If f(x) = x³ - 5x² - 2x + 24 and x + 2 is a factor of f(x), then find all of the
zeros of f(x) algebraically.
All the zeroes of the polynomial x³ - 5x² - 2x + 24 are -2, 3, and 4.
What are the zeroes of a polynomial?The polynomial can be expressed as [tex]ax^{2} +bx+c=0[/tex], where a, b and c are real numbers. The numbers by which the polynomial expression values equal zero are termed zeroes of the polynomial.
The number of zeroes of the polynomial depends on the highest power of the polynomial.
Calculation:As x + 2 is one of the factor of f(x),
Now, dividing x³ - 5x² - 2x + 24 by x + 2, we get
Quotient = [tex]x^2-7x+12[/tex]
Remainder = 0
Now, factorizing the quotient by splitting the middle term,
[tex]x^2-3x-4x+12=0[/tex]
[tex]x(x-3)-4(x-3)=0[/tex]
[tex](x-3)(x-4)=0[/tex]
Now, equating both values to 0, we get
x = 3 and x = 4
All the zeroes of the polynomial x³ - 5x² - 2x + 24 are -2, 3, and 4.
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Find the number of degrees for the sum of the interior angles of a regular 12-sided figure.
Answer:
Sum of 12-sided polygon=1800°
Measure of each interior angle of a regular12-sided polygon=150°
6) Which transformation or set of transformations will map a point (x, y) onto the point (3x, 3y+4 )
a
a dilation of scale factor 3 through the origin followed by a translation of up 4 unit
b
a dilation of scale factor 3 through the origin followed by a translation of right 4 unit
c
a dialation of scale factor 3 through the point ( 4, 0 )
d
a dialation of scale factor 3 through the point ( 0, 4 )
5) Which discription of a figure and its image match the transformation described by (x, y) → (x+5, y )
a
The figure and its image are neither similar nor congruent, and the image has been streched horizontally.
b
The figure and its image are similar, and the image has been translated 5 unit up.
c
The figure and its image are similar, and the image has been translated 5 unit to the right.
d
The figure and its image are neither similar nor congruent, and the image has been streched vertically.
6. The transformation or set of transformations which map a point (x, y) onto the point (3x, 3y+4 ) is; Choice A; a dilation of scale factor 3 through the origin followed by a translation of up 4 unit.
5. The description of a figure and its image match the transformation described by (x, y) → ( x+5, y ) is; The figure and its image are similar, and the image has been translated 5 unit to the right.
Which transformations maps the given pre-image and image points?It follows from transformations that a transformation using a scale factor, k about the origin is represented as; ( x, y ) → ( kx, ky ).
Also a shift in the horizontal or vertical direction by k units is represented by; ( x, y ) → ( x ± k, y ± k ) intuitively and respectively.
On this note, the given transformations are as represented in the answer section above.
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Select the correct text in the passage.
iS John is a journalist. He went to a product demonstration for a new computer. Some of what he heard was informative, while the rest was meant to
persuade consumers to buy the product. Which two statements in the excerpt are persuasive rather than informative?
At the latest launch by the computer manufacturer Mintel Corporation, they demonstrated the latest smart technology in their new computer. The
computer has voice recognition software that can adapt the user's experience to his or her preferences. This is something no other computer can
do at present.
The computer also has touchscreen technology, is loaded with the latest apps, and comes with a free year's subscription to Adobe
Photoshop. This is the best buy on the market.
The two sentences meant to persuade are the following:
"This is something no other computer can do at present.
"This is the best buy on the market".
What are the sentences for persuasion?It should be noted that persuasion is used to make someone agree to a particular point. From the information, at the latest launch by the computer manufacturer Mintel Corporation, they demonstrated the latest smart technology in their new computer.
The computer has voice recognition software that can adapt the user's experience to his or her preferences. This is something no other computer can do at present.
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What is the value of the function shown when x = -5?
f(x) = x2 + 7
Answer:
-3
Step-by-step explanation:
f(-5) = (-5)2 + 7
= -10 + 7
= -3
Fractions on number line help!!!!!
Answer:
There are four small lines between 0 and 1 in the number line, they denote the decimals : 0.2, 0.4, 0.6 and 0.8. Put the SUM on the 0.4 line
A set of data has a normal distribution with a mean of 47 and a standard deviation of 8. Find the percent of data within the following interval.
from 39 to 55
The percent of data within the interval from 39 to 55 which is normally distributed is 68.26%.
What is Normal and Standard Distribution ?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.
A probability bell curve is more properly described as the normal distribution.The mean and standard deviation of a normal distribution are 0 and 1, respectively. It has a kurtosis of 3 and zero skew.Not all symmetrical distributions are normal, but all normal distributions are symmetrical.Natural occurrences frequently resemble the usual distribution.However, most price distributions in finance are not quite normal.A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardize it. Z scores provide the number of standard deviations from the mean that each value falls within.
Given in the problem mean is 47 and Standard Deviation(SD) is 8
Probability of data within 39 to 55 is
P(x<55) - P(x<39)
Let Z be the standard deviation :
[tex]\phi(Z) = \frac{x - mean}{SD}[/tex].
for X = 39
[tex]\phi(Z) = \phi(\frac{x - mean}{SD})[/tex] = [tex]\phi(\frac{39 - 47}{8}) = \phi(-1) = 1 - \phi(1) = 1-.8413 = .1587[/tex]
for X = 55
[tex]\phi(Z) = \phi(\frac{x - mean}{SD})[/tex] = [tex]\phi(\frac{55 - 47}{8}) = \phi(1) = .8413[/tex]
The percent of data within the interval from 39 to 55
(.8413 - .1587) = .6826 = 68.26%
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n- ? 1) When loan officers speak to people about taking out a loan for a certain principal, P at a certain monthly rate, they always have to balance two quantities, the monthly payment, m] with the number of payments, n] it takes to pay off the loan. These two vary inversely. All of these quantities can be related by the formula: Por 1-(1+r)¯" m= Calculate the monthly payment needed to pay off a $200,000 loan at 4% yearly interest over a 20-year period.. 110
[tex]m = \frac{200000.1/3}{1-(2/3)^{-240} }[/tex] is the monthly payment
What is Compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
According to given question:
Principle Amount (P) = $200, 000
Rate(r) = 4% yearly
Rate(r) = 4/12 % Monthly
Rate(r) = 1/3 % Monthly
Time = 20 years = 240 months
⇒ 240 is the number of payment needed to pay
n = 240
Therefore, the monthly payment needed to pay
⇒ [tex]m = \frac{P.r}{1-(1-r)^{-n} }[/tex]
⇒ [tex]m = \frac{200000.1/3}{1-(1-1/3)^{-240} }[/tex]
⇒ [tex]m = \frac{200000.1/3}{1-(2/3)^{-240} }[/tex]
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juan is trying to save pizza from dinner, so he can bring pizza to school for lunch he bought 1 3/7 od pepperoni pizza and ate 1 1/3 of the pepperoni pizza how much pizza does he have left to bring to school?
Answer:
i think 2/21 i think im wrong
Step-by-step explanation:
he table below models the cost, y, of using a high-efficiency washing machine and a standard washing machine over x number of years. Which equation represents the cost of the high-efficiency washing machine over a given number of years? Which equation represents the cost of the standard washing machine over a given number of years? After how many years of use would the washing machines cost the same amount? Which washing machine would be the more practical purchase if kept
How do I solve for x?
Apply arithmetic operations to both sides of the equation to bring the variable to one side and all other values to the other side in order to find the value of x. To determine the outcome, simplify the values.
Meaning of y = mx + b
The slope-intercept formula for a straight line is y = mx + b. m is referred to as the line’s slope and b is referred to as the line’s y-intercept in the equation y = mx + b for a straight line. Y = mx+b, where
Y ⇒ how far up or down is the line,
X ⇒ how far along is the line,
B ⇒ the value of y when x = 0 and
M ⇒ how steep the line is.
This is determined by m = (difference in y coordinates)/ (difference in x coordinates).
1. we have to determine a straight line equation that models the cost of High-Efficiency washing machine over the years;
Slope of the line = change in y / change in x
= [tex]\frac{550-525}{2-1}[/tex]
= 25
Equation will be
y= 25x+c
Where y is the cost of the High-Efficiency washing machine and x the number of years.
To find c we take points from table,
525= 25×1+ c
c= 525-25
c= 500
Therefore, y= 25x+ 500
2. we have to determine a straight line equation that models the cost of Standard washing machine over the years;
Slope of the line = [tex]\frac{430-400}{2-1}[/tex]
= 30
Equation will be,
y= 30x+c
where y is the cost of the Standard washing machine and x the number of years.
To find c we take points from table,
430= 30×1+ c
c= 430-30
c= 400
Therefore, y= 30x+ 400
3. Given the cost functions for both machines over the number of years, we simply equate the two equations and determine the value of x when both machines would cost the same amount;
y= 25x+ 500
y= 30x+ 400
Equating both equations,
30x+ 400= 25x+ 500
30x- 25x= 500-400
5x= 100
x =[tex]\frac{100}{5}[/tex]
x= 20
Therefore, the washing machines would cost the same amount after 20 years of use.
4. To determine which machine would be the more practical purchase if kept for 9 years we use the cost functions obtained in 1. and 2.
High-Efficiency washing machine
y= 25x+ 500
y= 25×9+ 500
y= 725
Standard washing machine
y= 30x+ 400
y= 30×9+ 400
y= 670
Therefore, the cost for the Standard washing machine is more practical.
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The ratio of females to males at a movie is 8 7 If there are 28 males how many females
are in the movie
Answer: 32 females
Step-by-step explanation:
28 divided by 7 = 4
so, multiply 8 by 4 as well.
Answer: 32 females are at the movie
Step-by-step explanation:
8(females):7(males)
x:28
28/7= 4
x=4x8
x=32
There are 32 females
please helppppp :(((
Answer: Crust and asthenosphere should be switched
Step-by-step explanation:
Brainliset please?
Answer:
Step-by-step explanation:
crust is the surface of the earth and the asthenosphere below it with currents that cause earthquakes.
how would increases in tolerable misstatement and assessed level of control risk affect the sample size in a substantive test of details
Increases in tolerable misstatement will decrease sample size and assessed level of control risk will Increase sample size in a substantive test of details.
Sample size will be decreased when there is an increase in tolerant misstatement because there is a deviation that does not impact the financial statement. An increase in the assessed level of control risk, on the other hand, will increase sample size because the risk of material misstatements has also increased.
Complete question:-
How would increases in tolerable misstatement and assessed level of control risk affect the sample size in a substantive test of details?
a. Increase in Tolerable Misstatement = Decrease sample size. Increase in Assessed Level of Control Risk = Decrease sample size
b. Increase in Tolerable Misstatement = Decrease sample size. Increase in Assessed Level of Control Risk = Increase sample size
c. Increase in Tolerable Misstatement = Increase sample size. Increase in Assessed Level of Control Risk = Decrease sample size
d. Increase in Tolerable Misstatement = Increase sample size. Increase in Assessed Level of Control Risk = Increase sample size
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PLEASE EXPLAIN AND SHOW YOUR WORK THANK YOU!!
Solve as a MIXED NUMBER:
-2.25 + 0.4x = -2.8
THANK YOU!
The value of x on the equation 2.25 + 0.4x = -2.8 is -0.1375.
How to calculate the value of x?A 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.
The equation is given as;
- 2.25 + 0.4x = -2.8
Collect the like terms
0.4x = -2.8 + 2.25
0.4x = -0.55
Divide
x = -0.55 / 0.4
x = - 0.1375
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A fast food outlet claims the mean waiting time in line is less than 3. 5 minutes. A random sample of 20 customers has a mean of 3. 7 minutes with a standard deviation of 1 minute. What will be the test statistic?.
Answer:
To determine the test statistic for this problem, we need to first calculate the standard error of the mean. This is given by the formula:
Standard error of the mean = Standard deviation / sqrt(n)
where n is the number of samples in the population. In this case, the standard deviation is 1 minute and the number of samples is 20, so the standard error of the mean is equal to 1 / sqrt(20) = 0.22.
We can now use this value to calculate the test statistic, which is given by the formula:
Test statistic = (Sample mean - Population mean) / Standard error of the mean
In this case, the sample mean is 3.7 minutes, the population mean is less than 3.5 minutes, and the standard error of the mean is 0.22. Since the population mean is less than 3.5 minutes, we will use 3.5 as the value for the population mean in our calculation. Plugging these values into the formula, we get:
Test statistic = (3.7 - 3.5) / 0.22 = 0.22 / 0.22 = 1
Therefore, the test statistic for this problem is 1. This value indicates that the sample mean is slightly higher than the population mean, but not by a significant amount.
16 - x^2
x^2 - 9y^2
1/25x^2 - 64y^2
Answer:
The solutions to the given equations are x = 4, x = -4, x = 3y, x = -3y, 1/5x = 8y, and 1/5x = -8y.
Step-by-step explanation:
These are all algebraic expressions, which are combinations of variables, numbers, and mathematical operations. The first expression, 16 - x^2, is an example of a difference of squares. The second expression, x^2 - 9y^2, is also a difference of squares. The third expression, 1/25x^2 - 64y^2, is a difference of squares with a fractional coefficient in front of the first term.
To solve an equation, we need to find the values of the variables that make the equation true.
For the first equation, 16 - x^2, we can solve it by adding x^2 to both sides to get rid of the negative sign. This gives us 16 = x^2, and then we can take the square root of both sides to get x = +/- 4. Therefore, the solutions to this equation are x = 4 and x = -4.
For the second equation, x^2 - 9y^2, we can solve it by factoring the left-hand side to get (x - 3y)(x + 3y) = 0. This means that the product of the two factors on the left-hand side must be equal to 0, so either x - 3y = 0 or x + 3y = 0. Solving each of these equations separately, we get x = 3y and x = -3y. Therefore, the solutions to this equation are x = 3y and x = -3y.
For the third equation, 1/25x^2 - 64y^2, we can solve it by factoring the left-hand side to get (1/5x - 8y)(1/5x + 8y) = 0. This means that the product of the two factors on the left-hand side must be equal to 0, so either 1/5x - 8y = 0 or 1/5x + 8y = 0. Solving each of these equations separately, we get 1/5x = 8y and 1/5x = -8y. Therefore, the solutions to this equation are 1/5x = 8y and 1/5x = -8y.
In summary, the solutions to the given equations are x = 4, x = -4, x = 3y, x = -3y, 1/5x = 8y, and 1/5x = -8y.
(9x -38)= (2x+42) find mf this exam is crazy
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
x=80/7
Decimal Form: x=11.428
or 11.44
Mixed Number Form: x=11 3/7
The school's math team has 14 new members this year, which makes a total of 34. The number of new members represents about what percent of the total membership?
41% of the math team's total members are brand-new recruits.
What is percentage ?It is the ratio of two integers expressed as a decimal fraction of a whole number. It is a statistic for contrasting two sets of data, and the % sign is used to describe it as a percentage.
Percentages are often and creatively used. For instance, a lot of data is published as percentages in the media, including bank interest rates, retail discounts, and inflation rates. Percentages are essential for grasping the financial aspects of daily living.
The percentage of the entire membership that the number of new members represents is determined to be
=(14/34)×100
=41 %
0.41 x 100 = 41%
This means that 41% of the club is new members!
Thus, the number of new members is 41% of the total membership of the maths team.
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Given: Angle R is congruent to Angle Q Segment AS is congruent to Segment AT Which of the following may not be true?
Angle 5 is congruent to Angle 6
Segment AR is congruent to Segment AQ
Segment RS is congruent to Segment TQ
Angle 2 is congruent to Angle 3
Charlotte bought a magazine for $5 and four boxes of candy. She spent a total of $25. How much did each box of candy cost?
Answer: $5
Step-by-step explanation: To calculate how much she spent on the 4 boxes of candy, we need to subtract 5 from 25, because we won't be including the cost of the magazine. So, therefore 25-5 is 20. So, now to find the cost for one, we need to set up a proportional relationship like this:
[tex]\frac{20}{4}[/tex] = [tex]\frac{?}{1}[/tex]
So, with that, we need to divide 4 by 20 to find the cost of 1. So, if you know, 20 divided by 4 = 5. So, therefore the cost of each candy box is $5. We can check our answer if we use the inverse operations, so our new equation would look like this:
5(4) + 5 = 25
We can check this, because we know 5 x 4 = 20, and 20 + 5 = 25. So 25 = 25, so it is $5.00
9. A straight line passes through points (2, 12) and (3, 8). What is the equation of the
line?
Help with question 4
Answer:
It is 11-9/16
Step-by-step explanation:
g(x) = x² - 4x²+x+6
The simplified expression of g(x) = x² - 4x² + x + 6 is g(x) = -3x² + x + 6
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
g(x) = x² - 4x²+x+6
Rewrite properly
So, we have the following representation
g(x) = x² - 4x² + x + 6
Evaluate the like terms
g(x) = -3x² + x + 6
The above expression cannot be further simplified
Hence, the solution is g(x) = -3x² + x + 6
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set the two equations to each other then solve for x y=2x-3
Answer:
The value of x is (y + 3)/2
Step-by-step explanation:
y = 2x - 3
y + 3 = 2x - 3 + 3
y + 3 = 2x
2x/2 = (y + 3)/2
x = (y + 3)/2
Thus, The value of x is (y + 3)/2
Answer:
x = (y + 3)/2
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ y = 2x - 3
Then the value of x will be,
→ y = 2x - 3
→ 2x - 3 = y
→ 2x = y + 3
→ x = (y + 3)/2
→ x = (y/2) + (3/2)
Hence, answer is x = (y + 3)/2.
What is the partial sum of terms 12 to 15 of the arithmetic sequence 100, 88, 76, 64, …?
The provided sequence's 12th through 15th terms add out to -200.
The formula is used to get the sum of n terms in an arithmetic sequence.
Sn = ((2×a₁)+(d×(n -1)))×(n/2)
where d is the common difference and a₁ is the first number in the series.
Finding the total of four words in a series that starts with 100, 88, 76 is necessary to solve this issue. These are the 12th through 15th terms.
General Term
The formula indicates what an arithmetic sequence's general term is.
aₙ = a₁ +d(n-1)
where d is the common difference and a is the first term.
The first term in the above sequence, a₁ is 100, and the common difference is...
d = 88 -100 = -12
Then the general term is
aₙ = 100 -12(n -1)
The 12–15 term total is what we need. This sub-first sequence's phrase is
a₁₂ = 100 -12(12 -1) = 100 -132 = -32
The following words in the series will all share a -12 common difference. The following sum formula may be used to get the total of the four terms:
Sₙ = (2·a₁+d(n -1))(n/2) . . . . . . . for a₁=-32, d=-12, and n=4
S₄ = (2·(-32) -12(4 -1))(4/2) = (-64 -36)(2) = -200
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Go step by step to reduce the radical
The reduced form of the radical √192 is 8√3.
How to reduce radicals?A radical is a symbol that represents a particular root of a number. Radical simply means square root of a number.
Therefore, the symbols for radical is √.
Let's reduce the radical accordingly,
√192
Let's find number you can multiply to get 192. One of the numbers will be a perfect square.
Therefore, the numbers are 64 and 3. 64 is the perfect square.
Therefore,
√192 = √64 × 3 = √ 8² × 3 = 8√3
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help me pleaseeeeeeee
Answer:
Step-by-step explanation:if angle a is 42 then b is 42 which means its 42 right, so its cos(42)=AB over 10, the last one its a educated guess.
If ABC is equilateral, solve for x
Plssssssssssssssssssss
the variability believed to be in the population, the acceptable margin of sample error, and the level of confidence required in your estimates of the population values describe the basic elements required to calculate the proper sample size for a survey. true false
The statement mentioned in the question is True.
The sample size of a survey is determined by the variability believed to be in the population, the acceptable margin of sample error, and the level of confidence required in estimates of the population values. These elements are important considerations when designing a survey because they help to ensure that the results of the survey are reliable and accurately reflect the characteristics of the population being studied.
To calculate the proper sample size for a survey, you need to first determine the size of the population being studied and the level of precision you want to achieve in your estimates. You also need to consider the level of confidence you want to have in your estimates and the acceptable margin of error for your survey. Once you have all of this information, you can use a sample size calculator or a statistical formula to determine the appropriate sample size for your survey.
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