Answer:178
Step-by-step explanation: I took the test :)
Answer:
The mass of the container is 178 kg.
Step-by-step explanation:
Since, the volume of a cylinder is,
[tex]V=\pi (r)^2 h[/tex]
Where r is the radius of the cylinder
And, h is its height
Here, r = 0.2 meters,
h = 1 meter,
So, the volume of the cylindrical container is,
[tex]V=\pi (0.2)^2(1)[/tex]
[tex]=3.14\times 0.04=0.1256\text{ cubic meters}[/tex]
Now,
[tex]Density = \frac{Mass}{Volume}[/tex]
[tex]\implies Mass = Density\times Volume[/tex]
Given, Density of the container = 1417 kg/m³,
By substituting the values in the above formula,
[tex]\text{Mass of the container}=1417\times 0.1256=177.9752\text{ kg}\approx 178\text{ kg}[/tex]
What is the determinant of m= {5 8 -5 4} ? 20 40 60 80
Answer:
60
Step-by-step explanation:
We have been given the matrix;
[tex]\left[\begin{array}{ccc}5&8\\-5&4\end{array}\right][/tex]
For a 2-by-2 matrix, the determinant is calculated as;
( product of elements in the leading diagonal) - (product of elements in the other diagonal)
determinant = ( 5*4) - (8*-5)
= 20 - (-40) = 60
Answer:
c. 60
Step-by-step explanation
math
The fibrous protein core formed by elongated cells that contains melanin pigment is the______?
Answer:
Cortex layer
Step-by-step explanation:
The fibrous protein core of the hair, formed by elongated cells containing melanin pigment, is the cortex layer
Answer:
The fibrous protein core formed by elongated cells that contains melanin pigment is the cortex.
(I need help as soon as i can! :-) Can you find the third angle measure in a triangle, if you know the other 2 angel measure?
Answer: Yes you can using the sum of internal angles in a triangle they add up to 180, so if you add the two given angle measures and them substract the result from 180 you will have the measure of the third angle. Hope this helps. :)
Step-by-step explanation:
Thaddeus and lan start at the same location and drive in opposite directions, but leave at different times. When they are 365 miles apart, their combined travel is 16 hours. If Thaddeus drives at a rate of 20 miles per hour and lan drives at a rate of 25 miles per hour, how long had each been driving?
Thaddeus has been driving____? hours and lan has been driving_____? hours.
I NEED HELP RIGHT NOW PLEASE
Answer:
Thaddeus: 7 hIan: 9 hStep-by-step explanation:
If Thaddeus drives the whole 16 hours, the distance between them is ...
distance = speed · time
distance = 20 mi/h · 16 h
distance = 320 miles.
It is 45 miles more than that. For each hour that Ian drives, their separation distance increases by (25 mph -20 mph)·(1 h) = 5 mi. Then Ian must have driven ...
(45 mi)/(5 mi/h) = 9 h
The rest of the 16 hours is the time that Thaddeus drove: 7 hours.
___
Let x represent the time Ian drives. Then 16-x is the time Thaddeus drives. Their total distance driven is ...
distance = speed · time
365 mi = (25 mi/h)(x) + (20 mi/h)(16 h -x)
45 mi = (5 mi/h)(x) . . . . . . . . subtract 320 miles, collect terms
(45 mi)/(5 mi/h) = x = 9 h . . . . . . divide by the coefficient of x
_____
Comment on the solution
You may notice a similarity between the solution of this equation and the verbal discussion above. (That is intentional.) It works well to let a variable represent the amount of the highest contributor. Here, that is Ian's time, since he is driving at the fastest speed.
To solve the problem, we need to set up two equations based on the information given in the problem. Solving the equations simultaneously gives Thaddeus has been driving for 7 hours and Ian has been driving for 9 hours.
Explanation:First, we'll define the variables. Let's say the time Thaddeus has been driving is T hours, and the time Ian has been driving is I hours. The total distance they covered is the sum of the distances each one traveled, which is 365 miles. Thaddeus travels at a rate of 20 mph, while Ian travels at 25 mph. This is represented by the equation 20T + 25I = 365.
Next, we know that the total time they have been driving is 16 hours, which gives us another equation, T + I = 16. Now we have a system of linear equations that we can solve simultaneously to find the values of T and I. The solution gives T = 7 hours and I = 9 hours. Hence, Thaddeus has been driving for 7 hours and Ian has been driving for 9 hours.
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If $22,000 is deposited in an account paying 3.85% interest compounded continuously, use the continuously compounded interest formula , A=Pe^rt, to find the balance in the account after 11 years.
A. $1,519,356.93
B. $33,600.60
C. $33,416.25
D. $25,416.25
Answer:
B
Step-by-step explanation:
In the equation for interest compounding continuously, the A stands for the amount after the compounding is done, the P is the initial amount invested, the e is Euler's number, the r is the rate in decimal form, and the t is the time in years that the money is invested. Setting up our equation with the given values looks like this:
[tex]A=22,000e^{(.0385)(11)}[/tex]
Multiply the rate with the time to simplify a bit to
[tex]A=22,000e^{.4235}[/tex]
Raise e to the power of .4235 on your calculator (hit 2nd then the ln button to get your e) and get
[tex]A=22,000(1.527297754)[/tex]
Multiply out to get $33600.55, but rounding up gives you B as your answer.
The balance in the account after 11 years is $33,600.6. Thus, the correct option is B.
What is continuous compounding?Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.
The equation is given as,
[tex]\rm P=P_o \times e^{rt}[/tex]
The balance in the account after 11 years is calculated as,
[tex]\rm P = \$22,000 \times e^{0.0385\times 11}[/tex]
Simplify the equation, then we have
P = $22,000 x 1.52729
P = $33,600.6
Thus, the correct option is B.
More about the continuous compounding link is given below.
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Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i + y j + 9 k S is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 8
[tex]S[/tex] is a closed surface with interior [tex]R[/tex], so you can use the divergence theorem.
[tex]\vec F(x,y,z)=x\,\vec\imath+y\,\vec\jmath+9\,\vec k\implies\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(x)}{\partial x}+\dfrac{\partial(y)}{\partial y}+\dfrac{\partial(9)}{\partial z}=2[/tex]
By the divergence theorem, the flux of [tex]\vec F[/tex] across [tex]S[/tex] is given by the integral of [tex]\nabla\cdot\vec F[/tex] over [tex]R[/tex]:
[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV[/tex]
Convert to cylindrical coordinates, setting
[tex]x=u\cos v[/tex]
[tex]y=y[/tex]
[tex]z=u\sin v[/tex]
The integral is then
[tex]\displaystyle2\int_{v=0}^{v=2\pi}\int_{u=0}^{u=1}\int_{y=0}^{y=8-u\cos v}u\,\mathrm dy\,\mathrm du\,\mathrm dv=\boxed{16\pi}[/tex]
The flux of a vector field across a surface is calculated using a surface integral, which involves integrating the dot product of the vector field and the differential area element over the surface. For closed surfaces, the outward orientation is used. Electric flux, the flux of the electric field across a surface, is mentioned as an example.
Explanation:The flux of a vector field across a surface can be calculated using a surface integral. For the given vector field F(x, y, z) = x i + y j + 9 k and the surface S defined as the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 8, the flux is evaluated by integrating F·dS over the surface S.
The orientation of the surface is important in this process. For a closed surface, the positive (outward) orientation is used. The normal vector at any point on the surface points from the inside to the outside, and this outward normal is used to compute the flux through a closed surface.
Conceptually, this is like breaking the surface up into infinitesimally small patches dA and summing up the contributions of the vector field F (in this case, x i + y j + 9 k) through each patch - this is referred to as electric flux in the context of electric fields. This calculation embodies the concept of electric flux, which is defined as the scalar product of the electric field and the area vector.
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Given: JK tangent, KH=16, HE=12 Find: JK.
Check the picture below.
A rectangle has an area of 12 square centimeters and a perimeter of 16 centimeters. Which of the following could be its dimensions? 2 cm and 6 cm 3 cm and 4 cm 1.5 cm and 8 cm 1 cm and 12 cm
Answer:
2 cm and 6 cm
Step-by-step explanation:
The product of the dimensions must be 12 cm². (All answer choices meet that requirement.)
Opposite sides of a rectangle are the same length, so the sum of the two dimensions must be half the perimeter, 8 cm. The sums of the answer choices are ...
8 cm7 cm9.5 cm13 cmOnly the first answer choice meets the requirement for a perimeter of 16 cm. The dimensions could be 2 cm and 6 cm.
6
×
2
Explanation:
For the rectangle
Length
=
ℓ
Breadth
=
b
Area is
12
cm
2
ℓ
b
=
12
Perimeter is
16
cm
2
(
ℓ
+
b
)
=
16
ℓ
+
b
=
8
Substitute
b
=
12
ℓ
from first equation
ℓ
+
12
ℓ
=
8
ℓ
2
+
12
=
8
ℓ
ℓ
2
−
8
ℓ
+
12
=
0
Use quadratic formula (
x
=
−
b
±
√
b
2
−
4
a
c
2
a
) to find
ℓ
ℓ
=
−
(
−
8
)
±
√
(
−
8
)
2
−
(
4
×
1
×
12
)
2
×
1
ℓ
=
8
±
√
16
2
ℓ
=
8
±
4
2
ℓ
1
=
8
+
4
2
=
6
ℓ
2
=
8
−
4
2
=
2
If
ℓ
1
is taken as length then
ℓ
2
is the breadth of the rectangle.
2nd term in expansion of the binomial theorem (4x+2y^3)^3 show work
I hope this helps with you
The diameter of a sphere is 12
inches. What is the appropriate
surface are, in square inches, of the
sphere if Surface Area = 4tr2?
Answer:
first u should find the radius .radius is half of diameter 12/2=6 so surface area of sphere is 4*3.142*6*6=452.448 square in
PLEASE ANSWER THIS... WILL VOTE FOR U
The answer is g(x) = (1/4 x)^2
It has a horizontal stretch of 4. Since it is horizontal it goes inside the parentheses and becomes the reciprocal of 4 which is 1/4
Hope this helped!
~Just a girl in love with Shawn Mendes
Evaluate: 54-75+81-(-27)+53
Hi the answer is 344
Answer:
140
Step-by-step explanation:
54-75=-21
-21+81=60
60-(-27)=87 or 60+27=87
87+53=140
What measure of the cylinder do 26 and 34 describe?
diameter and height i think
Answer:
they describe diameter and height
26-diameter
34-height
Choose the correct graph for the equation y=2x+3
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Solve for the indicated variable. Express numbers as integers or simplify fractions.
-288/5 or - 57.6 I used a calculator so I cannot solve step by step
The area of a triangle is 17.5 square meters. The height of the triangle is 3 meters less than twice its base. The base of the triangle is x meters. Complete the equation that represents this description and fill in the values for the base and height of the triangle.
Answer:
17.5 = (1/2)(x)(2x-3)base: 5 m; height: 7 mStep-by-step explanation:
The base is defined as x. The height is said to be 3 less than 2x, so is (2x-3).
The formula for the area of a triangle is ...
A = (1/2)bh
Filling in the given values, we have ...
17.5 = (1/2)x(2x-3)
35 = 2x^2 -3x . . . . multiply by 2
2x^2 -3x -35 = 0 . . . . put in standard form
(2x +7)(x -5) = 0 . . . . . factor
The base is 5 meters; the height is 2·5-3 = 7 meters.
The base and height of the triangle satisfying the given conditions are approximately 4.3 and 5.6 meters, respectively.
Explanation:The area of a triangle is given by the formula 1/2 * base * height. Here, the area is 17.5 square meters, the base of the triangle is x, and the height of the triangle is 3 meters less than twice its base, therefore the height is 2x-3. Plugging these values into the formula, we get 17.5 = 1/2 * x * (2x - 3).
To solve this equation for x, first simplify the right-hand side, yielding 17.5 = x*(2x - 3). Multiplying this out gives 17.5 = 2x^2 - 3x. Then, rearrange to get the equation in standard quadratic form, resulting in 2x^2 - 3x - 17.5 = 0.
Through using quadratic formula we can find the solution(s) to be approximately x = 4.3 or x = -2.0. Since a negative value for x ? the base of a triangle ? is not possible, we discard that solution. Thus, the base of the triangle is 4.3 meters, and the height would then be 2*4.3 - 3 = about 5.6 meters.
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Find the slope of the line that passes through the points (2.1) and (-1.-1).
Answer: The slope is [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
The slope can be calculated with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Then, knowing that the line passes through the points (2,1) and (-1,-1), we can substitute the coordinates into the formula.
In this case:
[tex]y_2=-1\\y_1=1\\x_2=-1\\x_1=2[/tex]
Therefore, the slope of the line that passes through the points (2,1) and (-1,-1) is:
[tex]m=\frac{-1-1}{-1-2}\\\\m=\frac{-2}{-3}\\\\m=\frac{2}{3}[/tex]
Find the value of x in each case. Give reasons to justify your solutions!
Answer:
x = 11°
Step-by-step explanation:
The parallel lines suggest we look to the relationships involving angles and transversals. The angle marked 33° and ∠CAB are alternate interior angles, hence congruent:
∠CAB = 33°
5x is the measure of the external angle opposite that internal angle and angle 2x of ΔABC, so it is equal to their sum:
5x = 2x + 33°
3x = 33° . . . . . . . . . subtract 2x
x = 11° . . . . . . . . . . . divide by 3
The maximum grade allowed between two stations in a rapid-transit rail system is 3.5%. Between station A and station B, which are 260260 ft apart, the tracks rise 7 and one half7
1
2 ft. What is the grade of the tracks between these two stations? Round the answer to the nearest tenth of a percent. Does this grade meet the rapid-transit rail standards?
The grade of the tracks between station A and station B is nothing%.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Answer:
2.9%
Step-by-step explanation:
The problem says the stations are 260 feet apart. Assuming that this is the horizontal distance between them, then the grade is:
7.5 / 260 × 100% = 2.9%
This is less than the maximum of 3.5%, so it meets the standards.
Please help me ASAP!!!!
Answer: A, inside the circle.
Step-by-step explanation: Because the radius is wider than 4, (4,-1) would be just inside the circle instead of outside. Using the radius, you could determine that all points on the circle extend 5 units from its center, which means that the overall circumference would be past (4,-1).
Hope this helps,
LaciaMelodii :)
Help please............
Answer:
(9x -2)(9x +2)
Step-by-step explanation:
Each of the terms in the difference is a perfect square, so the "perfect square trick" applies. The factors are the sum and difference of the square roots of the given terms.
√(81x²) = 9x√4 = 281x² - 4 = (9x +2)(9x -2)
Benji, a 12 kg Border terrier, requires daily injections of ampicillin 15% for 3 days. The dose rate is 7.5
mg/kg. How many mL per injection does Benji require? i just need to know how to set the problem up, using dimensional analysis.
The answer is:
Benji requires 90mL per injection.
Why?From the statement we know that dog's weight is 12 kg, and daily injections are required for 3 days, the dose rate is 7.5 mg/kg, so we need to calculate how many mL per injection does Benji require.
We have that:
[tex]Weight=12Kg\\\\Dose=7.5\frac{mL}{Kg}[/tex]
If the dose rate is 7.5 mL per each Kg, how many mL are required for 12 Kg? We can set it up using the following relation:
[tex]7.5mL=1Kg\\x=12Kg\\\\x=\frac{7.5mL*12Kg}{1Kg}=\frac{90mL.Kg}{1Kg}=90mL[/tex]
Hence, we have that there are needed 90 mL per injection.
Have a nice day!
The function f(x) is the wait time for an amusement park ride where x is the number of people in line. What is the practical domain for the function f(x)?
all integers
all whole numbers
all real numbers
all positive integers
Answer:
The domain would be the set of all whole numbers.
Step-by-step explanation:
Integers are { ......-3, -2, -1, 0, 1, 2, 3....}
Whole numbers are {0, 1, 2, 3, ...... }
Real numbers are all numbers except imaginary number,
Positive integers are {1, 2, 3, 4, ....}
Given,
In the function f(x),
x represents the number of people in line,
We know that number of people can not be negative and it can be 0,
Thus, the possible value of x are 0, 1, 2, 3,......
Also, the domain of a function is the set of all possible value of input,
Since, x represent the input for the function f(x),
Thus, the domain of f(x) would be the set of all whole number.
Second option is correct.
Use trigonometric ratios to solve the right triangle.
The length of leg DF is WARRAND -
The length of leg DE is
Answer:
DF = 21DE = 7√3Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Sin = Opposite/Hypotenuse
Side DF is opposite the marked angle, and the hypotenuse is EF, so ...
sin(60°) = (√3)/2 = DF/(14√3) . . . . . to solve, multiply by the denominator
DF = (√3)/2·(14√3) = 7·3 = 21
__
Likewise,
Cos = Adjacent/Hypotenuse
Side DE is adjacent to the marked angle, so ...
cos(60°) = 1/2 = DE/(14√3) . . . . . to solve, multiply by the denominator
DE = (1/2)(14√3) = 7√3
Serena is an account executive. She receives a base pay of $18 an hour plus a 15 percent bonus for all the sales she generates. Last week she generated $1,200 worth of sales. What is the minimum number of hours she could have worked to make $500?
PLEASE SHOW WORK.
Answer:
17.8 hours
Step-by-step explanation:
Serena's bonus on $1200 sales is 15%×$1200 = $180. In order to make $500 for the week, then she must have at least ...
$500 - 180 = $320
in hourly pay.
At $18 per hour, that requires she work $320/($18/h) = 17.77_7 h.
Serena must work a minimum of about 17.8 hours to make $500.
_____
Comment on the answer
The exact result of the computation is 17 7/9 hours. Many payroll departments record hours to the nearest 1/4 or 1/10 hour. For Serena's pay to be at least $500, she must work 17.8 (rounded to tenths) or 18.0 (rounded to quarters) hours.
There are 40 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 6 min and a standard deviation of 6 min.If a grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, the (approximate probability that he is through grading before the 11:00 P.M. TV news begins is probability isIf the sports report begins at 11:10 P.M., the probability that he misses part of the report if he waits until grading is done before turning on the TV is
Final answer:
To determine the probability of the instructor finishing grading before 11:00 P.M., calculate the expected time to grade 40 exams, determine the standard deviation, and then use the z-score to find the corresponding probability from the standard normal distribution.
Explanation:
To tackle these statistics problems, there are several concepts we need to apply including expected value, standard deviation, the central limit theorem, hypothesis testing, and probability. Since only one problem can be answered at a time, I'll focus on the first one you've mentioned about the grading times for exams.
The instructor's time to grade each paper is a random variable with an expected value of 6 minutes and a standard deviation of 6 minutes. When considering the grading of 40 papers, we can use the central limit theorem which suggests that the sum of these independent random variables will be approximately normally distributed given the large number of papers (n=40).
We first calculate the expected total time to grade 40 exams by multiplying the individual exam time's expected value by the number of exams: 6 minutes/exam * 40 exams = 240 minutes. Then, we calculate the standard deviation for the total grading time: 6 minutes/exam * √40 ≈ 37.95 minutes.
To find the probability that the instructor finishes grading before 11:00 P.M., we need to calculate the number of minutes from 6:50 P.M. to 11:00 P.M., which is 250 minutes. Next, we convert this problem into a z-score problem where we find the z-score corresponding to 250 minutes. Finally, we look up this z-score in a standard normal distribution table (or use statistical software) to find the corresponding probability.
Three trucks delivered potatoes to a warehouse. The first truck delivered 5 7/8 tons of potatoes, the second one 6 1/2 tons more. If the three trucks delivered 25 tons of potatoes in total, then how many tons were delivered by the third truck?
Answer:
12 5/8 tons were delivered by the third truck
Step-by-step explanation:
25 = 6 4/8 + 5 7/8 + x
25 = 12 3/8 + x
- 12 3/8
12 5/8 = x
Answer:
6 3/4
Step-by-step explanation:
5 7/8 * 2 +6 1/2 + X = 25
Do the algebra.
x = 6 3/4
i'm gonna need help with this one
Answer:
KM = 20
Step-by-step explanation:
Point V is the midpoint of KM, so ...
KV = VM
2.5z = 5z -10
10 + 2.5z = 5z . . . . . add 10
10 = 2.5z . . . . . . . . . subtract 2.5z
This is sufficient to answer the question:
KV = VM = 2.5z = 10
KM = KV + VM = 10 + 10
KM = 20
_____
In this case, it is not necessary to find the value of z. If you wanted to, you could divide by the coefficient of z in the last equation:
10/2.5 = z = 4
Lisa has developed a new product, and knows that the graph of function R models her revenue from selling the item, after deducting expenses, when she charges x dollars per unit.
Lisa wants to restrict function R to only model selling prices for which she will make a profit. Which interval should she use as the domain of the function?
Answer:
Choice B is correct; (10, 60)
Step-by-step explanation:
For Lisa to make a profit, the function R should assume a value greater than 0;
R > 0
We are to determine the interval of x values for which the above expression will be true.
From the graph, R(x) = 0 when x = 10. As x increases from 10 to 60, the value of R(x) remains positive, that is;
R(x) ≥ 0 for values of x in the interval (10, 60)
The domain that she should use in order to only model selling prices for which she will make a profit is thus;
(10, 60)
In triangle ABC, the side lengths are AB = 13, AC = 21, and BC = x. Write a compound inequality that represents the range of possible values for x.
Big fraction
Parentheses
Vertical bars
Square root
Root
Superscript (Ctrl+Up)
Subscript (Ctrl+Down)
Plus sign
Minus sign
Middle dot
Multiplication sign
Equals sign
Less-than sign
Greater-than sign
Less-than or equal to
Greater-than or equal to
Pi
Alpha
Beta
Epsilon
Theta
Lambda
Mu
Rho
Phi
Sine
Cosine
Tangent
Arcsine
Arccosine
Arctangent
Cosecant
Secant
Cotangent
Logarithm
Logarithm to base n
Natural logarithm
Bar accent
Right left arrow with under script
Right arrow with under script
Angle
Triangle
Parallel to
Perpendicular
Approximately equal to
Tilde operator
Degree sign
Intersection
Union
Summation with under and over scripts
Matrix with square brackets
The compound inequality representing the range of possible values for 'x' (side length BC) in the triangle ABC, given that side lengths AB=13 and AC=21, is 8 < x < 34.
Explanation:In the triangle ABC with side lengths, AB=13, AC=21, and BC=x, we use the triangle inequality theorem which states that the length of a side of a triangle is less than the sum of the lengths of the other two sides and more than the absolute difference between them. Applying this theorem to your specific situation, we get the compound inequality 8 < x < 34. This inequality represents the range of possible values for the side length x is BC.
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For triangle ABC with sides AB = 13, AC = 21, and BC = x, the range of possible values for x is[tex]\( 8 < x < 34 \)[/tex] based on the triangle inequality theorem.
In triangle ABC, the relationship among its side lengths is governed by the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
For the given triangle with side lengths AB = 13, AC = 21, and BC = x, we can express this relationship as a compound inequality. Let \[tex]( a \), \( b \), and \( c \)[/tex] represent the lengths of the sides of the triangle. According to the triangle inequality theorem, we have:
[tex]\[ a + b > c \][/tex]
Substitute the given values:
[tex]\[ 13 + x > 21 \][/tex]
Now, solve for[tex]\( x \)[/tex]
[tex]\[ x > 8 \][/tex]
Similarly, for the other pair of sides:
[tex]\[ 21 + x > 13 \][/tex]
Solving for \( x \):
[tex]\[ x > -8 \][/tex]
However, since side lengths cannot be negative, we disregard the second inequality. Therefore, the compound inequality representing the range of possible values for [tex]\( x \) is \( 8 < x < 34 \).[/tex] This means that any value of [tex]\( x \)[/tex] between 8 and 34 (exclusive) will satisfy the conditions for the given triangle.