The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).
What is a polynomial ?
A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) multiplied by coefficients.
where n is a non-negative integer (the degree of the polynomial), x is the variable, and (the coefficients of the polynomial). The highest power of x in the expression is n, and this term is called the leading term. The coefficient of the leading term, a_n, is called the leading coefficient.
To find the other linear factors of the polynomial function f(x) = x³ - 4x² - 3x + 18, we can use long division by dividing the polynomial function by (x + 2).
Here's how the long division would look like:
x³ - 4x² - 3x + 18
÷ x + 2
__________________________
x² - 6x - 20
÷ x + 2
__________________________
x - 22
÷ x + 2
__________________________
-20
here -20 is the remainder.
The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).
So, the other linear factors are x - 22.
Therefore, The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).
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Translate the sentence into an inequality.
Seven subtracted from b is less or equal to -18
If sentence be "Seven subtracted from b is less or equal to -18" then the inequality be b – 7 ≤ -18
What is meant by inequality?A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. Thus inequality emerges from an imbalance.
Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >, <, ≤ or ≥.
An inequality symbol represents that the expressions on each side are not equal. It indicates that the expressions on the left and right should be bigger or less than one another, or vice versa.
Let the given sentence be "Seven subtracted from b is less or equal to -18" then the inequality be b – 7 ≤ -18
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For each of the following graphs, the two given polygons are similar. Write precisely a single dilation (coordinates of center and coefficient) by which the image (labeled with primed letters) was obtained.
Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.
What is dilation?Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image. Resizing an object is accomplished through the transformation of dilation. The objects can be enlarged or shrunk using dilation. The result of this transformation is an image that has the same shape as the original shape. The size of the shape varies, though. A dilation should either stretch or contract the original shape. The term "scale factor" describes this transformation.
From the diagram:
Scale factor = A'B' / AB = 6/3 = 2
Center = (6, -6)
Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.
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Line ℓ has equation y=-x+4. Find the distance between ℓ and the point F(-1 7)
Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
To find the distance between a line and a point, we need to find the perpendicular distance from the point to the line. Here's the step-by-step process:
Find the equation of the line perpendicular to ℓ that passes through point F(-1, 7): Since the slope of line ℓ is -1, the slope of the perpendicular line will be the negative reciprocal of -1, which is 1. To find the equation of the line, we need a point and the slope. Point F(-1, 7) will be used, and the slope is 1.
Using the point-slope form of a line, we can write the equation of the perpendicular line passing through point F as: y - 7 = 1(x + 1). Simplifying, we get: y = x + 8.
To find the point of intersection between the two lines, we can substitute the equation of line ℓ into the equation of the perpendicular line:
-x + 4 = x + 8
Solving for x, we get x = 6. Substituting x = 6 into the equation of line ℓ, we get:
y = -6 + 4 = -2
So, the point of intersection between the two lines is (6, -2).
To find the distance between the point F and the line ℓ, we can use the distance formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) is the point F(-1, 7) and (x2, y2) is the point of intersection (6, -2).
So, substituting the values into the formula:
distance = √((6 - (-1))^2 + ((-2) - 7)^2) = √((7)^2 + (9)^2) = √(49 + 81) = √(130) = approximately 11.3
Therefore, the distance between the line ℓ and point F is approximately 11.3 units.
Suppose a turtle walks 3/8 of a mile in 50 minutes what is the unit rate
Answer:
3/400 per min
Explanation:
Divide the rate at which he can walk by the number how mins he can walk at that rate
Generally, the more someone exercises the less they will weigh (while also maintaining a proper diet). John has started exercising and eating healthy and has recorded his weight each week. Using a regression model, how much would you expect john to weigh at the end of week 8 if he continues with his new routine? (round your answer to the nearest tenth. ).
We would expect John to weigh approximately 216.4 pounds at the end of week 8.
To answer this question, we need to fit a regression model to the data to determine the relationship between the number of calories burned and John's weight. We can use linear regression to find the line of best fit that represents this relationship.
We can see that there is a negative relationship between the number of calories burned and John's weight, which is consistent with the statement that "the more someone exercises the less they will weigh." We can use linear regression to find the line of best fit that represents this relationship.
Using a linear regression model, we get the following equation:
Weight = 219.9 - 0.0007 * Exercise
We can use this equation to predict John's weight at the end of week 8 based on the number of calories he burned. Plugging in Exercise = 5000, we get:
Weight = 219.9 - 0.0007 * 5000
Weight = 216.4
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Samantha is trying to run for City Council, but she needs to have
500 total signatures on her petition in order to get on the ballot. She currently has 284 signatures and believes that her team of volunteers can get 28 signatures per day. Which of the following represents how many signatures Samantha expects to have in d days?
284 + 28d
500 - 28d
500 + 28d
284 - 28d
Answer:
284 + 28d
Step-by-step explanation:
Because she has 284 it is known
She plans to obtain 28/day
Therefor, it should be 248+28d
Read the following description of a relationship:
Victoria signed up for a gym membership 21 weeks after Monica.
Let a represent the number of weeks Victoria has been a member and b
represent the number of weeks Monica has been a member.
Find the value of b when a = 9.
b= _
When a = 9, b = -12. However, this result is not physically meaningful in this context because it implies that Monica signed up for a gym membership 12 weeks after Victoria, which contradicts the original statement.
What is algebraic expression ?
An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.
If Victoria signed up for a gym membership 21 weeks after Monica and we let a represent the number of weeks Victoria has been a member and b represent the number of weeks Monica has been a member, then we have a = b + 21.
Substituting a = 9, we get:
9 = b + 21
Solving for b, we subtract 21 from both sides:
b = 9 - 21
b = -12
Therefore, when a = 9, b = -12. However, this result is not physically meaningful in this context because it implies that Monica signed up for a gym membership 12 weeks after Victoria, which contradicts the original statement.
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Find the limit…………………….
Answer:
[tex]\frac{1}{22}[/tex]
Step-by-step explanation:
Limits:For these time of limit problems, we want to try to rewrite the equation in such a way that we can get some value, because in this case plugging in x=121, we simply get 0/0 which is indeterminate.
One thing you may or may not notice is that 11 and 121 are closely related, as 121 is just the square of 11... something important to solving this.
We have the fraction: [tex]\sqrt{x}-11[/tex], we want to possibly rewrite this into the denominator (x-121) to cancel out the two... well we can use the difference of squares. [tex](\sqrt{x}-11)(\sqrt{x}+11)=x-121[/tex] and we want to multiply the bottom by this amount as well, giving us the fraction:
[tex]\frac{x-121}{(x-121)(\sqrt{x}+11}[/tex]
Now we can cancel out the x-121 from the numerator and denominator, leaving us with:
[tex]\frac{1}{\sqrt{x}+11}[/tex]
and now we can directly plug in 121
[tex]\frac{1}{\sqrt{121}+11}=\frac{1}{11+11}=\frac{1}{22}[/tex]
Find the cardinal number for the set.
B = {x|XEN
and 5
Answer:
Step-by-step explanation:
Cardinality of a set refers to the number of elements in the set. There are two types of cardinality: finite and infinite. A set is considered to have finite cardinality if it has a finite number of elements, meaning that the elements can be counted. A set is considered to have infinite cardinality if it has an infinite number of elements and cannot be counted.
In the case of the set B = {x | x ∈ N and x > 5}, the set is comprised of all natural numbers greater than 5. The set of natural numbers is infinite, meaning that there are an infinite number of elements in the set B. As a result, the cardinality of the set B is also considered to be infinite.
The symbol "ℵ0" is used to represent the cardinality of the set of natural numbers, and it is often used to indicate the cardinality of infinite sets with the same size as the set of natural numbers. In this case, we can say that the cardinality of the set B is ℵ0, meaning that the set B has the same size as the set of natural numbers and therefore has infinite cardinality.
first combine like terms in 3/4a + 8 - 1/4a - 2
1/2a+6 is the simplified form of the expression 3/4a + 8 - 1/4a - 2
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 3/4a + 8 - 1/4a - 2
Three by four times of a plus eight minus one by four times of a minus 2.
In the given expression a is a variable and plus and minus signs are the operators.
3/4a + 8 - 1/4a - 2
3/4a and - 1/4a are the like terms
Add the like terms
3/4a - 1/4a +8 - 2
2/4 a +6
1/2a+6
Hence, 1/2a+6 is the simplified form of the expression 3/4a + 8 - 1/4a - 2
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What is the value of x? enter your answer, as a decimal, in the box. Do not round your answer.
The "value of x" in algebraic expression represented as "3x + 2 = 8" , in decimal form is 2.0 .
We have to solve the algebraic expression "3x + 2 = 8" for value of x, we first need to separate the "variable x" on one side of the equation.
So , we subtract "2" from both sides of expression ,
we get ;
⇒ 3x + 2 - 2 = 8 - 2 ;
Simplifying the left hand side, we get:
⇒ 3x = 6 ;
To solve for the variable x, we on divide both sides by 3 ;
⇒ 3x/3 = 6/3 ;
Simplifying, we get:
⇒ x = 6/3 = 2 .
Therefore, the value of x in the algebraic expression "3x + 2 = 8" is 2 , which is 2.0 when expressed as a decimal.
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The given question is incomplete , the complete question is
What is the value of x in the algebraic expression "3x + 2 = 8" ? Enter your answer, as a decimal . Do not round your answer.
The distance between two cities is 6160 kilometers. Convert the distance to miles. Round to the nearest mile.
Complete the sentence below.
0.075 is a hundred times smaller than
Answer:
0.075 is a hundred times smaller than 7.5
Step-by-step explanation:
evaluate expressions: a)10^5*10^6 b) 10^4*10^-2 c)10^8/10^4 d)10^9/10^-3
Simplify your answer. Type your answer using exponential notation.)
The solution to each of the exponent problems are;
a) 10¹¹
b) 10²
c) 10⁴
d) 10¹²
How to use laws of exponents?
The seven laws of exponents are;
1) Product of powers rule.
2) Quotient of powers rule.
3) Power of a power rule.
4) Power of a product rule.
5) Power of a quotient rule.
6) Zero power rule.
7) Negative exponent rule.
The given expressions are;
a) 10⁵ × 10⁶
= 10⁵⁺⁶
= 10¹¹
b) 10⁴ × 10⁻²
= 10⁴⁻²
= 10²
c) 10⁸/10⁴
= 10⁸⁻⁴
= 10⁴
d) 10⁹/10⁻³
= 10⁹⁻⁽⁻³⁾
= 10⁹⁺³
= 10¹²
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Equations 4 and 5 are not equivalent to any of the other equations.
What is a equation in math?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
The equations that are equivalent are:
2 + x = 5
Negative 5 + x = negative 2
x + 1 = 4
Subtracting 2 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.
Adding 5 to both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.
Subtracting 1 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.
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Tara has two store coupons. Coupon 1 gives her $10 off on one item. Coupon 2 gives her 10% off on one item. Tara can use both coupons together on one item in the store and choose which coupon to apply first. For an item that has an original price of x dollars, let f be the function that models the discount price of the item using only coupon 1 and let g be the function that models the discount price of the item using only coupon 2. The price of each item in this store is more than $20 . Which of the following statements best explains which coupon should be applied first when using both coupons to give Tara a lower price?
To give Tara a lower price, coupon 2 should be applied first.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Tara has two store coupons.
Coupon 1 gives her $10 off on one item.
Coupon 2 gives her 10% off on one item.
Tara can use both coupons together on one item in the store and choose which coupon to apply first.
For an item that has an original price of x dollars,
let f be the function that models the discount price of the item using only coupon 1,
and let g be the function that models the discount price of the item using only coupon 2.
The price of each item in this store is more than $20.
Let the price is $50.
So applying coupon 1 and then coupan2,
we get,
(50 - 10) - ($50 - $10) x 0.10 = $36
Now, apply coupon 2 and then coupon 1,
we get,
$50 x 0.10 - $10 = $35
Therefore, she should apply coupon 2 and then coupon 1.
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Please help me with the question pleaseeee
Answer:
∠1 and ∠3
Step-by-step explanation:
The other pair of vertical angles are ∠2 and ∠4
Evaluate the expression when c equals 3 and y = -7. -2c+y
Answer: That’s easy… The answer is -13
Step-by-step explanation: -2 x 3 + -7 = ?
-2 x 3 = -6
-6 + -7 = -13
Circles formula and answers please just need help
The radius of the circle is 7.8 cm.
What is a circle?
All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
Given that the area of a circle is 192 cm².
The area of a circle is πr², where r is the radius of the circle.
Assume that the radius of the circle is r.
Therefore,
πr² = 192
Divide both sides by π:
r² = 192/π
r² = 61.115
r = 7.817
r ≈ 7.8 cm
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A provider prescribes magnesium sulfate 0.5g/hr by continuous IV infusion. Available is magnesium sulfate 4,000mg in 50 mL of D5W. Determine how many mL/hr to administer
In order to infuse 0.5 grams of magnesium sulfate, 6.25ml must be administered in 1 hour.
Magnesium sulphate: what is it?A magnesium salt with the counterion sulfate is known as magnesium sulfate. It functions as a medication called, anaesthetic, tocolytic, anti-arrhythmia, analgesic, fertilizer, anticonvulsant, cardiovascular medication, analgesic, and all of the above. Drug is used to treat constipation temporarily.
Additionally, it is employed as a soaking solution to treat minor sprains, bruises, muscular aches, joint stiffness, and fatigued feet. A cleanse and soaking solution, this medication Magnesium sulfate, also known as Bath, is a natural compound used for a variety of therapeutic and physiological benefits.
xml = 0.5*50 (cross multiplication)
4
So xml = 6.25ml
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The box plot shows the times for sprinters on a track team.
A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 44, 48, 50.5, 53, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.
Which of the following is the five-number summary for this data?
Min = 42, Q1 = 44, Median = 50, Q3 = 54, Max = 56
Min = 41, Q1 = 43, Median = 49.5, Q3 = 56, Max = 58
Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56
Min = 44, Q1 = 45, Median = 49, Q3 = 56, Max = 58
The summary of the given data is Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56 . So option C is correct.
What is the median?The middle number of data in a collection is known as the median. Three alternative metrics are employed in mathematics to determine the average value for a given group of integers. They are the median, mode, and mean. The measures of central tendency are this trio of measurements.
Median = [(n/2)th term + {(n/2)+1}th term]/2 (for even)
Median = {(n+1)/2}th term (for odd)
Based on the given information,
we can see that the box plot shows the values of 44, 48, 50.5, 53, and 56.
These values represent the minimum, lower quartile (Q1), median, upper quartile (Q3), and maximum, respectively.
Therefore, the five-number summary for this data is:
Min = 44,
Q1 = 48,
Median = 50.5,
Q3 = 53,
Max = 56
So the answer is: Min = 44, Q1 = 48, Median = 50.5, Q3 = 53, Max = 56
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Solve the following polynomial equation. y3+8=0
f(1) = 25
f(n) = f(n-1)(-1/5)
f(3) = ??
Answer: = 1 (look at the image for the solution)
Step-by-step explanation:
Find the number of solutions for the given equation for 0° ≤ θ ≤ 360°.
sin2x - 2sinx - 3 = 0
1
2
3
4
0
The number of solutions to the trigonometric equation is; 1 solution which is x = 270°
How to find the trigonometric solution?The trigonometric equation is given as;
sin²x - 2sin x - 3 = 0
Now, factorizing this gives us;
(sin x - 3)(sin x + 1) = 0
Thus, we now have;
sin x - 3 = 0
sin x = 3
At this point, x has no real solution
For the second factor, we have;
sin x + 1 = 0
sin x = -1
x = sin⁻¹ -1
x = 270°
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you deposit $1000 in an account that pays 3.5% annual interest compounded monthly. when is your balance at least $1200? round your answer to nearest hundredth.
The balance will be at least $1200 after 8.18 months, if you deposit $1000 in an account that pays 3.5% annual interest compounded monthly.
What is compound interest?The result of earning interest on a principal amount as well as the accumulated interest from earlier periods is known as compound interest. It occurs when money is reinvested rather being paid out, allowing interest to be generated on the principle and accrued interest over the next month.
The balance of an account with an initial deposit of $1000 earning 3.5% annual interest compounded monthly will reach $1200 after 8.18 months.
To find the time it takes for the balance to reach $1200, we can use the formula for compound interest, A = P[tex](1 + r/n)^{nt}[/tex],
where P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, P = 1000, r = 0.035, n = 12 (because the interest is compounded monthly), and t is the unknown variable. We can rearrange the formula to solve for t:
t = (A/P) / (1 + r/n)
Plugging in the values, we get
t = (1200/1000) / (12(1 + 0.035/12))
which simplifies to
t = 8.18 months
Therefore, it will take 8.18 months for the balance of the account to reach $1200.
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The jacket's original price is $65.00. It is on sale for 40% off. You have to pay 5% sales tax. What is the final price for the jacket?
Answer:
To find the final price for the jacket, we need to first calculate the amount of the discount and then add the sales tax.
The amount of the discount is $65.00 * 40% = $26.00. So the price after the discount is $65.00 - $26.00 = $39.00.
The sales tax is $39.00 * 5% = $1.95. So the final price for the jacket is $39.00 + $1.95 = $40.95.
Step-by-step explanation:
Answer:
he final price for the jacket is $40.95.
Step-by-step explanation:
First, let's calculate the discount for the jacket:
Discount = $65.00 * 40% = $26.00
The price of the jacket after the discount is:
$65.00 - $26.00 = $39.00
Next, let's calculate the sales tax:
Sales tax = $39.00 * 5% = $1.95
Finally, let's add the sales tax to the discounted price to find the final price:
Final price = $39.00 + $1.95 = $40.95
So, the final price for the jacket is $40.95.
Find x. Use law of sine. Round to the nearest tenth.
Answer:
9.5
Step-by-step explanation:
Law of sine:
[tex]\frac{SideXY}{sinZ^{o}} = \frac{SideZY}{sinX^{o}} = \frac{SideXZ}{sinY^{o}}[/tex]
Sum of interior angles = 180°:
∴∠Z° = 180° - 63° - 41°
∠Z° = 76°
∴[tex]\frac{14}{sin76^{o}}[/tex]= [tex]\frac{x}{sin41^{o}}[/tex]
Cross- multiplication is applied:
(x)(sin76°) = (14)(sin41°)
x has to be isolated and made the subject of the equation:
x = [tex]\frac{[(14)(sin41^{o})]}{sin76^{o}}[/tex]
x = 9.466
x = 9.5 (Rounded to the nearest tenth)
Which system has infinitely many solutions? A) 2x + y = 7 4x - 2y = 14 B) 3x - y = 2 x - 3y = -2 C) x+y = 3 x + y = 4 D) 2x + y = 5 4x + 2y = 10
The system of equations which has infinitely many solutions as required to be determined is; Choice D; 2x + y = 5 and 4x + 2y = 10.
Which among the answer choices has infinitely many solutions?By the standards of linear geometry, two equations have infinitely many solutions when their graphs coincide and in which case, they have the same slope and y-intercept.
Therefore, the system of equations which satisfy the said criterion is; 2x + y = 5 and 4x + 2y = 10.
Ultimately, the correct answer is; Choice D; 2x + y = 5 and 4x + 2y = 10.
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The correct mix for a batch of concrete is 6:3:2 in terms of sand, gravel and cement. The batch is to have 3300 pounds of these ingredients. How many of each are needed?
pounds of sand
pounds of gravel
pounds of cement
Answer:
1,800 lbs of sand
900 lbs of gravel
600 lbs of cement
Step-by-step explanation: 11*300=3,300. 300*6=1,800, 300*3=900, and 300*2=600. This is correct because if you add 1,800+900+600 you get 3,300.
Please help me with this please
The measure of the angles are 60 degrees each
How to determine the measure of the anglesFrom the question, we have the following parameters that can be used in our computation:
AOB = 138 degrees
Also, we have:
The line OX bisects the angle AOB
Using the above as a guide, we have the following:
AOX = AOB/2 = 138/2 = 69
Also, we have
XOB = AOB/2 = 138/2 = 69
Hence, the angles are 69 degrees each
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