The dimensions of the rectangle is length = 5ft and width = 3ft
Define System of equation
A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied—in other words, the locations at which all of these equations intersect.
Let,
x = length of rectangle
y = width of rectangle
Next, set up system of equation
We have given, the length of a rectangle is 5 ft more than twice its width.
x = 2y + 5 --------(a)
Next, The area of the rectangle is 33 ft²
xy = 33 ----------(b)
x = 33/y
substitute the value of x in eq(a)
x = 2y + 5
33/y = 2y + 5
33 = 2y² + 5y
2y² + 5y - 33 = 0
Factor it,
2y² + 11y - 6y - 33 = 0
y( 2y + 11) - 3( 2y + 11) = 0
(y - 3) (2y + 11) = 0
Split the values,
y - 3 = 0 and 2y + 11 = 0
y = 3 and y = -11/2 (ignore this as width cannot be -ve)
Substitute y = 3 in eq(b)
x * 3 = 33
x = 11
So, we get
length = 11 ft and width = 3 ft
Hence, the dimensions of the rectangle is length = 5ft and width = 3ft
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Is algebra from Islam?
Therefore , the algebra is derived from Islam word Arabic al‐jab used by its founder.
What is algebra?Mathematical branch known as algebra deals with symbols and the rules governing their manipulation. These characters, which are now expressed as Latin and Greek letters, stand for variables, or quantities without set values, in elementary mathematics. Similar to how sentences illustrate the connections between particular words, in algebra,
Here,
The word algebra is derived from the Arabic word al‐jabr, which its creator, Muhammad ibn Mūsā al‐Khwārizmī, used in the title of his work.
Al-Jabr wa-l-muqbalah, which dates to the ninth century (The Science of Equations and Balancing).
Therefore , the algebra is derived from Islam word Arabic al‐jab used by its founder.
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What is called histogram?
A, B, C and D are points on the circumference of a circle, and the center is O. AC is the diameter of the circle. AC and BD intersect at E.
Answer:
[tex]m\angle DAC=35^{\circ}[/tex]
Step-by-step explanation:
Arc [tex]BC=50^{\circ}[/tex] (inscribed angle theorem)
Arc [tex]AB=130^{\circ}[/tex] (semicircle)
[tex]m\angle ADB=65^{\circ}[/tex] (inscribed angle theorem)
[tex]m\angle DEA=80^{\circ}[/tex] (linear pair)
[tex]m\angle DAC=35^{\circ}[/tex] (angle sum of a triangle)
A kangaroo chases a rabbit that starts 150 feet ahead of the kangaroo. for every 12-foot leap of the kangaroo, the rabbit leaps 7 feet. how many leaps would the kangaroo have to make to catch up to the rabbit?
The kangaroo must take at least 23 leaps to catch up to the rabbit.
To catch up to the rabbit, the kangaroo must travel a total distance of 150 feet. For every 12-foot leap of the kangaroo, the rabbit leaps 7 feet, so the kangaroo must take one more leap than the rabbit in order to cover the same distance.
The number of leaps the rabbit takes can be found by dividing the distance the rabbit travels (150 feet) by the distance the rabbit leaps in each jump (7 feet):
150 feet / 7 feet/leap = 21.43 leaps
Since the kangaroo must take one more leap than the rabbit, the kangaroo must take 21.43 + 1 = 22.43 leaps to catch up to the rabbit.
However, since the number of leaps must be a whole number, the kangaroo must take at least 23 leaps to catch up to the rabbit.
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The number of leaps the rabbit takes can be found by dividing the distance the rabbit travels (150 feet) by the distance the rabbit leaps in each jump (7 feet):
150 feet / 7 feet/leap = 21.43 leaps
Since the kangaroo must take one more leap than the rabbit, the kangaroo must take 21.43 + 1 = 22.43 leaps to catch up to the rabbit.
What fraction has the same value as 25% ?
Answer: 1/4
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
We know that 25% is equal to the decimal 0.25. So, we can convert the decimal into a fraction
To do so, we need to write the fraction 0.25 x 100 / 100.
Solving the top part (100 x 0.25), we get 25/100.
Next, we need to simplify this fraction. The GCF (greatest common factor) of both numbers is 25, so we divide 25 by 25 and 100 by 25.
This leaves us with 1/4, and our answer.
How many solutions can we get by solving these equations 3x 2y 5 2x 3y 7?
By resolving these equations, we can arrive at one solution.
To find the number of solutions to a system of equations, you can solve the system either by graphing the equations or by using algebraic methods such as substitution or elimination.
If the equations are compatible (meaning that there is at least one combination of values for the variables that satisfies both equations), then the system has at least one solution. If the equations are independent (meaning that they are not related to each other and cannot be derived from each other), then the system has exactly two solutions. If the equations are dependent (meaning that one of the equations can be derived from the other), then the system has exactly one solution. If the equations are incompatible (meaning that there is no combination of values for the variables that can satisfy both equations), then the system has no solutions.
In this case, the equations are 3x + 2y = 5 and 2x - 3y = 7. To find the number of solutions to this system, you can either graph the equations or solve the system using algebraic methods.
Using algebraic methods, you can start by solving one of the equations for one of the variables in terms of the other:
3x + 2y = 5
2y = -3x + 5
y = (-3/2)x + (5/2)
Then, you can substitute this expression for y into the other equation to solve for x:
2x - 3((-3/2)x + (5/2)) = 7
2x + (9/2)x - (15/2) = 7
(11/2)x - (15/2) = 7
(11/2)x = (15/2) + 7
(11/2)x = (15 + 14)/2
(11/2)x = 29/2
x = 29/11
Substituting this value for x back into the first equation, you can solve for y:
3(29/11) + 2y = 5
87/11 + 2y = 5
2y = 5 - 87/11
2y = (55 - 87)/11
2y = -32/11
y = -32/22
Therefore, the solution to this system of equations is x = 29/11 and y = -32/22. Since there is only one solution, this system has exactly one solution.
The complete question is:-
How many solutions can we get by solving these equations 3x + 2y= 5;2x -3y =7?
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Consider the linear equation. 5x+6y=−15 Which point represents a solution to the equation?
The point that represents a solution to the linear equation 5x + 6y = -15 is (-1, -5 / 3)
How to solve linear equation ?Linear equation can be represented in different form such as standard form, general form, slope intercept form and point slope form.
Therefore, let's find the solution to the linear equation.
5x + 6y = -15
Let's put the equation in slope intercept form.
5x + 6y = -15
6y = -5x - 15
divide through by 6
y = - 5 / 6 x - 15 / 6
y = - 5 / 6 x - 5 / 2
Therefore, the slope of the equation is -5 / 6 and the y-intercept is - 5 / 2.
Using the equation we can find the solution of the equation.
We will substitute the value of x to get y value.
Hence,
y = - 5 / 6 x - 5 / 2
using (-1, -5 / 3)
y = - 5 / 6 (-1) - 5 /2
y = 5 / 6 - 5 / 2
y = - 5 / 3
Hence, the solution is (-1, -5 / 3)
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find the exact length of the curve. y = 1 4 x2 − 1 2 ln(x), 1 ≤ x ≤ 4
The exact length of the curve of the equation y = 1/4 x² − 1/2 ln(x), 1 ≤ x ≤ 4 is 1.125
Here we have given an equation y = 1/4 x² − 1/2 ln(x) with the limit as 1 ≤ x ≤ 4.
Now, the arc length is calculated by differentiating the terms, then we get,
=> dy/dx = x/2 - 1/2x
Now, we have to apply these derivative on the arc length formula, then we get,
=> length = [tex]\int\limits^4_1 {\sqrt{1 + (\frac{x}{2} -\frac{1}{2x})^2 } } \, dx[/tex]
When we simplify this one then we get,
=> length = [tex]\frac{1}{2} \int\limits^4_1 {\sqrt{x^2 + 2 + \frac{1}{x^2} } } \, dx[/tex]
When we further simplify this one then we get,
=> length = [tex]\frac{1}{2} \int\limits^4_1 {x + \frac{1}{x} } \, dx[/tex]
Now, the result of the differentiation is
=> length = 1/2 [17/4 - 2]
=> length = 1/2 [9/4]
=> length = 1.125
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Is a square root always an irrational number?
No, a square root is not always an irrational number because the perfect square roots are rational number.
What is an irrational number?Any real number that cannot be written as p/q, where p and q are both integers, the quotient of two integers.
If a number is not a perfect square, the square root of that number is not rational.
For example, the square root is 4 is 2.
The square root of 9 is 3.
But whereas the square root of 5 is 2.23606797755555...... which is irrational
The square root of 8 is 2.8284271247555..... which is irrational.
So, therefore square root of a number is not irrational always it can be rational also.
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What is the first prime number?
A prime number is a positive integer greater than one that has no positive integer divisors other than one and itself. so The first prime number is 2.
What is a prime number?A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.
What is whole number?Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.
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when constructing an angle bisector, the compass must be used to make three arcs. do all three arcs need to have the same radius? explain.
When constructing an angle bisector, the compass should be used to make three arcs, but these arcs do not necessarily need to have the same radius.
To construct an angle bisector, you can follow these steps:
Place the compass on one of the angle's vertices, and draw an arc that intersects both sides of the angle.Without changing the compass width, draw a second arc that intersects the first arc and one of the sides of the angle.Without changing the compass width again, draw a third arc that intersects the second arc and the other side of the angle.The point where the third arc intersects the other side of the angle is the bisector of the angle.In step 1, the radius of the first arc can be any length, as long as it intersects both sides of the angle. The radius of the second and third arcs should be the same as the first arc because they are drawn using the same width setting on the compass. However, the radius of the second and third arcs does not need to be the same as the radius of the first arc. The important thing is that all three arcs are drawn using the same width setting on the compass so that they are all equidistant from the vertex of the angle.
The complete question is:-
When constructing an angle bisector, the compass must be used to make three arcs. Do all three arcs need to have the same radius? Explain.
- Yes, because then the marks are equidistant from each other.
- Yes, because you need the points of intersection of the angle and arcs to form a parallelogram.
- No; the second two arcs must have the same radius but it can be different from the first.
- No; any three radii will work.
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Using the area model divide, true or false, 79/7 is equal to 11 R 1. True False
Answer: false
Step-by-step explanation:
Tickets to the baseball game are on sale for $1.50 off the regular price. Dea buys 6 tickets. If her total cost is $51, what is the regular price of each ticket? Write and solve an equation of the form p(x±q)=r. Then write a sentence to explain your answer.
Answer:
Below
Step-by-step explanation:
6 (x-1.50) = 51 6 = number of tix x - 1.50 = sale price x = reg price
6x - 9 = 51
6x = 60
x = 10 dollar regular price
Which of the following is equivalent to −2(5p − 2q)?
−10p + 4q
−10p − 2q
−7p + 4q
−7p − 4q
the number of unbroken charcoal briquets in a twenty-pound bag filled at the factory follows a normal distribution with a mean of 450 briquets and a standard deviation of 20 briquets. the company expects that a certain number of the bags will be underfilled, so the company will replace for free the 5% of bags that have too few briquets. what is the minimum number of unbroken briquets the bag would have to contain for the company to avoid having to replace the bag for free? (a) 404 (c) 418 (e) 448 (b) 411 (d) 425
The minimum number of unbroken briquets the bag would have to contain for the company to avoid having to replace the bag for free is b) 411.
A standard deviation (or σ) is a degree of the way dispersed the records is with regards to the mean. Low standard deviation approach records are clustered across the mean, and excessive widespread deviation suggests records are greater unfold out. The interval of filled bags is at confidence interval of 95%. At 95% confidence interval, Z=1.96 (from Z tables).But, Z= (x-mean)/SD => 1.96 = (x-450)/20 => x (upper limit)= 20*1.96+450489 bags. Lower limit or minimum number bags to avoid replace= 450-1.96*20 =411 bags.
Therefore, the correct option is b.
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Which of the decimals in the problem should be represented as a negative rate? which two factors should ericka multiply to find the total variation in water level?.
The decimal that should be represented as a negative rate in this problem is the 2.2 millimeters per year because it represents a decrease in water level.
The two factors that Ericka should multiply to find the total variation in water level are the rate of change (2.2 millimeters per year) and the time period over which the change occurred (6.2 years). In other words, she should multiply 2.2 by 6.2 to find the total variation in water level.
A novel and somewhat paradoxical tool for monetary policy, negative interest rates are not common. The goal of negative interest rates is to encourage lending and spending rather than saving and hoarding. When cash is placed with a bank, it results in a storage fee rather than the chance to receive interest income. When cash is placed with a bank, it results in a storage fee rather than the chance to receive interest income.
The quantity you are measuring is said to be increasing over time if the rate of change is positive, whereas the opposite is true if the rate of change is negative.
The complete question is:-
Ericka is also in Mr. Whittaker’s science class and she recorded the variation in water level at a different part of the river. She observed that the water level there fell 2.2 millimeters per year over a period of 6.2 years This data is compared to the average annual trend, which shows the water level rising 1.8 mm/year. Which of the decimals in the problem should be represented as a negative rate? Which two factors should Ericka multiply to find the total variation in water level?
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What is the example of unique number?
If there are no duplicate digits, then and only then, is a number considered to be unique. For instance, unique numbers include 20, 56, 9863, 145, etc., but non-unique numbers include 33, 121, 900, 1010, etc.
Which number is the most distinctive?Any two items that are the only ones of their kind are equally unique. Unique is defined as the only one like it. There is not a singular most. Each number is distinct because there is only one other one like it. For instance, if you subtract a three-digit number, like 345, from its reverse, 543, you get a difference of 198.
How can I locate the UN's special number?If the number An'obtained is subtracted from a number An made up of n consecutive digits in ascending order by reversing the digits of An, then the difference is always a constant. This constant is termed as the Unique number Un.
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A una exposición asisten menos de 100 personas y se recaudan más de 260€ con entradas de 2€ y de 4 €. ¿Cuántas entradas de cada tipo han podido ser vendidas?
Based on the graph, a solution for the system of inequalities is 70 and 30.
The number of 2 pounds tickets sold are 70 tickets.The number of 3 pounds tickets sold are 30 tickets.How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of 2 pounds tickets sold and number of 3 pounds tickets sold, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of 2 pounds tickets sold.Let the variable y represent the number of 3 pounds tickets sold.Since less than 100 people attend an exhibition, we have;
x + y < 100 ..........equation 1.
Additionally, more than €260 is raised with tickets of €2 and €4;
2x + 4y > 260 ..........equation 2.
Next, we would use an online graphing calculator to graphically solve the system of linear inequalities. Hence, the required solution for the given system of linear inequalities is the point of intersection of the two (2) lines on the graph, which is given by the ordered pair (70, 30)
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Complete Question:
Less than 100 people attend an exhibition and more than €260 is raised with tickets of €2 and €4. How many tickets of each type could have been sold?
please help!!
Given the function p(x) = 5x(x - 3)² Find p(3):
Answer:
The answer is 35.
Step-by-step explanation:
The given polynomial is p(x) = 5x² -4x + 2 we substitute x = 3 in the polynomial:
p(3) = 5(3)² -4(3) + 2 = 5×9 - 12 + 2 = 45 - 12 + 2 = 47 - 12 = 35
Hence, p(3) =35
. a model proposed for nba basketball supposes that when two teams with roughly the same record play each other, the number of points scored in a quarter by the home team minus the number scored by the visiting team is approximately a normal random variable with mean 1.5 and variance 6. in addition, the model supposes that the point differentials for the four quarters are independent. assume the model is correct. (a) what is the probability the home team wins? (b) what is the conditional probability that the home team wins, given that is is behind 5 points by the end of halftime. (c) what is the conditional probability that the home team wins, given that it is ahead by 5 points at the end of the first quarter
a) The probability the home team wins is of: 0.7291 = 72.91%.
b) The conditional probability that the home team wins, given that is is behind 5 points by the end of halftime is of: 0.3409 = 34.09%.
c) The conditional probability that the home team wins, given that it is ahead by 5 points at the end of the first quarter is of: 0.9015 = 90.15%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for each quarter are given as follows:
Mean: 1.5.Standard deviation: square root of 6 = 2.45.Hence for each case, the mean and the standard deviation are given as follows:
Entire game -> Four quarters -> [tex]\mu = 6, \sigma = 9.8[/tex]After halftime -> Two quarters -> [tex]\mu = 3, \sigma = 4.9[/tex]After the first quarter -> Three quarters -> [tex]\mu = 4.5, \sigma = 7.35[/tex]The probability of the home team winning is the probability of X being greater than zero for four quarters, hence it is one subtracted by the p-value of Z when X = 0, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (0 - 6)/9.8
Z = -0.61
Z = -0.61 has a p-value of 0.2709.
1 - 0.2709 = 0.7291 = 72.91%.
When the home team is down five points at the end of the halftime, the probability of winning is P(X > 5) for two quarters, hence one subtracted by the p-value of Z when X = 5 as follows:
Z = (5 - 3)/4.9
Z = 0.41
Z = 0.41 has a p-value of 0.6591.
Z = has a p-value of 0.6591.
1 - 0.6591 = 0.3409 = 34.09%.
When the home team is up five points at the end of the first quarter, the probability of winning is P(X > -5) for three quarters, hence one subtracted by the p-value of Z when X = -5.
Z = (-5 - 4.5)/7.35
Z = -1.29
Z = -1.29 has a p-value of 0.0985.
1 - 0.0985 = 0.9015 = 90.15%.
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What is the value of log2 16 log 2 16?
We determine the value of log₂16 = 4 by using logarithm laws.
What is logarithm?
Logarithm is the alternative way of representing an exponent. The power at which a number is needed to raise to get the other values is termed as logarithm.
What does mean by log₂?It is called log base 2 or binary logarithm. It is the inverse of the power of function 2.
How do we calculate the value of log₂ 16?We stated before that log base 2 is an inverse expression of the power 2. let N is a real positive number and x is the number of exponents. Now, logarithm form of the exponent is written as log₂ N = x
2ˣ = N
We are given, log₂ 16
N= 16
log₂16 = x
2ˣ =16
we know that 2⁴ =16
hence, x= 4
hence, log₂ 16 = 4
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What is range in set?
In a list or collection of numbers, the range is the difference between the lowest and highest integers. Place all the numbers in order before attempting to determine the range.
what is range ?The statistics' range is the difference between the highest and lowest values for a specific data collection. The range could also be expressed as the difference between the highest and lowest observation. The sample interval is calculated as the greatest value less the smallest value. The sample range is a crucial measure of variability for continuous variables.
here
The x values for a function like f are contained in this collection (x).
The collection of numbers that the function assumes is known as its range.
Following the insertion of an x value, the function outputs this sequence of values.
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Solve the equation
22 = -13 + a
The equation 22 = -13 + a gives the value a = 35.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 8 is an equation.
We have,
22 = -13 + a
Add 13 on both sides.
22 + 13 = a
a = 35
Thus,
The value of a is 35.
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What should I Do here? I need steps pls......:)
Answer:
Step-by-step explanation:
Domain is constant since there are no value that x could be to make this not a possible answer
First f(x)=3x+5 y=3x+5 then y+5=3x so (y+5)/3
inverse is (x+5)/3
Then g(x)=x^2+6 y=x^2+6 then y-6=x^2 so then x= \sqrt{y-6}
inverse is \sqrt{y-6}
find the area of the region bounded by the given curves. y = 6x^2 ln x, y = 24 ln(x)
The area of the region bounded by the given curves is [tex]32lnx-\frac{58}{3}[/tex]
Given curves,
y = [tex]6x^{2} lnx[/tex]
y = 24lnx
We will find the intersection points of these two curves by equating and then solving.
The intersection of these two curves will be at x = 1,2.
The area under the curves,
A = [tex]\int\limits^2_1 {(24lnx-6x^{2} lnx)} \, dx[/tex]
To solve, concentrate on the unbounded (indefinite) integral:
a = [tex]\int\limits {(24lnx-6x^{2} lnx)} \, dx[/tex]
= [tex]-6\int\limits {(lnx)(x^{2} -4)} \, dx[/tex]
We will use integration by parts to solve this integration.
[tex]\int\limits {u} \, dv=vu-\int\limits{v} \, du[/tex]
Let us assume,
u = lnx and v = [tex]\frac{1}{3}x^{3} -4x[/tex]
Therefore,
[tex]du = \frac{1}{x}dx[/tex]
[tex]dv=x^{2}-4[/tex]
Putting the values,
a = [tex]-6[(lnx)(\frac{1}{3}x^{3}-4x) - \int\limits{(\frac{1}{x} )(\frac{1}{3}x^{3}-4x)} \, dx ][/tex]
= [tex]-6[(lnx)(\frac{1}{3}x^{3}-4x) - (\frac{1}{9}x^{3}-4x)][/tex]
= [tex]-6(lnx)(\frac{1}{3}x^{3}-4x) + \frac{2}{3}x^{3}-24x[/tex]
Returning to the definite integral, now
A = [tex]\int\limits^2_1 {(24lnx-6x^{2} lnx)} \, dx[/tex]
= [tex][-6(lnx)(\frac{1}{3}x^{3}-4x) + \frac{2}{3}x^{3}-24x]^{2} _{1}[/tex]
= [tex]-6ln2(\frac{8}{3}-8)+\frac{16}{3}-48-\frac{2}{3}+24[/tex]
= [tex]32lnx-\frac{58}{3}[/tex]
Hence, The area of the region bounded by the given curves is [tex]32lnx-\frac{58}{3}[/tex].
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Write a rule for the reflection.
(x,y) = ( , )
The rule of the reflection of the triangle ABC to A'B'C' across the y-axis will be (x, y) to (-x, y).
What is a reflection of the point?It is the image of the point which is located in the opposite direction of a given point.
The rule of the refection will be given as,
Firstly, the rule for reflecting a point about the y-axis is;
While reflecting on the y-axis, we get the reflected points (x, y) by the coordinates (-x, y).
The standard of the impression of the triangle ABC to A'B'C' will be (x, y) to (- x, y).
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Juan is trying to factor x² + 7x+3 and makes the following table.
- see picture-
Juan concludes that x² + 7x+3 cannot be factored using integers.
a. Is Juan correct?
b. Comment on Juan's strategy and improve it if possible.
a. Yes Juan is correct.
b. The given quadratic equation can be solve by using quadratic formula.
What is a quadratic equation?
A quadratic equation is a polynomial equation with a maximum degree of two. Where a ≠ 0, the equation is given by ax² + bx + c = 0.
Given equation is x² + 7x + 3.
The given equation can't factorized by using middle term or splitting method.
Factorization of quadratic equations can be done in different methods. They are:
Splitting the middle term
Using formula
Using Quadratic formula
Using algebraic identities
Assume that x² + 7x + 3 = 0
x = [-7 ± √(7² - 4 × 1 × 3)]/ 2 × 1
x = [-7 ± √37]/ 2
The factors of quadratic polynomial is ( x - [-7 ± √37]/ 2).
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Which shows one way to determine the factors of x³ 12x² 2x 24 by grouping?
Therefore, the solution of the given problem is factors of the given equation are [tex]x^{2}[/tex](x - 12) - 2. (x - 12).
Examine the equation.An equation is a mathematical statement that is created by connecting two expressions using the equivalent sign. An example of an equation is 2x - 5 = 15. By resolving this equation, we may ascertain that the variable x has a value of 5.
Here,
The approach of grouping for factoring polynomials in this case is a progression from the method of identifying common factors.
In order to determine the factors of the given polynomial expression,
we are trying to find groups from the common factors in this case.
The components of [tex]x^{3}[/tex]- 12[tex]x^{2}[/tex] - 2x + 24 are hence
=> [tex]x^{2}[/tex](x - 12) -2 (x - 12)
=> [tex]x^{2}[/tex](x - 12) - 2. (x - 12).
Therefore, the factors of the given equation are [tex]x^{2}[/tex](x - 12) - 2. (x - 12).
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Is Y =- 3x proportional?
Yes, y = -3x is proportional because the ratios are equivalent, the equation is proportional.
Describe proportion.A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. '::' or '=' are used to indicate proportions. Using 2:5::4:8 as an example, 2/5 Equals 4/8 Here, the averages are 5 and 4 and the extremes are 2 and 8. A proportion is an equation that sets two ratios at the same value.
Given
y = -3x
Yes, Because the ratios are equivalent, the equation is proportional.
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How can you use transformations to verify that the triangles are similar?
Get the two triangles to face in the same direction, or in the same orientation, to check if they resemble one another.
What are triangles?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a three-sided polygon that is also referred to as a trine on occasion (less frequently). There are three sides and three angles in every triangle, some of which may be equal.
Get the two triangles to face in the same direction, or in the same orientation, to check if they resemble one another. You do this by twisting one form such that it is in alignment with the other. A rotation is the name given to such a change.
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