determines how much three-dimensional space it can fill.
If the diameter of the soccer ball is 12 inches.
So, Volume of box
= length x width x height
= 12 x 12 x 12
= 1728 inch³
and, Volume of ball
= 4/3 πr³
= 4/3π (6)³
= 864/3 π
= 288 π inch³
So, the volume of box which is not used
= 1728 - 288π
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ3
PLEASE ANSWER!!! WILL MARK BRAINLIEST :D
When Alina was hungry she ate c cookies, which was 30% of all the cookies she had. How many cookies did she have in the beginning?
Answers
0.30a=x
x/0.30
Sarawong is carrying six pages of math homework and four pages of english homework. a gust of wind blows the pages out of his hands and he is only able to recover seven random pages. what is the probability that he recovers at least five pages of his math homework
Answers
The probability that Sarawong recovers at least five pages of his math homework is 56.6%, using the combinatory principles of probability.
Explanation:
To solve the problem, we need to calculate the probability that Sarawong recovers at least five pages of his math homework after a gust of wind blows the pages out of his hands. This is a probability problem, which is under the field of mathematics. We first need to understand the total possibilities of the pages he could recover, which is combinations of six math pages and four English pages, that is 10 pages pick 7 pages. We add up the probabilities that he recovers 5, 6, or all 7 math pages. We also need to consider that there is no particular order in which the pages are recovered.
The total number of ways to select 7 pages from 10 can be calculated by 10 choose 7, which is 120.
The number of ways to select 5 math pages out of 6 and 2 English pages out of 4 is 6 choose 5 times 4 choose 2, which equals 60. The probability of this case is 60 / 120 which is 0.5.
The number of ways to select 6 math pages and 1 English page is 6 choose 6 times 4 choose 1, which is also 4. The probability is 4 / 120 which is 0.033.
The number of ways to select all math pages is 6 choose 6 and 4 choose 1, which totals 4. The probability is also 4 / 120 which is 0.033.
Therefore, the total probability that Sarawong recovers at least 5 of his math pages is 0.5 + 0.033 + 0.033 = 0.566, or 56.6%. This is the mathematical solution to the problem.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ12
3/x+2 = 2/x−1 pleasee help
Answers
[tex] \frac{3}{x} + 2 = \frac{2}{x} - 1 [/tex]
1) Start off by multiplying both sides by x to simplify the problem:
[tex]\frac{3}{x} + 2 = \frac{2}{x} - 1 \\ x(\frac{3}{x} + 2) = (\frac{2}{x} - 1)x\\ 3 + 2x = 2 - x [/tex]
2) Now isolate the x by moving all terms with x onto one side and all other terms onto the other side:
[tex]3 + 2x = 2 - x\\ 3x = -1[/tex]
3) Finally, divide by 3 on both sides to find the value of x:
[tex]3x = -1\\ x = \frac{-1}{3} [/tex]
------
Answer: x = [tex]\frac{-1}{3}[/tex]
A = LW ; for L whats the answer step by step
Answers
_________________________________________________
Explanation:
_________________________________________________
Given:
_________________________________________________
" A = LW " ; Solve for "L" ; {step-by step} ;
_________________________________________________
A = L * W ;
↔ L * W = A ;
Divide each side of the equation by "W" ;
to isolate "L" on one side of the equation; & to solve for "L" ;
→ { L * W } / L = A / L ;
to get:
→ W = L / A .
________________________________________________________
The answer is: " W = L / A " .
________________________________________________________
How many gallons of punch will sadie make?
Answers
Sadie will make 3 gallons of punch.
First, let's convert all the measurements to the same unit, such as gallons.
1 gallon = 4 quarts
1 gallon = 8 pints
1 gallon = 16 cups
Now, let's convert each ingredient:
1. Lemon-lime juice: 8 quarts = 8/4 = 2 gallons
2. Vanilla ice cream: 4 pints = 4/8 = 0.5 gallons
3. Orange juice: 8 cups = 8/16 = 0.5 gallons
Now, let's sum up the amounts of each ingredient:
2 gallons (lemon-lime juice) + 0.5 gallons (vanilla ice cream) + 0.5 gallons (orange juice) = 3 gallons
Complete question: Using 8 quarts lemon-lime juice , 4 pints vanilla ice cream , 8 cups orange juice .How many gallons of punch will Sadie make?
Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it.
The mail slot has the dimensions shown. The dotted line shows the widest part of the slot.
Answers
Answer: 25
Step-by-step explanation:
Pythagorean theorem
c=√a²±b²
So it was 7=A
And it was 24=b
solving that it gives us 25
This isn’t that much of help sorry but this is the basic info on how to solve it you can learn more by searching videos about the Pythagorean thermom.
Hope this helps-A
The maximum width of the slot is 25cm (Option A).
To find the maximum width of the mail slot, we need to calculate the length of the diagonal (the dotted line) in the rectangle. The diagonal of a rectangle can be found using the Pythagorean theorem.
Given:
- The length of the rectangle (one side) = 24 cm
- The height of the rectangle (other side) = 7 cm
The formula for the diagonal [tex]\( d \)[/tex] is:
[tex]\[ d = \sqrt{(length)^2 + (height)^2} \][/tex]
Substituting the given values:
[tex]\[ d = \sqrt{24^2 + 7^2} \][/tex]
[tex]\[ d = \sqrt{576 + 49} \][/tex]
[tex]\[ d = \sqrt{625} \][/tex]
[tex]\[ d = 25 \, \text{cm} \][/tex]
So, the maximum width of the mail slot is 25cm.
Full Question:
Joel is mailing a large envelope to his cousin. The envelope has pictures inside, so he doesn't want to bend it.
The mail slot has the dimensions shown. The dotted line shows the widest part of the slot.
What is the maximum width of the mail slot?
A) 25
B) 31
C) 22
D) 20
What’s 3.192 rounded to the nearest hundredth ?
Answers
What is the equation of the line perpendicular to 2x + 5y = 20 that contains the point (10, −4)?
Answers
1) first solve for y
5y= -(2x) + 20
y= -(2/5)x + 4
so the slope is -2/5 so perpendicular is m= 5/2
so now use point slope
y-y1=m(x-x1)
m=5/2 and point is (10,-4)
plug and chug
y+4 = (5/2) (x-10 )
y= 5/2x - 25 - 4
y=5/2x - 29
hope i didnt make an adding error
but thats how you do it.
hope that helps
What is the simple interest that is missing from the table? p $375 r 2.2% t 3 years
Answers
I = 375*0.022*3 = $24.75