[tex]\begin{cases} x = -3 &\implies x +3=0\\ x = 2 &\implies x -2=0\\ x = 4 &\implies x -4=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{ ( x +3 )( x -2 )( x -4 ) = \stackrel{0}{y}}\implies (x+3)(x^2-6x+8)=y \\\\\\ x^3-6x^2+8x+3x^2-18x+24=y\implies \boxed{x^3-3x^2-10x+24=y}[/tex]
What is the highest common factor of 25, 75 and 150?
The required highest common factor of 25, 75, and 150 is 25.
What is the highest common factor?
The highest common factor (HCF) of two or more numbers is the largest number that divides all of the numbers exactly.
To find the HCF of 25, 75, and 150, we can first find the prime factorization of each number and then look for the common factors.
Prime factorization of 25, 25 = 5²
Prime factorization of 75:, 75 = 5² × 3
Prime factorization of 150, 150 = 2 × 3² × 5²
The largest factor that all three numbers have in common is 5², which is 25.
So, the HCF of 25, 75, and 150 is 25.
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7/40 x 1/2 =?
Simplest form, please and thank you! (The slashes are fractions not division)
Answer: 7/80
Step-by-step explanation: This is already the simplest form of this fraction.
Answer: 7/80
Step-by-step explanation:
lol please help me
Given y = 2/5 x make a chart of the first eleven inputs and outputs, and then write the ordered pairs. Start with the input of 0 and end on 10. Leave the numbers in improper fraction form.
THANK YOU SO MUCH
If an object is projected vertically upward with a velocity of 29.4 m/s from a height of 30 m, then its height h above the ground in meters after t seconds is given by h = 30 + 29.4t - 4.9t^2. What is the maximum height the object will reach?
If you could show work, that would be excellent. Thank you!
Answer:
Step-by-step explanation:
we can determine the maximum height using the expression given after finding the value of time at which the object reaches the maximum height. In order to find the time at which the object reaches the maximum height we need to use one of the UAM formulas.
and the compatible UAM formula is: vf=vi+at, we use UAM formula because the object is uniformly accelerating due to gravitational force.
vf=vi+at, at the point where the object reaches the maximum height its velocity will be zero so vf=0 and vi=29.4m/s.
given
a=-9.8m/s^2
vf=0
vi=29.4m/s
t=?
0=29.4-(9.8)t
-29.4= -9.8t
t= 29.4/9.8
t=3 seconds, it takes 3 seconds to reach the maximum height starting from a height of 30m.
h=30+29.4(3)-4.9(3)^2
h=30+88.2-44.1
h=118.2-44.1
h=74.1 m
is 6(-b+8) and 2(-3b+4) equivalent expressions.
Answer:
They are not equivalent expressions
Step-by-step explanation:
Let's expand each expression and see if they are the same
6(-b + 8) = 6 x (-b) + 6 x 8 = -6b + 48
2(-3b + 4) = 2 x (-3b) + 2 x 4 = -6b + 8
So while the terms -b are the same, the constants are different
Hence the two expressions are not equivalent
What calculator is used for pre-calculus?
A scientific calculator is typically used for pre-calculus.
This type of calculator is designed to handle more advanced mathematical functions, such as trigonometry, logarithms, and exponents, which are commonly used in pre-calculus.
It is important to have a scientific calculator for pre-calculus because it allows you to easily solve more complex equations and perform calculations quickly and accurately.
Additionally, many scientific calculators have graphing capabilities, which can be useful for visualizing equations and understanding how they behave. Overall, a scientific calculator is an essential tool for pre-calculus and can help you succeed in the course.
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In a triangle ABC, AB=AC. If D is the mid-point of the side BC, prove that:
i) AD is perpendicular to BC.
ii) AD bisects angle BAC
Answer:
Step-by-step explanation:
Given: In triangle ABC, AB = AC and D is the midpoint of BC.
To prove:
i) AD is perpendicular to BC.
We can prove this by using the midpoint theorem, which states that a line segment connecting the midpoints of two sides of a triangle is perpendicular to the third side and half as long as the third side.
Since D is the midpoint of BC, we have BD = DC. Thus, the line segment AD connects the midpoints of sides AB and AC of triangle ABC.
By the midpoint theorem, AD is perpendicular to BC and AD = BC / 2.
ii) AD bisects angle BAC
We can prove this by using the fact that if two line segments are perpendicular and one is an altitude of a triangle, then the two line segments divide the triangle into four smaller triangles that are congruent by SAS congruence.
Since AD is perpendicular to BC, we have two right triangles, ABD and ACD. By the Pythagorean theorem, we have AB = AC, which means that ABD and ACD are congruent by SAS congruence.
Since ABD and ACD are congruent, we have angle BAD = angle CAD. Also, since angle BAC is the sum of angles BAD and CAD, we have angle BAC = 2 * angle BAD.
Therefore, by substitution, we have angle BAC = 2 * angle CAD. This means that angle CAD is half of angle BAC, or in other words, AD bisects angle BAC.
Hence, we have proved that in triangle ABC, AD is perpendicular to BC and AD bisects angle BAC.
find missing value
i rlly need help thanks
Answer:
x = 9
Step-by-step explanation:
if three or more parallel lines are intersected by two or more transversals, the parallel lines divide the transversals proportionally , that is
[tex]\frac{3}{x}[/tex] = [tex]\frac{2.5}{7.5}[/tex] = [tex]\frac{1}{3}[/tex] ( cross- multiply )
x = 3 × 3 = 9
which ration is the largest 18: 5 or 27: 25
A small theater had 9 rows of 27 chairs each. Workers just removed 7 of these chairs. How many chairs are left?
Answer:
236
Step-by-step explanation:
number of chairs left = total chairs - 7 chairs
total chairs = 9 × 27
= 243
243 - 7
= 236
Answer: 236
Step-by-step explanation:
We have to figure out how many chairs there are in total so you will do 9*27. That is 243. If 7 were removed, you would do 243-7 which is 236. Therefore, there are 236 chairs left.
what sources of errors are included in the margin or error?
These are some of the main sources of error that can contribute to the margin of error in a survey or study.
What is the margin of error?The margin of error in a statistical survey or study is a measure of the uncertainty or variability in the results.
Here,
The margin of error reflects the potential difference between the sample estimate and the true population value. The margin of error is calculated by taking into account various sources of errors, including,
Sampling error: Sampling error arises from the fact that the sample is only a subset of the population and thus may not perfectly represent the population. The larger the sample size, the smaller the sampling error.
Other various sources are non-response error, Coverage error, Measurement error, Response bias, Weighting error, and Model error.
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the ________ is the positive square root of the sample variance.
The standard deviation is the positive square root of the sample variance.
Describe Standard Deviation?Standard deviation is a measure of the spread or dispersion of a set of data from its mean (average) value. It tells us how much the individual values in a dataset deviate from the average value. In other words, it indicates the extent to which the data points are spread out or clustered around the mean.
The formula for standard deviation is the square root of the variance, which is calculated by finding the average of the squared differences between each data point and the mean. The standard deviation is expressed in the same units as the original data and is denoted by the symbol "σ" for the population standard deviation or "s" for the sample standard deviation.
A small standard deviation indicates that the data points are clustered around the mean, while a large standard deviation indicates that the data points are spread out over a wider range. The standard deviation can be used to determine the range of values within which the majority of the data points lie. For example, if the standard deviation is 2, then about 68% of the data points will be within 2 standard deviations of the mean.
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please help me on this
In ΔJKL, l = 920 inches, j = 880 inches, and ∠K=157°. Find the length of k, to the nearest inch.
In the triangle ΔJKL, the length of side k found using the law of cosines is approximately 1764 inches.
What is meant by the law of cosines?
The law of cosines, commonly referred to as the cosine formula or cosine rule, is a relation in trigonometry that links the lengths of a triangle's sides to the cosine of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them.
If ABC is a triangle, then as per the statement of cosine law, we have:
c = [tex]\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}[/tex]
where,
c = length of side c
a = length of side a
b = length of side b
γ = angle opposite c
Given a triangle, ΔJKL
The length of side l= 920 inches
The length of side j = 880 inches
∠K = 157°
According to the law of cosines,
k² = l² + j² - 2.l.j . cos K
= 920² + 880² - 2 * 920 * 880 * cos (157°)
= 846400+ 774400 - (-1490481.46)
= 3111281.46
k = 1763.88 = 1764 inches.
Therefore the length of side k found using the law of cosines is approximately 1764 inches.
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A ticket to an all day concert is priced at $115, plus an additional 9% sales tax.
Which of the following statements correctly describes how to find the total cost of the ticket?
The total cost of the ticket is 125.35 dollars.
How to find the total cost?A ticket to an all day concert is priced at $115, plus an additional 9% sales tax.
The statements that describes how to find the total cost of the ticket can be represented as follows:
sale tax = 9% of 115
sale tax = 9 / 100 × 115
sale tax = 1035 / 100
sale tax = 10.35 dollars
Therefore,
total cost = 10.35 + 115
total cost = 125.35 dollars
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15 solids and liquids found in the house.
What are the mass 15 solids and volume of the 15 liquids.
Please help.
15 solids found in the house and their mass are:
Toilet paper roll - 0.25 kgCan of soda - 0.35 kgCoffee mug - 0.2 kgBooks - 0.5 kg (per book)Pillow - 0.7 kgLamp - 1.5 kgChair - 4 kgTelevision - 15 kgSofa - 30 kgMattress - 20 kgTable - 10 kgBlanket - 1.5 kgShoes - 0.5 kg (per shoe)Lampshade - 0.2 kgPlates - 0.1 kg15 liquids and volumes of these liquids :
Glass of water - 250 mLShampoo bottle - 500 mLDish soap bottle - 750 mLLaundry detergent bottle - 1.5 LMilk carton - 1 LCooking oil bottle - 2 LHand sanitizer bottle - 50 mLToilet cleaner bottle - 750 mLSpray bottle of cleaner - 500 mLKetchup bottle - 500 mLMustard bottle - 250 mLVinegar bottle - 1 LCooking spray can - 200 mLLiquid soap dispenser - 500 mLMouthwash bottle - 500 mLWhat are some typical solids and liquids in the house ?Some typical solid objects that can be found in a typical house would be chairs, tables, televisions, lamps and lampshades and tableware like plates, bowls, and spoons.
As for liquids, there is milk, mustard and ketchup. Then there are the cleaning liquids such as shampoos and hand sanitizers.
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The table shows ordered pairs of the function y=8-2x. What is the value of y when x = 8?
-20
-8
8
48
The numerical value of y in the function y = 8 - 2x when x equals 8 is -8.
What is the numerical value of y when x equals 8?A function is simply a relationship that maps one input to one output.
Given the function in the question;
y = 8 - 2x
x = 8y = ?To determine the value of y, replace all occurrences of x in the function with 8 and simplify.
y = 8 - 2x
Plug in x = 8
y = 8 - 2( 8 )
y = 8 - 16
y = -8
Therefore, the value of y is -8.
Option B) -8 is the correct answer.
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Question 5
Tickets to Greendale High School soccer game cost $7 for adults and $5 for students. There is a total of 150 tickets
sold for $850. How many adult tickets are sold and how many student tickets are sold?
Part A
Write a system of equations that represents the situation.
x + y =
Part B
x + 5y =
Solve the system of equations. Express the coordinates as decimals if necessary.
Part C
Interpret the solution.
there are __ adult tickets and __ student tickets sold
Answer:
Part A
x + y = 150
Part B
7x + 5y = 850
Part C
Solution is x = 50, y = 100
there are 50 adult tickets and 100 student tickets sold
Step-by-step explanation:
Let x = number of adult tickets and y= number of student tickets
We have the following equation
x + y = 150 (1) =>total number of tickets
7x + 5y = 850 (2) > total cost of x adult and y student tickets
Multiply (1) x 5:
5x + 5y = 750 (3)
Subtract (2) - (3)
7x + 5y - (5x + 5y) = 850 - 750
7x - 5x + 5y - 5y = 100
2x = 100
x = 50
y = 150 - 50 = 100
The circumference of a circle is 260.62 feet. What is the radius of the circle? Use 3.14 for π.
[tex] \: [/tex]
[tex] \rm{ {π ( pi ) = \bold{3.14}}}[/tex][tex] \: [/tex]
To find:-[tex] \rm{radius= ?}[/tex][tex] \: [/tex]
By using formula:-[tex] \boxed{ \rm{Circumference \: of \: circle \: = \bold{2πr}}}[/tex][tex] \: [/tex]
Solution:-[tex] \rm{C = 2 π r}[/tex][tex] \: [/tex]
[tex] \rm{260.62 = 2 × 3.14 × r}[/tex][tex] \: [/tex]
[tex] \rm{260.62 = 6.28r}[/tex][tex] \: [/tex]
[tex] \rm{r = \cancel\frac{260.62}{6.28} }[/tex]
[tex] \: [/tex]
[tex] \underline{ \boxed{ \rm{ \red{ \: r = 41.5 \: }}}}[/tex]
[tex] \: [/tex]
The radius of circle is 41.5.
hope it helps! :)
what is the name of the relationship between ∠1 and ∠4?a. corresponding angles
b. alternate interior angles
c. obtuse angles
d. adjacent angles
The name of the relationship is b. Alternate interior angles.
Alternate interior angles are two angles that are located on opposite sides of a transversal line, but within the same two lines. When two lines are cut by a transversal line, the alternate interior angles are always congruent, meaning that they have the same measure.
In this case, angles ∠1 and ∠4 are alternate interior angles. Alternate interior angles are formed when two parallel lines are cut by a transversal line. When this happens, corresponding angles are formed on the same side of the transversal.
The alternate interior angles are the two angles that are on opposite sides of the transversal. These angles are also congruent, meaning that they have the same measure.
To summarize, alternate interior angles are two angles that are located on opposite sides of a transversal line and within the same two lines. In this case, angles ∠1 and ∠4 are alternate interior angles, meaning that they have the same measure.
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AGAIN HELP!!!!!!!!!!!!!!!STILL TRYING TO TEACH MYSELF LOL
How many pounds in 73.5 kg?
There are 2.20462 pounds in one kilogram.
Therefore, to convert 73.5 kilograms to pounds, you would multiply 73.5 by 2.20462.
The calculation is as follows:
73.5 kg * 2.20462 pounds/kg = 162.04101 pounds
So, there are approximately 162.04101 pounds in 73.5 kilograms.
By the definition conversion of units means the conversion between different units and the measurements of the same quantity done by either the process of multiplication or division.
In maths, conversion is referred as the process of changing the value of one form to another for example inches to millimeters, or liters to gallons.
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How do you find the expression for the nth term in an exponential sequence.
Example:-
1, 3, 7, 15
Answer:
Step-by-step explanation:
Ans:n^th=2n-1
we are going to use the formula of arithmetic sequence.
We need to find the first term of the sequence which is 1 and find the difference between any two number.
Then simply multiply the different by (n-1)
Finally add the result with first term which is 1.
Han calculated the volume of a cylinder. Han said, “I used the formula V=[tex]\pi r^{2} h."[/tex]
Do you agree with Han's strategy? Explain your reasoning.
Han's strategy is correct, as V = πr²h is the exact formula for the volume of a cylinder of radius r and height h.
How to obtain the volume of a cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
This is the exact formula used by Han, hence the strategy is correct.
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A 6 month loan has $5,000 in proceeds and a discount rate of 10%. Determine the face value
Answer:
the face value of the loan is $5,263.16.
Step-by-step explanation:
To determine the face value of the loan, we need to use the formula:
Face Value = Proceeds / (1 - Discount Rate * Time)
where "Time" is the time period of the loan in years.
Since the loan is for 6 months, we need to convert this time to years by dividing it by 12. Therefore, "Time" = 6/12 = 0.5 years.
Now, we can substitute the given values into the formula:
Face Value = 5,000 / (1 - 0.1 * 0.5)
Face Value = 5,000 / (1 - 0.05)
Face Value = 5,000 / 0.95
Face Value = $5,263.16 (rounded to the nearest cent)
Therefore, the face value of the loan is $5,263.16.
The box plot represents the number of hours of battery life in different cell phones.What is maximum battery life?
Answer:
The maximum battery life is 27 hours
Step-by-step explanation:
The box plot represents the number of hours of battery life in different cell phones.
We have to find the maximum battery life.
What is box plot?
The box plot is a type of chart often used in explanatory data analysis.
Now,
By figure the maximum life of a battery is 27 hours.
Hence, The maximum battery life is 27 hours.
What is the value of 20 in asl
To calculate the mathematical value of 20, you would use the : 20 x 1 = 20. This means that 20 multiplied by 1 is equal to 20. Therefore, the value of 20 in ASL is equal to 20.
ASL stands for American Sign Language. It is the visual language used by the deaf and hard of hearing communities to communicate. In ASL, the sign for the number 20 is done by holding up both hands with the palms facing out and fingers spread apart. The hands are then moved together in a circular motion with the fingers crossed at the end. This sign is also used to represent the mathematical concept of multiplication. To express the value of 20 in ASL, you would sign the number 20 by making the above mentioned sign, and then sign the word "equals". To calculate the mathematical value of 20, you would use the formula: 20 x 1 = 20. This means that 20 multiplied by 1 is equal to 20. Therefore, the value of 20 in ASL is equal to 20.
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What happens to the value of the expression 5/x+5 as x decreases from a large positive number to a small positive number?
The value of the given expression increases, because as x decreases, 5/x increases
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, what happens to the value of the expression 5/x+5 as x decreases from a large positive number to a small positive number,
We know that, If the denominator of the fraction is decreased, the value of a fraction is increased while the numerator remains unchanged.
Therefore, if the value of x in the given starts decreasing the value of the whole fraction will start increasing.
Hence, the value of the expression increases, because as x decreases, 5/x increases
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what is the value of 130 kph in mph
To convert kilometers per hour (kph) to miles per hour (mph), we use the following formula: mph = kph x 0.621371. This is because there are 0.621371 miles in a kilometer.
To calculate the value of 130 kph in mph, we can simply plug the value into the formula: mph = 130 x 0.621371 = 80.78 mph. Therefore, the value of 130 kph in mph is 80.78 mph. To further understand how this conversion works, we can break down the calculation into its basic components. First, we divide 130 by 1. That gives us 130. Then, we multiply 130 by 0.621371, which gives us the result of 80.78. Therefore, the value of 130 kph in mph is 80.78 mph. The above formula and calculation can be used to convert any value from kph to mph. All we need to do is plug the kph value into the formula and we will get the equivalent mph value. It is important to note that the conversion from kph to mph is not exact, as there are slight variations in the exact value of a kilometer. However, this formula provides a good approximation and is accurate enough for most purposes.
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What is the value today of $5,100 per year, at a discount rate of 7. 9 percent, if the first payment is received 6 years from today and the last payment is received 20 years from today?.
The present value of the payment is: $25,015.42
Now, According to the question;
An annuity is series of equal annual payments or receipts made for a certain number of years.
A delayed annuity is that which the first cash flow occurs at a time later than year one.
A standard annuity is that which the first cash flow occurs a year from now.
An advanced annuity is that which first cash flow occurs immediately or now.
$5,100 per where the first payment occurs in year 6 and end 20 years from today is an example of a delayed annuity.
Present Value = A ×( 1 - (1+r)^(-n))/r
= 5,100 × ( 1 - (1+0.079)^(-11))/0.079
= 36,586.01
Present Value = Future Value × (1 + r)^(-n)
Present Value = $ 36,586.01 × (1+0.079)^(-5)
Present value = $25,015.42
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