Answer:
The three integers are 13,14,15
Step-by-step explanation:
Let x be the first integer
x+1 be the second integer
x+2 be the third integer
The sum of the three integers is 42
x+ (x+1) + (x+2) = 42
Combine like terms
3x+3 = 42
Subtract 3 from each side
3x+3-3 = 42-3
3x= 39
Divide by 3
3x/3 = 39/3
x = 13
x+1 = 14
x+2 = 15
The three integers are 13,14,15
A park has a large circle painted in the middle of the playground area. The circle is divided into 444 equal sections, and each section is painted a different color. The radius of the circle is 10 \text{ meters}10 meters10, space, m, e, t, e, r, s. What is the area AAA of each section of the circle? Give your answer in terms of pi. A=A=A, equals \text{m}^2m 2 m, start superscript, 2, end superscript
Answer:
The area of each section of the circle is [tex]A=25\pi\ m^{2}[/tex]
Step-by-step explanation:
we know that
Each section represent a quarter of circle
The area of a quarter of circle is equal to
[tex]A=\frac{1}{4}\pi r^{2}[/tex]
we have
[tex]r=10\ m[/tex]
substitute
[tex]A=\frac{1}{4}\pi (10)^{2}[/tex]
[tex]A=25\pi\ m^{2}[/tex]
A company will make a cereal box with whole number dimensions and a volume of 100 cubic centimeters. if cardboard costs $0.05 per 100 square centimeters, what is the least cost to make 100 boxs
Answer:
The best dimension to use to have the least cost to make 100 boxes is 5 x 5 x 4. It only costs $6.50 to make 100 boxes.
Step-by-step explanation:
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
ANSWER
Step 3
EXPLANATION
The given polynomial expression is:
[tex]2 {p}^{2} - 3p - 7 - (3 {p}^{2} + p - 5)[/tex]
Fatau correctly expanded the parenthesis in the first step.
[tex]2 {p}^{2} - 3p - 7 - 3 {p}^{2} - p + 5[/tex]
Fatau also correctly grouped the like terms to obtain:
[tex](2- 3) {p}^{2} + (- 3 - 1)p + (- 7 + 5)[/tex]
Fatau committed a mistake at the third step.
Instead of obtaining,
[tex] - {p}^{2} - 4p - 2[/tex]
He mistakenly got:
[tex]{p}^{2} - 2p +2[/tex]
(WORTH 30 POINTS PLS HELP LAST DAY OF ONLINE SCHOOL) !!!! The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.
Answer:what is the table
Step-by-step explanation:
Amber has 5/2 pouns of salt dough for a project. She writes this equation to show 5/2.
5/2= 5 × 1/2
Draw a model to show the equation is true.
Well... for starters:
[tex]
\frac{5}{2}=5\times\frac{1}{2} \\
\frac{5}{2}=\frac{5}{1}\times\frac{1}{2}
[/tex]
And the rule is [tex]\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}[/tex]
Therefore:
[tex]\frac{5}{2}=\frac{5\times1}{1\times2}\Longrightarrow\boxed{\frac{5}{2}=\frac{5}{2}}[/tex]
Derrick needs to figure out how he’s doing on his test scores so far this year. You can help by calculating the mean and the median to get an overall picture of his scores. Below are all of his scores: 25, 40, 68, 85, 95, 98, 70, 78, 85, 100 What is Derrick’s mean test score so far? What is Derrick’s median test score so far? Which gives a better picture of his scores?
Answer: Derrick’s mean test score= 74.4
Derrick’s median test score = 81.5
Better picture of his scores is given by Median.
Step-by-step explanation:
The given data : 25, 40, 68, 85, 95, 98, 70, 78, 85, 100
[tex]\text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Number of observations}}\\\\\Rightarrow\ \text{Mean}=\dfrac{744}{10}=74.4[/tex]
For Median , Arrange the data in order
25, 40, 68, 70, 78, 85, 85, 95, 98, 100
Median = Mean of two middle most value
[tex]\text{Median}=\dfrac{78+85}{2}=81.5[/tex]
Since the data set has outlier (25) and mean is affected by outlier.
So the better picture of his scores given by median value.
Answer:
(A) 74.4 (B) 81.5 (C) Median (Look below or dont)
Step-by-step explanation:
3. A jewelry store buys small boxes in which to wrap the items that it sells. The diagram below shows one of the boxes. The diagram is not drawn to scale.
What are the lateral area and the surface area of the box to the nearest whole number? Use the large 15cm x 6cm rectangles on the top and bottom as the bases.
A) 47 cm² ; 275 cm²
B) 95 cm² ; 365 cm²
C) 47 cm² ; 365 cm²
D) 95 cm² ; 275 cm²
Answer:
1) The lateral area is LA=95 cm²
2) The surface area is SA=275 cm²
The answer is the option D) 95 cm² ; 275 cm²
Step-by-step explanation:
we know that
The surface area of the box (rectangular prism) is equal to
SA=2B+LA
where
B is the area of the base
LA is the lateral area of the box
Find the lateral area
LA=PH
where
P is the perimeter of the base
H is the height of the box
substitute
LA=2[15+6](2.26)=94.92 cm²
Round to the nearest whole number
LA=95 cm²
Find the area of the base B
B=(15)(6)=90 cm²
Find the surface area of the box
SA=2B+LA
substitute the values
SA=2(90)+95=275 cm²
At a manufacturing plant where switches are made, it is a known fact that 2% of all switches are defective. If two switches are used in a device, what is the probability that exactly one switch is good?
Answer:
The probability that exactly one switch is good is
[tex]P(x) =0.0392[/tex]
Step-by-step explanation:
The probability that a switch is defective is:
[tex]P(D) = \frac{2}{100} =0.02[/tex]
The probability that a switch is not defective is
[tex]P(D') = 1-P(D)=0.98[/tex]
Therefore, if two switches are selected, the probability that exactly 1 is good is:
[tex]P(1=1)=P (D) P (D ') + P (D') P (D)[/tex]
[tex]P(x)=(0.02)(0.98) + (0.98)(0.02)[/tex]
[tex]P(x) =0.0392[/tex]
Answer:
P (exactly one good switch) = 0.0392
Step-by-step explanation:
We know that 2% of all switches are defective.
P (defective) = [tex]\frac{2}{100} =0.02[/tex]
So P (not defective) = 1 - P (defective) = [tex]1-0.02=0.98[/tex]
Now we have to find the probability of one good switch out of 2 that are used in a device.
P (exactly one good switch) = [tex] (0.02 \times 0.95) + (0.02 \times 0.95) [/tex] = 0.0392
SOMEONE PLEASE JUST ANSWER THIS FOR BRAINLIEST!!!
Answer:
2 a^4 -2a^2b^2 -6b^4
Step-by-step explanation:
C = 7a^4 + 5a^2b^2 -3b^4
D = 5a^4 +7a^2b^2 +3b^4
C-D = 7a^4 + 5a^2b^2 -3b^4 - ( 5a^4 +7a^2b^2 +3b^4)
Distribute the minus sign
7a^4 + 5a^2b^2 -3b^4 - 5a^4 -7a^2b^2 -3b^4
I like to line them up vertically
7a^4 + 5a^2b^2 -3b^4
- 5a^4 -7a^2b^2 -3b^4
--------------------------------------
2 a^4 -2a^2b^2 -6b^4
This parabola opens to the left.
x=1/4y^2
A. True
B. False
Answer:
B. False
Step-by-step explanation:
Given an equation of the type x = a(y-x)^2 + h, We know that If the "y" is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left.
Like the y is squared and the "a" is positive then it opens to the right, so it's false
What transformations are needed to change the parent cosine function to y=3cos(10(x-pi))?
Answer:
The graph of [tex]y=cos(x)[/tex] is:
*Stretched vertically by a factor of 3
*Compressed horizontally by a factor [tex]\frac{1}{10}[/tex] .
*Moves horizontally [tex]\pi[/tex] units to the rigth
The transformation is:
[tex]y=3f(10(x-\pi))[/tex]
Step-by-step explanation:
If the function [tex]y=cf(h(x+b))[/tex] represents the transformations made to the graph of [tex]y= f(x)[/tex] then, by definition:
If [tex]0 <c <1[/tex] then the graph is compressed vertically by a factor c.
If [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor c
If [tex]c <0[/tex] then the graph is reflected on the x axis.
If [tex]b> 0[/tex] The graph moves horizontally b units to the left
If [tex]b <0[/tex] The graph moves horizontally b units to the rigth
If [tex]0 <h <1[/tex] the graph is stretched horizontally by a factor [tex]\frac{1}{h}[/tex]
If [tex]h> 1[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{h}[/tex]
In this problem we have the function [tex]y=3cos(10(x-pi))[/tex] and our parent function is [tex]y = cos(x)[/tex]
The transformation is:
[tex]y=3f(10(x-\pi))[/tex]
Then [tex]c =3>1[/tex] and [tex]b =-\pi < 0[/tex] and [tex]h=10 > 1[/tex]
Therefore the graph of [tex]y=cos(x)[/tex] is:
Stretched vertically by a factor of 3.
Also as [tex]h=10[/tex] the graph is compressed horizontally by a factor [tex]\frac{1}{10}[/tex] .
Also, as [tex]b =-\pi < 0[/tex] The graph moves horizontally [tex]\pi[/tex] units to the rigth
How can you find the area of a triangle using the Law of Sines?
Explanation:
One formula for the area of a triangle is ...
Area = (1/2)ab·sin(C)
This presumes you know the measures of two sides and the angle between them. The Law of Sines is typically used where you know all the angles and only one side measure.
You would use the law of sines to find an additional side measure, then make use of the above formula for area.
To find the area of a triangle using the Law of Sines, you need to determine the lengths of two sides and the measure of the angle opposite one of those sides. Plug those values into the Law of Sines formula and solve for the missing side or angle.
Explanation:The area of a triangle can be found using the Law of Sines by following these steps:
First, determine the lengths of two sides of the triangle and the measure of the angle opposite one of those sides.Use the Law of Sines formula, which states that the ratio of the length of a side to the sine of its corresponding angle is constant for any triangle: a/sin(A) = b/sin(B) = c/sin(C).Plug the values you have into the formula and solve for the missing side or angle.Once you have all three sides or two sides and an angle, you can use Heron's formula or the formula for the area of a triangle (A = 1/2 * base * height) to find the area of the triangle.
For questions 4-5, find the volume of the cylinder in terms of pi.
4. height 8, radius 3.8
5. height 14, radius 5
Answer:
hope it helps you!!!!!!!!
The volume of a cylinder with a height of 8 and a radius of 3.8 is 115.52π cubic units, and with a height of 14 and a radius of 5, it is 350π cubic units.
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height of the cylinder.
For question 4 with a height of 8 and a radius of 3.8, the volume would be: V = π(3.8)²(8) = 115.52π cubic units.
For question 5 with a height of 14 and a radius of 5, the volume would be: V = π(5)²(14) = 350π cubic units.
These calculations illustrate how to determine the volume of cylinders using their respective dimensions, providing a fundamental understanding of geometric principles and applications.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The bar graph shows the z-score results of four contestants in a bowling contest.
The contestants bowled Round 1 and bowled Round 2 two months later.
Which contestant had the worst score for Round 1?
Answer: d) Easton
Step-by-step explanation:
Let's evaluate Round 1 (blue) for each bowler:
Jimmy --> the lowest score is 0.5 SD below the mean
Claudia --> the lowest score was the mean
Easton --> the lowest score is 0.75 SD below the mean
Cynthia --> the lowest score was the mean
The person that had the worst game is: Easton
Answer:
easton
Step-by-step explanation:
I did the test
Is this graph continuous at x=1?
Answer:
Step-by-step explanation:
By my definition, no. There's a continuity up to and including just before 1 approaching from the left, and there's a continuity just after 1 going to the right. But 1 itself has a special definition h(x) = 4 when x = 1 and that makes it discontinuous.
In the synthetic division problem shown below, what number belongs in the place of the question mark?
Answer:
7
Step-by-step explanation:
The full solution is:
1 |...1.....3.....-5.....7
.............-1....-2......7
__________________
.......1.....2.....-7.....14
So the answer is 7
The question doesn't provide enough information to answer it properly, as it doesn't specify the polynomial or the divisor necessary for synthetic division. Synthetic division involves dividing a polynomial by a linear divisor, but without the set polynomial and divisor, the number that would belong in the place of the question mark can't be determined.
Explanation:Unfortunately, the information provided doesn't clearly indicate the format or context of a synthetic division problem. Synthetic division typically involves dividing a polynomial by a linear divisor. The elements of the polynomials are numbers, specifically the coefficients of the polynomial terms. The repetition in your question about various Car X, Car Y and dots at various hash marks appears to be irrelevant data as it does not correlate with the synthetic division problem.
However, to apply synthetic division, we would need a specific polynomial to carry out the process. In synthetic division, a box is drawn, the coefficients of the polynomial are written in that box, and then the divisor is placed outside the box. From there, the numbers inside the box are manipulated, in a step-by-step manner, based on the divisor. The numbers derived from this process are the coefficients of the answer. Without this specific data, we cannot accurately determine what number belongs in the place of the question mark.
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A triangle with a base of 1/4 meter has an area of 8 square meters. What is the height, in meters, of the triangle? A. 1 B. 12 C. 32 D. 64
Answer:
D.64
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Givens
A = 8 square meters.
B = 1/4 meter
h = ?
Formula
A = 1/2 B * h
Solution
8 = 1/2 1/4 * h Combine
8 = 1/8 * h Multiply by 8
8*8 = 1/8 * 8 * h
h =64 m
D answer
==============
I had to edit this to get it. Give the brainliest to the other responder.
Math practice please help
Answer:
[tex]y=-\frac{1}{2}+7\frac{1}{2}[/tex]
Step-by-step explanation:
Let
x ----> the time in hours
y ----> the height of the candle in inches
we have the points
(1,7) and (4,5.5)
step 1
Find the slope m
[tex]m=(5.5-7)/(4-1)\\ m=-1.5/3=-0.5[/tex]
step 2
Find the equation of the line into slope point form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-0.5\\ (x1,y1)=(1,7)[/tex]
substitute
[tex]y-7=-0.5(x-1)\\ y-7=-0.5x+0.5+7[/tex]
[tex]y=-0.5+7.5[/tex]
[tex]y=-\frac{1}{2}+7\frac{1}{2}[/tex]
what is the volume of the cone below?
Answer:
V = 3408 pi unit^3
Step-by-step explanation:
Volume of a cone is given by
V = 1/3 pi r^2 h
We know the radius is 12 and the height is 71
V = 1/3 * pi * (12)^2 *71
V = 1/3 * pi * 144 *71
V = 3408 pi unit^3
Answer:
[tex]Volume=3408 \pi[/tex] [tex]units^3[/tex]
Step-by-step explanation:
Given that radius of the cone is r = 12 units
Given that height of the cone is h = 71 units
Now question says to find the volume of the given cone.
So plug these values into formula of volume of the cone.
[tex]Volume=\frac{1}{3}\pi r^2h[/tex]
[tex]Volume=\frac{1}{3}\pi (12)^2(71)[/tex]
[tex]Volume=\frac{1}{3}\pi (144)(71)[/tex]
[tex]Volume=\frac{1}{3}\pi (10224)[/tex]
[tex]Volume=\frac{10224 \pi}{3}[/tex]
[tex]Volume=3408 \pi[/tex] [tex]units^3[/tex]
Hence correct choice is D.
What is the exact area of a circle with radius 5?
10
25
25π
10π
How do you solve the inequality -2x > -10
Divide both sides by -2.
Add 10 to both sides
Add 2 to both sides.
Divide both sides by -2 and reverse the inequality.
the radius of this question 25pi
Answer:
Step-by-step explanation:
(1) The formula for the area of a circle of radius r is A = πr².
If the radius is 5 units, then the exact area of the circle is A = π(5 units)², or A = 25π units².
The third possible answer is the correct one.
(2) To solve -2x > -10, we must isolate x.
Divide both sides by -2, remembering that if we divide an inequality by a negative number, we must reverse the direction of the inequality sign:
-2x > -10
----- ------- → x < 5
-2 -2
The first possible answer is the correct one: Divide both sides by -2.
Mark wants to visit the 10 colleges he is considering attending. He can only spend the night at 3 of them. What is the probability that he spends a night at Rutgers University, a night at the University of Miami, and a night at Clemson University?
Final answer:
The probability that Mark spends a night at Rutgers University, the University of Miami, and Clemson University is 1/720, or approximately 0.00139.
Explanation:
To find the probability that Mark spends a night at Rutgers University, a night at the University of Miami, and a night at Clemson University, we assume that these choices are made without replacement from the 10 colleges he is considering. As he can only spend the night at 3 of them, his first choice has a 1 in 10 chance of being Rutgers University, his second choice a 1 in 9 chance of being the University of Miami, given that his first choice was Rutgers, and his third choice a 1 in 8 chance of being Clemson University, given that his first two choices were Rutgers and the University of Miami.
The overall probability is the product of these independent probabilities:
Probability = (1/10) × (1/9) × (1/8) = 1/720
Therefore, the probability is 1/720, or about 0.00139 when rounded to five decimal places.
Please help with math?
Use the given graph to determine the limit, if it exists.
roughly 1.5
since it says the limit as x approaches 2- it means that you are going from the left (from the negative ie 2-). If it said 2+ you would go from the right. So you should start on the left at the end of that line and follow it until it gets essentially at where 2 is. Then record that value which in this case about 1.5
The limit of the function as x approaches 2 is 3.
Explanation:In mathematics, a limit is a value that a function 'approaches' as the input (or variable) 'approaches' some value. To find the limit using the given graph, we need to examine the behavior of the function as it approaches a particular value. In this case, we look for the value the function approaches as x approaches a specific number.
From the graph, we can see that as x approaches 2 from the left side, the y-values approach 3. Similarly, as x approaches 2 from the right side, the y-values also approach 3.
Therefore, the limit of the function as x approaches 2 is 3.
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What is the probability of rolling a 6 on a die?
1/5
1/6
5/6
1/4
What is the probability of not rolling a 6 on a die?
Answer:
Step-by-step explanation:
There's only 1 '6' on an ordinary die with 6 sides, so the probability of rolling a 6 is 1/6.
That of NOT rolling a 6 is the complementary probability: 1 - 1/6 = 5/6.
Please simplify, 50 points.
(sin Θ - cos Θ) - (sin Θ + cos Θ)^2
Answer choices are attached.
Answer:
The trigonometric equation (sin Θ − cos Θ)^2 − (sin Θ + cos Θ)^3 can be simplified by:Using x for Θ: (sinx - cosx)^2 - (sinx + cosx)^2 = (sin^2 x - 2sinxcosx + cos^2 x) - (sin^2 x + 2sinxcosx + cos^2 x) = - 2 sinx cosx - 2 sinx cosx = - 4 sinx cosx = - 2sin(2x)
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Expand (sinΘ + cosΘ)²
= sinΘ - cosΘ - (sin²Θ + 2 sinΘcosΘ + cos²Θ)
= sinΘ - cosΘ - sin²Θ - 2sinΘcosΘ - cos²Θ
= sinΘ - cosΘ - 2sinΘcosΘ - (sin²Θ + cos²Θ)
= - 2sinΘcosΘ - cosΘ + sinΘ - 1 → D
A circular pizza that is 18 inches in diameter is cut into 8 equal slices. What is the area of a single slice?
Answer:
31.8 in^2
Step-by-step explanation:
The area of a circle is pi×radius^2.
r=.5d=18/2=9
A=(3.14159)(9^2)=(3.14159)(81)=254.5
And if each peice is of equal area, the area of one peice will equal:
254.5/8=31.8
The area of single slice is 31.7925 inch².
What is area of circle?The area of a circle is pi times the radius squared (A = π r²). Learn how to use this formula to find the area of a circle when given the diameter.
Given:
diameter= 18 inches
radius= 9 inches
Area of pizza
=πr²
=3.14*9*9
=254.34 inch²
Now, area of 8 equal slices=254.34 inch²
area of 1 equal slices=254.34 /8
= 31.7925 inch²
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The area of the circular base of a cylinder is 36 square units. The height is 2
Answer:
24 π
Step-by-step explanation:
First step is to determine the radius of the base. We have the area, so we can easily determine the radius. The base is a circle, and the area of a circle is given by A = π * r² , so r² = A / π
r² = (36 π) / π = 36
So, r = 6
The lateral surface of a cylinder is given by the following:
L = 2* π * r * 2
Now that we have r, we can easily calculate it:
L = 2 * π * 6 * 2 = 24π, second choice listed
Use the following half-life graph to answer the following question:
A graph titled half-life graph of a radioactive isotope is shown with mass remaining on the y axis from 0 to 60 grams and time on the x axis from o to 6 minutes. A curve connects the points 0, 50 and 1, 25 and 2, 12.5 and 3, 6.25 and 4, 3.125 and 5, 1.5625.
The graph is attached.
What is the mass of the radioactive isotope remaining at 2.0 minutes? (5 points)
A. 25.0 mg
B. 12.5 mg
C. 6.25 mg
D. 3.13 mg
Answer:
The correct answer is 12.5.
Step-by-step explanation:
When looking at the x axis, you locate the 2. After 2 minutes, the point connects at (2,12.5). Therefore, the correct answer is 12.5.
Answer:
At t = 2 minutes, remaining quantity of the radioactive element is 12.5 mg.
Step-by-step explanation:
To get the answer of this question we will solve this further with the help of the equation [tex]A_{t}=A_{0}e^{-kt}[/tex]
where k = decay constant
t = time for decay
[tex]A_{0}[/tex] = Initial quantity taken
From the graph attached we can say that 50 mg of a radioactive element remained half in 1 minute.
So the equation becomes
[tex]50=25e^{-k(1)}[/tex]
Now we take natural log on both the sides of the equation
ln50 = ln[25.[tex]e^{-k}[/tex]
3.912 = ln25 + [tex]ln(e^{-k})[/tex]
3.912 = 3.219 + (-k)lne
3.912 - 3.219 = -k [since lne = 1]
0.693 = -k
k = -0.693
Now we will calculate the remaining quantity of the element after 2 minutes
[tex]A_{t}=50.e^{-(0.693)(2)}[/tex]
= [tex]50.e^{-1.386}[/tex]
= [tex]\frac{50}{e^{1.386}}[/tex]
= [tex]\frac{50}{3.9988}[/tex]
= 12.50 mg
Now we confirm this value from the graph.
At t = 2 minutes, remaining quantity of the radioactive element is 12.5 mg.
the length of a rectangle is five times its width.
if the area of the rectangle is 320 yd^2, find its perimeter.
? yd
ANSWER
96 yd
EXPLANATION
Let the width of the rectangle be w, then, the length of the rectangle will be:
[tex]l = 5w[/tex]
The area of a rectangle is calculated using the formula:
[tex]Area=l \times w[/tex]
[tex]Area=5w \times w[/tex]
[tex]Area=5 {w}^{2} [/tex]
It was given that, the area of the rectangle is 320yd²
[tex]320=5 {w}^{2} [/tex]
Divide both sides by 5.
[tex]64 = {w}^{2} [/tex]
Take square root of both sides to get:
[tex]w = 8yd[/tex]
This means the length is
[tex]l = 5 \times 8 = 40yd[/tex]
The perimeter of a rectangle is given by:
P=2(w+l)
We plug in the values to get:
[tex]P=2(40 + 8) = 2 \times 48 = 96yd[/tex]
The perimeter is 96yd
Verify the equation.
1/tan^2(x)=cot^2(x)
csc^2(x)-1=cot^2(x)"trigonometric identity"
What is an attribute of a fractional equation?
there are multiple variables.
there are variables in the denominator of all involved fractions
there is a variable in the denominator of at least one involved fraction.
there are variables in the numerator of at least one involved fraction?
its either a half or part of what its worth
Answer:
There is a variable in the denominator of at least one involved fraction.Step-by-step explanation:
The actual definition of a fractional equation could be:
[tex]\frac{a}{x}+\frac{b}{x+1}=c[/tex]
In words, fractional equations are those which has variables in the denominator of a fractional term, that doesn't mean that all fractions must have a unknown denominator, but at least one of the denominators should have a variable.
Therefore, according to its definition, the right answer is third option.
In addition, other options don't make sense, multiple variables is not necessarily the case for fractional equations. Similarly, not all denominators must have variables. And, having variable only in the numerators don't define the equation as fractional.