Polynomial of degree 4 in factored form is x(x+3)(x-4)(x-8) = 0
The Standard form of polynomial with degree 4 is ax⁴ + bx³ + cx² + dx + e
Zeros of the polynomial is the points where the polynomial becomes zero.
According to the question,
The zeros of the polynomial are -3 , 4 , 0 , 8
Let equation of polynomial f(x) be
f(x) = ax⁴ + bx³ + cx² + dx + e ------------------(1)
Sum of zeros = -b/a = -3 + 4 + 0 + 8
= 9
Sum of product of two zeros = c/a = (-3× 4 ) +(0 × 4) + (0 × 8) + (8× -3)
= -12 + 0 + 0 -24
= -12 - 24
= -36
Sum of product of sum of three zeros = -d/a = ( -3×4×0) + ( 4×0 ×8 ) + (0×8×-3) + (-3×4×8)
= 0 - 96
= -96
Product of all four zeros = e/a = (-3×4×0×8)
= 0
So, b = -9 , c =-36 , d = 96 and e = 0
Substituting value in equation (1),
Hence , the required polynomial = x⁴ -9x³ -36x²+96x
Factored form ,
x⁴ -9x³ -36x² +96x = 0
=> x(x³ - 9x² - 36x + 96) = 0
=> x(x+3)(x-4)(x-8) = 0
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A photocopier takes 8 seconds to make 20 copies. How long will it take to make 45 copies?
Answer: 18
Step-by-step explanation:
8--20
x--45
x=45*8/20
x=18
Scarlett and Kamila are throwing a pizza party. They invited 436 students from school. Each pizza was cut into 6 pieces. How many pizza should they order?
Answer:
73 pizzas
Step-by-step explanation:
Scarlett and Kamila are throwing a pizza party. They invited 436 students from school. Each pizza was cut into 6 pieces. How many pizza should they order?
pizzas are cut into 6 slices so:
436/6 = 72.66 pizzas
Because you cannot order a partial pizza round up to:
73 pizzas
Choose the compound inequality that represents each phrase.
All real numbers that are less than –3 or greater than or equal to 5
A. x < –3 or x > 5
B. x < 5 or x > –3
C. x < –3 or x > 5
D. x < –3 or x < 5
i NEED HELP QUICK AGAIN
Answer: 3 1/3
Step-by-step explanation:
Each tick mark marks 1/3 of a space. A is at - 3 1/3. The absolute value of any number is positive and is just the number of spaces a dot is from zero. You can’t have a negative distance, so the answer is 3 1/3.
Find all values of m for which the equation has two real solutions
(m - 3)r² + 9r - 2 = 0
The value of m for equation (m - 3)r² + 9r - 2 = 0 is 57/8.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
The given equation is (m - 3)r² + 9r - 2 = 0
For the equation to have real and equal roots, the discriminant should be 0.
b²-4ac=0
a=m-3, b=9, c=-2
plug in the values in discriminant
81-4(m-3)(-2)=0
81-4(-2m+6)=0
81+8m-24=0
8m+57=0
m=57/8=7.125
Hence, the value of m for equation (m - 3)r² + 9r - 2 = 0 is 57/8.
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a divided by 4 is equal to For a= 7
Answer:
no no lose me das las respuestas
What mixed number is represented on the number line shown here?
Answer:
The mixed number is 1 and 2/5. If it is split into 5 parts.
Step-by-step explanation:
No explanation sorry!
Answer:
Step-by-step explanation:
We already know how to represent whole numbers on the number line. Let us consider the image shown, here, the digits 0 and 1 are represented on the number line.
Representation of 0 and 1 on The Number Line
If we divide the number line into two equal parts, as shown in the figure below, what value does that mid-point hold? Half of what the graduation between 0 and 1 holds.
So, the point represents (1-0)/2 = ½
Fraction - Representation Of Fraction On The Number Line
Thus we saw, to represent a fraction on the number line, we need to divide the line segment between two whole numbers into n equal parts where n represents the denominator of the fraction. For example, if we have to represent the fraction 1/5 on the number line, hence, we need to divide the line segment between 0 and 1 into five equal parts, where the first point as shown in the figure represents the fraction 1/5, the second represents 2/5 and so on.
Fraction Representation
We must note that, 0/5 = 0 here and 5/5 = 1.
Here you have seen the representation of proper fraction on the number line. To represent improper fractions, you first convert them into mixed fractions. The same procedure, as shown above, is used with the whole number as the starting point.
In the general multiple regression equation, which of the following variables represents the Y-intercept? Select one: O a. b1 O b. X1 c. d. a
Answer:
it is a since using the pythagoras theorium the brainly bahahaha
IXL need finished fast please Help fast !
Jasmine evaluated the expression 10 - (-3)
and says it is equal to 7. Is she right? If not, what was her mistake?
Jasmine was not right in evaluating the expression. She didn't multiply the subtraction signs.
How to evaluate an expression?An algebraic expression consists of unknown variables, numbers and arithmetic operators.
To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.
Therefore, let's evaluate Jasmine expression.
10 - (-3)
we have to open the bracket by multiplying the negative signs.
- × - = +
Hence,
10 - (-3) = 10 + 3 = 13
Therefore, Jasmine is wrong. Her mistake was not multiplying the minus sign.
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You want to buy a new car. You can afford payments of $425 per month and can borrow the money at an interest rate of 4% compounded monthly for 5 years. How much interest do you pay?
He would pay $8500 interest if he can afford payments of $425 per month and can borrow the money at an interest rate of 4% compounded monthly for 5 years.
Define interest.The expense of borrowing money is interest. It equates to a fee or additional charge the borrower pays the lender for the loaned amount, and is sometimes stated as a percentage. When you make a payment on a loan with simple interest, the money first goes toward the interest for that month and the rest is applied to the principal. Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
Given,
Principal = $425
Rate = 4%
Time = 5 years
Interest = Principal × Rate × time
Interest:
= 425 × 4×5
= 8500
He would pay $8500 interest if he can afford payments of $425 per month and can borrow the money at an interest rate of 4% compounded monthly for 5 years.
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A truck can be rented from Company A for $100 a day plus $0.30 per mile. Company B charges $50 a day plus $0.80 per mile to rent the same truck. Find the number of miles in a day at which the
rental costs for Company A and Company B are the same.
Atmiles, the rental costs are the same from either company.
Answer:
100 miles
Step-by-step explanation:
Let m be the number of miles.
[tex]100 + .30m = 50 + .80m[/tex]
[tex]100 = 50 + .50m[/tex]
[tex].50m = 50[/tex]
[tex]m = 100[/tex]
Answer:
100
Step-by-step explanation:
You can put into a graph such as desmos and see where the lines intersect. the x value of the intersection is the answer you want.
Please Help It would mean a lot!!
Answer:
30 x n - 60 = 20 x n
1 day
80
Step-by-step explanation:
What is the exact solution to the equation 10x=23?
Answer:
x = 2.3
Step-by-step explanation:
you divide both sides of the equation by 10
A map has a scale of 1/2 inch
equals 25 miles. How many
miles are 8 inches?
According to the given scale, 400 miles are 8 inches.
Scale
Scale refers the ratio that defines the relation between the actual figure and its model. And it is used in maps to represent the actual figures in smaller units.
Given,
A map has a scale of 1/2 inch equals 25 miles.
Here we need to find how many miles are 8 inches.
Through the given question we know that,
1/2 inches = 25 miles.
Then the 1 inch is equal to,
1 inch = 25 x 2 = 50 miles.
Therefore, the miles equivalent of 8 inches is written as,
=> 8 x 50
=> 400 miles.
Therefore, 8 inches is equal to 400 miles.
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At how many seconds s will the two bottles have the same amount of water if Jason and Pedro start drinking from each of their bottles at the same time ?
The time at which the two bottles will have the same amount of water, using linear functions, is of:
26 seconds.
What is a linear function?The slope-intercept representation of a linear function is given by the rule shown as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the numeric value of the function when the input x is of zero.For the functions in this problem, we have that:
The slope is the rate of water they drink per second.The intercept is the initial amount of water that they have.Hence the functions are given as follows:
Jason: J(x) = 20 - x.Pedro: P(x) = 65 - 2.5x.The time at which they have the same amount is x for which:
P(x) = J(x)
65 - 2.5x = 20 - x
1.5x = 45
x = 45/1.5
x = 30 seconds.
However, at this time, the amount would be of:
J(30) = 20 - 30 = -10.
Which is a negative amount of water, not possible, hence they would have the same amount when Jason finishes, hence:
65 - 2.5x = 0
2.5x = 65
x = 65/2.5
x = 26 seconds.
Missing InformationThe problem is:
Jason's water bottle has 20 ounces of water, and he is drinking ata rate of 1 ouncer per second. Pedro's water bottle contains 65 bunces of water, and he is drinking at a rate of 2.5 ouncers per second. At how many seconds, s, will the two bottles have the same amount of water if Jason and Pedro start drinking from each of their bottles at the same time?
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Which two points on the number line are
opposites?
points A and B
points B and C
points C and D
points A and D
The point B and C are opposite to each other.
A number line is a mathematical visual representation of numbers on a straight line. The digits on a number line are positioned sequentially at regular intervals throughout its length. It frequently appears horizontally and might go on forever in any direction.
As seen from the number line, point A is one unit left of -1 which is -2. Since each mark is a difference of 1 and to the left is a negative value, point B is midway between -1 and 0 is half of -1 which is -0.5, point C is midway between 0 and 1 is basically half of 1 which is 0.5 and point D is halfway between 1 and 2 is exactly that 1.5
As per the numerical values of the given points, the two that are opposites to each other are points B and C. They both have a value of 0.5 on each end of the number line, one being negative while the other is positive, thus they are opposites of each other.
Therefore, points B and C are opposite to each other.
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The given question is incomplete. Here is the complete question:
Which two points on the number line are opposites? A number line goes from negative 2 to positive 2 in increments of 1. There are 4 equal spaces between each number. Point A is 1 mark to the left of negative 1. Point B is halfway between negative 1 and 0. Point C is halfway between 0 and 1. Point D is halfway between 1 and 2.
i need help asap with this question
Answer: B
Step-by-step explanation:
The width = 23/4
The length = 2 × the width = 2 × 23/4 = 23/2
The perimeter of the rectangle = 2 ( length + width)
= 2 (23/2 + 23/4 )
= 2 ( 69/4)
= 69/2
= 34 .1/2
which expression is equivalent to i233?
O 1
O -1
O i
O -i
i is expression is equivalent to i233.
What is mathematical expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.Given i233
We know that i2 = -1 , if we square (i2) we get (-1)2 = 1
So, if i is multiplied to (i2), we get i3 = (-1).i = -i
Again if i is multiplied to i3 , we get i4 = (-i).i = -i2 = -(-1) = 1
Hence, all even powers of i after 2, will give answer as 1
The sequence will continue as a cycle as i, -1, -i, 1
So, i233 can be rewritten as i232 + 1= i232.i
i233 = (i2)116 .i = (-1)116 . i
Since the power 116 is even , the term becomes 1.i = i
Therefore, i233 = i
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Mindy owns 20 pairs of shoes and every week she purchases two more pairs.And she destroys one. How long will it take for her closet to have 50 pairs of shoes?
Write an equation and solve.
Answer:
y = x + 20
30 weeks
Step-by-step explanation:
The given scenario can be modelled using the linear equation:
[tex]y=mx+b[/tex]
where:
m is the rate of change (slope).b is the initial value (y-intercept.Mindy initially owns 20 pairs of shoes. Therefore, the initial value is b = 20.
If Mindy purchases 2 pairs but destroys 1 pair each week, then she is gaining 1 pair of shoes each week. Therefore, the rate of change is m = 1.
Therefore, the equation is:
[tex]y=x+20[/tex]
where:
x is time in weeks.y is the number of shoes Mindy owns.To find how long it will take for Mindy's closet to have 50 pairs of shoes, substitute y = 50 into the equation and solve for x:
[tex]\implies 50=x+20[/tex]
[tex]\implies 50-20=x+20-20[/tex]
[tex]\implies 30=x[/tex]
[tex]\implies x=30[/tex]
Therefore, it will take Mindy 30 weeks to have 50 pairs of shoes in her closet.
- 9 + 5z - 12z = 15 help please
Answer: z=24/7
Step-by-step explanation:
A scuba diver descends in the water at a rate of 23.5 feet per minute for 2.6 minutes. He immediately changes course when he sees a large fish and ascends at a rate of 28 feet per minute for 2 minutes. What is the scuba diver's position relative to sea level after the 4.6 minutes? Enter your answer as a decimal in the box.
Answer:
Step-by-step explanation:
t is given that a scuba driver descends in water for 2.8 minutes at a rate of feet per minute.
Let's assume the descending position as negative.
The position at which the scuba driver will be after 2.8 minutes is :
= - feet per minute × 2.8 minutes
= - 57.4 feet
Now , he sees a large fish and changes his direction and starts diving ascending at a rate of 25 feet per minute for 2 minutes.
Let's assume the ascending position as positive.
So , The position at which the scuba driver will be after 2 minutes after seeing large fish is :
= 25 × 2
= 50 feet
So , the scuba diver's position relative to sea level after the 4.8 minutes will be :
= -57.4 + 50
= -7.4 feet
This meant Scuba driver is 7.4 feet below sea level.
Amit sold 3 shells last week for $5 each
and 2 more shells this week for $5 each.
Show two ways to determine how much
money Amit made in the two weeks.
The two ways to determine how much money Amit made in the two weeks are,
$5(3 + 2) = $25 and $5(3) + $5(2) = $25.
What is shell?
A hard, protective outer layer is typically produced by an animal that lives in the sea and is referred to as a shell, seashell, or simply a shell. The animal's body includes the shell. Beachcombers regularly discover empty seashells washed up on beaches.
Given: Amit sold 3 shells last week for $5 each.
And 2 more shells this week for $5 each.
So, the equation which represent the total money is,
$5(3) + $5(2) = $15 + $10 = $25.
Also we can express this equation as,
$5(3 + 2) = $5(5) = $25
Therefore, the two ways to determine how much money Amit made in the two weeks are,
$5(3 + 2) = $25 and $5(3) + $5(2) = $25
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How can a polynomial expression be factored completely?
Answer:
Step-by-step explanation:
To factor the GCF out of a polynomial, we do the following:
Find the GCF of all the terms in the polynomial. Express each term as a product of the GCF and another factor. Use the distributive property to factor out the GCF.
hope it helps!
find the size of angle x
Answer: 14 is bigger than 8 and x is smaller than 8 so x would be a small number, i bet that x is = to 3 cm
Step-by-step explanation:
I don't know for SURE though :)
Devaughn is 13 years younger than Sydney. The sum of their ages is 43 . What is Sydney's age?
Answer:
30 years
Step-by-step explanation:
subtract devaughn's age from the sum of ages
*
Hamburger meat is priced at $5.98
for 1.3 pounds of meat. What is the
the price per pound?
Your answer
The price per pound of meat is $4.60.
How to calculate the price of meat?Given that hamburger meat is priced at $5.98 for 1.3 pounds of meat.
It should be noted that to find the cost per pound of meat, we will need to divide the value given.
This will be:
= Cost of meat / Pound of meat
= $5.98 / 1.3
= $4.6
The price is $4.60.
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cual es El promedio de 12,16 y 23
Answer:
17
Step-by-step explanation:
Se suman todos los números y se divide por el número de números.
¡¡¡Espero que esto ayude!!!
(Translated to English: You add all the numbers together and divide by the number of numbers. I hope this helps!!!)
A new car costs $24,250, which is approximately 110% of what a comparable car cost 3 years ago. What did the car cost 3 years ago?
The car's cost 3 years ago was $22,045.45.
According to the question,
We have the following information:
A new car costs $24,250, which is approximately 110% of what a comparable car cost 3 years ago.
Now, let's take the cost of car 3 years to be $x.
So, we have the following expression:
110% of x = 24250
110x/100 = 24250
Using the cross multiplication method:
110x = 24250*100
Dividing both sides by 110 will give us the value of x which is the required cost of car:
x = 2425000/110
x = $22045.45
Hence, the car's cost 3 years ago was $22,045.45.
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Which of the following is an equation of a line that is parallel to y = 6x - 2 and has a y-intercept of (0, 3)
A-y = 3x + 6
B-y = 6x - 3
C-y = 3x - 6
D-y = 6x + 3
The equation of a line which is parallel to the given line; y = 6x - 2 as required in the task content is; Choice D-y = 6x + 3.
Equation of parallel lines.It follows from the task content that the equation of a line which is parallel to the given equation; y = 6x - 2 is to be determined.
First, by comparison the given equation with the slope-intercept model of a linear equation; y = mx + c. where m is slope and c is y-intercept.
Slope, m = 6.
Hence, since parallel lines are lines which have equal slopes.
The slope of the required line is therefore; 6 and it's y-intercept (0, 3) has a y-coordinate of; 3.
The required equation of the line is therefore; y = 6x + 3.
The correct answer choice among the answer choices is; Choice D; y = 6x + 3.
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