In the triangle, we will use the Law of Cosines to find the value of angle q. angle q in the triangle is approximately 61.2° (rounded to one decimal place).
What is Law of Cosines?The Law of Cosines is a mathematical formula used in trigonometry to find the length of a side or an angle in a triangle.
The formula can be used to find the length of a side or an angle in a triangle, given the length of the other sides and angles.
The Law of Cosines is particularly useful when only two sides and the angle between them are known, or when only two angles and the side between them are known.
To use the Law of Cosines, you need to identify the sides and angles that you know and plug them into the formula. Then, you can use algebra to solve for the unknown side or angle.
The Law of Cosines is related to the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side.
The Law of Cosines can also be used in three-dimensional geometry to find the distance between two points in space.
The Law of Cosines is a useful tool in many fields, including engineering, physics, and computer graphics, and is widely used in solving geometric problems.
In this triangle, we have x = 66.1 cm, y = 22.8 cm, and angle f = 23.3º. We want to find angle q, which is opposite side x.
We can use the Law of Cosines to find the value of cos(q), and then use the inverse cosine function to find the value of q in degrees.
cos(q) = (x² + y² - x²)/(2xy)
cos(q) = (66.1² + 22.8² - 22.8²)/(2 * 66.1 * 22.8)
cos(q) = 67.8664/150.6448
cos(q) = 0.449
q = cos⁻¹(0.449)
q = 61.2°
Therefore, angle q in the triangle is approximately 61.2° (rounded to one decimal place).
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Which pile of laundry has more shirts?
Pile 1
Three pants two shirts
Pile 2
Two shirts 4 pants
Answer:111
Step-by-step explanation:
1111
What goes in the blank box?
On solving the linear equation y = 3/2x - 29, the missing value for x is obtained as 14.66.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The table shows the points (18,-2) and (16,-5).
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[-5 - (-2)]/[16 - 18]
(-5 + 2)/(-2)
-3/-2
3/2
So, the slope point is obtained as m = 3/2.
The equation becomes - y = 3/2x + b
To find the value of b substitute the values of x and y in the equation -
-2 = 3/2(18) + b
-2 = 27 + b
b = -2 - 27
b = -29
So, the value for b is -29.
Now, the equation becomes -
y = 3/2x - 29
To find the missing value substitute the value of y = -7 in the equation -
-7 = 3/2x - 29
3/2x = -7 + 29
3/2x = 22
x = 22 × 2/3
x = 44/3
x = 14.66
Therefore, the value of x = 14.66.
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1. Which of the following could be used to find the value of z in the figure? 38° x ft 32 ft 52° 25 ft
Answer:
The value of z can be found using the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. In other words, if a, b, and c are the lengths of the sides of a triangle opposite angles A, B, and C, respectively, and A, B, and C are the angles opposite sides a, b, and c, respectively, then: a/sin(A) = b/sin(B) = c/sin(C). This can be used to solve for the unknown side length.
Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 12 miles. If the two airplanes are 20 miles apart, how far has the eastbound airplane traveled?
The eastbound airplane has traveled 16 miles.
This can be determined using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the distance the northbound airplane has traveled (12 miles) is one side of the triangle, the distance the eastbound airplane has traveled is the other side, and the distance between the two airplanes (20 miles) is the hypotenuse.
So, we can set up the equation as:
(distance eastbound airplane)^2 + 12^2 = 20^2
Solving for the distance eastbound airplane, we get:
distance eastbound airplane = sqrt(20^2 - 12^2) = sqrt(256 - 144) = sqrt(112) = 16 miles
use the following equation to determine the ratio of the displacement thickness to the boundary layer thickness.
The formula the ratio of the displacement thickness to the boundary layer thickness is u = δ / 2
The term displacement thickness is defined as the distance by which the body surface should be shifted in order to compensate for the reduction in mass flow rate on account of boundary layer formation.
Here we need to find the way to determine the ratio of the displacement thickness to the boundary layer thickness.
As we all know that the boundary layer thickness. ideal fluid viscous force is neglected but in actual viscous stresses are prominent within the boundary layer.
AS we all also know that when fluid flows past a solid body the fluid particles adhere to the boundary and the condition of no-slip occurs.
Here the term non-slip conditions means the velocity of the fluid at body surface will be same as the velocity of body.
Then it can be calculated by using the following formula,
=> u = δ / 2
Complete Question:
Here by using the equation u/U = y/δ and to determine the ratio of the displacement thickness to the boundary layer thickness.
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use the centroid therom and the fogure for exercises 5-8 QU RS and PT are medians of PQR rs = 21 VT=5 find each length
The length of RV is 14, SV is 7, TP is 15 and VP is 10. The solution has been obtained using centroid theorem.
What is centroid theorem?
According to the centroid theorem, the centroid of a triangle is located at a distance of 2/3 between the vertex and the midpoint of the sides.
In the given figure, V is the centroid of the triangle
The medians RS and PT intersect at V.
Now, since V divides each median in the ratio 2:1, therefore,
⇒VT = 1/3 of PT
⇒PT = 3*VT
Since, VT=5
⇒PT = 15 = TP
So, VP = PT - VT
⇒VP = 15-5
⇒VP = 10
Similarly,
⇒RV = 2/3 of RS
Since, RS = 21, therefore,
⇒RV = 2/3 of 21
⇒RV = 14
So, SV = RS-RV
⇒SV = 23-14
⇒SV = 7
Hence, the length of RV is 14, SV is 7, TP is 15 and VP is 10.
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The complete question is attached below
The bond indenture for the 10-year, 9% debenture bonds issued January 2, 20Y5, required working capital of $100,000, a current ratio of 1.5, and a quick ratio of 1.0 at the end of each calendar year until the bonds mature. At December 31, 20Y6, the three measures were computed as follows:
$52 hundred is introduced to the December 31, 20Y6.
What is proportion?A proportion is a unit of fairness possession in the capital inventory of a corporation, and may discuss with devices of mutual funds, restrained partnerships, and actual property funding trusts. Share capital refers to all the stocks of an enterprise. The proprietor of stocks in a employer is a shareholder (or stockholder) of the corporation.
Note that proportion is an indivisible unit of capital, expressing the possession dating among the employer and the shareholder.
Given that bond indenture for the 10-year, 9% debenture bonds issued January 2, 20Y5, required working capital of $100,000, a current ratio of 1.5, and a quick ratio of 1.0 at the end of each calendar year until the bonds mature.
The profits acquired from the possession of stocks is a dividend. There are extraordinary varieties of stocks consisting of fairness stocks, bonus stocks, proper stocks, and worker inventory choice plan stocks.
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find the coordinates of point $p$ along the directed line segment $ab$ , from $a\left(-3,\ 2\right)$ to $b\left(5,-4\right)$ , so that the ratio of $ap$ to $pb$ is $2$ to $6$ . the coordinates are $p\text{(}$ , $\text{)}$ .
The coordinates of point p along the directed line segment ab are [tex]$p(-1,-2)$[/tex]
Let the coordinates of point p be (x,y)
The ratio of ap to pb is 2 to 6, so we have [tex]$$\frac{|ap|}{|pb|} = \frac{2}{6}$$[/tex]
We can calculate the distances between points $a$ and $p$ and points $p$ and $b$ using the distance formula as follows:
[tex]$$|ap| = \sqrt{(x+3)^2+(y-2)^2}$$$$|pb| = \sqrt{(5-x)^2+(y+4)^2}$$[/tex]
We can use the ratio of the distances to set up a proportion to solve for $x$ and $y$:
[tex]$$\frac{|ap|}{|pb|} = \frac{2}{6} \implies \frac{\sqrt{(x+3)^2+(y-2)^2}}{\sqrt{(5-x)^2+(y+4)^2}} = \frac{2}{6}$$\\[/tex]
Solving for $x$ and $y$, we get $x = -1$ and $y = -2$.
Therefore, the coordinates of point $p$ along the directed line segment $ab$ are [tex]$p(-1,-2)$[/tex]
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Find the smallest value of m such that the product of 189m is a perfect square
Answer: 7
Step-by-step explanation:
First, we need to prime factorize the number 189,
189 = 3 × 3 × 3 × 7 × m
From the factors we can see that there is no pair of same numbers for 7, so if we replace m with 7, we can get a perfect square.
Hence the answer is 7
we are given a classifier that performs classification on r 2 (the space of data points with 2 features (x1, x2)) with the following decision rule: h(x1, x2)
The decision rule given is x1 + x3 – 10 ≥ 0, which can be rearranged to x1 + x3 ≥ 10. This forms a line in the R2 space, and any point on or above this line will be classified as 1, while any point below this line will be classified as 0.
To draw the decision boundary, we can plot the line x1 + x3 = 10 on a graph with the x1 and x3 axes. The region above the line, where x1 + x3 ≥ 10, would be shaded to indicate that it is where the classifier predicts 1.
It is important to note that the classifier predicts 1 if x1 + x3 – 10 ≥ 0, but in the explanation above I have used x1 + x3 = 10 to draw the decision boundary, this is because x1 + x3 – 10 ≥ 0 is equivalent to x1 + x3 ≥ 10.
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How many pounds of chamomile tea that costs $18.10 per pound must be mixed with 12 lb of orange tea that costs
$ 12.22 per pound to make a mixture that costs $14.74 per pound?
lb
9 pounds of Chamomile tea needed to make a mixture that costs $14.74 per pound
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
let:
x pounds of Chamomile tea needed
Therefore,
18.10X + 12.22(12) = 14.74(12 + x)
18.10X + 146.64 = 176.88 + 14.74x
3.36X = 30.24
X = 9 pounds
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If 4√5 = √n, the value of n is
A. 10
B. 20
C. 80
D. 100
Every person has blood type O, A, B, or AB. A random group of people are blood-typed, and the results are shown in the table. A 2-column table with 4 rows is shown. The first column is labeled Blood Type with entries O, A, B, AB. The second column is labeled Number of People with entries 22, 20, 6, 2. Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is . The probability that a randomly chosen person from this group has type AB is . The probability that a randomly chosen person from this group has type B or type AB blood is .
The probabilities for each type of blood are given as follows:
Type B: 12%.Type AB: 4%.Type B or Type AB: 16%.How to obtain the probabilities?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
The total number of people is given as follows:
22 + 20 + 6 + 2 = 50.
6 people have type B, hence the probability is given as follows:
6/50 = 0.12 = 12%.
2 people have type AB, hence the probability is given as follows:
2/50 = 0.04 = 4%.
8 people have either type B or type AB, hence the probability is given as follows:
8/50 = 0.16 = 16%.
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find the equation of a line (or a set of lines) passing through the terminal point of a vector a and in the direction of vector b.
The equation of a line passing through the terminal point of a vector a and in the direction of vector b is r = a + λb.
In math the equation of a straight line is y = m x + c
where m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.
Here we need to find the equation of a line (or a set of lines) passing through the terminal point of a vector a and in the direction of vector b.
Based on the general form of the equation of the line, the vector form of the equation of a line passing through a point having a position vector a, and parallel to a vector line b is written as,
=> r = a + λb.
Where λ refers the constant term.
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Points A and B are 10 units apart. Points B and C are 4 units apart. Points C and D are 3 units apart. If A and D are as close as possible, then the number of units between them is
A. 0 B. 3 C. 9 D. 11 E. 17
A perimeter longer than 50 for any point, C satisfies the area requirement.
Consequently, we have a base-10 triangle whose area is 100. Since the area is equal to half the product of base and height, the object's height is then 20.
The next two sides. If one of the sides is exactly 20 inches tall (when it coincides with the height, forming a right triangle), the other side must be strictly greater than 20 inches tall (being the hypotenuse), in which case the perimeter must be greater than 50.
Alternately, both sides could be longer than 20 because neither side is a height. Once more, the perimeter exceeds 50.
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The full question
In a given plane, points A and B are 10 units apart. How many points C are there in the plane such that the perimeter of triangle ABC is 50 units and the area of triangle ABC is 100 square units?
Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation? Group of answer choices
(1)x + y = -2
x - y = -10
(2) x - y = -10
x + y = 2
(3) x + y = -10
x - y = -2
(4) x = -2
y = 5
Answer: The answer is 3
Step-by-step explanation:
Write and solve a proportion for the following problem.
In a recent survey for the student council, Dominique found that 150 students
out of a total of 800 students on campus did not like soda. If half of the student
body was going to attend a dance, how many students could she expect would
want soda?
The students expected to like soda are 324
How to determine the number of studentsfrom the question, we have the following parameters that can be used in our computation:
150 students out of a total of 800 students on campus did not like soda.
This means that
650 students out of a total of 800 students on campus like soda.
i.e. 800 - 150 = 650
When half of the students are considered, we have
Soda = 650/2
Evaluate
Soda = 325
Hence, the number of students is 325
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rhombus is inscribed in rectangle as shown. segments and are parallel to . segments and are parallel to . if and what is the area of rectangle ?
The perimeter of the rectangle WXYZ is 96 cm.
Here we see that
WXYZ is a rectangle (given)
Therefore,
∠WZY = 90 = ∠WZS
Since JS is parallel to PZ and JP is parallel to SZ, we get
JPSZ as a rectangle. Similarly, PKWQ, SYMR, and XQRL are rectangles.
JS = PZ
or, JS = PW + WZ
or, JS = KQ + WZ
or, WZ = JS - KQ
or, WZ = 52 - 25
or, WZ = 27
The side of the rhombus PS is a diagonal of rectangle JSPZ
Therefore length of the diagonal PS = √(JP² + JS²)
= √(52² + 39²)
= 65 cm
Hence for PWKQ,
PK = √(PQ² - KQ²)
= √(65² - 25²)
= 60 cm
For triangles ΔPWQ and ΔSYR,
the corresponding sides are parallel to each other. Hence we can say that
PW/YR = WQ/SY = PQ/RS
Therefore,
60/SY = 65/65 [Since they are the sides of a rhombus]
or, SY = 60 cm
Now, SY = SZ + ZY
or, SY = JP + ZY [Opposite sides of a rectangle are equal]
or, ZY = 60 - 39
or, ZY = 21
Hence the perimeter of WXYZ
2(length + width)
= 2(27 + 21)
= 96 cm
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Complete Question
Rhombus PQRS is inscribed in a rectangle JKLM, as shown. Segments PZ and XR are parallel to JM. Segments QW and YS are parallel to JK. If JP = 39 cm, JS = 52 cm, and KQ = 25 cm, what is the perimeter of rectangle WXYZ?
the perimeter of a rectangle is 700 feet. let x represent the width of the rectangle. write a quadratic function for the area a of the rectangle in terms of its width.
The perimeter of a rectangle is 700 feet. A quadratic function for its area in terms of its width is A(w) = 350w - w²
The formula for the perimeter of a rectangle is given by:
p = 2w + 2l
While its area is:
A = w x l
Where:
w = width
l = length
Substitute p = 700 ft.,
700 = 2w + 2l
700 = 2(w + l)
w + l = 350
l = 350 - w
Substitute l = 350 - w into the formula of area:
A = w x l
A = w (350 - w)
A(w) = 350w - w²
Hence, the expression is: A(w) = 350w - w²
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connsider the rectangle with a width of 18 in and a length of 39 in, write a ratio of the length to the width and simplify
Answer: 13:6
Ratio of length to width = 39:18
Divide both by 3 to simplify
13:6
In circle I, IJ = 2 and the area of shaded sector = . Find the length of JLK.
Express your answer as a fraction times T.
J
H
K
C
Given that IJ = 2, we know that IJ is the radius of the circle.
The area of the shaded sector is given as . Since the area of a sector is given by (angle of sector/360) * pi * r^2, we can set up the equation:
(x/360) * pi * 2^2 =
Solving for x:
x = (180/pi)*
We know that the arc JLK corresponds to the angle x, thus the length of JLK is (x/360)2pi*IJ = (x/180)*IJ * T = (180/pi) * T.
The number of papers ms. Motley grades increases exponentially as
time goes on. On the first day she grades 9 papers , on the second day she grades 27 papers and on the third day she grades 31 papers
How many will she grade in five days?
After many days will it take her to grade 6,000 papers?
The number of papers that Ms. Motley will grade in five days would be = 46 papers (approximately).
How to calculate the number of paper?The number of papers Ms. Motley graded in first day = 9 papers
The number of papers Ms. Motley graded in the second day = 27 papers
The number of papers Ms. Motley graded in the third day = 31 papers
The average number of she graded for the three days is calculated as follows;
9+27+31 = 67/3 = 27.3 papers.
If in 3 days = 27.3 papers
5. days = X papers
Make X papers the subject of formula;
X papers = 5× 27.3/3
= 136.5/3
= 45.5 papers
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how to calculate the area of a circle
Answer:
The area of a circle is pi multiplied by the radius squared (A = π r²)
The radius (r) is the distance from the center of the circle, to the edge of the circle.
Example:
if you have a circle with radius 2, the area would be:
r = 2
A = π (2)²
A = π(4)
A = 4π
Answer:
Area can be calculated by the formula = [tex]\pi r^{2}[/tex]
Step-by-step explanation:
We can calculate the area of a circle with the formula,
Area of Circle = [tex]\pi r^{2}[/tex]
Where r replicates the radius of the circle
Two beetles sit at the top edge of the house roof. The roof has two faces. The first face is such that the horizontal shift by 3 cm along this face means 2 cm shift vertically. Simultaneously the beetles start moving downwards, the first beetle by the first face, the second -- the second face of the roof. The first beetle moves twice as fast as the second beetle. Find the altitude of the second beetle above the first beetle when they will be 72 cm apart horizontally, if the second face of the roof is perpendicular to the first face?Need ANSWER ASAP
The altitude of the second beetle above the first beetle when they are 72 cm apart horizontally is 14.4 cm.
How do you find the altitude of the second beetle?In order to find the altitude of the second beetle, let x be the altitude of the second beetle above the first beetle.
The horizontal distance between the two beetles is 72 cm.
The first beetle moves twice as fast as the second beetle, so the vertical distance between them is 2x.
Therefore, the equation for the problem is:
3x + 2x = 72
5x = 72
x = 14.4 cm
Therefore, the altitude of the second beetle above the first beetle when they are 72 cm apart horizontally is 14.4 cm.
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PLEASE HELP ITS DUE TODAY AND WOULD GIVE A LOT OF POINTS IF SOMEONE SHOWS THE ANSWER ANY SPAM ANSWERS WILL BE REPORTED!
To find the slope of the line given the points (0,2) and (1,0), we can use the formula: m = (y2 - y1) / (x2 - x1).
m = (0 - 2) / (1 - 0) = -2
Using point-slope form, we can write the equation of the line as:
y - 2 = -2 (x - 0)
y = -2x + 2
To get the inequality we just need to change the equation to the inequality by replacing the equal sign with the inequality sign.
So the linear inequality for the points (0,2) and (1,0) is:
y >= -2x + 2
5% of batteries produced at a factory are defective. Use the binomial model to find the probability that 1 battery in a pack of 16 is defective.
The probability that 1 battery in a pack of 16 is defective is approximately 0.3706 or 37.06%.
How to evaluate using the binomial modelThe binomial model can be used to calculate the probability of a specific number of successful outcomes (in this case, defective batteries) in a fixed number of trials (in this case, 16 batteries) with a constant probability of success (in this case, 5%) for each trial.
The probability of 1 defective battery in a pack of 16 can be calculated using the formula:
P(X = 1) = (¹⁶C₁) × (0.05)¹ × (0.95)⁽¹⁶⁻¹⁾
where (¹⁶C₁) is the binomial coefficient, which is equal to 16.
So;
P(X = 1) = (¹⁶C₁) × (0.05)¹ × (0.95)⁽¹⁶⁻¹⁾
P(X = 1) = 16 × 0.05 × 0.95¹⁵
P(X = 1) = 0.3706
Therefore, the probability that 1 battery in a pack of 16 is defective is approximately 0.3706 or 37.06%.
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And chemical reaction one or more new substances are created. Are new atoms created?
No, new atoms are not created in a chemical reaction. Atoms are rearranged or combined to form new compounds. The total number of atoms before and after the reaction is the same. This is known as the law of conservation of mass.
What is chemical reaction?The law of conservation of mass states that in a closed system, the total mass of the reactants (the substances before the reaction) is equal to the total mass of the products (the substances after the reaction). This means that the atoms present in the reactants must also be present in the products, but in different combinations or arrangements.
Therefore, It's important to note that in some reactions, atoms can be transformed into different forms, for example, a carbon atom can be transformed into a carbon dioxide molecule, but the mass of the atoms remains the same.
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Written as a simplified polynomial in standard form, what is the result when (x+5) 2 is subtracted from 1 1? Answer:
The expression for the simplified polynomial would be - x² - 10x - 24.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the polynomial ( x + 5 )² is subtracted from 1. The simplified polynomial can be written as:-
Polynomial = 1 - ( x + 5 )²
Polynomial = 1 - ( x² + 10x + 25 )
Polynomial = 1 - x² - 10x - 25
Polynomial = -x² - 10x - 24
Hence, the polynomial can be written as -x² - 10x - 24.
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Plsssss helpppppppp!!!!
Answer:
3. f
4. b
5. a, x
Step-by-step explanation:
3.
a/f = f/c
f² = ac
f = √ac
Answer: f
4.
x/b = b/c
b² = cx
b = √cx
Answer: b
5.
x/k = k/a
k² = ax
k = √ax
Answer: a, x
-5x + -4 + 1 - 4x
show your work to combine "like terms"
Answer:
-9x + -3
Step-by-step explanation:
1. Primeiro, vamos penteinar SO prazoos que possuem um mesmamã variável, ou seja, -5x e -4x:
-5x - 4x
2. Agora, vamos penteinar SO prazoos que possuem o mesmo coeficiente, ou seja, 1 e -4:
-5x - 4x + 1 -
4 3. Por fim, vamos penteinar SO prazoos que possuem o mesmo coeficiente, ou seja, -4 e 1:
-5x - 4x + -4 + 1