Could someone help me with this? I need to solve for X. Here is the problem.
Answers
The two angles given are vertical angles, which mean they are equal to each other.
2x + 2 = 3x -52
Add 52 to both sides:
2x + 54 = 3x
Subtract 2x from both sides:
54 = x
Rewrite as x = 54
Answer: x = 54
Related Questions
find the measure of angle b
NO LINKS
Answers
Answer:
[tex]39^{\circ} + b= 180^{\circ} (linear \: pair)\\b= 180 - 39\\\boxed{b = 141^{\circ}}[/tex]
If Jim weights 100 pounds, what mass in kilograms does the person on the other side need to be for the sessão to be balanced?
Answers
Answer:
45.359237
Step-by-step explanation:
I believe this is the answer because if u convert u get 45.35
centeral school is hosting a "central has talent" show they will award various prices for the best 3 acts in the show first place wins the most money, and each susequent place after 1st wins $50 less then the previous place. let x equal the amount of money first place wins what expressions represent the total amount of prize money.
Answers
Answer:
The expression represent the total amount of price money is 3x-150.
The expressions let X be the amount of money for first place. This means X-50 would be the amount of second place because each subsequent place after 1st wins $50 less than the previous place. Thirds, would be X-50-50 or X-100.
That is X = first place and each place after that is 50 less so 2nd place would be x - 50 and third place would be x - 100.
Thus the total amount of money would be all of the values combined which is
x + (x - 50) + (x - 100)
Combinimg the like terms
What is the combinimg the like terms?
To combine like terms, we have to add the coefficients and keep the variables the same. We add like terms to make one term.
x+x-50+x-100
3x-150
3x - 150
Therefore the option b is correct.
So the expression represent the total amount of price money is 3x-150.
Step-by-step explanation:
In how many ways can 8 people be seated in a row of chairs if three of the people, John, Wilma, and Paul, refuse to sit in three consecutive seats?
Answers
Answer:
I think it's easiest to count the ways that they can consecutively sit together and subtract this from the total number of seating arrangements.
There are 6 groups of 3 consecutive seats. Within each group there are 3!=6 ways the three people can be arranged
Then the remaining 5 people can be arranged 5!=120 ways in the remaining seats.
So there are 6*6*120 = 4320 arrangements where they DO sit consecutively
There are 8! = 40320 total arrangements.
So there are 40320 - 4320 = 36000 arrangements where the 3 do not sit consecutively.
Step-by-step explanation:
Hello people ~
The given figure shows a cone of height "h cm" and base-radius "r cm" that is made from a wooden spherical solid of radius 10 cm. The volume of the cone is cm³.
(a) Show that r² =20h-h²
(b) Express V in terms of h
(c) Hence, find the value of h such that the volume of the cone is a maximum.
Answers
Cone details:
height: h cmradius: r cmSphere details:
radius: 10 cm================
From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.
Using Pythagoras Theorem
(a)
TO² + TU² = OU²
(h-10)² + r² = 10² [insert values]
r² = 10² - (h-10)² [change sides]
r² = 100 - (h² -20h + 100) [expand]
r² = 100 - h² + 20h -100 [simplify]
r² = 20h - h² [shown]
r = √20h - h² ["r" in terms of "h"]
(b)
volume of cone = 1/3 * π * r² * h
===========================
[tex]\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)[/tex]
[tex]\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)[/tex]
[tex]\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)[/tex]
[tex]\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)[/tex]
To find maximum/minimum, we have to find first derivative.
(c)
First derivative
[tex]\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )[/tex]
apply chain rule
[tex]\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}[/tex]
Equate the first derivative to zero, that is V'(x) = 0
[tex]\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0[/tex]
[tex]\Longrightarrow \sf 40h-3h^2=0[/tex]
[tex]\Longrightarrow \sf h(40-3h)=0[/tex]
[tex]\Longrightarrow \sf h=0, \ 40-3h=0[/tex]
[tex]\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}[/tex]
maximum volume: when h = 40/3
[tex]\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )[/tex]
[tex]\sf \Longrightarrow maximum= 1241.123 \ cm^3[/tex]
minimum volume: when h = 0
[tex]\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)[/tex]
[tex]\sf \Longrightarrow minimum=0 \ cm^3[/tex]
Answer:
(a) see step-by-step
[tex]\textsf{(b)}\quad V=\dfrac{20}{3} \pi h^2-\dfrac13 \pi h^3[/tex]
[tex]\textsf{(c)}\quad h=\dfrac{40}{3}[/tex]
Step-by-step explanation:
Part (a)A right triangle can be drawn with vertices at the center O, the base angle of the cone and the center of the base of the cone (see annotated image).
Side lengths of the formed right triangle:
Hypotenuse = radius of sphere = 10 cmHeight = height of cone - radius of sphere = (h - 10) cmBase = base radius of cone = r cmUsing Pythagoras' Theorem [tex]a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
[tex]\implies r^2+(h-10)^2=10^2[/tex]
[tex]\implies r^2+h^2-20h+100=100[/tex]
[tex]\implies r^2+h^2-20h=0[/tex]
[tex]\implies r^2=20h-h^2[/tex]
Part (b)[tex]\textsf{Volume of a cone}=\dfrac13 \pi r^2h[/tex]
(where r is the radius and h is the height)
Substitute the expression for [tex]r^2[/tex] found in part (a) into the equation so that volume (V) is expressed in terms of h:
[tex]\begin{aligned}V & =\dfrac13 \pi r^2h\\\\ \implies V & =\dfrac13 \pi (20h-h^2)h\\\\ & = \dfrac13 \pi (20h^2-h^3)\\\\ & = \dfrac{20}{3} \pi h^2-\dfrac13 \pi h^3 \end{aligned}[/tex]
Part (c)To find the value of h such that the volume of the cone is a maximum, differentiate V with respect to h:
[tex]\begin{aligned}V & =\dfrac{20}{3} \pi h^2-\dfrac13 \pi h^3\\\\ \implies \dfrac{dV}{dh} & =2 \cdot \dfrac{20}{3} \pi h-3 \cdot \dfrac13 \pi h^2\\\\ & = \dfrac{40}{3} \pi h- \pi h^2\\\\ & = \pi h\left(\dfrac{40}{3}-h\right)\end{aligned}[/tex]
Set it to zero:
[tex]\begin{aligned}\dfrac{dV}{dh} & =0\\\\ \implies \pi h\left(\dfrac{40}{3}-h\right) & = 0\end{aligned}[/tex]
Solve for h:
[tex]\begin{aligned} \pi h & = 0 \implies h=0\\ \dfrac{40}{3}-h & =0\implies h=\dfrac{40}{3}\end{aligned}[/tex]
Substitute the found values of h into the equation for Volume:
[tex]\begin{aligned}\textsf{when}\:h=0:V &=\dfrac{20}{3} \pi (0)^2-\dfrac13 \pi (0)^3\\\\ \implies V & =0\sf \:cm^3\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{when}\:h=\dfrac{40}{3}:V &=\dfrac{20}{3} \pi \left(\dfrac{40}{3}\right)^2-\dfrac13 \pi \left(\dfrac{40}{3}\right)^3\\\\ \implies V & =\dfrac{32000}{27} \pi -\dfrac{64000}{81} \pi\\\\ & = \dfrac{32000}{81} \pi \\\\ & = 1241.123024..\sf \:cm^3\end{aligned}[/tex]
Therefore, the value of h such that the volume of the cone is a maximum is:
[tex]h=\dfrac{40}{3}[/tex]
a store sells trail mix in a 5-pound bag. one serving of trail mix is 114 grams. 1 pound ≈ 454 grams. what is the approximate number of servings in a 5-pound bag of trail mix, rounded to the nearest tenth?
Answers
Explanation: Here if 1 pound= 454 grams you would times it by 5 for the 5 pound bag. You would next divided your answer (2,270) by 114 grams because that equals 1 serving. what ever your answer then is how many servings.
find the perimeter of the square if the side length of the square is (3a+6b) units
a. 24a+12b
b. 12a+24b
c. 4a+6b
d. 12a-24b
Answers
Answer:
B
Step-by-step explanation:
Length of one side= 3a+6b
Perimeter= sum of 4 sides= 4(3a+6b) = 12a+24b
Please, help! 20 points
Mrs. Garcia’s class sold burgers for $1.36 each and Mr. Runner’s class sold salads for $1.65 each. Together, the classes sold 79 items and earned $118.17 for their school.
(a) Write a system of equations that model the problem.
x + s = 79 1.36(x) + 1.65(s) = 118.17
(b) Solve the systems of equations from part a.
(c) Whose class sold more items?
(d) Which class earned more money?
Answers
The 42 burgers are sold by Mrs. Garcia's class at $57.12 and 37 salad is sold by Mr. Runner’s class at $61.05.
What is a system of equation?A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.
Mrs. Garcia’s class sold burgers for $1.36 each and Mr. Runner’s class sold salads for $1.65 each. Together, the classes sold 79 items and earned $118.17 for their school.
(a) Write a system of equations that model the problem.Let x burgers are sold by Mrs. Garcia's class and s salad is sold by Mr. Runner’s class. Together, the classes sold 79 items for their school. Thus,
[tex]x + s = 79[/tex] .....1
Mrs. Garcia’s class sold burgers for $1.36 each and Mr. Runner’s class sold salads for $1.65 each. Together, the classes earned $118.17 for their school. Thus,
[tex]1.36(x) + 1.65(s) = 118.17\\1.36x + 1.65s = 118.17[/tex] ....2
(b) Solve the systems of equations from part a.Rewrite the first equation,
[tex]x + s = 79 \\ x = 79-s[/tex] .....3
Put this value of x in equation 2,
[tex]1.36(79-s) + 1.65s = 118.17\\107.44-1.36s + 1.65s = 118.17\\0.29s=118.17-107.44\\s=\dfrac{10.73}{0.29}\\s=37[/tex]
Put this value in equation 3,
[tex]x=79-37\\x=42[/tex]
(c) Whose class sold more items?42 burgers are sold by Mrs. Garcia's class and 37 salad is sold by Mr. Runner’s class. Thus, Mrs. Garcia's class sold more items.
(d) Which class earned more money?Money earned by Mrs. Garcia's class by selling 42 burger at $1.36 each is,
[tex]M_x=1.36\times42\\M_x=57.12[/tex]
Money earned by Mr. Runner’s class by selling 37 salad at $1.65 each is,
[tex]M_s=1.65\times37\\M_s=61.05[/tex]
Thus, Mr. Runner’s class earned more money.
Hence, the 42 burgers are sold by Mrs. Garcia's class at $57.12 and 37 salad is sold by Mr. Runner’s class at $61.05.
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I need help
Answers please?
Answers
Answer:
Ethan sold 1/12 gallon more lemonade
Step-by-step explanation:
1 1/4 = 2/3 + x
x is the amount of lemonade Kayla sold
find least common denominator
1 3/12 = 8/12 + x
subtract 8/12 on both sides
15/12 - 8/12 = x
7/12 = x
7/12 = amount of lemonade Kayla sold
2/3 - 7/12 = how much more Ethan sold
8/12 - 7/12 = 1/12 gallon
Make y the subject of the formula [tex]x=a-2by^{2}[/tex]
Answers
Heyo!
RummySokka is here to help!!
Let's do this step-by-step explanation!
: Let's solve for the y.
[tex]x=a-2by^2[/tex]
Step 1: Flip the equation.
[tex]-2by^2+a=x[/tex]
Step 2: Add a- to your both sides.
[tex]-2by^2+a+a-a=x+-a[/tex]
[tex]-2by^2=-a+x[/tex]
Step 3: Divide both sides by -2b.
[tex]\frac{-2by^2}{-2b} =\frac{a+x}{-2b}[/tex]
[tex]y^2=\frac{a-x}{2b}[/tex]
Step 4: Take square root.
[tex]y=\sqrt{\frac{a-x}{2b} }[/tex] [tex]or[/tex] [tex]y-\sqrt{\frac{a-x}{2b} }[/tex]
Answer:
[tex]y=\sqrt{\frac{a-x}{2b} }[/tex] [tex]or[/tex] [tex]y-\sqrt{\frac{a-x}{2b} }[/tex]
Hopefully, this helps you!!
RummySokka~
Which theorem or postulate proves the
two triangles are similar?
76/5
20
16
19
Not drawn to scale.
SA Postulate
SSS Theorem
AA Postulate
SAS Theorem
Answers
Answer:
AA postulate the two triangles are similar
Nicolas was testing H_0: \mu=24H 0 :μ=24H, start subscript, 0, end subscript, colon, mu, equals, 24 versus H_\text{a}: \mu\neq24H a :μ =24H, start subscript, start text, a, end text, end subscript, colon, mu, does not equal, 24 with a sample of 121212 observations. His test statistic was t=-1.79t=−1.79t, equals, minus, 1, point, 79. Assume that the conditions for inference were met. What is the approximate P-value for Nicolas' test?
Answers
Considering the hypotheses tested, it is found that the p-value for Nicolas's test is of 0.101.
What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 24, that is:
[tex]H_0: \mu = 24[/tex]
At the alternative hypotheses, it is tested if it is different, hence:
[tex]H_1: \mu \neq 24[/tex]
As we are testing if the mean is different of a value, we have a two-tailed test, with t = -1.79 and 12 - 1 = 11 df. Hence, using a t-distribution calculator, the p-value is of 0.101.
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To find the distance an object has traveled, you use the formula D=RT; where D=distance, R=rate and T=time.
What was the rate a person drove if they traveled 313.5 miles in 6 hours?
A. 52.23 miles per hour
B. 52.25 miles per hour
C. 1,811 miles per hour
D. 18,810 miles per hour
Answers
Answer:
52.25 MPH
Step-by-step explanation:
Using the formula given D=RT we simply plug in values,
313.5=6R
313.5/6=R
52.25=R
Ralphie's dad has a nutritionist who instructed him to consume less than 2,187 calories per day. He has already consumed 1,571 calories today and wants to eat some fruit bars that are 64 calories each. Which of the following inequalities could be used to solve for x, the number of fruit bars Ralphie's dad can eat without going over his calorie allotment?
Answers
Answer:
1571 + 64x < 2187
Step-by-step explanation:
PLEASE HELP ME WITH THIS
Select the correct answer.
Function h is nonlinear, and h(4) = 2. Which equation could represent function h ?
Answers
Answer:
C
Step-by-step explanation:
H(4) simply means that where there is X, it must be substituted by the value 4
So lets see step by step:
A. h(4)=2 (incorrect)(there is no X to substitute on the right side and it is stated that H is non linear. This 2 would mean that H is a straight line)
B. (4)^3 -4= 60 (incorrect as answer needs to be 2)
C. 2^4 - 14=2 (correct, as answer is 2 and equation is non linear)
D. 1/2 (4) +3 = 5 (incorrect)
Hence your answer is C
WHATS IS PLS TELL ME PLS 10 X 10
Answers
Answer:
100
Step-by-step explanation:
10x10=100
What is the range of f(x) = (three-fourths) Superscript x – 4?
{y | y > –4}
Left-brace y vertical line y greater-than three-fourths right-brace
{y | y < –4}
Left-brace y vertical line y less-than three-fourths right-brace
Answers
Using exponential function concepts, it is found that the range of f(x) is given by:
{y | y > –4}
What is the range of an exponential function?An exponential function is defined by:
[tex]y = ab^x + k[/tex]
The value of k is the asymptote of the function, hence the range is {y|y>k}.
In this problem, the function is given by:
[tex]f(x) = \left(\frac{3}{4}\right)^x - 4[/tex]
Hence k = -4 and the range is {y | y > –4}.
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Answer:
the answer is A
Step-by-step explanation:
i got it right on edge 2022
Joel made a scale drawing of a boarding school. A building at the school is 16 millimeters wide in the drawing. The actual building is 20 meters wide. What is the scale of the drawing?
Answers
Answer:
Step-by-step explanation:
.8 millimeters :1 meters
Answer: 5 METERS ACCORDING TO IXL
Step-by-step explanation:
Which of the following sets of ordered pairs does not represent a function?
Answers
Answer:
d
Step-by-step explanation:
find the equation of the line passing through the points (1,5) and (3,9)
Answers
Answer:
[tex]\boxed{\sf{2}}[/tex]Step-by-step explanation:
Use the slope formula.
[tex]\underline{\text{SLOPE:}}[/tex]
[tex]\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{Rise}{Run} }[/tex]
[tex]\sf{y_2=9}\\\\\\\sf{y_1=5}\\\\\\\sf{x_2=3}\\\\\\\sf{x_1=1}[/tex]
[tex]\sf{\dfrac{9-5}{3-1} }[/tex]
Solve.
[tex]\sf{\dfrac{9-5}{3-1}=\dfrac{4}{2}=\boxed{\sf{2}}[/tex]
Therefore, the slope is 2, which is our answer.I hope this helps. Let me know if you have any questions.
Jade can travel 42 miles in 4 hours. Please calculate Jade's rate of speed. (round to 2 decimal places)
Answers
Answer:
10.50 Miles per hour
Step-by-step explanation:
42/4 = 10.50 easy
Point A is located at (-3, -6) and is translated 6 units down. What are the coordinates of point A?
(-3,-12)
(-9, -6)
(-3, 0)
(3, -6)
Answers
Answer:
-3, -12
Step-by-step explanation:
Only the y coordinate should change. A translation of -6 units would be -12 meaning it is (-3, -12)
PLEASE HELP!! WILL MARK BRAINLIEST!
which statement describes the graph and orientation of the parametric equations x = 16 cos r and y = 16 sin t?
A. The graph is a circle with a radius of 4. The orientation is counterclockwise as t increases.
B. The graph is a circle with a radius of 16. The orientation is counterclockwise as t increases.
C. The graph is the circle with the radius of 4. The orientation is clockwise as t increases.
D. the graph is a circle with a radius of 16. the orientation is clockwise as t increases.
Which is the polar form of the parametric equations x = 3t and y = t^2
A. r = 9 sec theta
B. r = 9 tan theta sec theta
C. r = 9tan^2 theta
D. r = 9sec^2 theta
Answers
From the graph and orientation of the parametric equations: A. the graph is a circle with a radius of 4. The orientation is counterclockwise as t increases.
How to find a polar function?In geometry, the relationship between the rectangular coordinates (x, y) and polar coordinates (r, t) is given by these polar functions:
x = rcost and y = rsint.
Where:
t is the angle.r is the radius of a circle.Mathematically, the standard form of the polar equation of a circle is given by;
x² + y² = r²
Given the following data;
x = 16cost ⇒ x² = 16cos²t
y = 16sint ⇒ y² = 16sin²t
Evaluating, we have:
x² + y² = 16
r² = 16
r = √16
Radius, r = 4.
Also, the orientation is counterclockwise as t increases because the angle gets bigger (increases).
How to determine polar form of the parametric equations?x = 3t .....equation 1.
y = t² .....equation 2.
Making t the subject of formula in eqn. 1, we have:
t = x/3 .....equation 3.
Substituting eqn. 3 into eqn. 2, we have:
y = (x/3)²
rsinθ = (rcosθ/3)²
rsinθ = r²cos²θ/9
9rsinθ = r²cos²θ
9sinθ = rcos²θ
r = 9sinθ/cos²θ
r = 9 × (sinθ/cosθ) × 1/cosθ
r = 9tanθsecθ.
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On average, Margo scores a goal for her field hockey team every 2 out of 3 shots. Margo uses a number cube to simulate her next three shots. She assigns 1 to 4 as goals and 5 and 6 as missed shots. Why does this assignment of numbers on the number cube make it a valid simulation?
Answers
Answer:
Margo makes 2/3 shots and making 4 shots and missing 2 shots equals 6 so 4/6 reduces to 2/3.
Step-by-step explanation:
4/6 = 2/3
The cone and cylinder above have the same radius, r, and height, h. The volume of the cone is 90 cubic centimeters.
What is the volume of the cylinder?
Answers
Answer:
[tex]\huge\boxed{\sf Volume\ of\ cylinder = 270\ cm^3}[/tex]
Step-by-step explanation:
Volume of cone = 90 cm³
Volume of cylinder = ?
Always remember:
Volume of cylinder = 3 × volume of cone
Volume of cylinder = 3 × 90
Volume of cylinder = 270 cm³
[tex]\rule[225]{225}{2}[/tex]
kono divides the numerator and denominator of 48 over 72 by the greatest common factor to simplify the fraction in one step. by what number does he divide?
Answers
Answer:
24
Step-by-step explanation:
[tex]\sf Given\:fraction:\dfrac{48}{72}[/tex]
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
So the greatest common factor (GCF) of 48 and 72 is 24.
Therefore, to simplify the fraction, divide the numerator and denominator by 24:
[tex]\sf \implies \dfrac{48}{72}=\dfrac{48 \div 24}{72 \div 24}=\dfrac{2}{3}[/tex]
Answer:
24
Step-by-step explanation:
The Greatest Common Factor (GCF) is the biggest common number by which 2 numbers can be formed when multipliedFactors of 48 and 72
48 : 1, 2, 3, 4, 6, 8, 12, 16, [24], 4872 : 1, 2, 3, 4, 6, 8, 9, 12, 18, [24], 36, 72⇒ 24 is the GCFSolving
[tex]\frac{48}{72} = \frac{2*24}{3*24} = \frac{2}{3}[/tex]Write a rule for the nth term of the sequence. Then find a20. Assume the first termis a₁. 86, 79, 72, 65…
Answers
Answer:
an = a(n-1) - 7
Step-by-step explanation:
the second term is smaller than the first term 7.
a20 = a19 - 7
a19 = a18 - 7
=> a20 = (a18 - 7) - 7
Then you can accumalate until a1
-> a20 = a1 - 19*7 = 86 - 19*7 = -47
factor the polynomial
28c - 12
Answers
Answer:
28c-12 and it would be 4(7e-3 and i did not copy from googe i did this on my own
Step-by-step explanation:
Answer:
4(7c - 3)[tex] \: [/tex]
Step-by-step explanation:
So, here we are to factor the polynomial :
[tex] \\ \longrightarrow \sf \qquad28c - 12\\ \\[/tex]
[tex]\longrightarrow \sf \qquad4(7c - 3)\\ \\[/tex]
Some points to know :
Factorisation is the reverse process of multiplucation.The Factorisation is the process of finding two or more expressions such that their product is the given expressionFind the error(s). PLEASE HELP!!!!!
Answers
Answer:
see explanation
Step-by-step explanation:
the tan , sin , cos ratios are used to find sides and angles in a right triangle.
There is no indication on the diagram that the triangle is right.
then the use of the tan ratio is an error if the triangle is not right.
Dan purchased a set of knitting needles for $11 and 6 identical packs of yarn. The total cost was $89.
How much did each pack of yarn cost?
Answers
Answer:
13$
Step-by-step explanation:
Dan purchased a set of knitting needles for $11 and 6 identical packs of yarn. The total cost was $89.
How muc[tex]rweds[/tex]h did each pack of yarn cost?
The total cost of each pack of yarn is $13.
What is a total cost?The total cost of an item is the sum of the cost of all items that are purchased. Total cost for more items can be found by multiplying the number of items and the cost of the individual item.
For the given situation,
There are two items purchased knitting needles and packs of yarn.
Cost of knitting needle = $11
Number of packs of yarn purchased = 6
Total cost = $89
Let the cost of yarn be x.
The cost of the yarn can be find by using the equation,
Total cost = Cost of knitting needle + (number of yarn purchased × x)
⇒ [tex]89=11+6x[/tex]
⇒ [tex]6x=78[/tex]
⇒ [tex]x=13[/tex]
Hence we can conclude that the cost of each pack of yarn is $13.
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