The given example is inductive reasoning.
What is inductive reasoning?The method of arriving at a conclusion based on a series of observations is known as inductive reasoning. It is not a valid method of proof in and of itself.
We have the information that. Janelle got invited to a shopping spree with a friend and is supposed to meet her at the mall at 4:00 p.m. when she has gone to the mall in the past,
she has noticed that it takes about two hours for her to travel to the mall. she has also noticed that it takes her 30 minutes to get ready before leaving her apartment. she concludes that she needs to start getting ready at 0:30 p.m.
The given information is giving us the series of the data like we are having a sequence of the timing at what time what she did so we have a series of observations here.
Therefore the given example is inductive reasoning.
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a
ОЈ
6(3+2d) = 54
I need that answer
Answer:
d = 3
Step-by-step explanation:
6*3=18
2d*6=12d
54-18 = 12d
36/12 = 12d/12
d = 3
Answer:
d = 3
Step-by-step explanation:
6 ( 3 + 2d ) = 54
First, solve the brackets.
18 + 12d = 54
Take 18 to the right side.
12d = 54 - 18
12d = 36
Divide both sides by 12.
d = 3
What does s(8) = 6.0 mean in terms of this problem?
A.A tree that is 6 years old is 8 meters tall.
B.A tree that is 8 years old is 6 meters tall.
C.8 different trees are 6 meters tall.
D.6 different trees are 8 meters tall.
Answer: C i think.
Step-by-step explanation:
8 different trees multipled by s equal to 6 meters tall in total.
Which angle is complementary to ∠EAD?
Answer: C
Step-by-step explanation:
Complementary angles have measures that add to 180 degrees, so since angle EAD measures 20 degrees, we need an angle that measures 70 degrees. This is angle DAB.
A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 23 times, and the man is asked to predict the outcome in advance. He gets 20 out of 23 correct. What is the probability that he would have done at least this well if he had no ESP
The probability that he would have done at least this well if he had no ESP is 0.99979
What is the probability of determining that he would have done well with no ESP?To determine the probability, we need to first find the probability of doing well with ESP.
The probability of having 20 correct answers out of 23 coin flips is:
[tex]\mathbf{=(\dfrac{1}{2})^{20}}[/tex]
Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:
[tex]\mathbf{=(\dfrac{1}{2})^{3}}[/tex]
There are [tex](^{23}_{20})[/tex] = 1771 ways to get 20 correct answers out of 23.
Therefore, the probability of doing well with ESP is:
[tex]\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}[/tex]
= 0.00021
The probability that he would have at least done well if he had no ESP is:
= 1 - 0.00021
= 0.99979
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What is the probability that you would land on a R and then a P?
Answer:
multiply the probability of the first event by the second.
Step-by-step explanation:
Use the specific multiplication rule formula. Just multiply the probability of the first event by the second. For example, if the probability of event A is 2/9 and the probability of event B is 3/9 then the probability of both events happening at the same time is (2/9)*(3/9) = 6/81 = 2/27.
Answer:
[tex]\frac{1}{26} * \frac{1}{26} = \frac{1}{676} = .00148.[/tex]
Step-by-step explanation:
Multiply the probability of P by the probability of Q.
In which the probability of P is equal to [tex]\frac{R}{Total NumberOf LettersInAlphabet} = \frac{1}{26}[/tex]
In which the probability of Q is equal to [tex]\frac{P}{Total NumberOf LettersInAlphabet} = \frac{1}{26}[/tex]
There's a 1 in 676 chance that you'd randomly pick R, put the tile back in, and then pick P in a sack of 26 letters of the latin alphabet.
There is 2.50m of rope and 11.5 inch pieces are cut. How many centimeters of rope will be left over?
Answer:
1.42 cm
Step-by-step explanation:
2.5 m = 98.4251 inches
98.4251 in / 11.5 in =8.5587
.5587 inches left over =1.42 cm
There will be 18.87 centimeters of rope left over.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Examples:
1 hour = 60 minutes
1 minute = 60 seconds
1 km = 1000 m
We have,
Let's convert the length of the rope to inches.
1 meter = 39.37 inches
2.50m = 98.43 inches
Now,
The number of 1.5-inch pieces.
= 98.43 / 11.5
= 8.55 pieces
Now,
11.5 inches pieces are cut.
This means,
= 98.43 - (8x11.5)
= 7.43 inches
Now,
1 inch = 2.54 cm
7.43 inch = 18.87 cm
Thus,
There will be 18.87 centimeters of rope left over.
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Find the equation of the line with Slope = −7 and passing through (7,−54 . Write your equation in the form y=mx+b
.
The equation of the line with Slope = −7 and passing through (7,−54) is y = -7x - 5
Equation of a lineThe equation of a line in pint slope form is expressed as:
y - y1 = m(x-x1)
where
m is the slope = -7
(x1, y1) = (7, -54 ) is the point on the line
Substitute
y + 54 = -7(x -7)
Write in slope intercept form
y + 54 = -7(x -7)
y + 54 = -7x + 49
y = -7x - 5
Hence the equation of the line with Slope = −7 and passing through (7,−54) is y = -7x - 5
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How many cubes with side lengths of
1
3
cm
3
1
cmstart fraction, 1, divided by, 3, end fraction, start text, space, c, m, end text does it take to fill the prism?
4
3
cm
3
4
cm
5
3
cm
3
5
cm
2
cm
2 cm
cubes
The number of 1/3 cm-cubes that would fill the rectangular prism is approximately 20 cubes.
What is the Volume of a Cube?Volume = a³, where a is the side length.
What is the Volume of a Rectangular Prism?Volume = lwh
Given the following:
a = ⅓ cml = 4/2 cm = 1/2 cmw = 2/2 cm = 1 cmh = 3/2 cmVolume of the rectangular prism = (1/2)(1)(3/2)
Volume of the rectangular prism = (1/2)(1)(3/2) = 0.75 cm³
Volume of the cube = (⅓)³ = 0.037 cm³
Number of cubes that would fill the prism = 0.75/0.037 ≈ 20 cubes.
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How to solve for x and what does x equal in this?
Answer:
10
Step-by-step explanation:
give brainliest please!
hope this helps :)
so these two angles add up to 180 degrees
7x -3 + 12x -7 = 180
7x+12x=180+7+3
19x=190
x=10
to check if this is true we can input 10 for x in each side.
7(10)-3 = 67
12(10)-7 = 113
113+67 = 180
Please Help! The value of m is:
Answer:
The value of m in the figure is 28.
Step-by-step explanation:
When we look at the figure, we see that 6 and 21, are connected with parallel lines to 8 and m. We can also see that 21 is dilated from 6. When dilating, we multiply or divide by a number, to get the extended or shortened length. (Just keep multiplication and division in mind)
To get m, we can do the same that we did to get 21, from 6.
To get 21 from 6, you must divide 21 by 6. So when we do the same thing to 8, we should get m.
21 / 6 = 3.5
Now that we have the dilation of 3.5, we simply multiply that by 8.
3.5 * 8 = 28
The value of x in the figure is 28.
[tex]\\ \rm\dashrightarrow \dfrac{m}{8}=\dfrac{21}{6}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{m}{8}=\dfrac{7}{2}[/tex]
[tex]\\ \rm\dashrightarrow 2m=56[/tex]
[tex]\\ \rm\dashrightarrow m=28[/tex]
The table shows information about the population of a town. emily takes a random sample of 90 people from the town. 40 of these people have not been to their doctor in the last year. work out an estimate for the number of people in the town who have not been to their doctor in the last year (2 marks)]
The estimate for the number of people in the town who have not been to their doctor in the last year is 7062.
What are population and sample?It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
Total population = 1819 + 6150 + 2003 + 5918 = 15890
Emily takes a random sample of 90 people from the town.
40 of these people have not been to their doctor in the last year.
The estimate for the number of people in the town who have not been to their doctor in the last year:
= (40/90)×15890
= 7062.22 ≈ 7062
Thus, the estimate for the number of people in the town who have not been to their doctor in the last year is 7062.
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PLEASE HELPP! RIGHT ANSWERS ONLY!!!
Answer:
[tex] \large {\boxed{ \sf{y = 2x + 5}}}[/tex]
Step-by-step explanation:
Suppose the slope of the line is k.
So,
[tex] \large {\bold {k = \frac{7 - ( - 1)}{1 - (3)} = \frac{7 + 1}{1 + 3} = \frac{8}{4} = 2 }}\\ [/tex]
So the line:
[tex] \large \bold{ \frac{y - 7}{x - 1} = k = 2 } \\ [/tex]
[tex] \: [/tex]
So,
[tex] \large \bold{y - 7 = 2(x - 1)}[/tex]
[tex]\large \bold{y - 7 = 2x - 2}[/tex]
[tex]\large \bold{y = 2x - 2 + 7}[/tex]
[tex]\large \bold{y = 2x + 5}[/tex]
[tex]{\rule{200pt}{4pt}}[/tex]
[tex] \large \bold{-N} \frak{unx-}[/tex]
Answer this question in 20 mins timer start now or else the question will go away and u would give point 25 points Ready Set GOOOO!!
Answer:
cost of a doughnut is $0.75
cost of a cookie is $0.60
Step-by-step explanation:
As you wrote:
Let x = doughnuts
Let y = cookies
The first sentence of the problem (alexandra) can be written as:
[tex]2x + 3y = 3.30[/tex]
The second sentence of the equation (briana) can be written as:
[tex]5x + 2y = 4.95[/tex]
We must now solve for either [tex]x[/tex] or [tex]y[/tex] in this system of equations.
I will solve for [tex]x[/tex] in this example.
First we need to multiply the first equation by [tex]2[/tex] and the second equation by [tex]3[/tex]. This is so both equations have [tex]6y[/tex] as a term.
Equation 1:
[tex]2(2x + 3y) = (3.30)2\\4x + 6y = 6.60[/tex]
Equation 2:
[tex]3(5x + 2y) = (4.95)3\\15x+6y=14.85[/tex]
Now that both equations have [tex]6y[/tex] as a term, we can subtract Equation 1 from Equation 2. This will remove y from the equation and allow us to solve for x.
[tex](15x+6y) - (4x+6y) = (14.85) - (6.60)\\11x = 8.25\\\boxed{x = 0.75}[/tex]
We now know the cost of a doughnut is $0.75. Now we can solve for the cost of a cookie through substitution.
[tex]2x + 3y = 3.30\\2(0.75) + 3y = 3.30\\1.50 + 3y = 3.30\\3y = 1.80\\\boxed{y = 0.6}[/tex]
Now we know the cost of a cookie is $0.60.
These are the answers,
- Kan Academy Advance
A fish swims at a speed of 12 miles per hour a boy swims at a speed of 4.44 feet per second. How much faster does the fish swim than the boy in yards per minute?
3ft = 1yd
5280= 1 mile
Answer:
I don't know it
Step-by-step explanation:
try with an textbook you have
Please help me solve this composite shape step by step
Answer:
73 cm²
Step-by-step explanation:
Areas and volumes of composite figures are found by dividing the figure into shapes you have formulas for. Sometimes that will be a sum of shapes, and sometimes it will involve the difference of shapes.
__
setupThis shape can be decomposed into two rectangles by extending the horizontal line. (This is the dashed line shown in the attachment.)
The width of the top rectangle will be the sum of the lengths of the labeled horizontal segments:
4 cm + 5 cm + 3 cm = 12 cm
The height of the top rectangle, and the dimensions of the bottom rectangle (square) are shown in the given figure.
The area of each rectangle is the product of its width and height.
A = WH
__
solutiontop rectangle area = WH = (12 cm)(4 cm) = 48 cm²
bottom rectangle area = WH = (5 cm)(5 cm) = 25 cm²
Area = top rectangle area + bottom rectangle area = (48 cm²) +(25 cm²)
Area = 73 cm²
The area of this composite shape is 73 cm².
_____
Additional comment
The figure will fit into a rectangle that is 9 cm high by 12 cm wide. From that rectangle, a rectangle 5 cm high and 4 cm wide is removed from the lower left, and a rectangle 5 cm high and 3 cm wide is removed from the lower right. Figuring the area this way, we find it to be ...
figure area = bounding rectangle area - removed areas
= (9 cm)(12 cm) -(5 cm)(4 cm) -(5 cm)(3 cm) = 108 cm² -20 cm² -15 cm²
= 73 cm²
Which expression is equivalent to
By taking a common factor, we will see that the equivalent expression is:
[tex]12*\sqrt[3]{6c}[/tex]
How to find the equivalent expression?
Here we start with the expression:
[tex]5*\sqrt[3]{6c} + 7*\sqrt[3]{6c}[/tex]
Notice that if we define:
[tex]\sqrt[3]{6c} = u[/tex]
We can rewrite our expression as:
[tex]5u + 7u[/tex]
Now we can take the common factor u to write:
[tex](5 + 7)u = 12u[/tex]
Now if we replace u y the cubic root, we will get:
[tex]12*\sqrt[3]{6c}[/tex]
So the correct option is the third one.
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Graph the inequality.
2x+5y> -15
Answer: See attached
Step-by-step explanation:
[] Since the inequality uses greater than (>) and not greater than or equal to (≥), the line will be dashed.
[] The inequality is greater than (>) so we will shade above the line as values "above" are greater.
Answer:
here is what i got
Step-by-step explanation:
Evaluate the following expression.
(-3)-² =
Answer:
The answer to this is 9.
Step-by-step explanation:
First of all, you wrote the expression wrong, but that's okay. It's supposed to be written as (-3)².
Second of all, since multiplying two negatives makes a positive and squaring is just multiplying the integer to itself, then -3×-3=9. I hope this helps! :)
Step 1: Choose a point on the line, such as (2, 5).
Step 2: Choose another point on the line, such as (1, 3).
Step 3: Count units to determine the slope ratio. The line runs 1 unit to the right and rises 2 units up, so the slope is StartFraction one-half EndFraction.
Step 4: Substitute those values into the point-slope form.
y – y1 = m(x – x1)
y – 3 = y minus y 1 equals m left-parenthesis x minus x 1 right-parenthesis. (x – 1)
Which of Talia’s steps is incorrect?
Step 1 is incorrect because it uses a point that is not on the line.
Step 2 is incorrect because it uses a point that is not on the line.
Step 3 is incorrect because it shows an incorrect ratio for the slope.
Step 4 is incorrect because it shows an incorrect substitution of (1, 3) into the point-slope form.
The step of Talia that's incorrect.The step that is incorrect is: C. Step 3
How to find the slope?The slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.
Thus, we get:
Slope = rise/ run
Calculating the slope using two points on the line, (2, 5) and (1, 3), we have:
Slope (m) = (5 - 3)/(2 - 1)
Slope (m) = (2)/(1)
Slope (m) = 2
This shows that the ratio of the slope calculated by Talia was wrong. The step that is incorrect is: C. Step 3
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3x² - 12x +9=0 using quadratic formula
Answer:
The quadratic equation 3x² - 12x + 9 = 0 has two real roots when solved:
x₁ = 1 and x₂ = 3
Step-by-step explanation:
✍ An equation of type ax² + bx + c = 0, can be solved, for example, using the quadratic formula:
[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{b^{2}-4ac } }{2a} }[/tex]
either
[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta} }{2a} }[/tex]
where
[tex]\bf{\Delta=b^{2}-4ac }[/tex]
Identify the coefficients
a = 3, b = -12 and c = 9
Calculate the discriminant value
Δ = b² - 4ac
Δ = (-12)² - 4.3.9 = 144 - 12.9
Δ = 144 - 108 = 36
Enter the values of a, b and the discriminant value in the quadratic formula
[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta } }{2a} }[/tex]
[tex]\boldsymbol{x=\dfrac{-(-12\pm\sqrt{36} }{2\cdot3 } }[/tex]
[tex]\boldsymbol{x=\dfrac{(12\pm\sqrt{36} }{6 } \ ==== > \ (Solution \ general) }[/tex]
As we can see above, the discriminant (Δ) of this equation is positive (Δ> 0) which means that there are two real roots (two solutions), x₁ and x₂.
[tex]\boldsymbol{x_{1}=\dfrac{-12-\sqrt{36} }{6}=\dfrac{12-6}{6}=\dfrac{6}{6}=1 \ === > (First \ solution) }[/tex]
To find x₁, just choose the positive sign before the square root. Later,
[tex]\boldsymbol{x_{1}=\dfrac{12+\sqrt{36} }{6}=\dfrac{12+6}{6}=\dfrac{18}{6}=3 \ === > (Second \ solution) }[/tex]
Please Help I Don't Understand!
Answer:18
Step-by-step explanation:
Answer:
C. 16
Explanation:
[tex]\rightarrow \sf \dfrac{9}{4} = \dfrac{x+2}{8}[/tex]
cross multiply
[tex]\rightarrow \sf \dfrac{9(8)}{4} = x + 2[/tex]
simplify integers
[tex]\rightarrow \sf 18 = x + 2[/tex]
exchange sides
[tex]\rightarrow \sf x =18-2[/tex]
subtract integers
[tex]\rightarrow \sf x =16[/tex]
The area of a circle is 64л сm². What is the circumference, in centimeters? Express your answer in terms of pi
A coordinate plane with a line passing through points (1, 2) and (4, 4)
The slope of the graphed line is . Which formulas represent the line that is graphed? Check all that apply.
y – 1 = (x – 2)
y – 2 = (x – 1)
y – 4 = (x – 4)
f(x) = x +
f(x) = x +
A straight line is represented by a linear equation given below.
The points are given as (1, 2) and (4, 4).
Start by calculating the slope (m)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
So, we have
[tex]m=\frac{4-2}{4-1} \\m=\frac{2}{3}[/tex]
What is the slope-intercept form of the line?The equation in slope-intercept form is then calculated as:
[tex]y=m(x-x_1)+y_1[/tex]
So, we have:
[tex]y=\frac{2}{3}(x-1)+2\\ \\y=\frac{2}{3}(x-4)+4\\[/tex]
Expand
[tex]y=\frac{2}{3}(x-1)+2\\ y=\frac{2}{3} x-\frac{2}{3}+2[/tex]
Take LCM
[tex]y=2/3x+4/3[/tex]
Multiply through by 3
3y=2x+4
So, the possible equations are:
.[tex]3y=2x+4\\y=\frac{2}{3}x+\frac{4}{3} \\y=\frac{2}{3}(x-1)+2\\y=\frac{2}{3}(x-4)+{4}[/tex]
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Answer:
B
C
E
Step-by-step explanation:
other dudes are wrong
Subtract.
5x²-5x+1
(2x² +9x-6)
OA. 3x² - 4x+7
OB. 3x² + 4x-5
OC. 3x² +14x-5
OD. 3x²-14x+7
SUBMIT
Answer:
C) [tex]3x^2-14x-5[/tex]
Step-by-step explanation:
[tex](5x^2-5x+1)-(2x^2+9x-6)\\\\5x^2-5x+1-2x^2-9x-6\\\\3x^2-14x-5[/tex]
The subtraction of the given expressions gives D. 3x² - 14x + 7.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given are two expressions.
5x² - 5x + 1 and 2x² + 9x - 6
We have to find the difference of the given expression.
(5x² - 5x + 1) - (2x² + 9x - 6)
= 5x² - 5x + 1 - 2x² - 9x + 6
Operating the like terms together,
= (5x² - 2x²) + (-5x - 9x) + (1 + 6)
= 3x² - 14x + 7
Hence the correct option is D.
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Find the value of x. Round to the nearest tenth. B 18 19 A 22° C x = [? ]° X X Law of Sines: sin A a sin B b = sin C C
Answer:
23.292°
Step-by-step explanation:
see the attachment photo.
The value of x to the nearest tenth is 23.3°.
What is Law of Sines?Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.
That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,
a / sin A = b / sin B = c / sin C
Given is a triangle ABC.
Using the law of sines,
AB / Sin C = BC / Sin A
We have to find the angle A.
Substituting,
18 / sin 22 = 19 / sin x
18 × sin(x) = 19 × sin (22°)
sin(x) = (19 × sin (22°)) / 18
sin x = 0.3954
x = 23.29° ≈ 23.3°
Hence the value of x is 23.3°.
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-2b + 9 = 25
ones step and two step equation Screenshot of example
Answer:
b = -8
Step-by-step explanation:
-2b + 9 =25
-9 = -9
-2b = 16
/-2 /-2
b = -8
Simplify 1- cos^2 Θ / cos^2 Θ
Answers
sin2 θ
cos2 θ
tan2 θ
1
[tex]\\ \rm\Rrightarrow \dfrac{1-cos^2\theta}{cos^2\theta}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{sin^2\theta}{cos^2\theta}[/tex]
[tex]\\ \rm\Rrightarrow tan^2\theta[/tex]
Option C
Answer:
Trigonometric identities
[tex]\large \begin{aligned}\cos^2 \theta + \sin^2 \theta & = 1\\\implies \quad \quad \sin^2 \theta & = 1 - \cos^2 \theta\\\\\tan \theta=\dfrac{\sin \theta}{\cos \theta} \end{aligned}[/tex]
Therefore, using the identities, the given expression can be simplified as follows:
[tex]\large\begin{aligned}\implies \dfrac{1- \cos^2 \theta}{\cos^2 \theta} & = \dfrac{\sin^2 \theta}{\cos^2 \theta}\\\\& = \tan^2 \theta\end{aligned}[/tex]
Write an equation that represents the line.
Step-by-step explanation:
a general line equation is
y = ax + b
"a" being the slope is the line, "b" being the y-intercept (the y value when x = 0).
we see from the 2 marked points (by we could choose any points on the line) that
y changes by 2 units, when x changes by 3 units.
so the slope is 2/3.
we use one point (1, 2) to solve for b
2 = 2/3 × 1 + b = 2/3 + b
6/3 = 2/3 + b
4/3 = b
and the full equation is
y = 2/3 x + 4/3
the diagram shows a right angled triangle .
Answer:
the image should help.
Step-by-step explanation:
image explains everything.
Please could you explain this step by step I’m really stuck.
Answer:
x = -2.5
x = 2
Step-by-step explanation:
Hello!
We can remove the denominators by multiplying everything by it.
Solve:
[tex]\frac{5}{x + 3} + \frac4{x + 2} = 2[/tex][tex]5 + \frac{4(x + 3)}{x + 2} = 2(x + 3)[/tex][tex]5 + \frac{4x + 12}{x + 2} = 2x + 6[/tex][tex]5(x + 2) +4x + 12 = (2x + 6)(x + 2)[/tex][tex]5x + 10 + 4x + 12 = 2x^2 + 6x + 4x + 12[/tex][tex]9x + 22 = 2x^2 + 10x + 12[/tex]Let's make one side equal to 0.
[tex]0 = 2x^2 + x - 10[/tex]Solve by factoring, and then the zero product property.
[tex]0 = 2x^2 + x - 10\\[/tex]Multiply 2 and -10. You get -20. Think of two number that multiply to -20, and add to 1. If we think about the standard form of a quadratic, [tex]ax^2 + bx + c[/tex], think two numbers that equal "ac" and add up to "b".
[tex]0 = 2x^2 - 4x + 5x - 10[/tex][tex]0 = 2x(x - 2) + 5(x - 2)[/tex][tex]0 = (2x + 5)(x - 2)[/tex]Using the zero product property, set each factor to 0 and solve for x.
2x + 5 = 0The two answers are x = -2.5, and x = 2.
Answer:
x = -5/2, 2
Step-by-step explanation:
Given:
[tex]\displaystyle \large{\dfrac{5}{x+3}+\dfrac{4}{x+2} = 2}[/tex]
With restriction that x-values cannot be -3 and -2 else it will turn the expression as in undefined.
First, multiply both sides by (x+3)(x+2) to get rid of the denominator.
[tex]\displaystyle \large{\dfrac{5}{x+3}\cdot (x+2)(x+3)+\dfrac{4}{x+2} \cdot (x+2)(x+3) = 2 \cdot (x+2)(x+3)}\\\\\displaystyle \large{5(x+2)+4(x+3) = 2(x+2)(x+3)}[/tex]
Simplify/Expand in:
[tex]\displaystyle \large{5x+10+4x+12 = 2(x^2+5x+6)}\\\\\displaystyle \large{9x+22=2x^2+10x+12}[/tex]
Arrange the terms or expression in quadratic equation:
[tex]\displaystyle \large{0=2x^2+10x+12-9x-22}\\\\\displaystyle \large{2x^2+x-10=0}[/tex]
Factor the expression:
[tex]\displaystyle \large{(2x+5)(x-2)=0}[/tex]
Solve like linear equation as we get:
[tex]\displaystyle \large{x=-\dfrac{5}{2}, 2}[/tex]
Since both x-values are not exact -2 or -3 - therefore, these values are valid. Hence, x = -5/2, 2