To find the zeros of a polynomial algebraically, you can use the following steps:
Write the polynomial in standard form, with the terms arranged in descending order of the degree of the term. For example, if the polynomial is 3x^2 - 2x + 5, it is already in standard form.
Set the polynomial equal to zero. For example, if the polynomial is 3x^2 - 2x + 5, you would set the equation equal to zero like this:
3x^2 - 2x + 5 = 0
Use the quadratic formula to find the solutions (i.e., the zeros) of the equation if the polynomial is a quadratic (degree 2). The quadratic formula is:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the polynomial, and sqrt represents the square root.
For example, if the polynomial is 3x^2 - 2x + 5, the solutions would be:
x = (-(-2) +/- sqrt((-2)^2 - 4 * 3 * 5)) / (2 * 3)
x = (2 +/- sqrt(4 - 60)) / 6
x = (2 +/- sqrt(-56)) / 6
Since the square root of a negative number is not a real number, there are no real solutions (zeros) for this polynomial.
Use the Rational Root Theorem to find the solutions of the equation if the polynomial is not a quadratic. The Rational Root Theorem states that if a polynomial of degree n has a rational root p/q (where p and q are integers and q is not equal to zero), then p must be a divisor of the constant term and q must be a divisor of the coefficient of the term of highest degree.
For example, if the polynomial is x^3 - 2x^2 + x - 6, the constant term is -6 and the coefficient of the term of highest degree is 1. The divisors of -6 are -6, -3, -2, -1, 1, 2, 3, and 6. The divisors of 1 are 1 and -1. Therefore, the possible rational roots of this polynomial are -6, -3, -2, -1, 1, 2, 3, and 6.
To find the actual roots, you can try each of these numbers as a root and see if it works. For example, if you try -6 as a root, you would get:
(-6)^3 - 2(-6)^2 + (-6) - 6 = 0
(-216) - (-72) + (-6) - 6 = 0
-144 - 6 - 6 = 0
-156 = 0
This equation is not true, so -6 is not a root of the polynomial. You can repeat this process for each of the other possible rational roots until you find all of the roots of the polynomial.
A car travels at an average speed of 68 miles per hour. How long does it take to travel 357 miles?
Jelani has twice as much money on his subway pass as Alexis. If they both add $20 to their passes, Jelani will have 1.5 times as much on his pass as Alexis. Write an equation to represent this situation. How much do Jelani and Alexis have on their subway passes now?
Answer:
x = 2x
x + 20 = 2x + 20
And,
1.5(x + 20) = 2x + 20
x = 20 i.e. Alexis
And, Jelani be 40
Step-by-step explanation:
Given that
Jelani has twice as much as Alexis
And, both can added $20
Jelani will have 1.5 times as much on his pass on Alexis
We need to write an equation also the amount does Jelani and Alexis have
So,
Let us assume the alexis be x
And, Jelani be 2x
Now
x = 2x
x + 20 = 2x + 20
And,
1.5(x + 20) = 2x + 20
1.5x + 30 = 2x + 20
-0.5x = -10
x = 20 i.e. Alexis
And, Jelani be 40
60 workers can complete a work in 21 days. How long will it take to complete the some work if 10 more workers were added?
Answer:
Step-by-step explanation:
set 1 is the work, then 60 works finish 1/21 per day. [tex]\frac{1}{21*60}[/tex] is the work for per workers. so, the days for 70 workers is [tex]\frac{21*60}{70}=18[/tex] days.
it will spend 18 days to complete
simplify 3a - 2(8 +4a)
help pleaseeeeee
Answer:
-5a - 16
Step-by-step explanation:
Mark as Brainllest
t(28 – 8) = 24(28 – 8)
- 24 1)
Answer:
24(24)
Step-by-step explanation:
[tex] \rm \mapsto \: t(28 - 8) = 24(28 - 8) \\ \rm \mapsto \: t(24) = 24(24) \\ \rm \mapsto \: 24t = 576 \\ \rm \mapsto \: t = \frac{576}{24} \\ \rm \mapsto \: t = 24[/tex]
The solution to the equations are
a) The quantity ( 28 - 8 ) represents the discounted price of the tickets
b) The total cost of the 24 tickets is given by the equation A = $ 480
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the cost of 24 tickets be represented as A
Now , the equation will be
The initial cost of a ticket = $ 28
The discounted cost of the ticket = $ 8
So , the final cost of the ticket = $ 28 - $ 8 = $ 20
Now , the cost of t tickets = 20t
So , when the value of t = 24
Substitute the value of t in the equation , we get
The cost of 24 tickets A = 20 ( 24 )
On simplifying the equation , we get
The cost of 24 tickets A = $ 480
Therefore , the value of A is $ 480
Hence , the equation is A = $ 480
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The function f(x) = 10(1. 015)* shows the balance in a savings account as time increases. What does the 10 represent?
A)
The interest the savings account earned for the first year.
B)
The annual interest rate of the savings account.
C)
The number of years the savings account has earned interest.
D)
The starting balance of the savings account.
The 10 represent in the function f(x) = 10(1. 015)* shows the balance in a savings account as time increases is the starting balance of the savings account.
Therefore the answer is D) The starting balance of the savings account.
The compound interest formula is used to calculate the total interest earned on a principal amount over a period of time, where the interest is compounded at regular intervals. The formula is:
A = P(1 + r)^(t)
Where:
A is the final amount (principal + interest)
P is the principal (initial) amount
r is the annual interest rate (expressed as a decimal)
t is the number of years the money is invested or borrowed
The function f(x) = 10(1. 015)* shows the balance in a savings account as time increases.
So 10 represents the principal (initial) amount
0.014 represents the annual interest rate (expressed as a decimal)
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An ice cream factory makes 310 quarts of ice cream in 10 hours how many quarts could be made in 48 hours what was the ate per day
The factory can make 744 quarts of ice cream per day.
To find out how many quarts of ice cream could be made in 48 hours, we can use the principle of proportionality. Since the factory makes 310 quarts of ice cream in 10 hours, we can set up a proportion:
310 quarts / 10 hours = x quarts / 48 hours
To solve for x, we can cross multiply:
310 quarts * 48 hours = 10 hours * x quarts
x = (310 quarts * 48 hours) / 10 hours = 1480 quarts
So the factory could make 1480 quarts of ice cream in 48 hours.
To find the rate per day, we need to divide the number of quarts made per hour by the number of hours in a day. Since there are 24 hours in a day, we can calculate the rate per day as:
rate per day = (310 quarts / 10 hours) * 24 hours = (31 quarts/hour) * 24 hours = 744 quarts/day
So the factory can make 744 quarts of ice cream per day.
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Which point represents the approximate location of 388 squared
Answer:
Point D
[tex] \sqrt{388} = 19.7 \\ between \: 19 \: and \: 20[/tex]
need help with this
Answer:
im sorry what exsactly is the question?
Step-by-step explanation:
What is the most specific name that can be given to a figure with the following coordinates?
(-10, 8), (-7, 13), (3, 7), and (0, 2)
A. rectangle
B. square
C. trapezoid
D. parallelogram.
Answer:
a. rectangle
Step-by-step explanation:
i just used desmos so i have no idea how to explain it
Mrs. Harris took 6 oranges out of the refrigerator and cut them into wedges, each wedge represents 1/6 of the entire orange. Her children at 3/4 of the wedges.
A) how many wedges did her children eat
B) how many wedges are left?
can someone help me?
Answer:
Step-by-step explanation:
The solution is the point where the 2 lines intersect.
If they intersect where x = 1 and y = 2 the solution is (1, 2).
Solve the following equation for mathwatch
3x-1/2= x+5/5
0.75 i think
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x=34x=34
Decimal Form:
0.75
Click on the assignment icon to receive a printout of this construction assignment. Do the assignment and be ready to give it to your teacher for grading if it is requested.
The Construction is shown below.
What is Perpendicular line?Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Given:
a) Steps for perpendicular line:
To cross the line segment, draw two arcs.Create two more intersecting arcs.Connect the initial point to the intersection of the arcs.b) Perpendicular Bisector for triangle
Draw arcs with the same radius that are centered at X and Y by opening the compass more than halfway.These two arcs come together at two locations. They will be referred to as points P and Q.The line segment M, which is the perpendicular bisector of the line segment S, should be drawn by placing the ruler where the arcs meet (that is, by connecting points P and Q).we are going to proceed in the same way on all three sides of the triangle to draw its three perpendicular bisectors (Ma, Mb and Mc)So, if we extend the bisector they can meet inside, at center and outside the triangle.
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Monty is working on a formula to determine the amount of profit (P) he will make when he sells his pottery. He has already spent $50 on materials and plans to sell each pot for $5. If x represents the number of pots he sells, which formula represents Monty's profit from his sales?
Answer:
P=5x-50
Step-by-step explanation:
Profit is represented by P.
$5 is what Monty plans to sell each pot for and x represents how many pots he sells.
therefore 5x-50=P
a smallercircle passes through the center of, and is tanget to a larger cirlc the area of the smaller circle is 9 square units. What is teh area of the larger circle in square units
36 square units make up the larger circle's surface area.
We can use the fact that the smaller circle is tangent to the larger circle and passes through its center to find the area of the larger circle. Since the radius of the smaller circle is tangent to the larger circle, the radius of the larger circle is double the radius of the smaller circle.
Let's call the radius of the smaller circle "r" and the radius of the larger circle "R". We know that R = 2r.
We know that the area of a circle is given by the formula A = πr^2.
We know that the area of the smaller circle is 9 square units, we can use this formula to find the radius:
A = πr^2 => r^2 = 9/π => r = sqrt(9/π)
Now we can use the formula of the area of a circle with R-value to get the area of the larger circle:
A = πR^2 => A = π(2r)^2 => A = 4πr^2 => A = 4π(9/π) => A = 36
So the area of the larger circle is 36 square units
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What is the area of the quadrilateral below?
15 m
4 m
O A. 30 square meters
OB. 45 square meters
C. 60 square meters
OD. 75 square meters
Answer:
C
Step-by-step explanation:
A = Base x height
Base = 15
height = 4
= 60 square meter
Answer:
it is c because all I did was algarithims so yes it would be c
Rewrite 7[tex]x^{\frac{1}{2}[/tex] as a radical expression
Marshall has $8.25 totally in his collection, consisting of quarters and nickels. The number of nickels is three more than the number of quarters. How many nickels and how
many quarters does Ross have?

Answer:
where did Ross come from? is that just misplaced or what. or am I reading it all wrong
How do you multiply FG?
FG cannot be multiplied because it is not a numerical value.
Multiplication is a mathematical operation that involves multiplying two numerical values together to produce a single numerical result. In order for multiplication to be possible, both values must be numerical values. FG is not a numerical value, which means that it cannot be multiplied. In order for FG to be multiplied, it would need to be replaced with a numerical value, such as a number or an expression that can be evaluated to a number. Without a numerical value, multiplication is not possible. Multiplying numerical values is done by taking the product of the two values, meaning that the result of the multiplication is the sum of each value multiplied by itself the number of times the other value is. For example, if you were to multiply 3 and 4, the result would be 12 because 3 multiplied by itself 4 times is 12, and 4 multiplied by itself 3 times is also 12. Without numerical values, this operation cannot be performed.
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A bag of
.5 red marbles
.6 blue marbles
.3 green marbles
.4 black marbles
.2 yellow marbles
A marble will be drawn from the bag and replaced 100 times how many green and black marbles will be drawn?
The number of green and black marbles will be 15 and 20 black marbles respectively.
How to illustrate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
We have the following information:
5 red marbles
6 blue marbles
3 green marbles
4 black marbles
2 yellow marbles
Total marble = 20 marbles
The number of green marbles:
= 3/20 × 100
= 15
The black marbles will be:
= 4/20 × 100
= 20
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temperature of an oven in a laboratory rises until it reaches a maximum temperature of 32°C. The oven then stops heating and reactivates only when the temperature goes down to a minimum of 18°C. At 12:00 pm, the oven starts at room temperature, which is 18°C, and takes 3 hours to reach 32°C Write a function in the form 0(t)= Acos(bt)+c, that represents the temperature of the oven, O. in terms of the number of hours, t, since 12:00pm. Then, sketch the function on the provided grid for one full cycle. Be sure to scale your axes trig.
Answer:
123456789123345
Step-by-step explanation:
PLEASE HELP
WILL GIVE BRAINLIEST
Answer:
[tex]\frac{9}{10}[/tex] + [tex]6\frac{1}{5}[/tex] = [tex]7\frac{1}{10}[/tex]
Answer:
look at the picture i sent .....
The picture shows a shed. Find the length, AB, of the roof.
The length AB of the roof is 3.20 m.
What is the Pythagorean theorem.
The Pythagorean theorem is one that can be used to determine the value of the unknown side of a right triangle when given two of its sides.
The theorem states that;
/Hyp/^2 = /Adj/^2 + /Opp/^2
Considering the given picture of the shed, draw a perpendicular to B from a point C on parallel line A. So that the length of AB can be referred to as the hypotenuse of triangle ABC.
Now applying the Pythagorean theorem, we have;
/Hyp/^2 = /Adj/^2 + /Opp/^2
/AB/^2 = /2/^2 + /2.5/^2
= 4 + 6.25
/AB/^2 = 10.25
AB = (10.25)^ 1/2
AB = 3.20
Thus, the length of AB of the roof is 3.20 m.
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What are the 3 steps for solving a quadratic equation?
Determine what a, b, and c are worth. the quadratic formula in writing. After that, enter the values for a, b, and c. Simplify.
what is quadratic equation ?A quadratic polynomial in a single variable is represented by the expression x ax2+bx+c=0, which is a quadratic equation. a 0. Since it is a second order polynomial, the Fundamental Theorem of Algebra guarantees that it has at least one solution. Simple or difficult solutions are both possible. The term "quadratic equation" refers to an equation that is quadratic. It must square at least one word, according to this indication. One of the common solutions for quadratic equations is the formula "ax2 + bx + c = 0." where the variables "X" are undefined and are numerical coefficients or constants a, b, and c.
given
steps are
Find out what a, b, and c are worth.
Quadratic formula: write it down.
Add the values of a, b, and c after that. Simplify.
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Kenneth opened a savings account and deposited $300.00 as principal. The account earns
14% interest, compounded annually. What is the balance after 8 years?
Use the formula A = P1+
P(1 + r/n)", where A is the balance (final amount), P is the principal
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
$855.78
Step-by-step explanation:Interest, in this context, is the amount of money a saving account can earn over time.
Compound Interest Formula
There are 2 types of interest: simple and compound. For this question, we are going to use the compound interest formula. This formula is [tex]A = P(1+\frac{r}{n})^{nt}[/tex]. As stated in the question, A is the total balance, P is the principal, r is the interest rate, n is how often the interest is compounded, and t is time.
Variables
The values of these variables for this question are as follows:
P = 300.00The principal is the initial amount, and the question states that the account starts at 300 dollars.
r = 0.14The question says the interest rate is 14%, so we can convert this to the decimal 0.14.
n = 1If something is compounded annually, it is compounded once a year, so n must be 1.
t = 8If we want to find the balance after 8 years, we should set t equal to 8.
Solving for A
To find A, all we have to do is plug the variables into the formula.
[tex]A = 300(1+\frac{0.14}{1})^{1*8}[/tex]This can be rewritten as:
[tex]A=300(1.14)^8[/tex]Solve this to find that A ≈ 855.78. After 8 years, the balance will be $855.78.
* I WILL GIVE BRAINLIEST TO THE CORRECT ANSWER*
A circle has a circumference of 10 millimeters. What is the circle's diameter? Use 3.14 for pi and round your answer to the nearest tenth.
Answer:
To find the diameter divide the circumference by pi
10÷3.14
=3.2 mm
HELP
Answers available are on the picture
Answer:
[tex]360 = 2\pi \\\\90 = \frac{2\pi }{4} =\frac{\pi }{2} \\\\180 = \pi \\\\270 = \frac{6\pi }{4} = \frac{3\pi }{2}[/tex]
I need to know the andwer to 0.03 divided by 0.81 in division of decimals
Answer: 0.0370 (Italic part repeats forever)
Step-by-step explanation:
Answer: 0.037...
Step-by-step explanation:
Please help! Will give brainiest to correct person!! No links please!
Answer:
39 inch
Step-by-step explanation:
Answer:
H=39.0625
Step-by-step explanation:
D=32in
R=1/2d=32/2=16
Volume of cylinder:pi r^2h
V=pir^2h
10000pi=16^2hpi
256h=10000
h=39.0625