A polynomial function with real coefficients that has the given zeros -1, 8, 3, -21 is x^4−11x^3−197x^2−297x+504.
In the given question we have to find a polynomial function with real coefficient that has the given zeros -1, 8,3, -21.
The given zeros are -1, 8,3 - 21.
Let the variable is x.
So the factor from the given zeros are
(x-1), (x+8), (x+3), (x-21)
To find the polynomial we multiply the factors to each other.
=(x-1)(x+8)(x+3)(x-21)
We firstly multiply the factor with the pair of two using the distributive property.
={x(x-1)+8(x-1)}{x(x+3)-21(x+3)}
=(x^2-x+8x-8)(x^2+3x-21x+63)
Simplifying
=(x^2+7x-8)(x^2-18x+63)
=x^2(x^2+7x-8)-18x(x^2+7x-8)+63(x^2+7x-8)
=(x^4+7x^3-8x^2)-(18x^3+126x^2-144x)+(63x^2+441x-504)
=x^4+7x^3-8x^2-18x^3-126x^2+144x+63x^2+441x-504
=x^4−11x^3−197x^2−297x+504
Hence, a polynomial function with real coefficients that has the given zeros -1, 8, 3, -21 is x^4−11x^3−197x^2−297x+504.
To learn more about polynomial function from zeros link is here
brainly.com/question/17158670
#SPJ1
find the quadratic function
For the quadratic function y = ax² + bx + c , for which graph passes through the points (2, 31), (3 , 45) , (1, 19) is given by y = x² + 9x + 9.
As given in the question,
Standard form of quadratic function,
y = ax² + bx + c
Graph of the quadratic function passes through the points (2, 31),
(3 , 45) , (1, 19) .
When passes through (2, 31)
31 = 4a + 2b + c __(1)
Passes through (3,45)
45 = 9a + 3b + c __(2)
Passes through (1, 19)
19 = a + b + c __(3)
Multiply 9 to (3) and subtract (2) from it,
9a + 9b + 9c =171
9a +3b + c = 45
6b + 8c = 126 ____(4)
Now, Multiply 4 to (3) and subtract (1) from it,
4a + 4b + 4c =76
4a +2b + c = 31
2b + 3c = 45____(5)
Multiply 3 to (5) and subtract (4) from it,
6b + 9c = 135
6b + 8c =126
c = 9
Substitute c= 9 in (5) we get,
2b + 3(9) = 45
⇒ b = 9
Now , substitute b = 9, c = 9 in (3) we get,
a + 9 + 9 = 19
⇒ a = 1
Required quadratic function is :
y = x² + 9x + 9
Therefore, for the quadratic function y = ax² + bx + c , for which graph passes through the points (2, 31), (3 , 45) ,(1, 19) is given by y =x² + 9x + 9.
Learn more about quadratic function here
brainly.com/question/18958913
#SPJ1
v- 15
------- = 2
2
What is the answerrr :D
Answer:
Can you tell me what i'm supposed to be finding
Step-by-step explanation:
Which of the following is a figure consisting of two rays with the same endpoint? (1 point)
O Angle
O Circle
O Line
O Vertex
Answer would be Angle as it has 2 rays and the same endpoint
y=-2x+10 rewrite in y=mx + b form
Answer:
it would already be in it the y is alone
Answer:
View explanation.
Step-by-step explanation:
y = -2x+10
M is the slope or how much the y value increases every time the x value increases by one. b is the y-intercept or when x=0.
It is already in y=mx+b form.
In a town, 100 people need 600 liters of water to drink everyday. At a festival time how many liters of water do they need to drink with their 50 guests?
The amount of water needed to drink with their 50 guests is 900 liters.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
In a town, 100 people need 600 liters of water to drink every day.
This can be written as,
100 people = 600 liters of water
50 guests are added.
The number of people = 100 + 50 = 150 people.
Now,
100 people = 600 liters of water
Multiply 150/100 on both sides.
150 people = 150/100 x 600 litres of water
150 people = 900 liters of water
Thus,
The amount of water needed to drink with their 50 guests is 900 liters.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
1. (8x10^5)+(9x10^4) in standard form
2. (5x10^-1)+(5x10^-2) in standard form
3. Work out (3.5x10^11)x(2x10^15) give answer in standard form
4. (9x10^4)x(2x10^6) in standard form
5. (8x10^10) divided by (2x10^6) in standard form
6. (4.9x10^-13) divided by (7x10^4) in standard form
7. (8x10^4)-(9x10^3) in standard from
8. (7x10^-3)-(4x10^-4) in standard from
9. (3x10^7)x(3x10^12) in standard form
10. (9x10^2)x(2x10^4) in standard form
11. (1.2x10^13) divided by (6x10^2) in standard form
12. (4.5x10^9) divided by (9x10^-2) in standard form
Answer:
1. 8.9x10^5
2. 5.05x10^1
3. 7x10^26
4. 1.8x10^11
5. 4x10^4
6. 7x10^-18
7. 7.1x10^4
8. 6.6x10^-3
9. 9x10^19
10. 1.8x10^7
11. 2x10^10
12. 5x10^10
What is the equation of the trend line in the scatter plot?
Use the two yellow points to write the equation in slope-intercept form. Write any coefficients
as integers, proper fractions, or improper fractions in simplest form.
PLS RN!!
The equation in slope intercept form is y = -4x + 24.
From the graph:
yellow points are (6,0) and (4,8).
slope intercept form is y = mx + c.
slope m = 8 - 0 / 4 - 6
= 8/-2
= -8/2
= -4
Substitute m and (6,0)
y = mx + c
0 = -4*6 + c
c = 24
y = mx + c
y = -4x + 24.
Therefore The equation in slope intercept form is y = -4x + 24.
Learn more about the slope intercept form here:
https://brainly.com/question/9682526
#SPJ1
I need help with this please
Answer:
No they are not
Step-by-step explanation:
6.23x10^2=623
62,300/10^3=62.3
623>62.3
-Hope this helped
If the original quantity is 5 and the new quantity is 7, what is the percent of change?
HElp if your good whit money
According to the concept of card payment, the true statement is "If you purchase an item using debit card, the money will deducted from your bank account".
Card payment:
Card payment refers any transaction whereby the Card is used to settle bills or to pay for certain goods and/or services at a Post Office branch.
Given,
Here we need to find the true statement according to the purchase.
While we looking into the given options,
The first option is incorrect because it says there is no interest for credit card purchase. This one is wrong because we have to pay interest for credit card purchase.
The second option is wrong because it tells that the money will be deducted from your account. If anyone can purchase using the credit card the money will only be deducted at the end of the month with some interest on it.
The third option is incorrect because debit card transaction are truly based on the amount within you account so it is not a borrowed one.
Therefore, the final statement is the correct one.
To know more about Card payment here.
https://brainly.com/question/16557697
#SPJ1
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
[tex]y \ \textgreater \ x^{2} -1[/tex]
[tex]y\leq -x^{2} +4[/tex]
The solution set of the inequalities can be identified by investigating the coefficient of x^2
How to interpret graph of a parabolaThe graph of a parabola is represented by a curve as used in the graphs attached in the equation
Parabolic graphs are also called graph of quadratic equation
The equation is usually in this form
y = ax^2 + bx + c
when it is "y =" it is a vertical parabola the graph will either opens up or down
The coefficient of "x^2" which is "a" says if the curve opens upwards or downwards. when a is:
positive the parabola opens upwards andnegative means the parabola opens downwardsy > x^2 - 1 "a" is positive hence opens upwards
y ≤ -x^2 + 4 "a" is negative hence opens downwards
Learn more about interpretation of quadratic equation here:
https://brainly.com/question/29395769
#SPJ1
Use the relationship among the three angles of any triangle to solve.
Two angles of a triangle have the same measure and the third angle is 66° greater than the measure of the other two.
Find the measure of each angle.
1. Measure of the top angle is (?)
2. Measure of the bottom left angle is (?)
3. Measure of the bottom right angle is (?)
Answer:
1. 104
2. 38
3. 38
Step-by-step explanation:
3x + 66 = 180
3x = 114
x = 38
The Gonzalez family drove 342 miles in 6 hours. The Wilson family drove 472 miles in 8 hours.
Which family traveled at the higher rate of speed and what was this rate?
Question 2 options:
A:Gonzalez; 57 mi/h
B: Gonzalez; 59 mi/h
C: Wilson; 57 mi/h
D: Wilson; 59 mi/h
Warning: Whoever Answers this wrong will be reported :l
If the Wilson family drove 472 miles in 8 hours. The family that traveled at the higher rate of speed and rate is: D: Wilson; 59 mi/h
How to find the rate of speed?'Using this formula to find the speed
Speed = Distance /Time
Let plug in the formula
Rate of speed for Gonzalez family
Rate of speed = 342 ÷ 6
Rate of speed = 57 mph
Rate of speed for Wilson family
Rate of speed = 472 ÷ 8
Rate of speed = 59 mph
Therefore the correct option is D.
Learn more about rate of speed here:https://brainly.com/question/26046491
#SPJ1
HELPPP so the man bought a tv worth $1,700, and then each week he continued to spend $700 weekly WHAT IS THE EXPRESSION???? HELP (variable is X)
Solve the system by substitution.
y = x + 6
y = 3x
Answer:
y=9
x=3
Step-by-step explanation:
Answer:
x = 3y = 9Step-by-step explanation:
y = x + 6y = 3xBring one of the equations into the other one:
3x = x + 6
3x - x = 6
2x = 6
x= 3
Then, bring the found value to find the value other variable:
y = 3x = 3(3) = 9
view picture please!!!
Answer:
70/3
Step-by-step explanation:
[tex]f(0)=\frac{140}{1+5e^{-2(0)}} \\ \\ =\frac{140}{1+5(1)} \\ \\ =\frac{140}{6} \\ \\ =\frac{70}{3}[/tex]
What is 54 divided by 6,539 equal
Answer:
0.00825814344701024621501758678697
Step-by-step explanation:
Use a calculator please<3
6.
Using a line of best fit equation to predict values between actual data points is an example of
O extrapolation
O correlation
O linear relation
O interpolation
For the given line of best fit, equation which represents the prediction of values between the actual data points is representing an example of interpolation.
As given in the question,
Given line of best fit equation,
Here prediction is to be done for the values which are between the actual data points.
The predicted values are within the range.
Predicted values represents either extrapolation or interpolation
If predicted values are outside the actual points it is extrapolation.
Here it is between the actual data points.
So, it is interpolation.
Therefore, for the given line of best fit, equation which represents the prediction of values between the actual data points is representing an example of interpolation.
Learn more about equation here
brainly.com/question/10413253
#SPJ1
6. There were 200 tickets sold for a woman's basketball game. Tickets for students
were $0.50 each and for adults they were $0.75 each. The total amount of money
collected was $132.50. How many of each type of ticket were sold?
Answer:
70 students and 130 adults
Step-by-step explanation:
Find the area of the circle pictured above.
Round your answer to the nearest tenth
Answer:
A ≈ 314.2 units
Step-by-step explanation:
To find the area of the circle, we will use the given formula. We are given the diameter (d), 20, and the radius (r) is half of the diameter. 20 units / 2 = 10 units for our radius (r).
A = πr²
A = π(10)²
A ≈ 314.15927
Now, we are asked to round to the nearest tenth.
A ≈ 314.2 units
What is the value of the expression below when w=8?
w-2
The value of the expression w-8 is 6 when w=8
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is w minus 8
w-2
The w is the variable and 2 is the number and minus is the operator
Now given variable w is 8
So substitute the value 8 in the expression w-2
8-2=6
Hence 6 is the value of the expression w-2 when w=8
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ1
how do I put 8x=26+14y in standard form
The standard form of the equation of the given straight line is 4x + (-7)y = 13.
We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation is given below.
8x = 26 + 14y
We need to convert this equation to standard form. The standard form of an equation for a straight line is given below.
Ax + By = C
We need to rearrange the given equation so that it matches the correct format. The equation is written below.
8x - 14y = 26
We can simplify the equation further by dividing the whole equation by two.
4x + (-7)y = 13
Hence, the standard form of the equation is 4x + (-7)y = 13.
To learn more about equations, visit :
brainly.com/question/10413253
#SPJ1
What is the coordinate for midpoint D?
Answer:
B
Step-by-step explanation:
You Basically need to find halfway between 5a and -3 which has a difference of 8 so halfway is 4 so 3a +4=a
and as it is on the same line it would be (a,-2b)
HELP IM GOING TO FAIL
Answer:
23) $248,943.75
24) $384
Step-by-step explanation:
23) 266,250/100= 2662.5 which is 1%
2662.5×6.5=17,306.25 which is 6.5%
Since it is a mark up we subtract 17,306.25 from 266,250 to find the
original price.
24) 320÷10=32 which is 10%
32×2= 64 which is 20%
Since it is a discount we add 64 to 320 to find the original price.
;)
17a^3+19a^3-25a^3-(-17a^3+19a^3-25a^3). PLEASE HELP!!!!!!!
Answer:
34a^3
Step-by-step explanation:
Since every term is alike we can add and subtract freely
(I wont be writing a^3 on every term to make this less confusing)
17 + 19 - 25 - (-17 + 19 - 25)
first the parenthesis do what is inside the parenthesis
17 + 19 - 25 - (-23)
now add everything
11 - (-23)
simplify
11 + 23
34
everything of course has a^3 at the end so
34a^3 is the answer
Multiply. −16√3⋅5√3 Enter your answer by filling in the boxes.
Answer:
-240
Step-by-step explanation:
−16√3⋅5√3
-16(5)√(3*3)
When you multiply numbers with the same radical (in this case square root) the numbers inside the radical can be multipled with each other. The numbers outside (in this case -16 and 5) should also be multiplied with each other.
-16(5)√9
-80√9
-80*3
-240
Point n is located at (3, 5). If point n is translated 3 units right and 2 units down, the new coordinates will be.
The revised coordinates for the indicated site are (6, 3).
Given information;
Location of Point n (3, 5). The new coordinates will be if point n is moved 2 units down and 3 units right.
To get new coordinates we have to transform given points;
Transformation of the coordinate system:
Defining new coordinate systems on the plane frequently involves coordinate transformations. The transformation's u- curves are representations of vertical lines with the form u- constant, while the v- curves are representations of horizontal lines with the form v- constant.
∴ (3, 5) ⇒ (3 + 3, 5 - 2)
⇒ (6, 3)
Hence, (6, 3) are the new coordinates of the given point.
To learn more about coordinate system click here:
brainly.com/question/28571033
#SPJ4
Finding Angle Measures When Parallel Lines Are Cut By a Transversal
Answer:
Below
Step-by-step explanation:
3 6 and 7 = 82 °
1 4 5 8 = 180 - 82 = 98 °
question is on image
The equation of the line that passes through the point (-6, 6) and (-3, 7) is y = 1 / 3 x + 8
How to find equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + c
where
m = slope of the linec = y-interceptHence, the line passes through the point (-6, 6) and (-3, 7)
m = slope = 7 - 6 / -3 + 6
m = 1 / 3
Therefore, the y-intercept of the line can be found using (-6, 6)
y = 1 /3 x + b
6 = 1 / 3 (-6) + b
6 = -2 + b
b = 6 + 2
b = 8
Therefore, the equation of the line is y = 1 / 3 x + 8
learn more on equation of a line here: brainly.com/question/16992545
#SPJ1
the cost of using a parcel service is r dollars for the first 3 pounds and s dollars for each additional pound. which of the following expressions represents the cost, in dollars, of sending a parcel that weighs 9 pounds?
a) r+3s
b) r+6s
c) 3r+6s
d) 3r+9s
e) 9r+9s
Answer:
The correct answer is: c) 3r + 6s
Step-by-step explanation:
the first 3 pounds are always going to be r dollars, then every additional pound will be s dollars.
Since we have a package that weighs 9 pounds; 3 pounds will cost r dollars and 6 pounds wills cost s dollars.
example:
lets say that r = 10 and s = 5
the first 3 pounds will cost 10 dollars and then every pound after would be 5 dollars
so:
3(10) + 6(5)
This is just an example, since we don't know the actual values of r and s, we just use those variables.