The polynomial divided by (x + 3), with quotient is x² - x + 8, and remainder of -5 is f(x) = x³ + 2x² + 5x + 19
What is the polynomial division algorithmThe polynomial division algorithm states that for two polynomials, f(x) and g(x), where the degree of g(x) a divisor is less than or equal to the degree of f(x), there exist unique polynomials, q(x) the quotient and r(x) the remainder, such that f(x) = g(x)q(x) + r(x) and the degree of r(x) is less than the degree of g(x). This is also known as synthetic division.
f(x) = (x + 3)(x² - x + 8) + (-5)
but expansion;
f(x) = x³ + 3x² - x² + 8x - 3x + 24 - 5
f(x) = x³ + 2x² + 5x + 19
Therefore, the polynomial f(x) = x³ + 2x² + 5x + 19 divided by (x + 3), will give the quotient x² - x + 8, and remainder of -5.
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[tex]\sqrt{45)[/tex]
The required solution to the given radical expression √45 is 3√5.
What are the radical expressions?Any expression that contains a radical symbol is considered a radical expression. To find the square roots, cubic roots, and higher, radical symbols are used. For example, √7, √6, and √11 are in the radial form.
The radical expression is given in the question
√45
As per the given question, the required solution would be as:
√45 = √(3 × 3 × 5)
√45 = 3√5
Thus, the solution to the given expression is 3√5.
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what do you enjoy yourselves 200 times by you don't even listen to me and I got rid of 100 times
Answer: ? what is the question
Step-by-step explanation:
These two images show steps in a proof of the Pythagorean theorem. Which of the following statements about the proof is false?
Brainliest if correct.
A. the area of the interior square in step 2 is equal to the combined area of the two interior squares in step 1.
B. The triangles in step 1 have the same combined area as the triangle in step 2.
C. The area of the interior square in step 2 is equal to c2 + ab.
D. The proof shows that a2 + b2 = c2.
Step 2's inside square has a larger area than Step 1's two interior squares taken together.
Explain about the Pythagoras theorem?According to the Pythagorean theorem, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the two shorter sides.
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Assume that the triangle ABC has sides measuring a, b, and c, and that a2 + b2 = c2. A second triangle with sides of lengths a and b and a right angle should be built. The hypotenuse of this triangle has length c = a2 + b2, matching the length of the hypotenuse of the first triangle according to the Pythagorean theorem.
According to the Pythagorean theorem, two squares added together equal the square of the longest side.
The Pythagoras theorem's equation is as follows:
H² = P² + B²
The procedures of proving the Pythagorean theorem are depicted in these two pictures.
Step 2's inside square has a larger area than Step 1's two interior squares taken together.
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Solve 3x − 2 = 37. a 2 b 5 c 7 d 9
Answer: x = 13
Step-by-step explanation:
To solve, we will isolate the variable.
Given:
3x − 2 = 37
Add 2 to both sides equation:
3x = 39
Divide both sides of the equation by 3"
x = 13
May I have help on this math question please? thank you if you do!
The rate of change of the function is: 2.
The y-intercept/initial value is: 3.
How to Find the Rate of Change and Initial Value of Linear Function?The rate of change is also the slope of a function, which is calculated as, m = change in y / change in x.
Given the points, (0, 3) and (2, 7):
Rate of change/slope (m) = (7 - 3) / (2 - 0)
m = 4/2
m = 2
To find the initial value/y-intercept (b), substitute m = 2 and (x, y) = (0, 3) into y = mx + b:
3 = 2(0) + b
3 = 0 + b
3 = b
b = 3
y-intercept = 3.
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Bob has 3/5 as many stamps as Barry. If Barry has 120 stamps, how many more stamps does he have than Bob?
If Barry has 120 stamps and Bob has 3/5 as many stamps as Barry, you can set up the proportion:
3/5 = x/120
Where x is the number of stamps Bob has. To solve for x, you can cross-multiply:
3 * 120 = 5 * x
Simplifying:
360 = 5x
x = 72
So, Bob has 72 stamps. To find out how many more stamps Barry has than Bob, you can subtract the number of stamps Bob has from the number of stamps Barry has:
120 - 72 = 48
Barry has 48 more stamps than Bob.
Answer: 72
Multiply 120 by 3/5 to get Bob's amount of stamps.
based on the healthy people 2030 initiative, what is one change that should be made in school cafeterias? a. reducing the number of protein choices b. frying potatoes in saturated fats for shorter periods of time c. removing soda pop from the lunchroom d. adding candy to vending machines e. increasing the size of vegetable servings on lunch choices
The Healthy People 2030 initiative goals of reducing obesity and promoting a healthy lifestyle.
One change that should be made in school cafeterias is to reduce the number of protein choices. This can be done by decreasing the amount of red meat, poultry, and fish in the cafeteria by at least 50%. The number of vegetarian and vegan options should also be increased. This would reduce the amount of saturated fat and cholesterol that students are consuming and help them to make healthier food choices. It would also help to reduce the environmental impact of the cafeteria by reducing the amount of animal products being consumed. This change would help schools to meet the Healthy People 2030 initiative goals of reducing obesity and promoting a healthy lifestyle.
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Explain how rectangles are related to squares.
Enter rectangles or squares in the answer boxes. Words may be used more than once.
Answer:
Rectangles
Squares
A square is a special type of rectangle. All squares are rectangles, but not all rectangles are squares. In a square, all four sides are equal in length (congruent), making it a special case of a rectangle where all angles are right angles and all four sides have the same length. In contrast, a rectangle can have sides of different lengths.
The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 246.7 and a standard
deviation of 62.5. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below.
a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or
between 59.2 and 434.2?
b. What is the approximate percentage of women with platelet counts between 184.2 and 309.2?
a) The approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 59.2 and 434.2 is of 99.7%.
b) The approximate percentage of women with platelet counts between 184.2 and 309.2 is of 68%.
What is defined by the Empirical Rule?These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:
68% of the measures within one standard deviation of the mean.95% of the measures within two standard deviation of the mean.99.7% of the measures within three standard deviation of the mean.Hence the percentages are given as follows:
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if JKLM is a parallelogram what is measure angle K
PLEASE HELP
JKLM is a parallelogram with four sides and four angles, meaning its measure of angle K is equal to the measure of angle M.
What is a parallelogram?A parallelogram is a quadrilateral having four equal-length sides and opposing sides that are parallel. It is a two-dimensional form with two pairs of parallel sides and equal angles on all sides.
JKLM has four sides and four angles if it is a parallelogram. Because it is a parallelogram, the opposite sides of the figure will be parallel, as will the opposite angles. This signifies that the angle K measure is equal to the angle M measure. As a result, if the measure of angle M is known, the measure of angle K may be calculated.
For example, if angle M is 70 degrees, then angle K is also 70 degrees. In general, if the measure of angle M is x, the measure of angle K must be x as well.
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a) if a leaf completes the color transformation, what is the probability that it will complete the textural transformation?
the probability that it will complete the textural transformation
is 0.90334.
Let A be the event that a leaf completes the color transformation and B be the event that a leaf completes the textural transformation.
n(A) = 243 + 26 = 269
n(B) = 243 + 13 = 256
n (A∩ B) = 243
n(S) = 243 +26+13+18 = 300
Finding the Probability of the event that the leaf completes the color transformation by using the Probability of an event formula
P(A)= 269 / 300
= 0.89667
p(A∩ B) = 243/300
= 0.81
By using the conditional probability of a leaf completing textural transformation given a leaf completing color transformation
P(B/A) = p(A∩ B) / P(A)
= 0.81/0.89667
= 0.90334
The conditional probability of a leaf completing textural transformation given a leaf completing color transformation is 0.90334
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The complete question is :
The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by type of transformation completed:
(a) ) If a leaf completes the color transformation, what is the probability that it will complete the textural transformation?
Explain how you can model 3x2/4
You can model 3x2/4 as the mathematical expression that represents the division of the product of 3 and 2 by 4. The result of this expression is 3/2.
What is division of a product in mathematics?In mathematics, division is an arithmetic operation that is the inverse of multiplication. Given two numbers, the quotient is the number of times the second number "fits into" the first number.
The product is the result of multiplying two or more numbers together. Dividing a product is the process of finding out how many times one of the factors in the product can be taken to equal the product.
For example, if the product is 12 and the divisor is 3, then the quotient is 4, because 3 x 4 = 12
So, in the example 3x2/4, the product of 3 and 2 is 6 and we divide it by 4 to get the quotient of 3/2.
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magine you are painting a series of towers built from cubes. You are going to paint only the exposed faces of the cubes. If the tower you paint has 25 exposed faces, how many cubes are in the tower?
Answer: 6
Step-by-step explanation:
4x + 1 = 25
4x = 24
x = 6
PLS HELP IF SOMEONE KNOWS THE ANSWER!!!!!!!!!!
Answer:
see below.
Step-by-step explanation:
1. g(x) = 2^(x-5) +3
2. g(x)= 1/3 * 2^x
3. f(x) was vertically stretched by 3. K value is 3. The Y intercept became augmented by 3 folds.
4. k value = 5, the curve basically got "lifted" up by 5 units.
a study suggests that 35% of all business executives are willing to switch companies if offered a higher salary. if a recruiter randomly contacts a simple random sample of 100 executives, what is the probability that over 41% will be willing to switch companies if offered a higher salary?
The probability that 41% of the sample will be willing to switch companies is 0.0024.
To find the exact probability that over 41% of a random sample of 100 executives will be willing to switch companies if offered a higher salary, we can use the cumulative distribution function (CDF) of the binomial distribution.
The CDF is given by the formula:
P(X <= x) = (n x) p^x (1-p)^(n-x)
Where x is the number of successful outcomes, n is the number of trials, and p is the probability of success in each trial.
To find the probability of getting over 41% of the sample willing to switch companies, we need to find the probability of getting 42 or more successful outcomes (people willing to switch companies) out of 100 trials.
So we need to find P(X <= 42) + P(X <= 43) + .... + P(X <= 100) = 1 - P(X>=41)
P(X<41)= 1 - 0.9976 = 0.0024
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suppose in mathlandia 11 peak dollars is equivalent to 22 sal dollars if a hamburger is 45 peak dollars what is the cost of the hamburger in sal dollars
The cost of the hamburger in sal dollars will be 90
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
Suppose in Mathlandia 11 peak dollars is equivalent to 22 sal dollars. Then the ratio of the sal dollar to the peak dollar will be constant. Then the ratio is given as,
Ratio = 22 / 11
Ratio = 2
If a hamburger is 45 peak dollars. Then the number of sal dollars is given as,
⇒ 2 x 45
⇒ 90
The cost of the hamburger in sal dollars will be 90
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. All of the following are true about robo-advisors, EXCEPT…
*
Robo-advisors generally have lower fees than a traditional financial advisor
Robo-advisors generally have a higher account minimum than a traditional financial advisor
Robo-advisors use an algorithm to automate the investing process
Robo-advisors generally invest your portfolio based on your goals and risk tolerance
False: Robo-advisors often invest your account in accordance with your objectives and risk tolerance.
what is amount ?aggregate aiming to figure out the amount total number, or time needed. The amount in front of you or being thought about is quite active. the final outcome, its significance, or its import. three accountings: principal, interest, and the third. Word forms include amounts, amounting, and amounted. supple noun How much something is, much you have, the amount that you require or how many you get is its quantity. He needs that much cash to get by.
given
It is true that robo-advisors typically charge less than a traditional financial advisor.
It is true that robo-advisors typically require larger account minimums than a traditional financial advisor.
It is true that robo-advisors automate the investing process using an algorithm.
False: Robo-advisors often invest your account in accordance with your objectives and risk tolerance.
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On a graph, the line representing Tony's distance covered with respect to time would be speed is Mark's. meters per minute and the unit rate for Mark is 2 3227 Mark's line. So, Tony's walking
Tony's walk speed exists 2 meters per minute slower then Tony's walk speed.
What is meant by equation?An equation in algebra is an equality claim that includes one or more variables or unknowable things.
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Two expressions joined by an equal sign form a mathematical statement known as an equation.
A number, a variable, or a mix of both plus certain operation symbols make up an expression. An equal sign separates two expressions that make up an equation.
Tony : d = 108m
Tony walks 108 meters per minute
Mark : (10,1100),(20,2200)
slope = (2200 - 1100) / (20 - 10) = 1100/10 = 110 meters per minute
Therefore, Tony's walk speed exists 2 meters per minute slower then Tony's walk speed.
The complete question is:
Tony writes an equation to represent the distance he walks in meters, d, in relation to the number of minutes he walks, m. d = 108m Mark has created a table to record the number of minutes it took him to walk different distances in meters. Time (minutes) Distance (meters) 10 1,100 20 2,200 40 4,400 Assuming that Tony and Mark both walk at a constant rate, the unit rate for Tony is meters per minute and the unit rate for Mark is meters per minute. On a graph, the line representing Tony’s distance covered with respect to time would be Mark’s line. So, Tony’s walking speed is Mark’s.
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How do I solve by multiplying Imaginary Numbers? (10√-6) (√42)
HElp quick pleaseHElp quick pleaseHElp quick pleaseHElp quick pleaseHElp quick pleaseHElp quick pleaseHElp quick pleaseHElp quick pleaseHElp quick please
The non linear equation is Option B.
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the non linear equation be represented as A
Now , the value of A is
The equation can be calculated as a linear equation if the slope of the point remains the same
So , when the slope m is constant , it will be a linear equation
a)
Let the first point be P ( 2 , 5 )
Let the second point be Q ( 4 , 17 )
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 17 - 5 ) / ( 4 - 2 )
Slope m = 12 / 2
Slope m = 6
Let the third point be R ( 7 , 35 )
Let the fourth point be S ( 13 , 47 )
Now , the slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope m = ( 47 - 35 ) / ( 13 - 7 )
Slope m = 12 / 6
Slope m = 2
Hence , the slope between the points is not the same and the equation of line will not be a linear equation
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Example 1: What is the probability of choosing a marble
2 questions with stripes? What is the complement of
choosing a marble with no design?
P(stripes)
P'(no design?
Answer:
The probability of choosing a marble with stripes, P(stripes), would be 0.2. The complement of choosing a marble with no design, P'(no design), would also be 0.2.
Step-by-step explanation:
1. The probability of choosing a marble with stripes, P(stripes), would depend on the proportion of marbles with stripes in the overall population of marbles available to choose from.
2. If, for example, there are 20 marbles with stripes and 80 marbles without stripes in a set of 100 total marbles, the probability of choosing a marble with stripes would be 20/100, or 0.2.
3. The complement of choosing a marble with no design, P'(no design), would be the probability of choosing a marble with stripes, or P(stripes).
4. This is because the complement of an event is the probability of the event not occurring.
5. So, if the probability of choosing a marble with stripes is 0.2, the probability of not choosing a marble with stripes (i.e. choosing a marble with no design) would also be 0.2.
Nora hired a plumber to come to her house. The equation
y = 35x + 50 represents the costs in dollars, y, of hiring the plumber for x hours. Interpret the y-intercept.
The meaning of the y-intercept is that Nora paid her plumber an initial fee of $50.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
x and y represents the data points.m represents the slope of a line.c represents the y-intercept of a line.What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
In this scenario, the y-intercept of this equation is 50 and it represents the initial fee being charged by the plumber.
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1. Circle C is centered at the origin. Is point (5, 5) on the circle? -8 -6 -4 -2 8 6 4 2 101 -2 -4 -6 -8 2 4 6 ++ 8
Answer: d
Step-by-step explanation:
put some clothes on
3. A unit cube is shown below. Which of these can best be measured by using unit
cubes?
Unit Cube
A. Weight
B. Area
C. Volume
D. Temperature
I unit
unif
Are true lines y= -1 and X =1 parallel, perpendicular, or neither? Explain
The lines, y = -1 and x = 1 are perpendicular lines.
What are Perpendicular Lines?If two lines are perpendicular to each other, it means they form right angle at the point of intersection, and also, they have slopes that are negative reciprocals to each other.
Also, vertical and horizontal lines are perpendicular to each other because horizontal line has a slope that is zero while vertical line has an undefined slope.
y = -1 is a horizontal line, while x = 1 is a vertical line. Therefore, we can concluded that, they are perpendicular to each other.
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i need to know how to find the gcf
The greatest positive integer that completely divides both of the numbers is known as the greatest common factor, or GCF. The GCF or HCF is composed of two or more non-zero integers.
In other words, the greatest common factor (GCF) among all the factors of the provided numbers is the case when there are two or more numbers. The Highest Common Factor of the Given Numbers is another name for it.
The approaches that are utilized to discover the GCF are listed below.
citing common elements:
Here, we list the common components of the given numbers and highlight those that are most frequently occurring.
main determinants:
In order to determine the highest common factors from both prime factor lists, we must write the given numbers as the product of prime numbers.
division strategy
Here, we must use the long division method to divide the greatest integer by the lowest number until the result is zero. The GCF of the given integers will make up the rest of the divisor when we reach the point where we have zero.
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Find the indicated real nth root(s) of a. n=2, a= -49
As, a = -49 is a negative number, so there is no real root for the integer.
What is square root?
A number's square root is a value that, when multiplied by itself, yields the original number. The other way to square an integer is to find its square root.
The expression is given as - a = -49
The value for n is n = 2
Find the nth root value for the expression a.
Since a = -49 is a negative number there is no real square root for the number.
If it would have been a = 49, then there would have been one real square root.
n=2 which generates √49.
This gives the value as 7.
Therefore, there are no roots for -49.
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A meteorologist drew the accompanying graph to show the changes in relative humidity during a 24-hour period in New York City. What is the range of this set of data?
The range of the data varies from 30 to 80. The correct answer is 30 < y < 80. The option C is correct
What are a domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
Given that there is a graph in which the y-axis represents relative humidity and the x-axis represents time.
The range will be the variation of the y value on the graph from minimum to maximum.
The y value varies from 30 to 80 from minimum to maximum respectively. The inequality can be written as 30 < y < 80.
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groups of 20 and more receive a 20% discount to the zoo. tickets range in price from $10.00 to $15.00 depending on your age. what is the range of the ticket prices after the discount is used
In a case whereby groups of 20 and more receive a 20% discount to the zoo. tickets range in price from $10.00 to $15.00 depending on your age. the range of the ticket prices after the discount is used is $8 to $12.
How can the Discounted ticket range be calculated?The concept that will be used is discount. Discount is the term used to describe a sum or a percentage subtracted from an item's usual selling price.
Since the ticket prices are been seen from the range from $10 to $15 so then we can say that the new range can have two figures reduced by 20%.
Then we can calculate the $10 after the discount as :
= [10 * (1 - 20%)]
= $8
Then we can calculate the $15 after the discount as :
=[ 15 * ( 1 - 20%)]
= $12
The we can calaculate the Discounted ticket range as
= $8 to $12
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complete question:
Groups of 20 or more receive a 20% discount at the LA Zoo. Tickets range from $10 to $15, depending on age. What is the range in ticket price after the 20% discount?
The bottom 30% of students failed the final examination. The mean score for the test was 120 and the standard deviation was 17. What was the passing score?
The passing score of the student when the standard deviation and mean are given is calculated to be 111.1.
Standard deviation = 17
Mean = 120
Percentage of students failed in the exam = 30%
Let us find Z such that P(Z< (X - 120)/17) = 0.3
By referring the table, the Z value corresponding to 0.3 probability is observed to be -0.525.
This means that (X - 120)/17 = -0.525
(X - 120) = 17 × -0.525
(X - 120) = -8.925
X = 120 - 8.925 = 111.07 ≈ 111.1
Thus, the required passing score is calculated to be 111.1.
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