How is the Remainder Theorem related to the process of synthetic division?
Answers
Answer:
The Remainder Theorem states that f(c) = the remainder. So if the remainder comes out to be 0 when you apply synthetic division, then x - c is a factor of f(x). by x - 2. Use the result to find all zeros of f
Related Questions
Find the product
3(z+4)(x-5)
Answers
Answer:
3zx-15z+12x-60
Step-by-step explanation:
first do parenthesis and distribute (z+4)(x-5) into zx-5z+4x-20
then distribute the 3 to get the answer
Solve the inequality for w.
w+7<20
Simplify your answer as much as possible.
0
Answers
Answer:
w<13
Step-by-step explanation:
Works identically to a normal single-variable equation.
Subtract 7 on both sides in order to isolate w--->w+7-7<20-7
The answer (which cannot be simplified any further) is w<13.
Answer:
w < 1`3
Step-by-step explanation:
Isolate the variable w on one side of the inequality sign.
w+7<20
w<20 - 7
w<13.
What is the probability of choosing a red marble or a green marble out of a bag containing 5 blue marbles, 3 red marbles, and 1 green marble?
Answers
Answer:
P(Red) = 1/3
Step-by-step explanation:
Total number of marbles = 15
5 red
6 green
4 blue
Sketch the graph of the quartic y=x^4-6x^3+12x^2-8x.
Answers
PLEASE HELP
Solve the following system algebraically. y = x^2 + 11 and y = –12x
Answers
Answer:
x^2+12x=-11
Step-by-step explanation:
Answer:
(-1, 12) and (-11, 132)
Step-by-step explanation:
what does 3 1/3 yard equal to in inches
Answers
Answer:
it is 120 i believe
Step-by-step explanation:
Answer: 120
Step-by-step explanation:
a yard is 3 feet
a foot is 12 inches
10ft x 12in = 120in
2+2=
a. 3
b. 5
c. 4
d. 7
Answers
Answer:
C
Step-by-step explanation:
2
+2
-----
4
5. Communicate Mathematical Ideas Two integers, a and b, have different
signs. The absolute value of integer a is divisible by the absolute value
of integer b. Find two integers that fit this description. Then decide if the
product of the integers is greater than or less than the quotient of the
integers. Show your work.
Answers
Answer: General rule for adding numbers
Two integers with the same signs
=> Once 2 integers has the same sign, then add.
For example
5 + 3 = 8 ( 5 and 3 are both positive numbers)
-5 + (-3) = -8 (5 and 3 are both negative number, thus we added the 2 numbers)
Two integers with different signs
=> When 2 integers has different sign, then do subtraction
For example
-5 + 3 (5 and 3 has different signs)
- 5 + 3 = 2
Two integers that vary in sign
=> When 2 integers vary in sign, then it will depend on the operator
For example
5 + (-3) (5 and 3 has different signs, but the process will vary with the operator and number sign)
When positive and negative = negative
5 – 3 = 2
Step-by-step explanation:
Two researchers make a test concerning standardized exam performance among senior high school students in one of two local communities. Researcher A tests performance from the population in the northern community, where the standard deviation of test scores is 110 ( ); Researcher B tests performance from the population in the southern community, where the standard deviation of test scores is 60 ( ). All other things being equal, which researcher has more power to detect an effect? Explain.
Answers
Answer:
Researcher B
Step-by-step explanation:
Normally, when all other things being equal, we usually say that power is higher when the standard deviation is small than when it is large.
Now, from researcher A, standard deviation is 110 while from researcher B, standard deviation is 60.
We can see that the standard deviation for researcher B is smaller than that of researcher A.
Therefore, we can conclude that since the standard deviation for researcher B is lesser than that of researcher A, it means that Researcher B will have more power to detect an effect.
Find the recursive definition for this sequence:
11, 24, 37, 50, 63, ...
A. f(0) = 13. f(n) = f(n + 11)
Answers
Answer:
D. f(0) = 11, f(n) = f(n-1) +13
Step-by-step explanation:
You want the recursive definition for the sequence ...
11, 24, 37, 50, 63, ...
First termThe first term is 11. This means the initial value for the recursive definition will be 11:
f(0) = 11 . . . . . eliminates choices A and B
Common differenceEach term of a recursive sequence is defined in terms of previous terms. That is, f(n) will be defined in terms of f(n-1). Here, the previous term has 13 added to it. (11 +13 = 24, for example).
The remaining part of the recursive definition is ...
f(n) = f(n -1) +13 . . . . . eliminates choice C
The recursive definition is ...
f(0) = 11f(n) = f(n-1) +13<95141404393>
PLLLLLLEEEEEEEEZZZZZZZZZ AAAAAANNNNSSSSSEEEEERRRRRR will give brainlist! One million dollars! A megayacht! FIVE STARS!
Plot 1 goes from 0 to 8. There are 2 images above 5, 2 above 6, 4 above 7, and 5 above 8. Plot 2 goes from 0 to 8. there are 5 images above 1, 2 images above 2, 4 images above 3, 3 images above 4, 1 image above 5, 1 image above 6, and 1 image above 8.
Use visual clues to decide which plot has the highest measure. No calculations should be necessary, although you may use them to verify your answers.
Highest mean:
Highest median:
Highest range:
Highest interquartile ranges:
Answers
Answer:
Highest mean:
✔ Plot 1
Highest median:
✔ Plot 1
Highest range:
✔ Plot 2
Highest interquartile ranges:
✔ Plot 2
Step-by-step explanation:
Answer:
Highest mean:
✔ Plot 1
Highest median:
✔ Plot 1
Highest range:
✔ Plot 2
Highest interquartile ranges:
✔ Plot 2
HELP ASAP Gina doesn’t agree with her town’s new policy about public playgrounds. The local newspaper’s editor has given her half a page to write an article supporting her position. Which two purposes should she consider while writing her article? to express to entertain to persuade to instruct
Answers
Answer:
to perduade and to instruct
Answer: To persuade
Step-by-step explanation:
She is trying to get them to change the policy
State the domain and range for the following relation. Then determine whether the relation represents a function.
Father Son
Gem Gale
Hesh Abby
Beni Sam
A. Domain : {Gem, Hesh, Gale}
Range : {Sam, Abby, Beni}
B. Domain : {Gale, Abby, Beni}
Range : {Gem, Hesh, Sam}
C. Domain : {Gem, Hesh, Sam}
Range : {Gale, Abby, Beni}
D. Domain : {Sam, Abby, Beni}
Range : {Gem, Hesh, Gale}
Does the relation represent a function?
A. The relation in the figure is a function because each element in the domain corresponds to exactly one element in the range.
B. The relation in the figure is a function because each element in the range corresponds to exactly one element in the domain.
C. The relation in the figure is not a function because the element Gale in the range corresponds to more than one element in the domain.
D. The relation in the figure is not a function because the element Sam in the domain corresponds to more than one element in the range.
Answers
Answer:
C. Domain : {Gem, Hesh, Sam}
Range : {Gale, Abby, Beni}
B. The relation in the figure is a function because each element in the range corresponds to exactly one element in the domain.
Step-by-step explanation:
The figure of the mapping is attached below.
From the diagram, the domain for the relation is the set of Fathers:
{Gem, Hesh, Sam}
The range is the set of Sons:
{Gale, Abby, Beni}
The relation is a function. This is because each element in the range corresponds to exactly one element in the domain.
A primary credit card holder's card has an APR of 11.99%. The current monthly balance, before interest, is $9,768.26. The cardholder makes a payment of $350 the first 11 months and then pays off the balance at the end of the 12th month. How much interest did the credit card holder pay?
Answers
Answer:
Thus, for making installment payments, the credit card holder incurred the additional cost of Option D.
Step-by-step explanation:
The credit card holder paid an additional D. $559.56 over the 12 months versus paying the balance in full before the end of the first month.
How is the additional payment determined?
The additional payment made by the credit card holder results from paying installments instead of clearing the balance in the first month.
Installment plans attract finance charges at an annual percentage rate (APR), which increases the total amount paid.
Therefore, the additional payment is the difference between the total installment payments and the credit card balance at the beginning of the first month.
N (# of periods) = 12 months
I/Y (Interest per year) = 11.99%
PV (Present Value) = $6,299.59
PMT (Periodic Payment) = $-350
Results:
FV = $3,009.15
Sum of all periodic payments = $3,850 ($350 x 11)
Total Interest = $559.57
The total amount paid over the 12 months = $6,859.15 ($3,009.15 + $3,850)
The total amount paid in full in the first month = $6,299.59
Additional payment made via installments = $559.56 ($6,859.15 - $6,299.59)
Thus, for making installment payments, the credit card holder incurred the additional cost of Option D.
2.414114111 is a rational number true or false
Answers
Solve the triangle. Round your answers to the nearest tenth. 27 degrees
Sorry never mind! Got it! Can’t delete!
Answers
One angle measure provided (27 degrees), to determine the lengths of the sides or the measures of the other Angles.
The triangle, we need more information about the triangle, such as the lengths of the sides or the measures of other angles. The given information, "27 degrees," only specifies one angle of the triangle, but it is not sufficient to solve the triangle completely.
To solve a triangle, we typically need at least three pieces of information, which can include side lengths, angle measures, or a combination of both. With only one angle measure provided (27 degrees), we are unable to determine the lengths of the sides or the measures of the other angles.
To fully solve the triangle, we would need additional information such as the lengths of the sides or measures of at least two more angles. Without this additional information, it is not possible to provide a complete solution or determine the lengths of the sides or the measures of the other angles in the triangle.
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Patricia was having fun playing a card game. To win the game, she
needed the next two cards dealt to be yellow cards. There are 12
cards left in the deck, and three are[yellow.
What is the probability that the two cards dealt to Patricia will both
be yellow?
Answers
Answer:
25
%
Step-by-step explanation:
te puedes subcribirte a mi canal se llama navegando con incognito
The probability that the two cards dealt to Patricia will both be yellow
is 1/4.
What is the probability?In mathematics, probability refers to the likelihood of an occurrence occurring. Simply put, how frequently the incidence occurs over a certain period of time.
Given, there are 12 cards left in the deck, and three are yellow.
To find the probability:
The probability= number of yellow cards in the deck / total number of cards in the deck.
= 3/12
= 1/4
Therefore, the probability is 1/4.
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what is the domain and range to y=|x+4|
Answers
Answer:
x ∈ (- ∞, + ∞) and y ∈ [0, + ∞)--------------------------
Given is the absolute value function.
It has no domain restriction but the range is not negative.
It can be shown as:
Domain: x ∈ (- ∞, + ∞)Range: y ∈ [0, + ∞)the enrollment of the Middle School drop by 168 students from 2015 to 2019 find average change in the number of students each year
Answers
We will find the average change as follows:
*First, we determine the points, those are:
(2015, x)
(2019, x - 168)
Now, the average change is determined as follows:
\(m=\frac{(x-168)-x}{2019-2015}\Rightarrow m=\frac{-168}{4}\Rightarrow m=-42\)So, the average change is -42 students per year.
***Explaination***
Since we are given two dates and two quantities we can interpret them as points.
We don't know the total number of students but we know the change over time, so we assign a random value to represent the total number of students, it will be "x" and it will be at "its maximum" in 2015.
So, we have our first point (2015, x)
Now, we know that the total number of students changed by -168 from 2015 to 2019, so in 2019 we will have "x - 168" students.
So, we have our second point (2019, x - 168).
*We know that the average change is given by the change on y divided by the change on x [The slope of both points], and since we have that the points follow (x1, y1) & (x2, y2), we will replace in the following expression [Slope]:
\(m=\frac{y_2-y_1}{x_2-x_1}\)Since we know the following:
\((x_1,y_1)=(2015,x)\)&
\((x_2,y_2)=(2019,x-168)\)We replace in the expression:
\(m=\frac{(x-168)-(x)}{(2019)-(2015)}\Rightarrow m=\frac{-168}{4}\Rightarrow m=-42\)So, the average change was -42 students per year.
Evaluate Combination (6,6)
Answers
Answer:
\( nCx = \frac{n!}{x! (n-x)!}\)
On this case n =6 and x =6 we got:
\( 6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1\)
Step-by-step explanation:
The utility for the combination formula is in order to find the number of ways to order a set of elements
For this case we want to find the following expression:
\( 6C6\)
And the general formula for combination is given by:
\( nCx = \frac{n!}{x! (n-x)!}\)
On this case n =6 and x =6 we got:
\( 6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1\)
Please help me!!!!!!!!!!!!!!!!!!!!!
fill in the blanks please!!
Words you can use are in the picture.
1. A comparison of one number to another by division is a ________.
2.________ name the same comparison.
3. A ratio that compares quantities with different units is a ________.
4. A _______ is a ratio, or rate, that compares a number to 100
5._______ a fraction or a ratio by dividing the numerator and denominator by a common factor.
Answers
Answer:
1. Ratio
2. Equivalent Ratios
3. Rate
4.Percent
5.Simplify
Sera had the number 548.She adds one to the tens and two to the units. What number would Sera end up with??
Answers
The number she'd have is:
560Explanation:
First, let's see which number is in the tens place and which number is in the ones place (the units place).
In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).
So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :
550
That's not all, since we also add 1 to the tens:
560
Hence, Sera ends up with 560.what is the value for x enter your answer in the box
Answers
Answer: x=26 degrees. These angles are complementary angles, meaning they add up to 90 degrees. if you do 90-64, you get 26 degrees.
Maria wrote the number 54,348. How many times greater is the 4 in the
thousands place, than the 4 in the tens place? *
10 times greater
100 times greater
1,000 times greater
10,000 times greater
Answers
2
Drag each equation to the correct location on the table.
Classify the quadratic equations based on the number of solutions.
20² +5=
2x² + 3x = 5
3x² + 2x =
One Solution
4x² + 12x =
Two Solutions
9 522 + 14 = 19
No Solution
Answers
The quadratic equations are classified as follows:
20² + 5 = 9 has no solution2x² + 3x = 5 has two solutions3x² + 2x = 22 has two solutions4x² + 12x = 19 has two solutionsWhat are the solutions of the quadratic equation?
If the discriminant of the quadratic equation is positive, then the equation has two real solutions.
If the discriminant is zero, then the equation has one real solution.
If the discriminant is negative, then the equation has no real solutions (but may have complex solutions).
Let's classify the given quadratic equations based on the number of solutions:
20² +5 = 9 is not a quadratic equation because it does not have a variable with a degree of two. Instead, it is just a number that evaluates to a false statement.
Therefore, it has no solution.
2x² + 3x = 5 is a quadratic equation with a = 2, b = 3, and c = -5. The discriminant is 3² - 4(2)(-5) = 49, which is positive.
Therefore, the equation has two real solutions.
3x² + 2x = 22 is a quadratic equation with a = 3, b = 2, and c = -22. The discriminant is 2² - 4(3)(-22) = 100, which is positive.
Therefore, the equation has two real solutions.
4x² + 12x = 19 is a quadratic equation with a = 4, b = 12, and c = -19. The discriminant is 12² - 4(4)(-19) = 400, which is positive.
Therefore, the equation has two real solutions.
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Drag each equation to the correct location on the table.
Classify the quadratic equations based on the number of solutions.
20² +5 = 9
2x² + 3x = 5
3x² + 2x = 22
4x² + 12x = 19
One Solution
Two Solutions
No Solution
Evaluate 4x^2 y^-3 for x=3 and y=-2
Answers
Answer:
36 and -1/8
Step-by-step explanation:
x^2 = 3^2 = 9 * 4 = 36
y^-3 = (-2)^-3 = -1/8
Answer:
-4.5.
Step-by-step explanation:
4x^2 y^-3
= 4x^2 / y^3
When x = 3 and y = -2
it is 4(3)^2 / (-2)^3
= 36 / -8
= -4.5.
If the value of a commodity decreases at a monthly rate of 0.8%, by what percentage does it decrease in a year?
Answers
If the value of a commodity decreases at a monthly rate of 0.8%, by 9.6 percentage it decreases in a year.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that, the value of a commodity decreases at a monthly rate of 0.8%,
We have to find by what percentage the rate decreases in a year.
If there are 12 months in a year, the rate decrease in a year obtained as,
=0.8 × 12
=9.6 %
Thus, if the value of a commodity decreases at a monthly rate of 0.8%, by 9.6 percentage it decreases in a year.
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In a year, the value of commodity decreases by 9.6%, at the monthly rate of 8%.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Monthly decrease rate of change in commodity = 0.8 %,
To find the percentage decrease in year,
Use ratio property,
In 1 month, commodity decreases 0.8%
In 12 months commodity decreases = 12 x 0.8 = 9.6 %
The value of commodity will decrease by 9.6% in a year.
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Points A' and B' are images of points A and B after a 270 degree rotation about the origin. If the slope of ray AB is 3, what is the slope of ray A'B'? Explain.
A. A rotation of 270 degrees would result in a line parallel to ray AB . Since the slopes of parallel lines are opposite reciprocals, the slope of ray A'B' is (Blank).
B. A rotation of 270 degrees would result in a line perpendicular to ray AB. Since the slopes of perpendicular lines are opposite reciprocals, the slope of ray A'B' is (Blank).
C. A rotation of 270 degrees would result in a line parallel to ray AB . Since the slopes of parallel lines are equal, the slope of ray A'B' is (Blank).
D. A rotation of 270 degrees would result in a line perpendicular to ray AB . Since the slopes of perpendicular lines are equal, the slope of ray A'B' is (Blank).
Answers
Answer:
B
Step-by-step explanation:
The population of a city was 10,000 in 2010. The population increase at an annual rate of 2.5% per year. Is the growth model function that represents the population of the city linear?
Answers
Answer:
The growth model that represents the population of this city is not linear--it is exponential:
\(f(t) = 10000( {1.025}^{t} )\)
\(t = 0 \: represents \: 2010\)
Evaluate the expression, writing the result as a simplified complex number.
To earn full credit be sure to show all steps and calculations. You may wish to do the work on paper and submit an image of that written work.
\frac{(2+i)(4-2i)}{1+i}
Answers
The simplified expression involving complex numbers is given as follows:
5 + 5i.
What are complex numbers?Complex numbers are number that have a real and an imaginary part, and are defined as follows:
z = a + bi.
In which:
a is the real part.b is the imaginary part.The basic relation of complex numbers is given as follows:
i² = -1.
The fraction for this problem is given as follows:
(2 + i)(4 - 2i)/(1 + i).
The numerator is simplified as follows:
(2 + i)(4 - 2i) = 8 - 4i + 4i - 2i² = 8 + 2 = 10.
Hence the fraction is of:
10/(1 + i).
To remove the complex number from the denominator, the entire fraction is multiplied by the conjugate of the denominator, hence:
10/(1 + i) x (1 - i)/(1 - i) = 10(1 + i)/(1 - i²) = 10(i + 1)/2 = 5 + 5i.
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