Answer:
A polynomial function f of least degree = f = x³ - 7x² + 36
The function in standard form = f = x³ - 7x² + 36
Step-by-step explanation:
As given, Leading coefficient of polynomial function = 1
Also given, zeroes of the function = -2, 3, 6
for root -2 : (x - (-2)) = (x + 2)
for root 3 : ( x - 3)
for root 6 : (x - 6)
Therefore, the polynomial function becomes -
f = 1(x+2)(x-3)(x-6)
⇒f = (x+2)(x² - 6x - 3x + 18)
⇒f = (x+2)(x² - 9x + 18)
⇒f = x³ - 9x² + 18x + 2x² - 18x + 36
⇒f = x³ - 7x² + 36
The polynomial function in standard form is [tex]f(x) = x^3 - 8x^2 +9x +18[/tex]
The zeros of the polynomial are given as:
[tex]Zeroes = -2,3,6[/tex]
Rewrite as:
[tex]x= -2,3,6[/tex]
Express the zeroes as an equation
[tex]x= -2[/tex], [tex]x =3[/tex] and [tex]x =6[/tex]
Equate to 0
[tex]x + 2 = 0[/tex], [tex]x -3 = 0[/tex] and [tex]x -6 = 0[/tex]
Multiply the equations
[tex](x + 1) \times (x - 3) \times (x - 6) = 0 \times 0 \times 0[/tex]
[tex](x + 1) \times (x - 3) \times (x - 6) = 0[/tex]
Expand
[tex](x^2 - 3x + x - 3) \times (x - 6) = 0[/tex]
[tex](x^2 - 2x - 3) \times (x - 6) = 0[/tex]
Expand
[tex]x^3 - 2x^2 - 3x -6x^2 +12x +18 = 0[/tex]
Collect like terms
[tex]x^3 - 2x^2 -6x^2 - 3x +12x +18 = 0[/tex]
[tex]x^3 - 8x^2 +9x +18 = 0[/tex]
Express as a function
[tex]f(x) = x^3 - 8x^2 +9x +18[/tex]
Hence, the function in standard form is [tex]f(x) = x^3 - 8x^2 +9x +18[/tex]
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What is the multiplicative rate of change of the
function?
Answer:
the multiplicative rate of change for the exponential change is 3
Step-by-step explanation:
Find each difference.
• (-5) – 6 =
.
35 – (-8) =
.
43 - (-1) =
Answer:
1=1
2=43
3=44
Step-by-step explanation:
the subtraction negative and the negative in the parentheses make a positive so instead of subtracting them you add them together
When completely factored, 8x + 2y - 4
Answer:...
-4+8x+2xy
Step-by-step explanation:
50 POINTS!!!!!!! WILL GET BRAINLIEST IF CORRECT!!!!!
Answer:
43
Step-by-step explanation:
give me stuff thats equivalent to 2/10
plz
i dont know my mafs
ACTON
Find the Percentage, Rate Of Base
1. What is 25% of 1258
Answer:________
2. 50 is what percent of 4502
Answer:________
3. 75 is 30% of what number?
Answer:________
Answer:
314.5
2252.5
250
Step-by-step explanation:
write an equation of a line in point slope form that has a slope of 1/4 and passes through the point (-1, -8)
Point-slope formula: y-y1=m(x-x1)
To fill it in, m is our slope, 1/4. y1 is -8 and x1 is -1.
y+8= 1/4(x+1) This is the formula filled in. If you noticed, the (-) signs that were in the formula changed to (+). This is because (- -) can be changed into (+).
y+8=1/4x+0.25
y=1/4x+8.25
Your answer is y=1/4x+8.25
I hope this was helpful :) please consider giving me brainliest
I need help please.
Answer:
5
Step-by-step explanation:
if you write a long list:111122333344555555566666677777888 you can see the number that occurs the most is 5.
A group of workers can plant 2/5 acres in 7/8 days. What is the unit rate in acres per day?
Four angles are shown below. Recall that an angle completing a full rotation measures 2π radians.

Angle A represents ____ of a full rotation.
Therefore, Angle A has a measure of___ radians.
Angle B represents___ of a full rotation.
Therefore, Angle B has a measure of ____ radians.
Angle C represents____ of a full rotation.
Therefore, Angle C has a measure of ___radians.
Angle D represents_____ of a full rotation.
Therefore, Angle D has a measure of ___radians.
Answer:
Step-by-step explanation: Angle A is 45 degrees so it represents 1/8 of a rotation. so it has a measure π/4 rads. Angle B is 90 degrees so it represent 1/4 of a rotation. so it has a measure of π/2 rads. Angle C represents 180 degrees so that represent 1/2 of a rotation so it has a measure of π rads. Angle D is 270 degrees so it represents 3/4 of a rotation . Therefore, Angle D has a measure of 6π/4.
The for angle A 1/8 and π/4, for angle B 1/4 and π/2, for angle C 1/2 and π, and for angle D 3/4 and 6π/4.
What is an angle?The measurement between the two lines is called an "Angle" when the two lines or rays converge at a common location.
From the figure attached:
Angle A represents 1/8 of a full rotation. Therefore, Angle A has a measure of π/4 radians.
Angle B represents 1/4 of a full rotation. Therefore, Angle B has a measure of π/2 radians.
Angle C represents 1/2 of a full rotation. Therefore, Angle C has a measure of π radians.
Angle D represents 3/4 of a full rotation. Therefore, Angle D has a measure of 6π/4 radians.
Thus, the for angle A 1/8 and π/4, for angle B 1/4 and π/2, for angle C 1/2 and π, and for angle D 3/4 and 6π/4.
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Answer this pleaseee !!
Answer:
D.
Step-by-step explanation:
m<F = m<B - Corresponding Angles Theorem
m<B + m<A = 180 - Adjacent Angles Theorem
180 - 105 = m<A
75 = m<A; therefore, m<A = 75.
Answer:
D.
Step-by-step explanation:
Because F and C are consecutive angles, they add up to 180°. So 180-105=75. Angle C is 75, which makes B wrong. After finding that C is 75°, then you use the verticle angles theorem to show that angle A is 75°. Hope this helps you.
Solve for r.
5r - -17r - 4r + -9 = 9
Answer:
r=1
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
5r−−17r−4r−9=9
5r+17r+−4r+−9=9
(5r+17r+−4r)+(−9)=9(Combine Like Terms)
18r+−9=9
18r−9=9
Step 2: Add 9 to both sides.
18r−9+9=9+9
18r=18
Step 3: Divide both sides by 18.
18r/18 = 18/18
r=1
Exercise 1.10.4: Mathematical statements into logical statements with nested quantifiers. info About Translate each of the following English statements into logical expressions. The domain is the set of all real numbers. (a) There are two numbers whose ratio is less than 1. (b) The reciprocal of every positive number is also positive. (c) There are two numbers whose sum is equal to their product. (d) The ratio of every two positive numbers is also positive. (e) The reciprocal of every positive number less than one is greater than one. (f) There is no smallest number. (g) Every number other than 0 has a multiplicative inverse. (h) Every number other than 0 has a unique multiplicative inverse.
Answer:
З x,y : ( x/y < 1, y/x < 1 )
Step-by-step explanation:
This is a bit somehow, I really do hope it doesn't confuse you. Here's your solution.
The domain in this question is one with a set of all real numbers. These real numbers needs the logical expressions of the English statements to be expressed with respect to real number. And so we're having
A) З x,y : ( x/y < 1, y/x < 1 )
B) ∀ Y : ( Y > 0 = 1/Y > 0 )
C) з x,y : ( x+y = xy )
D) ∀ x,y : [ ( x>0 ) ∧( y > 0 ) = (( x/y > 0 ) ∧ ( y/x > 0 ))
E ) ∀ y : [ ( y > 0 ) ∧ ( y < 1) = ( 1 / y > 1 )
F) n ( ( з x ∀ y ( x <y ) )
G) ∀x (( x ≠ 0 ) = ( зy ( xy = 1 ) ))
H) ∀x ( (x≠0) = ( з! y (xy = 1))
solve the following problem. round to one decimal place if necessary. if your answer is correct you will see an image appear on your screen
Answer:
theres no picture
Step-by-step explanation:
What should you do first to simplify 8 + (2 x 5) ?
Answer:
18
Step-by-step explanation:
8+(2)(5)
=18
Answer:
18
Step-by-step explanation:
8 + (2×5)
=8 + 10
= 18
hope this will help you ☺✌
a car is 180inches long. a truck is 75% longer then the car. how long is the truck?
Answer:
135 in.
Step-by-step explanation:
Need help on question hurry
Answer: C
Step-by-step explanation: it is c trust me
Courtney walks 5 laps around 1/4 mile track. how far does she walk?
Answer:
1 1/4 miles
Step-by-step explanation:
you need the previous answer to tell how to do the answer. "1232". Now that that's over with, onto the question.
The baker’s recipe for a loaf of bread calls for 12 ounces of flour. If he uses all of his flour to make loaves of bread, how many full loaves can he bake in two weeks?
Answer:
Step-by-step explanation:
1232 oz flour × (1 loaf)/(12 oz flour) = 102 loaves remainder 8 oz flour
what law of exponent is shown by (4³)⁴ = 4¹²
If FGH ~ KJH, find FH.
The required length of FH is obtained as 64.68.
What is the criteria for similarity of two triangles?Two triangles are said to be similar when either the ratio of their corresponding sides are equal or all the corresponding angles are equal.
Two similar triangles are the same in shape but not in size.
The given diagram shows two similar triangles as ΔFGH and ΔKJH.
Since the ratios of the corresponding sides of the two triangles are equal, the following equation can be written for the given case as,
(x + 8)/32 = (4x - 25)/52
=> 52(x + 8) = 32(4x - 25)
=> 52x - 128x = -32 × 25 - 52 × 8
=> -76x = -1716
=> x = 22.42
Thus FH = 4x - 25 = 4 × 22.42 - 25 = 64.68
Hence, the length of FH for the given case is 64.68.
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A 118° sector of a circle has an area of 75 square centimeters. To the nearest centimeter, what is the diameter of the circle?
please simplify- e⁵×e⁴
Answer:
e3x
Step-by-step explanation:
25% of 200. Find the percentage of the number
Answer:
50
Step-by-step explanation:
0.25 * 200 = 50
25% of 200 is 50
Answer:
50
Step-by-step explanation:
25% of 100 is 25 so add another 100 so u have to add 25
Each card in a set of cards has a different number from 1 to 12 written
on it. A student randomly chooses a card, records the number shown
on the card, and replaces the card. The table shows the results of the
student choosing a card 25 times.
Based on the data in the table, how
many of the next 125 cards the
student chooses could be expected
to have a number shown on the card
that is a multiple of 4?
Results
Answer: 35
Step-by-step explanation: i first divided 12 and 125 since there is 125 cards in total and 12 different cards which gives you 10 point something. There is 3 multiples of 4 so i multiplied 3x10 which gives you 30 and the closest answer is 35. You're welcome
Answer:
35
Step-by-step explanation:
got it right
7(-9a-3)-2a please help
Answer:
-65a -21 "that is the simplified version"
Answer:
-65a - 21
Step-by-step explanation:
7 ( -9a - 3 ) -2a
Distribute, multiply every term in the parenthesis by the term right outside of the parenthesis,
7 ( -9a - 3 ) - 2a
-63a - 21 - 2a
Simplify
-65a - 21
find the height of the cylinder if the volume is 340, and the length is 3
Answer:
113
Step-by-step explanation:
divide the volume with the length
The United States government wanted to determine what proportion of Americans approve of the current President so they conducted a survey of 2,000 randomly chosen Americans. Assume that the true proportion of Americans who approve of the president is 0.46. Determine what the mean and the standard deviation of the sampling distribution of the sample proportion would be. Round to 2 decimal places when necessary. The mean of the sampling distribution is .43 and the standard deviation of the sampling distribution is .05 .
Answer:
The mean of the sampling distribution is 0.46
The standard deviation of the sampling distribution is 0.01
Step-by-step explanation:
We use the central limit theorem to solve this question:
Central Limit Theorem
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.46, n = 2000[/tex]
So
Mean: [tex]\mu = p = 0.46[/tex]
Standard deviation: [tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.46*0.54}{2000}} = 0.01[/tex]
The mean of the sampling distribution is 0.46
The standard deviation of the sampling distribution is 0.01
The mean and the standard deviation of the sampling distribution of the sample proportion are 0.46 and 0.01 respectively
Proportion and standard deviation
The formula for calculating the standard deviation for a sample proportion is given as:
[tex]\sigma =\sqrt{\frac{p(1-p)}{n} }[/tex]
p is the proportionn is the sample sizeNote that p = mean = 0.46
To get the standard deviation:
[tex]\sigma =\sqrt{\frac{0.46(1-0.46)}{2000} }\\\sigma =\sqrt{\frac{0.46(0.54)}{2000} }\\\sigma = 0.01[/tex]
Hence the mean and the standard deviation of the sampling distribution of the sample proportion are 0.46 and 0.01 respectively.
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Mark has already earned money for mowing lawns over the summer when he takes a job at the local grocery store, earning $9.50 per hour. After working 16 hours at the grocery store, Mark has earned a total of $292. Write a linear equation to represent the amount of money m that Mark has earned this summer after working h hours at the grocery store.
Step-by-step explanation:
M=9.5 (16,292)
(y=mx+b)
292=9.5(16)+b
The linear equation m = 9.50 h + 140 represents the amount of money m that Mark has earned this summer after working h hours at the grocery store.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
Mark takes a job at the local grocery store, earning $9.50 per hour.
After working 16 hours at the grocery store, he earned a total of $292.
As per the given question, we can see points (16, 292)
Here earning $9.50 per hour can represent a slope of a linear function
Thus, M = 9.5 (16, 292)
The standard linear equation is given by,
⇒ m = Mx+b ....(i)
Substitute the values in the above equation,
292 = 9.5(16) + b
b = 292 - 152
b = 140
Substitute the value b = 140 in the equation(i),
⇒ m = 9.50 h + 140
Thus, the linear equation m = 9.50 h + 140 represents the amount of money.
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What are the dimensions of a 2x4x8
Answer: Many of you know this, but why is this a thing? You don't go to Subway and pay for a $5-footlong expecting to get 11 inches (although many of you will argue this is the case). And it's not just a 2x4: A 1x4 is actually ¾ inches by 3-½ inches; a 4x4 is actually 3-½ inches by 3-½ inches.
Step-by-step explanation:
If you are asking what they equal up too, your answer is 16
If this isn't, please correct me and I will give you a better answer