Answer:
The leading coefficient is 3
Step-by-step explanation:
Polynomials
Given the roots of a polynomial x1,x2,x3, it can be expressed as:
[tex]p(x)=a(x-x1)(x-x2)(x-x3)[/tex]
Where a is the leading coefficient.
We are given the roots x1=-6, x2=7i, x3=-7i, thus:
[tex]p(x)=a(x+6)(x-7i)(x+7i)[/tex]
Operating the product of the conjugated imaginary roots:
[tex]p(x)=a(x+6)(x^2+49)[/tex]
Knowing p(2)=1,272 we can find the value of a
[tex]p(2)=a(2+6)(4+49)=1,272[/tex]
Operating:
[tex]a(8)(53)=1,272[/tex]
[tex]424a=1,272[/tex]
Solving:
[tex]a=1,272/424[/tex]
a=3
The leading coefficient is 3
Answer:
3
Step-by-step explanation:
Tom buys some polos for $18 each.He has a coupon for $25 off the total price.If he pays $47, how many shirts,p,did he buy?
Answer:
he should have bought 4-5 unless he under paid but i'd say he bought 4 polo shirts
Step-by-step explanation:
How do you solve a 3x3 system of equations.
Answer: well it depends on what comes first but 9
Step-by-step explanation:
What is the perimeter of a rectangle whose width is (x - 7) units and whose length is (3x + 10) units?
Answer:
The answer is "(8x + 6) units".
Step-by-step explanation:
Formula of perimeter is:
[tex]\to \bold{P=2 \text{(Length +width)} }[/tex]
[tex]=2((3x+10)+(x-7))\\\\=2(4x+3)\\\\= 8x+6[/tex]
finding the slope of each line?
Answer:
1.) 5/1
2.) -7/8
3.) -4/2
Step-by-step explanation:
The formula of slope m= [tex]\frac{rise}{run}[/tex]
1.) rise=5 run=1
2.) rise=7 run=-8
3.) rise=4 run=-2
In which number is the digit 7 ten times larger than it is in the number 175?
A) 379
B) 607
C) 730
D) 7,513
Answer:
c 730
Step-by-step explanation:
because the 7 in 730 is one digit to the left
Answer:
C. 730
Step-by-step explanation:
The 7 in the original number is in the tens place. So if you multiply that by 10, the seven moves into the hundreds place.
Chase rode his roller skates around the block 5 times for a total of 1 mile yesterday. Today he wants to ride his roller skates 3/5 of a mile. How many times will he need to ride his roller skates around the block?
Assume that you are taking a multiple choice test that you have not studied for! The test only has 10 questions and each question has four possible answers. You plan to randomly guess on all 10 questions and the probability you get one correct is the same for all questions. Even though no studying took place, you really want a B. This means you would like to get 8 questions correct. How many combinations exist that yield 8 correct questions
Answer:
45
Step-by-step explanation:
To answer this question we will have to use the combination formula.
C(n,r) = n!/(n-r)!r!
n = population set = 10
e = sample set = 8 questions
Inserting into the formula we have:
10!/(10-8)!8!
= 3628800/2x40320
= 3628800/80640
= 45
So in conclusion, we have 45 combinations in existence that would yield 8 correct questions
can you help
thank you
Answer:
In first box: top left __7, in top right __4, on left top __9, left bottom __6.
In second box: top left __7, in top right __3, on left top __3, left bottom __5.
Step-by-step explanation:
Answer:
Here you go! I believe this is correct.
Use a number line to show the sum of 6+(-7) ?
Answer:
-1
Step-by-step explanation:
When you make the number line, go to the middle then move left once. Then mark that " -1 " and you put the dot over that.
It's hard to explain how to write number lines.
Anyways, the problem equals -1 because 6-7 is negative 1. The + is there to confuse you.
Mark brainliest if possible please :)
5. At the beginning of an experiment, there are ten bacterial cells in Petri Dish A and five bacterial cells in Petri Dish B. The number of bacterial cells
o in Dish A after h hours can be modeled with the equation a - 10(125)". The number of bacterial cells bin Dish B after h hours can be modeled
with the equation b - 5(25)" Based on this information, which of the following statements is true?
After one hour, the number of bacterial cells in Dish Ais equal to the number in Dish B
After one hour, the number of bacterial cells in Dish A is greater than the number in Dish B
After one hour the number of bacterial cells in Dish A is less than the number in Dish B.
After ten hours, there are approximately 125 bacterial cells in Dish A
After ten hours, there are approximately 50,000 bacterial cells in Dish B.
Swear no one answers but plz show work ?!
2+2 answer this and get 85 points
Answer:
4
Step-by-step explanation:
Thank you so much!! really appreciate it, I just need a few more points to become so thank you so much again!!:)
Answer:
4
Step-by-step explanation:
2+2=4
PLEASE HELP WILL GIVE CROWN
A submarine is 50 feet below sea level. It rises toward the surface for 12 seconds at a rate of 3 feet per second.
How many feet below sea level is the submarine when it is finished rising?
Answer:
14
Step-by-step explanation:
umm I don't know if im dumb but isn't it just 3 times 12 giving you 36 and than 50 minus 36 with an answer of 14
Plz help i only need c im confused lol 6th grade history
Answer:
War
Step-by-step explanation:
Criminals
Based on the survey results from 300 selected students in the Burbank School District (BSD), the 98% confidence interval used to estimate the population proportion of all BSD students who have access to a working computer at home was computed to be 48% to 60%. The following 2 subquestions require a numeric input, no work is necessary. [2 points] What number of students (out of the 300 sampled) have access to a working computer at home
Answer:
follows are the solution to this question:
Step-by-step explanation:
Please find the correct question in the attached file:
The formula for calculating the Confidence interval of proportion:
[tex]\to CI=\hat{p} \pm Z_{\frac{\alpha}{2}} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\to \hat{p}=\frac{\text{lower limit +upper limit}}{2}\\[/tex]
[tex]=\frac{0.48+0.60}{2}\\\\=\frac{1.08}{2}\\\\=0.54[/tex]
The number of learners with access to working at home on a computer:
[tex]= 0.54 \times 300 \\\\=162[/tex]
Lower limit =0.48
upper limit = 0.60
[tex]\to margin \ error = \frac{\text{upper limit - lower limit}}{2}\\[/tex]
[tex]=\frac{0.60-0.48}{2}\\\\=\frac{0.12}{2}\\\\= 0.06[/tex]
The total amount of time University students in the United States spend sleeping,grooming,eating and drinking and traveling is about?
Answer:
11.7 hours
Step-by-step explanation:
According to data gathered between the years of 2015-2020 from full-time University Students at various Universities throughout the US, it was discovered that they spend roughly 11.7 hours completing these tasks (sleeping, grooming, eating/drinking, and traveling) per day. This applies strictly to full-time University Students that have the responsibilities associated with that life such as studying, attending class, group projects, etc. and does not include extra activities such as cooking.
Find the dimension of the rectangular corral producing the greatest enclosed area given 200 feet of fencing. Anyone help me asap
Answer:Best corral has a width and length of 50 feet, enclosing an area of 2500 square feet. Let's calculate the width (W) of the rectangle as a function of it's length (L). So we have W = (200 - 2*L)/2 W = 100 - L Now the area of the rectangle is A = WL Substitute the equation for W. A = (100 - L)L A = 100L -L^2 Let's make an initial guess of 40 ft and add an error component of e. So we'll use the length of (40+e) and see what we get. A = 100L -L^2 A = 100(40+e) - (40+e)^2 A = 4000 + 100e - (1600 + 80e + e^2) A = 4000 + 100e - 1600 - 80e - e^2 A = 2400 + 20e - e^2 Now looking at those 2 "e" terms is interesting. It's pretty obvious that any negative value of e will cause those term to result in a value less than 0, and decrease the available area. Also any value of e greater than 20 will also cause those 2 values to sum to a negative value and decrease the area. But a value of e in the range of 0 to 20 will result in a positive value and cause the area enclosed to be larger. So it's obvious that 40 feet isn't optimal. Let's pick the middle of the e values that result in something positive (0+20)/2 = 10 and add that to our initial guess, getting a length of 50 and replace length by (50+e) and see what happens. A = 100L -L^2 A = 100(50+e) -(50+e)^2 A = 5000+100e -(2500+100e + e^2) A = 5000+100e - 2500 - 100e - e^2 A = 2500 - e^2 This looks quite promising. Any non-zero value of e will result in the area enclosed being smaller. So the idea value of e is 0. That means that the idea length of the rectangle is 50 feet. And that makes the width 50 feet as well. Mind, this problem could have been also solved using the first derivative of the equation A = 100L -L^2, which would have been A' = 100 - 2L, and then solving for 0. But I did this problem to demonstrate that you don't need to resort to calculus for every maximum type of problem.
Step-by-step explanation:
Find constants a , b, and c such that the function
y = ax2 + bx + c satisfies the differential equation y′′ + y′ − 2y = 4x2.
Answer: a = -2, b = -2, c = 1.
Step-by-step explanation:
We know that:
y = a*x^2 + b*x + c.
Then:
y' = 2*a*x + b
y'' = 2*a.
Then we can write the equation:
y′′ + y′ − 2y = 4x^2.
as:
2*a + 2*a*x + b - 2*(a*x^2 + b*x + c) = 4*x^2
To solve this, the first step is moving all the terms to the same side:
2*a + 2*a*x + b - 2*a*x^2 - 2*b*x - 2*c - 4*x^2 = 0
Now let's group terms with the same power of x.
(-4 - 2*a)*x^2 + (-2*b + 2*a)*x + (-2c + b) = 0
Now, this must be zero for all the values of x, then the parenthesis must be equal to zero:
-4 - 2*a = 0
-2*b + 2*a = 0
-2*c + b = 0
From the first equation:
-4 - 2*a = 0
-4 = 2*a
-4/2 = a
a = -2
And from the second equation:
-2*b + 2*a = 0
2*a = 2*b
a = b
b = -2.
From the third equation we have:
-2c + b = 0
-2c = b
c = b/-2 = -2/-2 = 1.
c = 1
Then our equation is:
y = -2*x^2 - 2*x + 1.
Be Helpful!
Your friend is absent from class today. They know that
we added integers, but they don't know how to do it
.
Explain to them how to add integers. Make sure that
your explanation works for all of the types of problems
that you've done today.
Answer:
Step-by-step explanation:
When you add integers you have either positive integers or negative integers. When you add positive integers, you just add normal. When you have negative integers, you have to see if the the larger number is positive or negative that will tell you if your answer is either negative or positive. Then you turn the negative into a positive then change the addition sign to a subtraction sign then solve.
A lumber supplier sells 96-inch pieces of oak. Each piece must be within ¼ of an inch of 96 inches. Write and solve an inequality to show acceptable lengths.
Answer:
[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]
Step-by-step explanation:
Given that a lumber supplier sells 96 inch Pieces of oak which must be within 1/4 of an inch.
This situation can be represented by the following absolute value inequality:
[tex]|x \: - 96| \: \leqslant \: \frac{1}{4} [/tex].
The absolute value can be thought of as the size of something because length cannot be negative. The length must be no more than 1/4 away from 96.
To simplify this, pretend this is a standard equality, |x-96| = 1/4. 1/4 is the range of acceptable length, 96 is the median of the range, and x is the size of the wood.
First apply the rule |x| = y → x = [tex]\pm[/tex]y
|x-96| = 1/4
x - 96 = [tex]\pm[/tex]1/4
x = [tex]96 \pm 1/4[/tex]
(These are just the minimum, and maximum sizes)
Now with a less than or equal to, the solutions are now everything included between these two values.
Therefore:
[tex]96 - 1/4 \: \leqslant x [/tex] [tex]\leqslant \: 96 + 1/4 [/tex]
With less than inequalities, you must have the lower value on the left, and the higher value on the right.
If x represents the size of the pieces, then the acceptable lengths are represented by this following inequality:
[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]
This is interpreted as x (being the size of the oak) is greater than or equal to 95 3/4, and less than or equal to 96 1/4 in inches.
The coordinates of point T are (0,3). The midpoint or ST is (1,4). Find the coordinates of point S.
The other endpoint is _
(type an ordered pair)
Answer:
[tex]S = (2,5)[/tex]
Step-by-step explanation:
Given
[tex]T = (0,3)[/tex]
[tex]Midpoint (M) =(1,4)[/tex]
Required
Determine the other end point (S)
Midpoint is calculated as thus:
[tex]M(x,y) = (\frac{S_x + T_x}{2},\frac{S_y + T_y}{2})[/tex]
This gives:
[tex](1,4) = (\frac{S_x + 0}{2},\frac{S_y + 3}{2})[/tex]
[tex](1,4) = (\frac{S_x}{2},\frac{S_y + 3}{2})[/tex]
Multiply through by 2
[tex]2 * (1,4) = (\frac{S_x}{2},\frac{S_y + 3}{2}) * 2[/tex]
[tex](2,8) = (S_x,S_y + 3)[/tex]
By comparison:
[tex]S_x = 2[/tex]
[tex]S_y + 3 = 8[/tex]
[tex]S_y = 8 - 3[/tex]
[tex]S_y = 5[/tex]
Hence:
The coordinates of S is
[tex]S = (2,5)[/tex]
anybody wanna answer for me ?????
Answer:
y=11x
Step-by-step explanation:
EX:
11(2)=22
Please help with this
a. r + (-s) = r - s
b. r - (-s) = r + s
c. -r + (-s) = -r - s
d. -r - (-s) = -r + s
Consider a conical tank, where the height of the tank is 12 meters, and and the diameter of the tank at the top is 8 meters. Water is leaking out of the bottom of a conical tank at an constant rate of 20,000 LaTeX: \text{cm}^3 / \text{min}cm 3 / min. Water is also being pumped in to the tank at a constant unknown rate (call it LaTeX: kk). The water level is currently 8 meters high, and the water level is rising at a rate of 2 LaTeX: \text{cm} / \text{min}cm / min. Find the rate LaTeX: kk at which water is being pumped in to the tank.
Answer:
The answer is below
Step-by-step explanation:
The height of tank = 12 m = 1200 cm, the diameter of the tank = 8 meters, hence the radius of the tank = 8/2 = 4 m = 400 cm
Let h represent the water level = 8 m = 800 cm. The radius (r) of the water level at a height of 8 m is:
r/h = radius of tank/ height of tank
r/h = 400/1200
r = h/3
[tex]\frac{change\ in\ volume}{change\ in \ time}=water\ in-water\ out\\ \\\frac{dV}{dt=} water\ in-water\ out\\\\V=\frac{1}{3}\pi r^2h\\ \\r=\frac{1}{3}h \\\\V=\frac{1}{3}\pi (\frac{1}{3}h )^2h\\\\V=\frac{1}{9} \pi h^3\\\\\frac{dV}{dt} =\frac{1}{3} \pi h^2\frac{dh}{dt}\\\\\frac{dh}{dt}=2\ cm/min,h=8\ m=800\ cm\\\\[/tex]
[tex]\frac{dV}{dt} =\frac{1}{3} \pi (800)^2(2)=426666.7\ cm^3/min\\\\\frac{dV}{dt=} water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-20000\ cm/min\\ \\water\ in=426666.7\ cm^3/min+20000\ cm/min\\\\water\ in=446666.7 \ cm^3/min[/tex]
A bread company has a total of 12 packages of buns to sell. Each package of buns contains 6 buns and sells for $2.50. The cost of the buns, in dollars, is a function of the number of packages bought.
Which of the following values are NOT in the domain of the function described?
a) -2
b) 0
c) 0.5
d) 6
e) 14
Answer:
a) -2, c) 0.5, e) 14
Step-by-step explanation:
The domain is the x value, which is the number of packages sold in this case.
a) -2: You can't sell a negative number of packages
c) 0.5: You can't sell half a package
e) 14: The company only has 12 packages
What is the x-intercept?
look at the picture.
Answer:
(0,0)
Step-by-step explanation:
The x-intercept is what the x value is when y = 0, and on this chart, when y=0, x=0 as well.
The endpoints of AB¯¯¯¯¯¯¯¯ are 8 and 16. Find the coordinate of the point P that partitions the segment in the ratio 3 : 1.
Answer:
The coordinates of the point P is 14.
Step-by-step explanation:
Let point A is at 8 and B is at 16.
P is the point where the line segment in the ratio 3 : 1.
This is also where P is [tex]\frac{3}{4}[/tex] rds the distance from A to B
The total distance is |16 - 8| = 8
The distance between point AB is 8 units.
[tex]\frac{3}{4}[/tex] of 8 is 6.
So, the point P is 6 units from A .
8 + 6 = 14
P is at 14
Hence, the coordinates of the point P is 14.
This also works if you go 1/3 from B.
-8 is 4 from -4 which is 1/3 of 12.
5
4. y = 1
D
1
1
1
I
B
Answer:
not sure what you need but I would be happy to help
Michael wanted to see what kitchen cleaner worked best for cleaning her counters. He used Lysol, Clorox, Pinesol, and just water. For each cleaner, he put 5 milliliters of grape juice on the counter, sprayed the cleaner, and wiped it with one paper towel.
Answer:
whichever paper towel observer's the most juice is the best brand
Kalvin sells bottles of water at baseball games he pays 0.75 per bottle and 3.78 for the ice to keep cold let b represent the number of bottles of water he buys c represent his total cost
Answer:
3.78+.75b=c
Step-by-step explanation:
