Multiplying a trinomial by a trinomial follows the same steps as multiplying a binomial by a trinomial. Determine the degree and maximum possible number of terms for the product of these trinomials: (x2 + x + 2)(x2 – 2x + 3). Explain how you arrived at your answer.
Answers
The product of the given trinomials will have a degree of 4, and since there are 9 terms, the maximum possible number of terms for the product is 9.egree of 4 and a maximum possible number of terms of 9.
When multiplying two polynomials, the degree of the resulting polynomial is the sum of the degrees of the two polynomials being multiplied.
In this case, both trinomials have a degree of 2.
The maximum possible number of terms in the product of two polynomials is the product of the number of terms in each polynomial.
For the first trinomial, there are 3 terms, and for the second trinomial, there are also 3 terms.
Multiplying these together gives a maximum possible number of terms of 9.
To arrive at this conclusion, you can use the distributive property, where each term in the first trinomial is multiplied by each term in the second trinomial, resulting in a total of 9 possible term combinations.
Therefore, the product of the two trinomials will have a dTo multiply two trinomials, like [tex]\( (x^2 + x + 2)(x^2 - 2x + 3) \)[/tex], you apply the distributive property repeatedly, multiplying each term in the first trinomial by each term in the second trinomial and then summing up the products.
Each term in the first trinomial needs to be multiplied by each term in the second trinomial, resulting in a total of [tex]\( 3 \times 3 = 9 \)[/tex] products.
Now, regarding the degree, when you multiply two polynomials, you add the degrees of the polynomials.
Here, both polynomials are of degree 2, so the resulting polynomial will be of degree 2 + 2 = 4.
Thus, the product of the given trinomials will have a degree of 4, and since there are 9 terms, the maximum possible number of terms for the product is 9.egree of 4 and a maximum possible number of terms of 9.
Related Questions
Given than line a is parallel to line b and that line c is parallel to line d, if m<13=(12x-22) & m<14=(9x-29), find m<2.
a 65
b 70
c 85
d 110
Answers
12x-22+9x-29=180
21x-51=180
x=11
m<2=m<14
m<2=70°
The measure of ∠2 is 70° .
What is corresponding angles?The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other and are equal in measure.
What is supplementary angles angles?When the sum of two angles is 180°, then the angles are known as supplementary angles. In other words, if two angles add up, to form a straight angle, then those angles are referred to as supplementary angles.
According to the question
line a is parallel to line b and c and d are transversal for them
line c is parallel to line d and a and b are transversal for them
m∠13 = (12x - 22)°
m∠14 = (9x - 29)°
Now
As, ∠13 and ∠14 forms supplementary angles .
i.e
m∠13 + m∠14 = 180°
12x - 22° + 9x - 29° = 180°
21x - 51° = 180°
21x = 180° + 51 °
21x = 231 °
x = 11°
So,
m∠13 = 12*11 - 22° = 110°
m∠14 = 9*11 - 29° = 70°
Now,
according to corresponding angles
m∠14 = m∠6 = m∠2 = 70°
Hence, the measure of ∠2 is 70° .
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Below are the functions of y = |x| and y = |x| – 3. How are the functions related?
a. The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is –3.
b. The functions have the same shape.
c. The y-intercept of y = |x| is 0, and the y-intercept of the second function is –3.
d. The functions have the same y-intercept.
Answers
Hope this helps u!!!
Let f(x)=x^3-7x^2+25x-39 and let g be the inverse function of f. What is the value of g'(0)? ...?
Answers
Below are the choices that can be found from other sources:
a) -1/25
b) 1/25
c) 1/10
d) 10
e) 25
f(x) = x^3 - 7x^2 + 25x - 39
f'(x) = 3x^2 - 14x + 25
Since g is the inverse function of f
f(g(x)) = x
Differentiate both sides of equation
f'(g(x)) g'(x) = 1
Now f(3) = 0, so g(0) = 3
g'(x) = 1 / f'(g(x))
g'(0) = 1 / f'(g(0))
g'(0) = 1 / f'(3)
g'(0) = 1 / 10
the form of a linear equation that shows the slope and one point is the...? ...?
Answers
Equations in point-slope form look like this: y - k = m(x - h) where m is the slope of the line and (h, k) is a point on the line (any point works). To write an equation in point-slope form, given a graph of that equation, first determine the slopeby picking two points.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
The form of a linear equation that shows the slope and one point is known as the point-slope form, which is written as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.
The form of a linear equation that shows the slope and one point is known as the point-slope form. Unlike the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept, the point-slope form is typically written as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.
For example, if you are given a slope of 3 and a point (2, 5), the equation of the line in point-slope form would be y - 5 = 3(x - 2). To visualize this, consider a line graph with the x-axis as the horizontal axis and the y-axis as the vertical axis.
If this was plotted, the line would rise 3 units on the vertical axis for every 1 unit it rises on the horizontal axis, illustrating the concept of slope as the rise over run, which is consistent along the entire length of a straight line.
Which ordered pairs are solutions to the inequality y − 4x ≤ −6?
Select each correct answer.
A.(1, 3)
B. (−2, −14)
C. (−1, −9)
D. (3, 5)
E. (0, −5)
Answers
The order pair given is (1, 3)
y-4x = 3-4(1) = -1
-1 is greater than -6
Therefore, this choice is wrong
Choice b:
The order pair given is (-2, -14)
y-4x = -14-4(-2) = -6
-6 is equal -6
Therefore, this choice is correct
Choice c:
The order pair given is (-1, -9)
y-4x = -9-4(-1) = -5
-5 is greater than -6
Therefore, this choice is wrong
Choice d:
The order pair given is (3, 5)
y-4x = 5-4(3) = -7
-7 is less than -6
Therefore, this choice is correct
Choice e:
The order pair given is (0, -5)
y-4x = -5-4(0) = -5
-5 is greater than -6
Therefore, this choice is wrong
Answer
b and d
Step-by-step explanation:
Evie was doing a science fair project by surveying her biology class. She found that of the 30 students in the class, 15 had brown hair and 17 had blue eyes and 6 had neither brown hair nor blues eyes. Determine the number of students who had brown hair and blue eyes.
Answers
Write five and three eights as an improper fraction and as a mixed number
Answers
43/8 (improper fraction)
5.375 (decimal)
Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina’s solution?
a. The cost of electricity is $0.17 per unit.
B. The cost of natural gas is $0.20 per unit.
C. The cost of electricity is $0.72 per unit.
D. The cost of natural gas is $0.83 per unit.
Answers
Answer:
The correct option is D. The cost of natural gas is $0.83 per unit.
Step-by-step explanation:
Consider the provided equation.
[tex]116y = 96.28[/tex]
We need to solve the above equation for y.
Divide both the sides by 116.
[tex]\frac{116y}{116} = \frac{96.28}{116}[/tex]
[tex]y=0.83[/tex]
Now consider the provided options.
Hence, the correct option is D. The cost of natural gas is $0.83 per unit.
Tony invested $5,500 in a four-year CD that paid 4.8% interest, but later needed to withdraw $475 early. If the CD’s penalty for early withdrawal was three months’ worth of interest on the amount withdrawn, how much of a penalty did Tony pay?
a.
$5.70
b.
$22.80
c.
$60.30
d.
$66.00
Answers
Answer:
It's A-$5.70 :))))
Step-by-step explanation:
The penalty will be $5.70 which corresponds to option A.
The question is about calculating the penalty for early withdrawal from a Certificate of Deposit (CD). Tony invested $5,500 in a CD at a 4.8% interest rate and withdrew $475 early.
To calculate the penalty, we first need to find three months' worth of interest on the amount withdrawn.
The annual interest on $475 at 4.8% is:
Interest = Principal × Rate × Time
Interest = $475 × 0.048 × 1 = $22.80
Since the penalty is three months' worth, we divide the annual interest by 4 (because there are four 3-month periods in a year):
Penalty = $22.80 / 4
= $5.70
What decimal is represented by this expanded form? 5 x 10,000 3 x 1,000 2 x 10 8 x 1 6 1/1,000 4 x 1/,000?
Answers
An equation that sets two fractions equal to each other is called a ____.
Answers
Final answer:
An equation that sets two fractions equal to each other is known as a proportion, where equivalent ratios or fractions indicate the same value. This maintains the equality governed by the rules of algebra, important when performing operations on both sides of an equation.
Explanation:
An equation that sets two fractions equal to each other is called a proportion. This type of equation indicates that two ratios or fractions are equivalent. For example, if we have ½ on one side of the equation and 2/4 on the other, we have a proportion because both fractions represent the same amount.
When we have fractions with the same value in the numerator and the denominator, such as ¹¹/₁₀⁰ for micrometers to meters, we can simplify this to 1 because the quantities cancel each other out. This is true by the rules of algebra, specifically the property that if we perform the same operation on both sides of an equality, the equation remains balanced. This concept is crucial when working with proportions and equations involving fractions.
It's also important to remember that when adding fractions, they must have a common denominator. Ratios and percentages are other forms of expressing relative sizes or amounts which can also be related back to fraction and proportion concepts.
Which answer describes the type of sequence?
3, 4, 5, 6, ...
A. neither arithmetic nor geometric
B. geometric
C. arithmetic
Answers
Valerie drives to and from work 5 days a week. the distance from her home to work is 6 miles. over the course of 5 days, her car uses 1/4 of a tank of gas.
Answers
Sara is burdened with debt and runs the risk of defaulting on her car loan. She is also late with her credit card payments. What action should Sara take to help her situation?
Answers
how to solve 4m+6p-8mp
Answers
Final answer:
The provided algebraic expression 4m+6p-8mp cannot be solved or simplified further without additional context, such as specific values for m and p or instructions for solving for one variable in terms of the other.
Explanation:
The original question, "how to solve 4m+6p-8mp", seems to be a request for simplification or to apply given values to an algebraic expression. Without specific values or instructions to solve for one of the variables, the expression cannot be "solved" in the conventional sense of finding a numerical answer. However, we can explore quick ways to simplify or rearrange such an expression if additional context or information were provided, such as values for m and p or instructions on solving for one variable in terms of the other.
if x>2, then x^2-a-6 / x^2-4=
Answers
We have to factorize the numerator and the denominator:
x² - x - 6 = x² - 3 x + 2 x - 6 = x ( x - 3 ) + 2 ( x - 3 ) = ( x - 3 ) ( x + 2 )
x ² - 4 = ( x - 2 ) ( x + 2 )
[tex] \frac{(x-3)(x+2)}{(x-2)(x+2)}= \frac{x-3}{x-2} [/tex]
WILL UPVOTE
what is the value of x in the following equation: 3x-15=4x+36
A.21
B.-51
C.-21
D.none of these
Answers
3x = 4x + 51
-x = 51
x = -51
________________________________________
Explanation:
________________________________________
Given: 3x − 15 = 4x + 36 ; Solve for "x" .
________________________________________
Let us subtract: "3x" from EACH side of the equation; AND
add: "15 to EACH side of the equation:
__________________________________________
→ 3x − 15 − 3x + 15 = 4x + 36 − 3x + 15 ;
__________________________________________
to get:
__________________________________________
→ 0 = x + 51 ;
___________________________________
→ Subtract "51" from EACH side of the equation; to isolate "x" on one side of the equation; and to solve for "x" ;
___________________________________
→ 0 − 51 = x + 51 − 51 ;
__________________________
→ - 51 = x ; ↔ x = - 51 ; which is: "Answer choice: [B]: -51".
___________________________________
→ Now, let us check our answer, "x = -51 ; by plugging in "-51" for "x" in the original equation, and seeing in both sides of the equation hold true when x = - 51 ;
______________________________
→ Given: 3x − 15 = 4x + 36 ;
→ Substitute "- 51 for "x" ;
→ Start with the "left-hand side" of the equation:
→ 3x − 15 = (3*-51) − 15 = -153 − 15 = -168 ; when x = -51 ;
→ Then, let us examine the "right-hand side" of the equation:
__________________________________________
→ 4x + 36 ; Substitute "-51" for "x" ;
→ (4*-51) + 36 = -204 + 36 = -168
→ Does the "left hand side" of equation = the "right-hand side of the equation" when: x = -51???
______________________________
→ That is, when x = -51, does: - 168 =? -168 ?? Yes!
_________________________
how do you round 17.92 to the tens
Answers
∧ ∧ this is the ones place
this is the tens place
if the ones place is lower then 5 you keep the tens the same. if the ones place is higher then 5 you round the tens place up one. so the answer is 17.90
A sports store donates basketballs and soccer balls to the boys and girls club. The ratio of basketballs to soccer balls is 7 : 6. The store donates 24 soccer balls. How many basketballs does the store donate?
Answers
To answer the above question, if the store donates 24 soccer balls the number of basketballs does the store donate is 28 basketballs
Answer:
Step-by-step explanation:
First you have to know that you if you divide 24 by 6 you would have to take 7 multiplied by 4 to get 28
What is bigger 5/6 or 13/18?
Answers
6 goes into 18 three times. If we multiply (5/6) by 3 on top and bottom you get
[tex]\frac{15}{18} [/tex]
Now we can compare numerators, since 15 > 13
[tex]\frac{5}{6} \ \textgreater \ \frac{13}{18}[/tex]
Use the area model to find the product of 28×32
Answers
List 12 spherical objects that would be around the home. Please do not list all balls, soccer ball, basket ball, etc.
Answers
If the function has jump discontinuity , infinite discontinuity , continuous , or the function has point discontinuity
X^3 + 7x^2 + 10x / x + 5
Answers
f(x) = x(x+5)(x+2) / (x+5)
f(x) = x(x+2)
The function is continuous everywhere/ in any domain.
The function x^3 + 7x^2 + 10x / (x + 5) is discontinuous at x = -5, where it has a jump discontinuity. The function is otherwise continuous and does not approach infinity, indicating no infinite discontinuity.
Explanation:The given function is x^3 + 7x^2 + 10x / (x + 5). To determine the continuity of the function, it's crucial to identify any values of x that would make the denominator zero since the function is undefined at these points.
In this case, if x is -5, the denominator will be zero, making the function undefined. Therefore, the function has a point of discontinuity or a jump discontinuity at x = -5.
The function does not have an infinite discontinuity because it never approaches infinity as x approaches any particular value. This function is continuous at every point except for x = -5. Therefore, "the function x^3 + 7x^2 + 10x / (x + 5) has one point of discontinuity at x = -5."
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Dan put's 11 dollars or his allowance in his savings account every week. how much money will he have affter 15 weeks
Answers
You multiply 11 and 15 in order to get your answer.
Hope this helps..
How do I convert 4/5 to a percent
Answers
= 80%
=0.8
Which of the following polynomials does not have real roots?
A. x2 - 17x - 7
B. -x4 + 4x2 + 6
C. x4 + 2x2 + 2
D. 2x2 - 13 ...?
Answers
proof
if a is a (real) is a root of x4 + 2x2 + 2, so
a4 +a2 +2 =0, it is impossible, because a4>0, a2>0 and 2>0
a4 +a2 +2 must be >0, so x4 + 2x2 + 2 doesnt have real roots
Answer:
C.
Step-by-step explanation:
x4 + 2x2 + 2 has no real roots
(Distribute , then simplify the remaining expression. Final answer must be in standard form) Please help !!
Answer correct for a brainliest and also a thanks ! Don't answer if you don't know it .
Answers
[tex]4x^2(2x^2+x-5) - x(x^3+5x^2-3) + 17[/tex]
[tex]4x^2(2x^2)+4x^2(x)+4x^2(-5) - x(x^3)-x(5x^2)-x(-3) + 17[/tex]
[tex]8x^4+4x^3-20x^2 - x^4-5x^3+3x + 17[/tex]
[tex]7x^4-x^3-20x^2+3x + 17[/tex]
So the final simplified answer to problem 22 is
[tex]7x^4-x^3-20x^2+3x + 17[/tex]
--------------------------------
Problem 23
[tex]-2x(x^3-6x^2+6)+4x^3-(5x^4+10x)[/tex]
[tex]-2x(x^3)-2x(-6x^2)-2x(6)+4x^3-(5x^4)-(10x)[/tex]
[tex]-2x^4+12x^3-12x+4x^3-5x^4-10x[/tex]
[tex]-7x^4+16x^3-22x[/tex]
So problem 23 simplifies to
[tex]-7x^4+16x^3-22x[/tex]
---------------------------------------------------------
Problem 24
[tex]4b[2a^2-5(3ab-2b^2)]+29ab^2[/tex]
[tex]4b[2a^2-5(3ab)-5(-2b^2)]+29ab^2[/tex]
[tex]4b[2a^2-15ab+10b^2]+29ab^2[/tex]
[tex]4b[2a^2]+4b[-15ab]+4b[10b^2]+29ab^2[/tex]
[tex]8a^2b-60ab^2+40b^3+29ab^2[/tex]
[tex]8a^2b-31ab^2+40b^3[/tex]
So problem 24 simplifies to
[tex]8a^2b-31ab^2+40b^3[/tex]
-------------------------------------------------
Problem 25
[tex]2y(6x-4x^2y)+13x^2y^2-6[/tex]
[tex]2y(6x)+2y(-4x^2y)+13x^2y^2-6[/tex]
[tex]12xy-8x^2y^2+13x^2y^2-6[/tex]
[tex]12xy+5x^2y^2-6[/tex]
The final answer for problem 25 is
[tex]12xy+5x^2y^2-6[/tex]
Clark Kent walks 3 miles west and then 4 miles north. How far is it for Superman to fly in a straight line back to his starting point? (It makes a right triangle.)
Question 16 options:
3 miles
5 miles
7 miles
9 miles
Answers
For this problem, a = 3, b = 4
c = √(3² + 4²) = √5² = 5
A statement we accept without proof is called a:
theorem
definition
postulate
term
Answers
For postulates, no evidence/proof is needed. It is always believed to be true.
Answer:
C. Postulate.
Step-by-step explanation:
We are asked to find the term that defines the given statement.
Theorem: We know that a theorem is proved by a chain of reasoning. Ir is not self evident.
Definition: We know that definition is a statement of the exact meaning of a word.
Postulate: We know that a postulate is a statement that is taken to be true without any proofs, therefore, postulate is the correct choice.
water flows from a faucet at a rate of 5 liters every 25 seconds. At this rate, how much water will flow form the faucet in 45 seconds. Make a table.