Answers
The factor form of the cubic equation y = x³ + 3 · x² + x + 3 is y = (x² + 1) · (x + 3).
How to factor a cubic equation
In this problem we find a cubic equation, that is, a polynomial of the form:
y = a · x³ + b · x² + c · x + d
Where a, b, c, d are the real coefficients of the polynomial. Herein we must use algebra properties to find the factor form of the expression:
y = a · Π (x - rₙ) for n = {1, 2, 3, ..., m - 1, m}
Where:
a - Lead coefficient.m - Grade of the polynomial.First, write the entire equation:
y = x³ + 3 · x² + x + 3
Second, use distributive property of real mumbers:
y = x² · (x + 3) + 1 · (x + 3)
Third, use distributive property of real numbers once again:
y = (x² + 1) · (x + 3)
To learn more on factoring polynomials: https://brainly.com/question/26354419
#SPJ1
Related Questions
HELP
Q1: e + -10.67 + 553⅝² - e × 8⅘⁴
Q2: 95⅚⁵ + -8⅚ + 1⅜
Q3: e⁸ + ⅓² × π × π³
Q4: φ⁸ ÷ 80 - 1⅗ + -108⅔
Answers
Answer:
Step-by-step explanation:
3
If f(x)=2x+1 and g(x)=x−5, find f(x)+g(x) to complete the polynomial
Answers
Answer:
[tex]\huge\boxed{\sf 3x -4}[/tex]
Step-by-step explanation:
Given functions:f(x) = 2x + 1g(x) = x - 5Add both equations.
f(x) + g(x):= 2x + 1 + x - 5
Combine like terms
= 2x + x + 1 - 5
= 3x - 4[tex]\rule[225]{225}{2}[/tex]
Answer:
f(x) + g(x) = 3x - 4
Step-by-step explanation:
The problem is,
→ f(x) + g(x)
Let's solve the problem,
→ f(x) + g(x)
→ (2x + 1) + (x - 5)
→ 2x + 1 + x - 5
→ (2x + x) + (1 - 5)
→ 3x +(-4)
→ 3x - 4
Hence, answer is 3x - 4.
At a local restaurant, Tony earns $12.50 per hour with a 13% deduction for taxes and social security. His
overall earnings are modeled by the expression, 12.5-0.13(12.5x), where a represents the number of
hours Tony worked.
Tony deposits 38% of his overall wages into his savings account. How many hours will he need to work to save
$1,000?
Answers
The total number of hours Tony will he need to work to save amount $1,000 is 242 hours.
Explain the term deductions on salary?Payroll deductions are sums of money taken out of an employee's overall pay to cover taxes, garnishments, and perks like health insurance. Income tax may be one of these with holdings, which make up the difference in gross pay or net pay. tax on social security.The given data for the question is-
Tony makes $12.50 per hour at a nearby restaurant after a 13% tax and social security deduction.The equation 12.5x - 0.13(12.5x), where an is the total number of hours Tony worked, is used to model his overall earnings.38% of Tony's total pay goes into the savings account.Thus,
38%(12.5x - 0.13(12.5x)) = 1000
0.38(10.875x) = 1000
x = 2631.57/10.875
x = 241.98
x = 242
Thus, total number of hours Tony will he need to work to save
$1,000 is 242 hours.
To know more about the deductions on salary, here
https://brainly.com/question/25267964
#SPJ1
Which graph represents the solution to the inequality −0.96 is greater than or equal to the product of a number and 0.3?
number line with closed circle on point negative 9.3 and arrow shaded to the right
number line with open circle on point negative 9.9 and arrow shaded to the left
number line with closed circle on point negative 3.2 and arrow shaded to the left
number line with closed circle on point negative 3.2 and arrow shaded to the right
Answers
The graph that represents the solution to the inequality −0.96 is greater than or equal to the product of a number and 0.3 number line with a closed circle on point negative 3.2 and arrow shaded to the left
What is the graph?Generally, To solve this inequality, we can start by multiplying both sides by the reciprocal of 0.3, which is 3. Doing so gives us the inequality:
−0.96 * 3 >= x * 0.3 * 3
Simplifying the right side gives us:
−0.96 * 3 >= x * 0.9
Then we can simplify both sides further:
−2.88 >= x * 0.9
Dividing both sides by 0.9 gives us:
−3.2 >= x
The solution to this inequality is all values of x that are less than or equal to -3.2.
The graph of this inequality would be a number line with a solid dot at -3.2, and a solid line extending to the left of -3.2, as shown below:
(graph with number line and solid dot at -3.2, and solid line extending to the left)
This graph represents the solution to inequality.
Read more about inequality
https://brainly.com/question/28823603
#SPJ1
Sam buys 10 tickets for $5
Sam spends $135 at fundraiser
S=
Answers
When Sam buys 10 tickets for $135 at fundraiser, the amount for each ticket will be $13.50.
How to illustrate the equation?It should be noted that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, Sam buys 10 tickets for $135 at fundraiser, the amount for each ticket will be:
= $135 / 10
=$13.50
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
Complete question
Sam buys 10 tickets for $135 at fundraiser. Calculate the amount for each ticket.
Select all of the following that are quadratic functions.
x=3y²-6y+5
y+3=-2x2+5
y=2x2−8x+6
y=-7x-4
y-3x=4x³-x² +9
y = 5 x(x +9)-8
y-2x²=3x-2x²+4
DONE
Answers
Step-by-step explanation:
For this select the function with the leading term with the power of 2
1 and 6 are the only quadratic function ( BECAUSE THEY ONLY HAVE FUNCTION WITH GREATEST POWER OF 2)
1/5(4x-2.5)=5(0.4+10)+3 1/3
Answers
The Value of x is 69.78 per given equation.
1/5(4x-2.5) = 5(0.4+10)+3 1/3
0.2(4x-2.5) = 5(0.4+10)+3.33
0.2(4x-2.5) = 5(10.4)+3.33
0.2(4x-2.5) = 52 + 3.33
0.2(4x-2.5)=55.33
4x-2.5 = 276.33
4x = 276.33+2.5
4x = 279.15
x = 69.78
So, the value of x is 69.78
To learn more about other example:
https://brainly.com/question/5055224?referrer=searchResults
When we reject the null and the null is true, we have a made a _________ __________.
Answers
When we reject the null and the null is true, we have a made a TYPE 1 ERROR
A null hypothesis is either true or false. Unfortunately, we do not know which is the case, and we almost never will. It is important to realize that there is no probability that the null hypothesis is true or that it is false, because there is no element of chance. For example, if you are testing whether a potential mine has a greater gold concentration than that of a break-even mine, the null hypothesis that your potential mine has a gold concentration no greater than a break-even mine is either true or it is false; you just don’t know which. There is no probability associated with these two cases (in a frequentist sense) because the gold is already in the ground, and as a result there is no possibility for chance because everything is already set.
To learn more about Type 1 error
https://brainly.com/question/29707785
#SPJ4
Using a given zero to write a polynomial as a product of linear factors: Real zeros
For the polynomial below, -1 is a zero.
g(x)=x³ + 3x² - 7x − 3
Express g(x) as a product of linear factors.
g(x) =
Answers
We can not write the polynomial g(x) as a product of linear factors.
What is polynomial?
Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents (No division operation by a variable).
Given:
g(x)=x³ + 3x² - 7x − 3 and x = -1 is a zero of g(x).
Since, if x = a is a zero of the polynomial then (x - a) is a factor of polynomial.
Here (x - (-1)) = (x + 1) is a factor of g(x).
First to check x = -1 is a zero of polynomial or not.
Plug x = -1 in g(x).
g(-1) = (-1)^3 + 3(-1)^2 - 7(-1) - 3
g(-1) = -1 + 3+ 7 - 3
g(-1) = 6
g(-1) ≠ 0
Hence, we can not write the polynomial g(x) as a product of linear factors.
To know more about polynomial, click on the link
https://brainly.com/question/2833285
#SPJ1
Two similar triangles have perimeters in the ratio of 2:7. The smaller
triangle has sides measuring 6 inches, 7 inches, and 8 inches. How long, in
inches, is the longest side of the larger triangle?
A) 18
B) 21
C) 28
D) 56
E) 74
Answers
Do the expressions (-2)(3) and (2)(-3) have the same value? Show your thinking .
Answers
(-x)(y) = -xy
(x)(-y) = -xy
Until this happens:
(-x)(-y) = xy
To qualify for the next marathon, a runner's time must be less than 314 hours. Indicate whether or not each runner will qualify for the next marathon.
who will qualify?
Answers
Answer:
(It's weird how I answered this question for someone else 12 minutes ago.)
There was no data provided but due to simple research i have conducted the following data
Qualifiers are in bold, italics and underlined.
Step-by-step explanations:
Chio- 3 1/5
Kevin- 3.2
Ojas- 3 8/30
Sydney- 3 13/60
Qualifiers: Chico, Kevin
let me know if this is incorrect data
What is an angle that is supplementary to BGD
Answers
Answer:
DGE and BGA
Step-by-step explanation:
Supplementary angles are two angles whose measures add up to 180°
so BGD + DGE = 180 or BGD + BGA = 180
so both DGE and BGA are supplementary to BGD
Whitch ones correct
A b c or d
Answers
Answer:
A. y = -1/2 x + 3/2
Step-by-step explanation:
An x-intercept of 3 means point (3, 0).
The line passes through points (3, 0) and (-5, 4).
y = mx + b
m = (4 - 0)/(-5 - 3) = 4/(-8) = -1/2
y = -1/2 x + b
0 = -1/2 × 3 + b
b = 3/2
y = -1/2 x + 3/2
In the following expression, both A and B are variables that can take positive values.
(A+7)*2^B
Which of these actions will cause the expression's value to increase?
Choose 2 answers:
Answers
Answer:
its 3/5 and 9/5
Step-by-step explanation:
HOPE IT HELP :D
Question is attached
Answers
A2=ar^2=1•3^2=9
A3=ar^3=1•3^3=27
Option D} none of the above
Answer:
D) None of the above------------------------------------
Let the numbers be:
1, x, y, z, 81Geometric means give us:
y² = 1*81 ⇒ y = 9Then:
y² = xz ⇒ xz = 81Given options give us:
A) 3*21 = 63 ≠ 81;B) 3*18 = 54 ≠ 81;C) Same as option A (must be a typo);Since all the above options are false, the answer is option D.
Name the slope and one point or
y-1=2(x+3)
Q
(__)
=_
m=
Answers
y=2x+7
i.e m= +2
Answer: M=2
y-intercept = (0,7)
x-intercept = (-7/2,0)
Step-by-step explanation:
The slope is already given in the equation, which is 2
M=2
y-intercept = (0,7)
x-intercept = (-7/2,0)
1 For 7-8, given two sides of a triangle, find a range of possible lengths for the third side 7. 4 cm, 17 cm 8. 24 ft , 52 ft
Answers
The range of possible lengths for the third side is [16.52,17.46] for 1st part and [46.13,57.27] for 2nd.
What is pythagoras theorem?
The Pythagorean theorem or Pythagoras' theorem could be a elementary relation in parabolic geometry between the 3 sides of a trigon.
Main Body:
To find range of possible lengths for the third side , we will use Pythagoras theorem : a²+b² = c²
7. 4 cm, 17 cm
4²+17²=c²
16+289=c²
305=c²
To undo the square you have to square root so
√ 305 =17.46
OR
17² = 4²+b²
289 -16 =b²
b = √273 = 16.52
range of possible lengths for the third side is [16.52,17.46]
8. 24 ft , 52 ft
24² =576
52² =2704
2704+576=3280
√3280 =57.27
OR
52² = 24²+b²
b²= 2704-576
b=√2128
b = 46.13
range of possible lengths for the third side is [46.13,57.27]
Hence the range of third side is found out.
To know more about Pythagoras theorem , visit:
https://brainly.com/question/231802
#SPJ1
Mackenzie ha ome red, yellow and blue marble. She ha 3200 more red marble than yellow marble. She ha 3840 more blue than yellow. She give 1490 blue marble away. How many more red marble than blue marble doe he have left?
Answers
We know that there are 850 more red marbles left than blue marbles by solving equations.
What are equations?The equals sign is used in mathematical equations to indicate that two expressions are equal.
An equation is a claim that demonstrates the equality of two mathematical expressions, according to algebra.
For instance, the word "equal" separates the formulas 3x + 5 and 14, which together form the equation 3x + 5 = 14.
So, a number of red marbles more than blue marbles is:
Mackenzie has 3200 more red than yellow marbles.
y + 3200 = r
Additionally, she has 3840 more blue than yellow marbles.
y + 3840 = b
Assume Mackenzie has one yellow marble, then.
1 + 3200 = 3201 red marbles
1 +3840 = 3841 blue marbles
She will have left over 2351 blue marbles after giving away 1490
3841 - 1490 = 2351
She now has 3201 red marbles and 2351 blue marbles.
r - b =?
3201 - 2351 = 850
Therefore, we know that there are 850 more red marbles left than blue marbles by solving equations.
Know more about equations here:
brainly.com/question/28937794
#SPJ4
Samon opened a bank account with 1. 25% imple interet. The total amount of interet Samon will earn after 20 year i $812. 50. What i the interet for one year?
Answers
162.5 is the simple interest for one year.
What does the term "simple interest" mean?
The principal of a loan or the initial deposit into a savings account serves as the foundation for simple interest.
Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
P = $812.50
T = 1 Year
S.I. = ?
R = 20
According to question,
S.I. = P * R* T/100
= 812.50 * 20 * 1/100
= 16250/100
= 162.5
Learn more about Simple interest
brainly.com/question/25845758
#SPJ4
your recipe for oatmeal cookies calls for 3 pounds 3 ounces of oats, you have a 25 pound bag. how many times can you make this recipe?
Answers
We can make 19 oatmeal cookies from the bag.
1 pound = 16 ounces
for making a single unit of oatmeal cookie it uses 21 ounces of oats.
We have 25 pound of oats in the bag which means we have 25 X 16 which is equal to 400 ounces of oats in the bag .
To find how much of oatmeal cookies can be made we have to divide the total amount of oats available in the bag divided by the number of ounces required in making of the single unit of oatmeal .
Therefore,
= 400 / 21
= 19.047
Which means 19 overall pieces of oatmeal can be prepared in the 25 pound of oats bag
To know more about weight conversion
https://brainly.com/question/17059091
#SPJ4
Noah is going to invest in an account paying an interest rate of 7% compounded continuously. How much would Noah need to invest, to the nearest hundred dollars, for the value of the account to reach $12,900 in 10 years?
Answers
The amount of money that Noah needs to invest would be = $ 6,558
What is interest rate?An interest rate is defined as the rate at which an individual receives an interest on an invested funds over a stipulated period of time.
The interest rate (R) = 7% = 0.07 (decimal form)
The time for the investment (T) = 10 years.
The present value of the account (A) = $12,900
n compounding frequency = 1
Using the formula;
A = P (1 +r/n) ^nt
12,900 = P ( 1 + 0.07) ^ 10
12,900 = P (1.07) ^10
12,900 =P 1.96715
P = 12,900/1.96715
P =$ 6,558
Learn more about simple interest here:
https://brainly.com/question/25793394
#SPJ1
What is the value of 9+21(13+5)? 287 395 387 540
Answers
The answer is C. 387
Step-by-step explanation:
9+21(13+5)
First do what is in parentheses:
9+21(13+5)
=9+21(18)
Next do 21(18) or 21 x 18:
9+21(18)
=9+378
The last step is to add:
9+378=387
The answer is C. 387
suppose we have trained 10 different models on the exact same training data, and magically, they all achieve 95% precision. is there any possibility these models could all be combined to achieve better performance? if so, how? if not, why?
Answers
If you train 10 distinct models on the same training data, try integrating them into a voting ensemble, which will eventually produce better results.
what is voting ensemble ?Voting is an ensemble technique for making predictions by combining the results of various models. The predictive performance of an ensemble is better than that of a single predictive model in a predictive modeling issue. This is accomplished by the model adding bias, which lowers the variance component of the prediction error
calculation
Voting ensembles frequently produce even better results, so try combining them.
The models should differ greatly for it to operate. 95 percent accuracy.
We will therefore get better results if we combine them.
If you train 10 distinct models on the same training data, try integrating them into a voting ensemble, which will eventually produce better results.
To know more about voting ensemble visit :-
https://brainly.com/question/18364291
#SPJ4
Answer for brainlist and hearts 19 points and show every step
Answers
To view the representation of graph of check the attached image.
What is called graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
Given that ;
Stewart's overdue assignment = 36
Per day he complete 4 overdue assignments.
To find : In how many days he complete all the overdue assignments
To complete 36 overdue assignments = 36/4
= 9 days
Therefore, In 9 days he complete all the overdue assignments
To learn more about graph check the given link
brainly.com/question/19040584
#SPJ1
help pleaseee dlkwekemmwnd right now
Answers
By using the property of congruency of triangles,
[tex]\angle[/tex]Y [tex]\cong[/tex] [tex]\angle[/tex]X has been proved
What is congruency of triangles?
Two triangles are said to be congruent if the corrosponding angles are equal and the corrosponding sides are equal.
There are different axioms of congruency. They are
SSS axiom, SAS axiom, AAS axiom, ASA axiom, RHS axiom
Z is the midpoint of XY [Given]
WZ [tex]\perp[/tex] XY [Given]
[tex]\angle[/tex]WZX [tex]\cong \angle[/tex]WZY [90° each]
XZ [tex]\cong[/tex] YZ [Z is the midpoint of XY]
WZ [tex]\cong[/tex] WZ [Reflexive property of congruency]
[tex]\Delta[/tex] WXZ [tex]\cong \Delta[/tex] WYZ [SAS axiom]
[tex]\angle[/tex]Y [tex]\cong[/tex] [tex]\angle[/tex]X [Corrosponding parts of congruent triangles are congruent]
To learn more about congruency of triangles, refer to the link-
https://brainly.com/question/2938476
#SPJ1
A science club has 13 members. The club bought b bumper stickers to split among its members. Write an expression that shows how many bumper stickers each member will get.
Answers
Answer: b/13
Step-by-step explanation:
Divide b by 13 to get b/13
pls help due now!!!!!!!!!!!
Answers
Answer:
B. x = 3
Step-by-step explanation:
3³ = 27
3 · 3 · 3 = 27
9 · 3 = 27
Take square root of both
X=3
Brainly pls
a student scores 68 on a geography test and a 249 on a mathematics test. the geography test has a mean of 80 and a standard deviation of 10. the mathematics test has a mean of 300 and a standard deviation of 34. if the data in both tests are distributed equally, which test did the student do better one?
Answers
The student did better in the test of Geography.
What is Standard Deviation ?The standard deviation is a measure of the amount of variation or dispersion of a set of values.
To solve this question, we will use the z-score formula to find the w test in which the student scored better. The z-score formula is;
z = (x - μ)/σ
Now, for Geography we have given :
Test score (x) = 68
Mean (μ) = 80
Standard deviation (σ) = 10
Thus, the z-score here will be :
z = (68 - 80)/10
z = -1.2
Similarly, for Mathematics we have given :
Test score (x) = 249
Mean (μ) = 300
Standard deviation (σ) = 34
Thus, the z-score here will be :
z = (249 - 300)/34
z = -1.5
Since the z-score for Geography is less than that of Mathematics, thus, we can conclude that the Geography test is the one in which the student scored better.
To learn more about Standard Deviation visit :
https://brainly.com/question/16985548
#SPJ4
Section
B
Determine whether the ordered pair
on the graph.
lies
1) (-3, 4): y = -2x +1
2) (2, 9): y = 6x-3
3) (4,3): 2x-5y = -7
4) (-5, 6): -8x +4y=10
5) (-1,0): -4y = 2x +3
6) (0₁-2): 6y=x+3
Answers
(4,3): 2x-5y = -7 is the ordered pair on the graph lies.
Define ordered pair.An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it can be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers. The coordinates of one point in the coordinate system are included in an ordered pair. An ordered pair of the form of a point's name is (x, y). The x-coordinate is represented by the first integer, and the y-coordinate by the second. You must place a dot at the coordinates of the ordered pair in order to graph a point.
Given
We enter the values of the variables into each equation to see if an ordered pair is a solution to the system of two equations. The ordered pair is the system's solution if it makes both equations true.
For this,
(4,3): 2x-5y = -7
Equating values,
2(4) - 5(3)
8 -15
-7
(4,3): 2x-5y = -7 is the ordered pair on the graph lies.
To learn more about ordered pair, visit:
https://brainly.com/question/28874341
#SPJ1