Answers
Answer:
The variable that has the highest power is considered to be the degree of polynomials in an algebraic equation.
A column:
1) [tex]4x^3[/tex] .
The degree is 3.
2)[tex]x^2+4[/tex].
The degree is 2.
3) [tex]x-2[/tex]
The degree is 1.
B column:
1) [tex]2x^2+1[/tex]
The degree is 2.
2) [tex]x^2-x[/tex]
The degree is 2.
3) [tex]x^3-5x^2+1[/tex]
The degree is 3.
A×B columns:
While Multiplying two terms in a equation, if the variables are same then multiply the constant value and sum the exponent value.
1) [tex](4x^3)(2x^2+1)[/tex].
=[tex]8x^5+4x^3.[/tex]
The degree is 5.
2) [tex](x^2+4)(x^2-x)[/tex].
=[tex]x^4-x^3+4x^2-4x[/tex].
The degree is 4.
3) [tex](x-2)(x^3-5x^2+1)[/tex].
[tex]=x^4-5x^3+x-2x^3+15x^2-3.\\=x^4-7x^3+15x^2+x-3.[/tex]
The degree is 4.
Related Questions
An irregular polygon is shown below:
The area of the irregular polygon is
square units.
Answers
Answer:
15 units²
Step-by-step explanation:
The figure is composed of 2 rectangles.
The rectangle on the left has
A = 4 × 3 = 12 units²
The rectangle on the right has
A = (3 - 2) × (7 - 4) = 1 × 3 = 3 units²
Thus area of figure = 12 + 3 = 15 units²
To find the area of an irregular polygon, divide it into regular shapes and sum their areas. The area of a square is simple: side length squared. When scaling, areas of similar shapes increase by the square of the scaling factor.
Explanation:Understanding Area CalculationTo calculate the area of an irregular polygon, we often need to divide it into regular shapes such as triangles, rectangles, or squares. Once we do that, we can calculate the area of each shape and then sum all the areas to find the total area of the irregular polygon. For instance, if an irregular shape fits within a square of side a, its area is less than a² based on the premise that the area of a circle inscribed in a square is smaller than the square's area yet larger than half. For a square, the calculation is relatively straightforward with the formula for area being side length squared (a²).
Calculating the area becomes even more important when applied to real-life examples, such as surveying land parcels which can have highly irregular outlines. The concept is similar to understanding the relationship between the area of a square and its side length when measuring larger plots of land like a state or a carpet on a house's blueprint. We use scales or conversion factors to translate a drawn measurement to actual size.
The comparison of areas can also be seen in the example where Marta's larger square's area is four times that of the smaller one because areas of similar shapes scale by the square of the scaling factor (in this case, 2).
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Expand to write an equivalent expression: -1/4(8x+12y
Answers
Answer:
-1/4(8x+12y)=-2x-3y
The expanded equivalent expression of -1/4(8x+12y) is -2x - 3y.
Explanation:The given mathematical expression is: -1/4(8x+12y). To expand and simplify this expression, we need to apply the distributive property of multiplication over addition, which means we multiply -1/4 with both 8x and 12y separately. So, the first step would be -1/4 * 8x which becomes -2x. Doing the same for the second term, -1/4 * 12y, the result will be -3y. Therefore, the equivalent expanded expression becomes
-2x - 3y
.
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Please show the steps to-
Julie has 81 pieces of jewelry.
She has twice as many earrings as she has necklaces.
Answers
Julie has 27 necklaces and 54 earrings.
Let's assume Julie has x necklaces. Since she has twice as many earrings as necklaces, she would have 2x earrings.
We know that Julie has a total of 81 pieces of jewelry, which includes both necklaces and earrings. Therefore, we can set up a system of equations to represent the given situation:
Equation 1: x + 2x = 81
In Equation 1, we add the number of necklaces (x) and the number of earrings (2x) together, resulting in 81, which is the total number of pieces of jewelry Julie has.
Now, we can solve Equation 1 to find the value of x:
3x = 81
x = 81 / 3
x = 27
So, Julie has 27 necklaces.
To find the number of earrings she has, we can substitute the value of x back into the equation:
2x = 2 * 27
2x = 54
Thus, Julie has 54 earrings.
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Complete Question:
julie has 81 pieces of jewelry. she has twice as many earrings as she has necklaces How many of each does julie have? Write a system of equations for the situation. (two seperate equations ). find the solution.
Final answer:
Using basic algebra, Julie has 27 necklaces and 54 earrings. We found this by setting up the equation 2N + N = 81, solving for N (number of necklaces), and then multiplying by 2 to get the number of earrings.
Explanation:
The student's question regarding Julie's 81 pieces of jewelry can be solved using basic algebra. We know that the number of earrings is twice the number of necklaces. Let's define the following:
Earrings (E) = 2NNecklaces (N) = NTotal jewelry (T) = E + NWe're given that T = 81, so we can substitute E with 2N to get the equation:
2N + N = 813N = 81N = 27Hence, Julie has 27 necklaces. Now we can find the number of earrings:
E = 2NE = 2 * 27E = 54Therefore, Julie has 54 earrings and 27 necklaces.
If the dilation is given: triangle ABC->Triangle ¨A¨B¨C under do.2 which of the following is the scale factor.
Answers
Answer:0.5
Step-by-step explanation:
EASY MATH 10 PTS + BRAINLIEST
If (6^2)^p = 6^10, what is the value of p?
a. 2
b. 3
c. 4
d. 5
Answers
Answer:
d. 5
Step-by-step explanation:
What is 3(x+3)+7x= ?
Answers
Answer:10x+9
Step-by-step explanation:
First you have to multipy the 3 into the parenthesis using distributive property.
After that you get 3x+9+7x.
Then you get 10x+9 because you can only combine like terms
B. Factor the polynomial 64x + 27y. If the
polynomial cannot be factored, write prime.
Answers
Answer:
PRIME
Step-by-step explanation:
the GCF of 64 and 27 is 1
>therefore the polynomial is already factored and can’t be factored further.
The first equation in the following system gives the
company's cost of making x purses. The second
equation gives the company's income for selling x
purses.
What are the solutions to the system of
equations?
(-23,400, 3,400) and (-1,170, 170)
(-1,170, -23,400) and (170, 3,400)
(274, 726) and (5,480, 14,520)
(274, 5,480) and (726, 14,520)
DONE
y=-0.01(x - 500)2 + 4.489
y = 20x
You used substitution to obtain the equation
0 = -0.01x2-10x+1,989 from the system
Intro
Answers
Answer:
option 2: (-1,170, -23,400) and (170, 3,400)
Step-by-step explanation:
correct answer for e2020
Answer:
B. (-1,170, -23,400) and (170, 3,400)
Step-by-step explanation:
100 points What scale factor was applied to the first rectangle to get the resulting image?
Enter your answer as a decimal in the box.
A rectangle with a short side of 6. An arrow points to a smaller rectangle with a short side of 1.5
Answers
Answer:
0.25
Step-by-step explanation:
Scale factor = ratio of the sides
Assuming the first rectangle is with shorter side 6,
Scale factor = 1.5/6 = 15/60 = 1/4 = 0.25
Divide the new length by the original length:
The arrow points from 6 to 1.5, so the new length is 1.5 and the original length was 6.
1.5 / 6 = 0.25. The scale factor was 0.25
How do you write 0.35 as a fraction in simplest form
Answers
Answer:It equals -7/20 because Here's how to convert 0.35 to a fraction... There is not much that can be done to figure out how to write 0.35 as a fraction, except to literally use what the decimal portion of your number, the .35, means. Since there are 2 digits in 35, the very last digit is the "100th" decimal place. So we can just say that .35 is the same as -35/100. The fraction -35/100 is not reduced to lowest terms. We can reduce this fraction to lowest terms by dividing both the numerator and denominator by 5. Why divide by 5? 5 is the Greatest Common Divisor (GCD) or Greatest Common Factor (GCF) of the numbers 35 and 100.
So, this fraction reduced to lowest terms is -7/20.
So your final answer is: 0.35 can be written as the fraction -7/20
Hope this helps... Plz mark me brainliest if the answer is correct... Stay safe and have a great weekend!!! :D
The sum of a number and two is equal to negative seven. Translate this sentence to an equation and then find the number.
-5
5
-9
9
Answers
Answer:
-9 is correct
Step-by-step explanation:
Answer:
-9
Step-by-step explanation:
<3
identity of survey, this is for math, can i get an explanation?
Answers
Answer:
Third statement: convenience sampling.Explanation:
The student used convenience sampling.
The population of the study is the entire population of students of the school.
Since it is time consuming to survey all the students, the high school volunteer student needs to survey a sample.
A systematic random sample would have used a procedure, algorithm, method (a system) to select a random sample. This is not what the student did, thus the first option is incorrect.
A voluntary sampling consits of volunteer people who agree to take part in the study and answer the survey. This isn't either how the sample was choosen, thus the second option is also incorrect.
A convenience sample is when the sample is chosen for the researcher's ease, i.e. convenience. In this case, the student decided to survey only members of his class instead of selecting a representative sample of all the classes. This sample is not random, since not every member of the population has equal chances to be chosen, but it is easy for the student to survey a group that is very close to him. Hence, the third statement is correct.
The was not an statrified sampling (fourth choice), since statrified sampling consists in creating different groups and chosing some members from every group. This is not what the researcher did.
Two angles are supplementary. If one angle measures 56 degrees, what is the measure of the second angle? A. 34 degrees B. 44 degrees C. 114 degrees D. 124 degrees
Answers
Supplementary angles add up to 180 degrees. If one angle measures 56 degrees, the other supplementary angle equals 180-56 which equals 124 degrees. So, the second angle measures 124 degrees.
Explanation:Supplementary angles are two angles that add up to 180 degrees. Therefore, if one of these angles measures 56 degrees, the other one must be the value that when added to 56 completes 180. We can find it by using the formula for supplementary angles: angle B = 180 - angle A.
So, to find the measure of the second angle, we subtract the measure of the first angle (56 degrees) from 180 degrees.
Angle B = 180° - 56° = 124°.
Therefore, the second angle measures 124 degrees (Choice D).
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PLEASE HELP ASAP PLEASE PLEASE PLEASE
Graph the solution to the scenario by dragging and dropping a circle/arrow onto the number line.
The roots of Billy's plant grew to 3 inches beneath Earth’s surface. Graph all the possible depths the roots can continue to grow.
Answers
Answer:
i am taking the test now and its going left on negative 3 open circle
Step-by-step explanation:
if angle B is two more than three times the measure of angle C, and angle B are
complementary angles, find each angle measure.
Answers
Set up a system of equations:
B=2+3C
B+C=90
The variable B is already solved, so plug into bottom equation:
2+3C+C=90
2+4C=90
4C=88
C=22
Plug C back in:
B+22=90
B=68
So B is 68 degrees and C is 22 degrees
Hope this helped!
Carl and Tamera want to compare tests in math class. They have taken six tests. Should they use the mean, median or mode to compare their scores? Explain your choice.
Answers
Answer:
Mean
Step-by-step explanation:
Ⓗⓘ ⓣⓗⓔⓡⓔ
Well, if they use the mean to compare their scores, it is basically just averaging them. If they each average their own scores, they can see who did better!
(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥
how do you simply this expression (x+2)-(1x-2)-12x
Answers
Answer:
4-12X
Step-by-step explanation:
Expression: (x+2)-(1x-2)-12x
First step: x+2-1x+2-12x
Second step: (2+2)+(x-1x-12x)
Third step: 4-12X
How do you Change 56/8 into a mixed number
Answers
The population of a city is currently 1500. It is expected to triple every
- years. Find the population after 30 years.
Answers
Answer:
135000
Step-by-step explanation:
1500 x 3 x 30
so u start out with ur number u have now then u multiply that by 3 because it triples every year and it askes the population in 30 years so its 1500x3x30 = 135000 ur welcome
Please hurry! (include graph for both)
1: Graph h(x)=2sin(2x)−3 . Use 3.14 for π .
2: Graph g(x)=4cos(2x)−2 . Use 3.14 for π .
Answers
See the graphs below
Explanation:FOR GRAPH 1:
Let's take:
[tex]f(x)=sin(x)[/tex]
Let's transform this function as follows:
Step 1. Horizontal compression by 1/2:
[tex]f(x)=sin(2x)[/tex]
Step 2. Vertical stretch:
[tex]f_{1}(x)=2sin(2x)[/tex]
Step 3. Vertical shifting 3 units down
[tex]f_{2}(x)=2sin(2x)-3[/tex]
Finally:
[tex]h(x)=f_{2}(x)=2sin(2x)−3[/tex]
The graph is shown in the First Figure below.
FOR GRAPH 2:
Applying a similar method we get:
Step 1. Horizontal compressionStep 2. Vertical stretchStep 3. Vertical shifting
The graph is shown in the Second Figure below.
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To graph h(x) = 2sin(2x) - 3 and g(x) = 4cos(2x) - 2, multiply the sine and cosine functions by 2 and 4 for amplitude, adjust the period by halving it due to the 2x factor, and shift vertically by -3 and -2 respectively.
Explanation:To graph h(x) = 2sin(2x) - 3 and g(x) = 4cos(2x) - 2, you can follow these steps:
Plot the basic sin(x) and cos(x) functions, remembering that for sine, the maximum and minimum values are 1 and -1, and the function starts at 0. For cosine, the function starts at its maximum value of 1.Multiply the sine and cosine values by their respective coefficients, 2 for h(x) and 4 for g(x), to stretch the amplitude accordingly.Incorporate the period change by understanding that the coefficient 2 in front of x will make the functions complete their cycles twice as fast, effectively halving the period to π instead of 2π.Finally, shift each graph vertically by the constants -3 for h(x) and -2 for g(x).The resulting graphs will show sine and cosine waves with adjusted amplitudes, periods, and vertical shifts. Remember to use 3.14 as an approximation for π to determine the x-values where key points like maxima, minima, and intercepts occur.
What does x equal in 10x=6x-12
Answers
Ben, Tracy, and Tran spent a total of $15 to go skating, they each rented skates at the park for n dollars.
Answers
The problem involves an algebraic expression where Ben, Tracy, and Tran each spend an equal amount, n, on skate rentals that total $15. By setting up an equation, we solve for n, which is $5 per person. This concept is related to understanding budget constraints in financial decision-making.
The student's question about Ben, Tracy, and Tran spending a total of $15 to go skating where they each rented skates for n dollars pertains to algebraic expressions and equations, which is a mathematics concept commonly explored in college-level courses. If we assume that each of them paid an equal amount for the skate rental, represented by n, then we can express the total cost as 3n because there are three individuals.
Given that the total cost was $15, we can set up an equation: 3n = $15. To find the cost of renting skates per person, we solve for n by dividing both sides of the equation by 3, resulting in n = $5. Therefore, each person paid $5 to rent the skates.
Understanding how to solve this problem helps in grasping the concept of budget constraints, as seen in the example of Janet Bain who must decide how to allocate a limited budget of $250 for activities such as skiing and horseback riding. This topic relates to the decision-making processes regarding spending within the constraints of a budget, which is essential in both personal and organizational finance.
what is 29/4 simplyfied?
Answers
Answer:
7 and 1/4 or 7.25
Step-by-step explanation:
28/4 = 7
1/4 = 0.25
7 + 0.25 = 7.25
Answer:
[tex]\frac{29}{4}[/tex] or [tex]7\frac{1}{4}[/tex]
Step-by-step explanation:
29/4 is the most simplified it can get, if you want it as a mixed fraction then it is 7 1/4.
6. 4x + 2y = 16
| 5x - 2y = 38
Answers
Answer:
2y-2y=0
9x=54
x=54/9
x=6
Dude is making 12 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $9 per pound and almonds cost $5.25 per pound. How many pounds of macadamia nuts and how many pounds of almonds should dude use for the mixture to cost $7.75 per pound to make
Answers
Number of pounds of macadamia nuts is 8 pounds and number of pounds of almonds is 4 pounds.
Step-by-step explanation:
Step 1:
Given total pounds of mixture = 12 pounds, cost of macadamia nuts per pound = $9, cost of almonds per pound = $5.25, total cost of mixture per pound = $7.75.
Let number of pounds of macadamia nuts be x and number of pounds of almonds be 12-x.
Step 2:
Form an equation using the above information.
⇒ 9x + 5.25 (12-x) = 12 × 7.75
⇒ 9x + 63 - 5.25x = 93
⇒ 9x - 5.25x = 30
⇒ 3.75x = 30
⇒ x = 8
Number of macadamia nuts is 8 pounds.
Step 3:
Calculate number pounds of almonds
⇒ Number of pounds of almonds = 12 - x = 4 pounds.
Which situation is an example of an observational study?
a.) Having a randomly selected group of students take a pen and paper test and comparing the results with another randomly selected group of students who took the same test on the computer?
b.) Polling voters about their favorite candidates in upcoming elections.
c.) Recording the reaction time of participants in a study who were asked to press a button as soon as they see a certain picture on a screen.
d.) Asking kids in a kindergarten classroom about the average number of pieces of fruit they eat each day.
Answers
Answer:
Step-by-step explanation:
C! hopes this helps
Which operation should you perform first when you simplify 63 − (2 + 54 × 6) ÷ 5?A addition B division C subtraction D multiplication
Answers
Answer:
Multiplication
Step-by-step explanation:
PEMDAS
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
-Since there are parentheses you do that first, so multiplication.
Final answer:
The first operation to perform when simplifying the expression is D: Multiplication, specifically within the brackets where it states 54 × 6. The answer is option D.
Explanation:
When simplifying the expression 63 − (2 + 54 × 6) ÷ 5, according to the order of operations, commonly known as PEMDAS or BEDMAS, we must first perform the operation in the Brackets (in American English, Parentheses are used instead of Brackets).
Within the brackets, the correct sequence of operations is Exponentiation, Multiplication/Division (from left to right), and then Addition/Subtraction (from left to right). Since there is no exponentiation in the brackets, we start with multiplication (54 × 6), which will affect the result within the brackets before performing the addition (2 + ...) and then division ÷ 5. Therefore, the first operation to perform is D: Multiplication.
What is the GCF (greatest common factor of 9 and 18?
Answers
Answer:
9
Step-by-step explanation:
How does 4 × 1/2 = 1 explain
Answers
Answer: The answer is not 1 it's 2
Step-by-step explanation:
Multiply 4*1 to get 4
Multiply 1*2 to get 2
Your answer should be 4/2 which equals 2
Solve the equation for x. For each step, describe the operation and/or property used.
5(2x - 4) - 11 = 4 + 3x
PLEASE HELP
Answers
Answer:
x = 5
Step-by-step explanation:
Start by distributing the 5 to remove parentheses. To do this multiply the numbers and variable in the parentheses by 5.
10x - 20 - 11 = 4 + 3x
Next. you want to get the variables to one side. This is done by subtracting 3x from both sides.
7x - 20 - 11 = 4
Now solve the -20 - 11.
7x - 31 = 4
You need to have the variable all by itself. To do this, first add -31 to both sides.
7x = 35
Finally divide by 7.
x = 5
Hope this helped.