The number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3
How to determine the number of real zeros?The equation of the function is given as:
f(x) = x^3 + 4x^2 + x - 6
Expand the function
f(x) = x^3 + 5x^2 - x^2 + 6x - 5x - 6
Reorder the terms of the function
f(x) = x^3 + 5x^2 + 6x - x^2 - 5x - 6
Factor the expression
f(x) = x(x^2 + 5x + 6) -1(x^2 + 5x + 6)
Factor out x -1
f(x) = (x^2 + 5x + 6)(x -1)
Expand
f(x) = (x^2 + 3x + 2x + 6)(x -1)
Factorize
f(x) = [x(x + 3) + 2(x + 3)](x - 1)
Factor out x + 2
f(x) = (x + 3)(x + 2)(x- 1)
The function has been completely factored;
And it has 3 linear factors
Hence, the number of real zeros of the function f(x) = x3 + 4x2 + x − 6 is 3
Read more about functions at:
https://brainly.com/question/7784687
#SPJ1
Question 1 of 10
f(x) = 3x³ - 2x² + 4x - 5
g(x) = 6x - 7
Find (f + g)(x).
Done!
Answer:
[tex](f+g)(x)=3x^3-2x^2+10x-12[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}f(x)=3x^3-2x^2+4x-5\\g(x)=6x-7 \end{cases}[/tex]
[tex]\begin{aligned}(f+g)(x) & = f(x)+g(x)\\& = (3x^3-2x^2+4x-5)+(6x-7)\\& = 3x^3-2x^2+4x-5+6x-7\\& = 3x^3-2x^2+4x+6x-5-7\\& = 3x^3-2x^2+10x-12\end{aligned}[/tex]
With full explanation from the internet like before
3x2-6x+5=0
Answer:
[tex]\sf x=1+i\sqrt{\dfrac{2}{3}} \ \quad and \quad \:x=1-i\sqrt{\dfrac{2}{3}}[/tex]
Explanation:
Given Expression:
3x² - 6x + 5 = 0Use the Quadratic Formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ \ ax^2 + bx + c = 0[/tex]
insert coefficients
[tex]\Longrightarrow \sf x = \dfrac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:3\cdot \:5}}{2\cdot \:3}[/tex]
[tex]\Longrightarrow \sf x = \dfrac{\left6\right\pm \sqrt{-24} }{6}[/tex]
[tex]\Longrightarrow \sf x = \dfrac{\left6\right\pm 2\sqrt{6}i}{6}[/tex]
[tex]\Longrightarrow \sf x =1 \pm i\dfrac{\sqrt{6} }{3}[/tex]
[tex]\Longrightarrow \sf x=1+i\sqrt{\dfrac{2}{3}}, \quad 1-i\sqrt{\dfrac{2}{3}}[/tex]
Use quadratic formula
[tex]\\ \rm\Rrightarrow x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{6\pm \sqrt{36-60}}{6}[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{6\pm\sqrt{-24}}{6}[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{6\pm2\sqrt{6}i}{6}[/tex]
[tex]\\ \rm\Rrightarrow x=1\pm \dfrac{sqrt{2}i}{\sqrt{3}}[/tex]
[tex]\\ \rm\Rrightarrow x=1\pm\sqrt{\dfrac{2}{3}}i[/tex]
find 3 solutions for y=-2x-4
Tasty Goodies Bakery recorded the desserts that were recently sold.
chocolate croissants 1
cookies 1
brownies 10
slices of pie 12
Considering this data, how many of the next 78 desserts sold should you expect to be slices of pie?
slices of pie
Answer:
36
Step-by-step explanation:
possibility of slices of pie is 12/24, = 1/2
78 desserts, how much i expect is slices of pie
78*(1/2) = 36
We should expect about 39 of the next 78 desserts sold to be slices of pie.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Out of 24 desserts sold, 12 were slices of pie.
Therefore, the proportion of slices of pie sold is 12/24 = 1/2.
To estimate the number of slices of pie in the next 78 desserts sold, we can multiply the proportion of slices of the pie by the total number of desserts sold:
(1/2) x 78 = 39
Therefore,
We should expect about 39 of the next 78 desserts sold to be slices of pie.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
ten students in Ashton class were randomly selected and asked how many phone call they made yesterday their answer where 1,0,10,2,9,15,0 and 3 find the mean of the data find the median of the data find the mode of the data find the range of the data
Answer:
Mean = 2.2
Median = 1
Mode = 0 and 1
Range = 9
Step-by-step explanation:
First arrange the number of calls from least to greatest.
0, 0, 0, 1, 1, 1, 2, 3, 5, 9
Mean is the average. Add the numbers together and divide by 10 since there are 10 numbers in total.
0 + 0 + 0 + 1 + 1 + 1 + 2 + 3 + 5 + 9 = 22
22/10 = 2.2
Mean = 2.2
Median is the middle number. Since there is an even amount of numbers, take the 5 and 6 number in the list, add them together and divide by 2. You are taking the average of the two numbers.
0, 0, 0, 1, 1, 1, 2, 3, 5, 9
1 + 1 = 2
2/2 = 1
Median = 1
Mode is the number that occurs the most.
0, 0, 0, 1, 1, 1, 2, 3, 5, 9
In the list the numbers 0 and 1 both occur 3 times.
Mode = 0 and 1
Range is the biggest number (9) minus the smallest number (0).
0, 0, 0, 1, 1, 1, 2, 3, 5, 9
9 - 0 = 9
Range = 9
Find the interquartile range (IQR) of the data in the dot plot below VV
(PLS HELP ME PLSSS)
The interquartile range of the data that is represented on the dot plot is: 2 chocolate chips.
What is the Interquartile Range?Interquartile range (IQR) = upper quartile - lower quartile.
Upper quartile (Q3) = center of the second half of the data = 5
Lower quartile (Q1) = center of the first half of the data = 3
Interquartile range (IQR) = 5 - 3
Interquartile range (IQR) = 2 chocolate chips.
Learn more about the interquartile range on:
https://brainly.com/question/4102829
#SPJ1
Which of the following is an even function?
Of(x) = (x - 1)²
Of(x) = 8x
Of(x)=x²-x
Of(x) = 7
COFFE
Sinte echinat
SUMPARNI
Answer:
Step-by-step explanation:
Please help! I’m really confused on this question
Answer:
noncollinear
Step-by-step explanation:
my guess sorry if im wrong
Jenna is a part-time receptionist at
the dentist's office. Her income last
year was $9,125. Her tax status is
single, she claims one exemption for
herself, and she plans on taking the
standard deduction. What is her
taxable income?
From the information provided, Jenna's taxable income is zero. See the explanation below.
How do you calculate taxable income?The formula for taxable income is given as:
Gross Income Less Standard Deduction.
Since the current effective standard deduction for singles is $12,950 Jenna doesn't need to file a tax return since tax cannot be a negative figure.
it is to be noted that the rate payable for individual single taxpayers in 2022 is $10% up to $10,275.
Learn more about Taxable income at:
https://brainly.com/question/24732919
#SPJ1
Find the mean of the following data. (a) 9, 7, 11, 13, 2, 4, 5, 5 (b) 16, 18, 19, 21, 23, 23, 27, 29, 29, 35 (c) 2.2, 10.2, 14.7, 5.9, 4.9, 11.1, 10.5 (d) 11/4, 21/2, 51/2, 31/4, 21/2
Answer:
a) 7 b) 24 c) 8.5 d) 11.4 (i think)
Step-by-step explanation:
An insurance company estimates that the value of a car depreciates by 20% each year (That also means it retains 80% of its value each year). The company used an exponential function to predict the value of a car, v, as a function of time, t, in years. Part A If the value of a brand new car is $32,000.00. Which expression can the company use to predict the value of the car? I need help plsssss
The expression, the company can use to predict the value of the car is v =32000 (0.8)^t
What is insurance company?The company which provides term life or accidental or death insurance in terms of money when one subjects to any of the conditions.
Given is an insurance company estimates that the value of a car depreciates by 20% each year (That also means it retains 80% of its value each year). The company used an exponential function to predict the value of a car, v, as a function of time, t, in years.
The rate of interest r in percentage = 100 - 20 = 80%
If the value of a brand new car is P =$32,000.00.
The value of car will be
value = P x r^t
v = $32,000 x(0.8)^t
Thus, this is the expression insurance company uses to find the value of car.
Learn more about insurance company.
https://brainly.com/question/16996203
#SPJ1
What is the third quartile of this data set?
20,21,24,25,28,29,35,37,39,42,44
A. 44
B. 29
C. 24
D. 39
Divide.
456 ÷ 7
64 R 1
64 R 2
65 R 1
65 R 2
i need help
Answer:
65 R 1
Step-by-step explanation:
Type the correct answer in the box.
The value of is .
A card is drawn from a deck of 52 cards what is the probability that it is a number 2?
Answer:
Step-by-step explanation:
Remark
The deck is divided into 4 different kinds of cards
clubs
diamonds
Hearts
Spades
Each kind of card has a 2
So there are 4 twos in a standard deck of cards.
Answer:
P(2) = 4/52P(2) = 1/13P(2) = 0.07692Which expressions will help you find the surface area of this right triangular prism? Select all that apply.
38 × 45
1/2 × 36 × 45
45 × 36
1/2 × 36 × 38
Convert MMCMLVII to Hindu-Arabic form
MMCMLVII in Hindu-Arabic is 2957
Counting in Hindu-ArabicThe Hindu-Arabic system uses the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 to count.
Analysis:
MM = 2000
+
CM = 900
+
L = 50
+
VII = 7
MMCMLVII = 2957
Learn more about Hindu-Arabic counting system: brainly.com/question/1542814
#SPJ1
Which of these choices show a pair of equivalent expressions? Check all that apply.
the answer is A.B
I mean the answer is a and b
1.012 - 0.809 +2.75
give me the answer
Answer:
2.953
Step-by-step explanation:
Following the order of operations, work from left to right for addition/subtraction.
Subtraction:
[tex]\begin{array}{r r r r r} ^0\diagup\!\!\!\!1 &. & ^10 & ^0\diagup\!\!\!\!1&^1 2\\ -\quad0&.&8&0&9\\\cline{1-5}0&.&2&0&3\\\cline{1-5} \end{aligned}[/tex]
Addition:
[tex]\begin{array}{r c c c r} 0 & . & 2&0&3\\ + \:\:2 &.& 7 & 5\\\cline{1-5}2&.&9&5&3\\\cline{1-5} \end{aligned}[/tex]
Therefore, the solution is 2.953
Let's see
1.012-0.809+2.752.75 can be written as 2.750
1.012-0.809+2.7500.203+2.7502.953Solve for x
x/8 = 3/5 give your answer as an improper fraction in its simplest form
Answer:
24/5
Step-by-step explanation:
x is 4.8, improper simplified is 24/5
If a tree grew 5 feet in n years, what was the average rate at which the tree grew, in inches per year?
Answer:
0.01
Step-by-step explanation:
so i divided 5 by 365 because 365 days or in a year so 5/365=0.01369863013 and usually just said as 0.01
Hope This Helped
solve the formula for h. B=1hm÷2
Answer:
[tex]\frac{2B}{1m} =h[/tex]
Step-by-step explanation:
[tex]B =\frac{1hm}{2}[/tex]
Multiply both sides by 2.
[tex]2B = 1hm[/tex]
To make h as the subject divide both sides by 1m.
[tex]\frac{2B}{1m} =\frac{1hm}{1m}[/tex]
Therefore,
[tex]\frac{2B}{1m} =h[/tex]
what is the answer here
Answer:
120m²
Step-by-step explanation:
Area¹ = (6*5) = 30*2 surfaces = 60m²
Area² =(6*6) = 36m²
Area of Triangle =(1/2*4*6) = 12* 2 surfaces = 24m²
Total surface area = 60 + 36 + 24 = 120m²
=/120m²
quadrilateral ABCD with angle B of 72 degree, angle C of 130 degrees, angle D of 67 degrees What is the measure of ∠A?
Answer:
[tex]m\angle A = 91^{\circ}[/tex]
Step-by-step explanation:
All angles in a quadrilateral must add up to [tex]360^{\circ}[/tex], so [tex]\angle A + \angle B + \angle C + \angle D = 360^{\circ}[/tex]
We can now solve for [tex]\angle A[/tex] by substituting [tex]\angle B, \angle C, \angle D[/tex] for the correct values.
[tex]\angle A + \angle B + \angle C + \angle D = 360\\\angle A + 72 + 130 + 67 = 360\\\angle A + 269 = 360\\\\\boxed{\angle A = 91^{\circ}}[/tex]
That is the answer
- Kan Academy Advance
Fizer Pharmaceutical paid $78 million on January 2, 2021, for 6 million shares of Carne Cosmetics common stock. The investment represents a 25% interest in the net assets of Carne and gave Fizer the ability to exercise significant influence over Carne’s operations. Fizer received dividends of $2 per share on December 21, 2021, and Carne reported net income of $28 million for the year ended December 31, 2021. The fair value of Carne’s common stock at December 31, 2021, was $28.50 per share.
The book value of Carne's net assets was $192 million.
The fair value of Carne's depreciable assets exceeded their book value by $48 million. These assets had an average remaining useful life of twelve years.
The remainder of the excess of the cost of the investment over the book value of net assets purchased was attributable to goodwill.
Prepare the appropriate journal entries related to the investment during 2021. (If no entry is required for a transaction/event, select "No journal entry required" in the first account field. Enter your answers in millions, (i.e., 10,000,000 should be entered as 10).)
The appropriate journal entries related to the investment during 2021 is: Debit Investment in Carne shares $78 million; Credit Cash $78 million.
Journal entriesJanuary 2, 2021
Debit Investment in Carne shares $78 million
Credit Cash $78 million
January 12, 2021
Debit Cash $12,000,000
($2 per shares x 6,000,000)
Credit Investment in Carne shares $12,000,000
December 21, 2021
Debit Investment in Carne shares $7,000,000
Credit Investment revenue $7,000,000
(25% x $28,000,000)
December 31, 2021
Debit Investment revenue $1,000,000
Credit Investment in Carne shares $1,000,000
[25% x ($48,000,000 ÷ 12 years)]
December 31, 2021
No journal entry for changes in fair value when using equity method.
Therefore the appropriate journal entries related to the investment during 2021 is: Debit Investment in Carne shares $78 million; Credit Cash $78 million.
Lear more about journal entries here:https://brainly.com/question/14279491
#SPJ1
This is for a test please answer
Answer:
25 = b
26 = c
Step-by-step explanation:
YOOOOO ITS MY LAST DAY OF SCHOOL HAVE SOME POINTS :D
AYEEE SAME WOOOO!!! HOPE YOU'RE HAVING A GREAT DAY :D
1. Desde el pie de un edificio se observa la parte superior de una torre con un ángulo de elevación de 45°. Desde la azotea del mismo edificio se observa la cúspide de la torre con un ángulo de depresión de 60°. El edificio es 20 m. más alto que la torre. Determinar ambas alturas.
Por razones trigonométricas, encontramos que las alturas de la torre y el edificio son de aproximadamente 11.548 metros y 31.548 metros, respectivamente.
¿Cómo determinar la altura de dos edificios?
En esta pregunta debemos utilizar conceptos de trigonometría para determinar la altura de los dos edificios. A continuación, tenemos las siguientes expresiones trigonométricas:
Diferencia entre las alturas del edificio y el torre
20 = r₁ · sin 60°
r₁ ≈ 23.094 m
Ahora determinamos el valor de r₂ mediante identidades trigonométricas:
r₂ = r₁ · (cos 60°/cos 45°)
r₂ = (23.094 m) · (cos 60°/cos 45°)
r₂ ≈ 16.330 m
Finalmente, obtenemos las alturas de cada edificio:
Torre
h = (16.330 m) · sin 45°
h ≈ 11.548 m
Edificio
h' = h + 20 m
h' = 11.548 m + 20 m
h' = 31.548 m
Por razones trigonométricas, encontramos que las alturas de la torre y el edificio son de aproximadamente 11.548 metros y 31.548 metros, respectivamente.
Para aprender más sobre razones trigonométricas: https://brainly.com/question/6904750
#SPJ1
A is the amount you pay for the purchase of a house that decreases the amount of the loan.
-closing payment
-closing cost
-origination payment
-down payment
The statement that completes the definition is (d) down payment
How to complete the definition?From the question, we have the following highlights:
The payment decreases the amount of loanThe payment is used for purchaseWhen a part payment is made to procure an item, the part payment is referred to as a down payment
The down payment fits the highlights (1) and (2) stated above
Hence, the statement that completes the definition is (d) down payment
Read more about down payment at:
https://brainly.com/question/1698287
#SPJ1
What is the spread of the data?
:...
58 59 60 61 62 63 64 65 66 67
Number of people who ride
the morning ferry
OA. 59 to 61 people
OB. 59 to 64 people
OC. 61 to 64 people
OD. 58 to 67 people