Answer:the answer is A
Step-by-step explanation:
The step is
Real number - rational(irrational)_ - integer - whole - then natural
The true statement regarding number sets are b. all irrational numbers are real numbers.
What are irrational numbers ?Irrational numbers are those numbers which have a non-repeating, non-terminating pattern after decimal place.
According to the given statements we have to determine which is true.
a. all integers are not whole numbers as 0 contains in the set of whole numbers but not in the set of integers.
b. all irrational numbers are real numbers this is a true statement because all the real numbers consist of rational and irrational numbers.
We don't need to check other options because we have been asked which of the following is true not which of the following is/are true.
learn more about number sets here :
https://brainly.com/question/17675434
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What is the equation of the line that passes through the point (6,14) and is parallel to the line with the following equation? y=-4/3x-1
Answer:
[tex]\displaystyle \boxed{y = -1\frac{1}{3}x + 22}[/tex]
Step-by-step explanation:
Parallel Equations have SIMILAR RATE OF CHANGES [SLOPES], so keep [tex]\displaystyle -\frac{4}{3}[/tex]as is and do this:
14 = −4⁄3[6] + b
14 = −8 + b
+ 8 + 8
_________
[tex]\displaystyle 22 = b \\ \\ y = -1\frac{1}{3}x + 22[/tex]
I am joyous to assist you at any time.
Boomer, the dog, eats 3\2 of dog food each week. How many grams of dog food will Boomer eat in 4weeks?'
Answer:
6 grams
Step-by-step explanation:
(3/2)*4 = 12/2 = 6
Answer:
[tex]\boxed{\sf 6 \ grams \ of \ food}[/tex]
Step-by-step explanation:
1 week = [tex]\frac{3}{2} g\ of \ the \ food[/tex]
Multiplying both sides by 4
4 weeks = [tex]\frac{3}{2} * 4[/tex]
4 weeks = 3 * 2 g of the food
4 weeks = 6 g of food
Please help me!!! I need this ASAP!!!
Answer:
number ten: x=5
number two: x=5³/5
Step-by-step explanation:
number ten:
4x + 3x - 9 = 26
4x + 3x = 26+9
7x = 35
x = 5
number two:
3x + 2x - 8 = 20
3x + 2x = 20+8
5x = 28
x = 5³/5
If 3 cats catch 3 mice in 3 minutes, how long will it take 100 cats to catch 100 mice?
Answer:
100 minutes
Step-by-step explanation:
It takes each of the 3 cats about 1 minute to catch one mouse. If the same goes for the 100 cats, it will take them 100 minutes to catch 100 mice.
Hope that helps.
Answer:
3 min
Step-by-step explanation:
These are all independent actions.
If you put 1 cat in a room with 1 mouse, it will take 3 min to catch the mouse.
If you put 2 cats in a room with 2 mice, they will act independently and it will take 3 min for each one to catch a mouse.
If you put 3 cats in a room with 3 mice, they will act independently and it will take 3 min for each one to catch a mouse.
If you put 100 cats in a room with 100 mice, they will act independently and it will take 3 min for each one to catch a mouse.
Each cat will finish at the same time — 3 min.
A tent is in the form of a right circular cylinder and cone. The radius of the cone and cylinder is 4 meters. The height of the cylinder and cone are 4.5 meters and 3 meters respectively. Find the outer surface area of the tent. (Assume π = 22 /7)
Answer:
176m²
Step-by-step explanation:
When we are asked to find the outer surface area of a geometric shape, it means to find the Lateral or Curved Surface Area of the shape. We are given two shapes above.
Step 1
Find the Outer surface area of the cone
Outer / Lateral surface area of a cone =
πrl
Where l = √r² + h²
r = 4 m
h = 3m
Outer surface area = 22/7 ×√4² + 3²
= 22/7 × √16 + 9
= 22/7 × √25
= 22/7 × 5
= 62.83185m²
Step 2
Find the outer surface area of a cylinder
= 2πrh
π = 22/7
r = 4m
h = 4.5
π = 22/7
Outer surface area of a cylinder = 2 × 22/7 × 4 × 4.5
= 113.09734m²
Step 3
The Outer Surface Area of the Tent = Outer Surface Area of the cone + Outer Surface Area of the cylinder
= 62.83185m² + 113.09734m²
= 175.92919m²
Approximately ≈ 176m²
Therefore, the outer surface area of the tent = 176m²
Triangle A″B″C″ is formed by a reflection over y = −3 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C″? coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3
Answer:
Option (3)
Step-by-step explanation:
This question is not complete; here is the complete question.
Triangle A″B″C″ is formed by a reflection over y = −3 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between ΔABC and ΔA″B″C″?
Coordinates of the vertices of the triangle ABC are,
A(-3, 3), B(1, -3) and C(-3, -3)
When triangle ABC is reflected over y = -3
Coordinates of the image triangle A'B'C' will be.
A(-3, 3) → A'(-3, -9)
B(1, -3) → B'(1, -3)
C(-3, -3) → C'(-3, -3)
Further ΔA'B'C' is dilated by a scale factor of 2 about the origin then the new vertices of image triangle A"B"C" will be,
Rule for the dilation will be,
(x, y) → (kx, ky) [where 'k' is the scale factor]
A'(-3, -9) → A"(-6, -18)
B'(1, -3) → B"(2, -6)
C'(-3, -3) → C"(-6, -6)
Length of AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(-3-1)^2+(3+3)^2}[/tex]
= [tex]\sqrt{52}[/tex]
= [tex]2\sqrt{13}[/tex]
Length of A"B" = [tex]\sqrt{(-6-2)^2+(-18+6)^2}[/tex]
= [tex]\sqrt{64+144}[/tex]
= [tex]\sqrt{208}[/tex]
= [tex]4\sqrt{13}[/tex]
Therefore, [tex]\frac{\text{AB}}{\text{A"B"}}=\frac{2\sqrt{13}}{4\sqrt{13}}[/tex]
[tex]\frac{\text{AB}}{\text{A"B"}}=\frac{\sqrt{13}}{2\sqrt{13}}[/tex]
[tex]AB(2\sqrt{13})=A"B"(\sqrt{13})[/tex]
Option (3) is the answer.
A conveyor belt carries supplies from the first floor to the second floor, which is 21 feet higher. The belt makes a 60° angle with the ground. How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot. If the belt moves at 75 ft/min, how long, to the nearest tenth of a minute, does it take the supplies to move to the second floor?
Hey there! I'm happy to help!
LENGTH OF CONVEYOR BELT
We are going to have to use some trigonometry. Let's think of this as a right triangle. The conveyor belt is the diagonal or the hypotenuse, while the ground is and the height of the room make a right angle as the legs.
We have a sixty degree angle between the conveyor belt and the ground. This is means that the 21 foot height is the opposite side of our right triangle. So, we are dealing with the opposite and the hypotenuse, so we will use the sine. The sine of an angle is equal to the opposite length divided by the hypotenuse length.
We will set up the following equation and solve for the length of our conveyor belt (c).
[tex]sin60=\frac{21}{c}[/tex]
We multiply both sides by c.
[tex]c(sin60)=21[/tex]
We divide both sides by sin60.
[tex]c=\frac{21}{sin60}[/tex]
If we evaluate this with a calculator, we get that c is equal to 24.2487113..., or 24 when rounded to the nearest foot.
So, the supplies travel 24 feet from one end to the other.
DURATION OF TRAVEL
We want to find how long it takes the supplies to move across the conveyor belt. We see that every minute, it moves 75 feet. We want to see how many minutes it will take to move 24 feet, as that is the length of the conveyor belt as we previously solved. Let's set up a proportion.
[tex]\frac{feet}{minute} =\frac{75}{1} =\frac{24}{m}[/tex]
We cross multiply, giving us the following equation.
75m=24
We divide both sides by 75.
m=0.32
We want to round to the nearest tenth of a minute, so it will take 0.3 minutes for the supplies to move to the second floor.
Have a wonderful day! :D
Find the area of the following shape.
Answer:
57 units^2
Step-by-step explanation:
First find the area of the triangle on the left
ABC
It has a base AC which is 9 units and a height of 3 units
A = 1/2 bh = 1/2 ( 9) *3 = 27/2 = 13.5
Then find the area of the triangle on the right
DE
It has a base AC which is 6 units and a height of 1 units
A = 1/2 bh = 1/2 ( 6) *1 = 3
Then find the area of the triangle on the top
It has a base AC which is 3 units and a height of 3 units
A = 1/2 bh = 1/2 ( 3) *3 = 9/2 = 4.5
Then find the area of the rectangular region
A = lw = 6*6 = 36
Add them together
13.5+3+4.5+36 =57 units^2
Answer:
Total Area = 57 sq. units
Step-by-step explanation:
will make it simple and short
Total Area = A1 + A2 + A3
A1 = (7 + 6) * 6/2 = 39 sq. units (area of a trapezoid)
A2 = 1/2 (9 * 3) = 13.5 sq. units (area of a triangle)
A3 = 1/2 (3 * 3) = 4.5 sq. units (area of a triangle)
Total Area = 39 + 13.5 + 4.5 = 57 sq. units
Please help! offering 25 points, 5 stars, and a thanks. Ive asked this 3 times now
Answer:
17 quarters
Step-by-step explanation:
Let q = quarters
n = nickels
.25q + .05n = 5.90
we have 16 more nickels than quarters so add 16 quarters to make them equal
n = q+16
Substitute
.25q + .05( q+16) = 5.90
Distribute
.25q+.5q+.80=5.90
Combine like terms
.30q +.8 = 5.90
Subtract .8 from each side
.30q = 5.10
Divide each side by .3
.3q/.3 = 5.1/.3
q = 17
Answer:
Gisel have:
17
quarters
Step-by-step explanation:
1 nickel = 5 cents
1 quarter = 25 cents
1 dollar = 100 cents
5,90 dollars = 5,9*100 = 590 cents
then:
n = t + 16
5n + 25t = 590
n = quantity of nickels
t = quantity of quarters
5(t+16) + 25t = 590
5*t + 5*16 + 25t = 590
5t + 80 + 25t = 590
30 t = 590 - 80
30 t = 510
t = 510 / 30
t = 17
n = t + 16
n = 17 + 16
n = 33
Check:
5n + 25t = 590
5*33 + 25*17 = 590
165 + 425 = 590
If Y varies directly as x
write down the equation
connecting y and x. If y = 10
when x=5, find the value
of y when x= 16
Answer:
32
Step-by-step explanation:
If y is 2 times as much as x, then 1 = 2
5 x 3 = 15 + 1 = 16
10 x 3 = 30 + 2 = 32, or 16 x 2 = 32
Please tell me if I'm wrong.
Help! Will give brainliest.
Answer:
A. You can see which shape the bases are, how many bases there are, how many faces there are, and how many edges there are.
B. The bases are ABC and DEF, and I know because they are two congruent triangles on two opposite sides of the shape.
Coherence
5. Simon's teacher asked him to e-mail her a copy of the outline for his essay on American
History: When drafting the e-mail, what level of diction should Simon use?
informal
formal
standard
foundational
Answer:
The correct option is;
Formal
Step-by-step explanation:
The common levels of diction are formal, informal, and popular, with formal diction being the most selective of the word choices
Formal diction is used when when communicating in a situation that is formal
Formal diction uses languages that is devoid of slang and grammatically correct
Formal language is precise, grammatically correct language that does not use slang used in communication for legal, professional, business and academic purposes.
Helpppp pleaseee!!! Thank you
Complete the recursive formula of the arithmetic sequence -15, -11, -7, -3,...−15,−11,−7,−3,...minus, 15, comma, minus, 11, comma, minus, 7, comma, minus, 3, comma, point, point, point.
Answer:
c(1) = -15
c(n) = c(n - 1) + 4
Step-by-step explanation:
Given arithmetic sequence is,
-15, -11, -7, -3...........
Common difference between each successive and previous term is,
d = -11 - (-15)
= -11 + 15
= 4
Since recursive formula of the arithmetic sequence is represented by,
a₁ = First term of the sequence
a(n) = a(n - 1) + d
where a(n) is the nth term and a(n-1) is the previous term of the nth term.
Form the given sequence,
c₁ = -15
c(n) = c(n - 1) + 4
Show that the equations x^2-7x+6=0 and y^2-14y+40=0 form a rectangle.Also find the joint equations of diagonals.
Answer:
1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The joint equations of diagonals are;
5·y = 56 - 6·x and 5·y = 6·x + 14.
Step-by-step explanation:
The equations are;
x² - 7·x + 6 = 0......................(1)
y² - 14·y + 40 = 0.................(2)
Factorizing equation (1) and equation (2) , we get
x² - 7·x + 6 = (x - 6)·(x - 1) = 0
Which are vertical lines at points x = 6 and x = 1
For equation (2) , we get
y² - 14·y + 40 = (y - 10)·(y - 4) = 0
Which are horizontal lines at point y = 4 and y = 10
The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The points of intersection of the equations are;
(1, 4), (1, 10), (6, 4), and (6, 10)
The end point of the diagonals are;
(1, 10), (6, 4) and (1, 4), (6, 10)
The slope of the diagonals are;
(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5
The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)
y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5
5·y = 56 - 6·x
The other diagonal is therefore;
y - 4 = 6/5×(x - 1)
y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5
5·y = 6·x + 14.
The joint equations of diagonals are therefore;
5·y = 56 - 6·x and 5·y = 6·x + 14.
Write a number sentence that
illustrates the associative property
of addition,
Please, someone help.
Answer:
ok so
faf
Step-by-step explanation:
Factor 20x2 + 25x – 12x – 15 by grouping.
1. Group terms with common factors.
2. Factor the GCF from each group.
3. Write the polynomial as a product of binomials.
(20x2 – 12x) + (25x– 15)
4x(5x – 3) + 5(5x – 3)
(5x – 3)(
x +
)
Please answer this question now
Answer:
AB = 72°
Step-by-step explanation:
The inscribed angle ADC is half the measure of its intercepted arc, thus
56° = [tex]\frac{1}{2}[/tex] ( m ABC ) ← multiply both sides by 2
112° = ABC
ABC = AB + BC = AB + 40, so
AB + 40 = 112 ( subtract 40 from both sides )
AB = 72°
With which set of information can you construct a unique triangle?
OA the measurements of all the angles
ОВ.
the lengths of two sides
OC. the measurements of two angles
OD. the lengths of all the sides
OE the measurement of one angle
Answer:
D
Step-by-step explanation:
This would be using the SSS.
Which means knowing three sides.
The other options do not relate to any of the SSS, SAS, ASA, RHS
Hope that helped!!! k
There are 10 students on the basketball team. The coach selects 3 of them to go to the basketball clinic. In how many ways can she choose 3 of the 10 students?
[tex]_{10}C_3=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot 3}=120[/tex]
Question :-
There are 10 students on the basketball team. The coach selects 3 of them to go to the basketball clinic. In how many ways can she choose 3 of the 10 students?Answer :-
The coach can choose 3 of the 10 students in 120 ways.[tex] \rule{200pt}{3pt}[/tex]
Combinations refers to the number of ways of selecting from a set when the order is not important. The number of combinations of n objects taken r at a time is given by [tex]\sf C(n, r) = \dfrac{n!}{(n - r)!r!}, n \geqslant r[/tex].
Solution :-
As per the provided information in the given question, we have been given that the number of combinations of 10 students taken 3 at a time. We have been asked to calculate the ways that she can choose 3 of the 10 students.
To calculate the ways that she can choose 3 of the 10 students, we will apply the formula below :-
[tex] \qquad \bigstar \: \: \: \boxed{ \sf{ \: \: C(n, r) = \dfrac{n!}{(n - r)!r!} \: \: }}[/tex]
Substitute the given values into the above formula and solve for C:
[tex]\sf:\implies{ C(n, r) = \dfrac{n!}{(n - r)!r!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10!}{(10 - 3)!3!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10!}{7!3!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10 \cdot 9 \cdot 8 \cdot \cancel{7!}}{ \cancel{7!}3!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10 \cdot 9 \cdot 8}{3 \cdot 2}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{720}{6}}[/tex]
[tex]\sf:\implies \bold{ C(10, 3) = 120 \: ways}[/tex]
Therefore :-
The coach can choose 3 of the 10 students in 120 ways.[tex]\\[/tex]
Learn more about combinations at https://brainly.com/question/11955073
Have a great day! <33
what are the factors of 47 (cuz im STUPID and i dont feel like doing this cuz im working on geogrophy)
Hey there! I'm happy to help!
The factors are the numbers you multiply to get 47. And they can't be fractions or numbers with fractions. They have to be integers (numbers without fractions).
So far, we see that we can multiply 1 and 47 to get 47. To see if there are any more, we see what numbers 1-10 we can divide by.
We cannot divide by 2 because 47 is odd.
We cannot divide by 3 because it gives us 15.6666...
We can't divide by 4 because 47 is odd.
We can't divide by 5 because 47 does not have a 5 or 0 in the ones place.
We can't divide by 6 because 47 is odd.
We can't divide by 7 because it gives us 6.714285....
We can't divide by 8 because 47 is odd.
We can't divide by 9 because it gives us 5.2222
And we obviously can't divide it by 10.
Therefore, the factors of 47 are 1 and 47. A number whose only factors are 1 and itself is called a prime number.
I hope that this helps! Have a wonderful day! :D
Answer: 47 is a prime number
The exponent of prime number 47 is 1 . Adding 1 to that exponent we get (1+1)=2
Factor of 47: 1, 47
1. Which monomial has the same degree as 6a2b8c? A 18t8 B 12p6q5 C 9a5b3c2 D 6w4x2y3z3
Answer: "B. [tex]12p^6q^5[/tex]
Step-by-step explanation:
The given monomial : [tex]6a^2b^8c[/tex]
Degree of this monomial = Sum of powers of variables=2+8+1= 11
Let's check all the options
A [tex]18t^8[/tex]
Degree = 8
B [tex]12p^6q^5[/tex]
Degree = 6+5 =11
C [tex]9a^5b^3c^2[/tex]
Degree = 5+3+2=10
D [tex]6w^4x^2y^3z^3[/tex]
Degree =4+2+3+3=12
We can see that only option B has degree 11.
So, the monomial has the same degree as [tex]6a^2b^8c[/tex] is "B. [tex]12p^6q^5[/tex] "
5y-5y^2-5+2+2y+3y^2-1
Answer:
7y - 2y² - 4
Step-by-step explanation:
5y - 5y² - 5 + 2 + 2y + 3y² - 1
5y + 2y - 5y² + 3y² - 5 + 2 - 1 (combine like terms)
7y - 2y² - 4
90 POINTS! HELP ASAP! Using one of the figures below, explain a strategy for calculating the area of the irregular polygon.
Answer:
area of polygon = 88 sq. units
Step-by-step explanation:
lets make it simple, short and accurate.
area of polygon = total area - total area of triangles
total area = 11 * 12 = 132
triangle 1 = 1/2 * 5 * 5 = 12.5
triangle 2 = 1/2 * 3 * 6 = 9
triangle 3 = 1/2 * 3 * 8 = 12
triangle 4 = 1/2 * 3 * 7 = 10.5
total area of triangle = 12.5 + 9 + 12 + 10.5 = 44
area of polygon = 132 - 44 = 88 sq. units
Answer:
The area of the irregular polygon:
88 units²
Step-by-step explanation:
The irregular polygon is insert in a rectangle
The strategy is:
1 - calculate the rectangle total area
2- calculate the area of each right triangle
3.- substracte the total area of the 4 right triangles from the area of the rectángule
then:
1.-
Ar = 12*11 = 132 units²
Ar = rectangle area
2.-
At₁ = (5*5)/2 = 25/2 = 12.5 units²
At₂ = (6*3)/2 = 18/2 = 9 units²
At₃ = (7*3)/2 = 21/2 = 10.5 units²
At₄ = (8*3)/2 = 24/2 = 12 units²
At total = 12.5 + 9 + 10.5 + 12 = 44 units²
At = right triangle areas
3.-
Ap = 132 - 44 = 88 units²
Please help Describe a way that you can remember the elements of the reflection matrices if you forget where the 1s, -1s, and 0s belong.
Step-by-step explanation:
Multiplying the vertex matrix with the matrix gives us a reflection matrix. The most common matrix reflections are seen as reflection in the x - axis as well as reflection in the y - axis.
It can also be reflect by 90 degree or by 180 degree.
So, one way to remember the elements is by multiplying the given matrix by a unit matrix. And on the other hand you can remember the elements remembering by what degree we are reflecting the matrix. This way makes it easier to remember the elements.
The explanation regarding the elements of the reflection is explained below:
The following information should be considered:
In the case when we Multiply the vertex matrix with the matrix so it provides the reflection matrix. The most common matrix reflections are seen as reflection in the x - axis as well as reflection in the y - axis. It can also be reflect by 90 degree or by 180 degree.Learn more: https://brainly.com/question/17961582?referrer=searchResults
x-6/2=2x/7 solve the equation
Answer:
x-6/2=2x/7
7x-42=4x
7x-4x=42
3x= 42
X = 42/3
Please help!!
can you explain how to do it cause my teacher didnt show us.
math question- If the spinner below is spun 500 times, then how many times could you expect to spin a D
thank you for you trying or helping!!
Answer:
500×4 =2400 I think would help u
The graph of a quadratic function intercepts the x-axis in two places and the y-axis in one place. According to the fundamental theorem of algebra, which of the following statements is correct? A. The quadratic function has no real zeros and two complex zeros. B. The quadratic function has one distinct real zero and one distinct complex zero. C. The quadratic function has two distinct real zeros and one distinct complex zero. D. The quadratic function has two distinct real zeros.
Answer: D. The quadratic function has two distinct real zeros.
There are no complex roots as a quadratic's roots are maxed out at 2. The fundamental theorem of algebra says that if you have an nth degree polynomial, then the max number of real roots is n.
This quadratic's roots are distinct because the two x intercepts are in different places. Each x intercept is a root.
A bag contains five tokens numbered 2, 3, 6, 7, and 8. Two tokens are taken in succession out of the bag without replacement. A) Create the probability distribution for "x" being the number of odd numbered tokens drawn. B) What is mean and variance of the probability distribution?
Answer and Step-by-step explanation:
A) Probability of taken two odd numbered token without replacement:
P(3) = 2/5 = 0.4
P(7) = 1/4 = 0.25
Construct a probability distribution:
X 3 7
p(X) 0.4 0.25
B) Mean of the probability distribution:
E(X) = ∑xp
E(X) = 3*0.4 + 7*0.25
E(X) = 2.95
Variance of the probability distribution:
V(X) = [tex]\Sigma X^{2}p - [E(X)]^{2}[/tex]
V(X) = [tex]3^{2}*0.4+7^{2}*0.25 - (2.95)^{2}[/tex]
V(X) = 7.1475
Mean and variance of the probability distribution are 2.95 and 7.145, respectively.
Find the conjugate of 2 - 5i and then calculate the product of the given complex number and its conjugate. (1 point)
Answer:
29
Step-by-step explanation:
conjugate of a+ib=a-ib
conjugate of 2-5i=2+5i
(2+5i)(2-5i)=2²-(5i)²=4-25i²=4-25(-1)=4+25=29
Answer:
29
i had the same question and 29 was the right answer
solve the following inequalitie and fin x
5/( + 2)(4 − )< 1
Answer: -1 < x < 3
Step-by-step explanation:
[tex]\dfrac{5}{(x+2)(4-x)}<1[/tex]
Step 1 The denominator cannot equal zero:
x + 2 ≠ 0 and 4 - x ≠ 0
x ≠ -2 4 ≠ x
Place these restrictive values on the number line with an OPEN dot:
<----------o-------------------o--------->
-2 4
Step 2 Find the zeros (subtract 1 from both sides and set equal to zero):
[tex]\dfrac{5}{(x+2)(4-x)}-1=0\\\\\\\dfrac{5}{(x+2)(4-x)}-\dfrac{(x+2)(4-x)}{(x+2)(4-x)}=0\\\\\\\dfrac{5-(-x^2+2x+8)}{(x+2)(4-x)}=0\\\\\\\dfrac{5+x^2-2x-8}{(x+2)(4-x)}=0\\\\\\\dfrac{x^2-2x-3}{(x+2)(4-x)}=0\\\\\\\text{Multiply both sides by (x+2)(4-x) to eliminate the denominator:}\\x^2-2x-3=0\\(x-3)(x+1)=0\\x-3=0\quad x+1=0\\x=3\quad x=-1[/tex]
Add the zeros to the number line with an OPEN dot (since it is <):
<----------o-----o----------o----o--------->
-2 -1 3 4
Step 3 Choose test points to the left, between, and to the right of the points plotted on the graph. Plug those values into (x - 3)(x + 1) to determine its sign (+ or -):
Left of -2: Test point x = -3: (-3 - 3)(-3 + 1) = Positive
Between -2 and -1: Test point x = -1.5: (-1.5 - 3)(-1.5 + 1) = Positive
Between -1 and 3: Test point x = 0: (0 - 3)(0 + 1) = Negative
Between 3 and 4: Test point x = 3.5: (3.5 - 3)(3.5 + 1) = Positive
Right of 4: Test point x = 5: (5 - 3)(5 + 1) = Positive
+ + - + +
<----------o-----o----------o----o--------->
-2 -1 3 4
Step 4 Determine the solution(s) based on the inequality symbol. Since the original inequality was LESS THAN, we want the solutions that are NEGATIVE.
Negative values only occur between -1 and 3
So the solution is: -1 < x < 3
