Inequalities are relationships like equalities, what makes it different from equalitites is that on both sides are different expressions that allows to comparate them without been equal, for this we have 4 types
≤ less or equal than
≥ greater or equal to
< less than
> greater than
some examples are:
[tex]\begin{gathered} 3x-3<50 \\ 5x-45>33x \\ x^2-15x<34 \end{gathered}[/tex]Another difference between inequalities and equalities is that in equalities we obtain 1,2 or 3 solutions accronding to the degree of the equation, in inequalities we can obtain infinite number of solutions.
3 7/9 + 4 10/12 I need help
Given the fraction 3 7/9 + 4 10/12
Add the numbers first
3 + 4 = 7
Then the fractions
7/9 + 10/12
The lowest common multiple of 12 and 9 ( the denominators) is 36
Divide the denominators by 36 and multiply the result with the numerators
(7*4 + 10 * 3)/36
= (28 + 30)/36
= 58/36
= 29/18
= 1 11/18
Add this to the sum of the wholes munbers done earlier
= 7 + 1 11/18
=8 11/18
1. A fruit punch recipe contains 8 ounces of pineapple juice and makes enough punch for 20 servings. If150 servings need to be prepared for a party, how many ounces of pineapple juice are needed?Let x =Proportion:Solution:2. Zach can read 7 pages of a book in 5 minutes. At this rate, how long will it take him to read the entire175 page book?Let x =Proportion:Solution:
Let x be the number of ounces.
A fruit punch recipe contains 8 ounces of pineapple juice and makes enough punch for 20 servings: Proportion:
[tex]\begin{gathered} \frac{\text{xoz}}{150servings}=\frac{8oz}{20\text{servings}} \\ \\ \frac{x}{150}=\frac{8}{20} \\ \\ \end{gathered}[/tex]Solution:
[tex]undefined[/tex]if m=24 and v=4 p=mv
p = 96 is the product of m = 24 and v = 4
What is multiplication ?In mathematics, a product is the outcome of multiplication, or an expression that identifies the things to be multiplied, known as factors.
Calculationm = 24
v = 4
p = mv
p = 24 * 4 = 96
p = 96
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A rectangular shaped parking lot is to have a perimeter of 792 yards if the width must be 168 yards because of a building code what will the length need to be?
The perimeter of rectangular shaped parkin is P = 792 yards.
The width of rectangula parking is w = 168 yards.
The formula for the perimeter of rectangle is,
[tex]P=2(l+w)[/tex]where l is length.
Substitute the values in the formula to determine the length of rectangular parking.
[tex]\begin{gathered} 792=2(l+168) \\ \frac{792}{2}=l+168 \\ l=396-168 \\ =228 \end{gathered}[/tex]So length need to be 228 yards.
a firefighter on the ground sees fire break through a window near the top of a building. The angle of elevation to the window seal is 28 degrees. The angle of elevation to the top of the building is 42 degrees. The firefighter is 75 ft from the building and her eyes are 5 feet above the ground. What Ruth window seal distance guess you report by radio to Firefighters on the roof
Problem:
A firefighter on the ground sees fire break through a window near the top of a building. The angle of elevation to the window seal is 28 degrees. The angle of elevation to the top of the building is 42 degrees. The firefighter is 75 ft from the building and her eyes are 5 feet above the ground. What Ruth window seal distance guess you report by radio to Firefighters on the roof?
Solution:
There are two big triangles, one of them is that formed by a fireman, the roof and the building foundation plus the height of the fireman as the vertices. So, the opposite side to the 42 degrees angle given is denoted by h_roof, and the adjacent side is 75 ft away from the building:
[tex]h_{roof\text{ }}=\text{ }75.tan(42^{\circ}\text{)}[/tex]that is:
[tex]h_{roof\text{ }}=\text{ (}75)(0.9004)\text{ = }67.53[/tex]Now, the other big triangle is formed by the fireman, the window, and the building foundation plus the height of the fireman as vertices:
[tex]h_{WIN}=75.\tan (28)[/tex]that is:
[tex]h_{WIN}=(75)(0.5317)=\text{ 39.}87[/tex]then, the difference between the heights is the roof-to-windowsill:
[tex]h=h_{roof}-h_{WIN}=\text{ }67.53-39.87\text{ = }27.66[/tex]Then, we can conclude that the correct answer is:
[tex]h=27.66[/tex]Expand 4(y + 5).4(y+5)= 1
ANSWER
[tex]4y+20=[/tex]EXPLANATION
We want to expand the expression:
[tex]4(y+5)[/tex]To do this, we apply the distributive property:
[tex]a(b+c)=(a\cdot b)+(a\cdot c)[/tex]Therefore, we have:
[tex]\begin{gathered} (4\cdot y)+(4\cdot5) \\ 4y+20 \end{gathered}[/tex]That is the answer.
You roll a six-sided die. What is the probability that it is an odd number or greater than three? Round your answer to the nearest thousandth. The probability is about
the total possible outcome of a die is 6
n(T) = 6
the sample space {1,2,3,4,5,6}
the odd numbers are {1,3,5}
thus n(O) = 3
numbers greater than 3 are {4,5,6}
thus n(>3) = 3
the probability of getting an odd number or a number greater than 3
is Pr(O) U Pr(>3)
[tex]\begin{gathered} Pr\text{ (O) = }\frac{n(O)}{n(T)}=\frac{3}{6}=\frac{1}{2} \\ Pr(>3)\text{ = }\frac{n(>3)}{n(T)}=\text{ }\frac{3}{6}=\frac{1}{2} \end{gathered}[/tex][tex]\begin{gathered} Pr\text{ (O U >3) = Pr(O) + Pr(>3)} \\ \text{ = }\frac{1}{2}\text{ + }\frac{1}{2}\text{ = 1} \end{gathered}[/tex]the probabilty of that it is an odd number or a number greater than 3 is 1.000 (nearest thousandth)
A manufacturer knows that their items have a normally distributed length, with a mean of 6.1 inches, and standard deviation of 0.5 inches.If one item is chosen at random, what is the probability that it is less than 6 inches long? (Give answer to 4 decimal places.)
..SOLUTION
[tex]\begin{gathered} Mean=6.1 \\ Standard\text{ deviation=0.5} \end{gathered}[/tex][tex]\begin{gathered} Z-score=\frac{x-mean}{standard\text{ deviation}}=\frac{6-6.1}{0.5}=-0.2 \\ \end{gathered}[/tex]The normal curve is given below.
Using statistical table, the probability is given as;
[tex]0.4207[/tex]solve the system of linear equations by elimination x+2y=13 -x+y=5
To solve the system
[tex]\begin{gathered} x+2y=13 \\ -x+y=5 \end{gathered}[/tex]we add the two equations to get:
[tex]\begin{gathered} x+2y=13 \\ -x+y=5 \\ --------------_{} \\ 0+3y=18 \end{gathered}[/tex]Dividing both sides by 3 gives
[tex]y=6[/tex]with the value of y in hand, we now put it in -x + y = 5 to get
[tex]-x+6=5[/tex]subtracting 6 from both sides gives
[tex]-x=-1[/tex][tex]x=1[/tex]Hence, the solution to the system is
[tex]\begin{gathered} x=1 \\ y=6. \end{gathered}[/tex]Solve the right triangle with a= 1.42 and b=17.1 . Round off the results according to the table below
A)
[tex]\begin{gathered} c=17.159 \\ A=4.747\text{\operatorname{\degree}} \\ B=85.253\operatorname{\degree} \end{gathered}[/tex]Explanation
Explanation
Step 1
c) to find the measure of the hypotenuse we can use the Pythagorean theorem, it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
[tex]a^2+b^2=c^2[/tex]Step 1
a) Let
[tex]\begin{gathered} a=1.42 \\ b=17.1 \end{gathered}[/tex]b) now, replace and solve for c
[tex]\begin{gathered} a^2+b^2=c^2 \\ 1.42^2+17.1^2=c^2 \\ 294.4264=c^2 \\ c=\sqrt{294.4264} \\ c=17.15885 \\ rounded \\ c=17.159 \end{gathered}[/tex]Step 2
angle A
to solve for angle A we can use tan function, so
[tex]tan\theta=\frac{opposite\text{ side}}{adjacent\text{ side}}[/tex]replace
[tex]\begin{gathered} tan\text{ A=}\frac{a}{b} \\ tanA=\frac{1.42}{17.1} \\ A=\tan^{-1}(\frac{1.42}{17.1}) \\ A=4.747\text{ \degree} \end{gathered}[/tex]Step 3
for angle B we can use tan function
let
[tex]\begin{gathered} opposit\text{ side=b} \\ adjacent\text{ side=a} \end{gathered}[/tex]replace and solve for angle B
[tex]\begin{gathered} tan\text{ B=}\frac{b}{a} \\ tanB=\frac{17.1}{1.42} \\ B=\tan^{-1}(\frac{17.1}{1.42}) \\ B=85.252\text{ \degree} \\ \end{gathered}[/tex]I hope this helps you
Joe jogged at 8mph. At this speed, how far can he get in 35 minutes?
We are required to find distance while we are given the speed and the time.
Distance is given as:
[tex]d=s\times t[/tex]where:
d = distance
s = speed = 8 miles per hour
t = time = 35 minutes
[tex]d=8\times\frac{35}{60}=4.67miles[/tex]Distance covered in 35 minutes is 4.67 miles
A car was valued at $27,000 in the year 1992. The value depreciated to $15,000 by the year 2000,A) What was the annual rate of change between 1992 and 2000?Round the rate of decrease to 4 decimal places.B) What is the correct answer to part A written in percentage form?%T-C) Assume that the car value continues to drop by the same percentage. What will the value be in the year2004value - $Round to the nearest 50 dollars,
If a car is valued at $27,000 in the year 1992
The value of the car depreciated to $15,000 by year 2000
The formula for the annual rate change is given below as,
[tex]A=P(1-r)^t[/tex]Where,
[tex]\begin{gathered} A=\text{ \$15,000} \\ P=\text{ \$27,000} \\ t=8\text{years (between 1992 and 2000)} \end{gathered}[/tex]a) Substitute the values into the formula above,
[tex]\begin{gathered} 15000=27000(1-r)^8 \\ \frac{15000}{27000}=(1-r)^8 \\ \frac{5}{9}=(1-r)^8 \\ \sqrt[8]{\frac{5}{9}}^{}=1-r \\ r=1-0.9292 \\ r=0.0708 \end{gathered}[/tex]Hence, the annual rate of change, r, is 0.0708 (4 decimal places)
b) The percentage form of the annual rate of change is,
[tex]=0.0708\times100\text{\% = 7.08\%}[/tex]Hence, the percentage form of the annual rate of change is 7.08%
c) If the car value continues to drop from 1992 to 2004, t = 12 years
The value of the car in the year 2004 will be,
[tex]\begin{gathered} A=P(1-r)^t \\ \text{Where P = \$27000} \\ t=12years \\ r=0.0708 \end{gathered}[/tex]Substituting the values into the formula above,
[tex]\begin{gathered} A=27000(1-0.0708)^{12} \\ A=27000(0.9292)^{12} \\ A=27000(0.4143)=\text{\$11186.1} \\ A=\text{\$111}90\text{ (nearest \$50)} \end{gathered}[/tex]Hence, the value in the year 2004 is $11190 (nearest $50)
hi. can you help me with number 16? I am unsure how to do the math here.
Given:
The distance between parallel celling and the floor is 10 ft.
The locus points are equidistant from the ceiling and the floor.
Required:
We need to find the distance between the locus plane and both the ceiling and the floor.
Explanation:
The locus of the points consists of the plane parallel to the floor and ceilings.
The locus plane is the midpoint of the distance between floor and ceilings since the locus points are equidistant from c
The mid-value of 10 feet is 5 feet.
The locus plane is 5 feet from both the ceiling and the floor.
Final answer:
The locus plane is 5 feet from both the ceiling and the floor.
What is 3ln5x=10? I have a test
Answer:
x=e^10/3
————
5
Step-by-step explanation:
Decimal Form:x=5.60632497
Managers of a sports arena’s parking garage keep track of the duration of time customers park their cars there. Shown in the stem and - leaf display below is a sample of 15 such parking duration (in minutes). Use the display to answer the questions that follow.
Step 1
A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).
[tex]198\text{ Minutes}[/tex]Step 2
[tex]\begin{gathered} In\text{ the 180s, we have;} \\ 182,183,186,189\text{ minutes} \\ The\text{ shortest parking duration in the 180's is 182} \\ Answer=182\text{ Minutes} \end{gathered}[/tex]Step 3
[tex]\begin{gathered} In\text{ the 160's, we have; 160,164,164} \\ Answer=3\text{ } \end{gathered}[/tex]Cook-It rice cooker has a mean time before failure of 42 months with a standard deviation of 3 months, and the failure times are normally distributed. What should be the warranty period, in months, so that the manufacturer will not have more than 9% of the rice cookers returned? Round your answer down to the nearest whole number.
From the statement, we have a normal distribution with:
• variable X = time before failure,
,• mean μ = 42 months,
,• standard deviation σ = 3 months.
We want to know for how much time the manufacturer will not have more than 9% of the rice cookers returned. So this is equivalent to finding the value x such that the probability of failure is lower than 9%:
[tex]P(X\leq x)=9\%=0.09.[/tex]We can compute this probability using the z-scores:
[tex]\begin{gathered} P(Z\leq z)=0.09, \\ z=\frac{x-\mu}{\sigma}\Rightarrow x=\mu+\sigma\cdot z=42+3\cdot z. \end{gathered}[/tex]We have the following table for z-scores:
The entries in the table represent the area under the curve, i.e. the probability. We must look for the closest value to the probability of 0.09. From the table, we see that the closest value to this probability is 0.091:
For this value we see that we have the z-score:
[tex]z=-1.34.[/tex]Replacing this value in the equation for x from above, we get:
[tex]x=42+3\cdot(-1.34)=37.98.[/tex]So we have found that for x = 37.98, we have:
[tex]P(X\leq x=37.98)=9\%=0.09.[/tex]This means that by a time x = 37.98 months, only 9% of the cookers will fail have failed. So the manufacturer must set a warranty period of 38 months to not have more than 9% of the rice cookers returned.
AnswerThe manufacturer must set a warranty period of 38 months to not have more than 9% of the rice cookers returned.
The stem-and-leaf plot shows student test scores. How many students score at least 17 points?Test ScoresStem Leaf0 681 5 5 7 8 992ooooKey: 17 = 17studentsPREV2125NEXTOOO$
We are given a data set in the form of a stem and leaf plot. This means that in the stem column we have the decimal digit and in the leaf column we have the units digits.
We are asked for the number of students that have scored at least 17, this means the number of students with a score that is greater or equal to 17. From the graph those scores are:
[tex]17,18,19,19,20,20,20,20[/tex]There are 8 students that scored at least 17.
2727. Boat Y and boat Z start traveling toward each other from 600 mile apart. Y istraveling at 35 mph, Z at 40 mph. How many hours will pass before theymeet?a. 7 b. 8 c. 9 d. 102828. Refer to problem 27. Y and Z start traveling toward each other from 600miles apart. Y is traveling at 35 mph, Z at 40 mph. How many miles will Ytravel before they meet?a. 400 b. 320 c. 350 d. 280
Given:
Speed of boat Y is 35 mph and speed of boat Z is 40 mph.
Both the boats are 600 miles a part.
how do you solve this problem?3 7/3+2 5/6=
Answer:
49/6
Explanation:
In order to add the mixed numbers given, we first convert the mixed numbers to improper fractions.
Now,
[tex]3\frac{7}{3}=3+\frac{7}{3}[/tex]The number 3 can be rewritten as
[tex]7=3\cdot\frac{3}{3}[/tex]which helps us rewrite our mixed fraction as
[tex]3+\frac{7}{3}=3\cdot\frac{3}{3}+\frac{7}{3}[/tex][tex]=\frac{9}{3}+\frac{7}{3}[/tex]adding the numerators gives
[tex]\frac{16}{3}[/tex]Hence,
[tex]3\frac{7}{3}=\frac{16}{3}[/tex]Similarly,
[tex]2\frac{5}{6}=2+\frac{5}{6}[/tex]the number 2 can be rewritten as
[tex]2=2\cdot\frac{6}{6}=\frac{12}{6}[/tex]therefore, the mixed number becomes
[tex]2+\frac{5}{6}=\frac{12}{6}+\frac{5}{6}[/tex][tex]=\frac{17}{6}[/tex]Hence,
[tex]2\frac{5}{6}=\frac{17}{6}[/tex]Now with mixed numbers rewritten as improper fractions, we are ready to add
[tex]3\frac{7}{3}+2\frac{5}{6}=\frac{16}{3}+\frac{17}{6}[/tex]rewriting 16/3 as 16/3 * 2/2 gives
[tex]\frac{16}{3}=\frac{32}{6}[/tex]therefore, we have
[tex]\frac{16}{3}+\frac{17}{6}=\frac{32}{6}+\frac{17}{6}[/tex]and now we just add the denominators to get
[tex]\frac{32}{6}+\frac{17}{6}=\frac{49}{6}[/tex]Hence,
[tex]3\frac{7}{3}+2\frac{5}{6}=\frac{49}{6}[/tex]which is our answer!
Hi, can you help me with this problem?A manufacturer has a monthly fixed cost of $42,500 and a production cost of $6 for each unit produced. The product sells for $11/unit.(a) What is the cost function?C(x)= (b) What is the revenue function?R(x)=(c) What is the profit function?P(x)= (d) Compute the profit (loss) corresponding to production levels of 6,000 and 11,000 units.P(6,000)=P(11,000)=
Given:
Fixed cost = b = $ 42,500
Production cost (Variable cost) /unit = m = $ 6/ unit
Let 'x' represent the number of unit, therefore the variable cost will be
[tex]6x[/tex]a) The cost function will be the sum of the fixed cost and the variable cost.
[tex]C(x)=6x+42500[/tex]b) The revenue function is the amount the product is sold per unit.
Recall: 'x' represents the number of units.
Therefore,
[tex]11\times x=11x[/tex]Hence, the revenue function R(x) is
[tex]R(x)=11x[/tex]c) The profit function is the difference between the revenue function and the cost function.
[tex]P\mleft(x\mright)=11x-\mleft(425000+6x\mright)=5x-42500[/tex]Hence, the profit function is
[tex]P\mleft(x\mright)=5x-42500[/tex]d) Let us compute the profit (loss) values when the units are 6000 and 11000
Using the profit function
[tex]P(x)=5x-42500[/tex]Therefore,
[tex]\begin{gathered} P(6000)=5(6000)-42500=30000-42500=-\text{ \$12500} \\ P(11000)=5(11000)-42500=55000-42500=\text{ \$12500} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} P(6000)=-\text{ \$12500 (which is a loss)} \\ P(11000)=\text{ \$12500 (this is a profit)} \end{gathered}[/tex]In some states, the amount of sales tax on an item is found by multiplying the cost of the item by 0.07. Find the sales tax of a DVD that costs $23.99. O $1.67 $1.68 $16.79 O $0.17
DVD = $23.99
Sales tax = (23.99 x 0.07)
= 1,679 = $1.68
solve 74 make sure to define the limits based on asymptotes don't just solve for the asymptotes
Explanation
[tex]f(x)=x^2(4x^2-\sqrt{16x^4+1})[/tex]2. A right prism has a square base of edge a and altitude h, write the formula for the total surface area
Given the shape in the question the total surface area of a prism is given by:
[tex]\begin{gathered} ph+2A \\ \text{where p=perimeter of the base} \\ h=\text{height} \\ A=\text{Area of the base} \end{gathered}[/tex]Since the right prism is square based, then we have:
[tex]\begin{gathered} \text{perimeter of a square = 4a where a is the edge of the square} \\ \text{Area of a square= a}^2 \end{gathered}[/tex]Hence, the formula for the total surface area of the prism is given by:
[tex]\begin{gathered} 4ah+2a^2 \\ \text{where a is the edge of the square and h is the height} \end{gathered}[/tex]what is the volume in cubic in of a cylinder with the height of 17 in and a base radius of 18in to the nearest tenth place
The volume V of a cylinder with radius r is the area of the base B (circle) times the height h . That is:
[tex]V=r^2\pi h[/tex]In our case, we have that r = 8 in and h= 17 in. Then, we have that the volume of the cylinder would be
[tex]V=r^2\pi h=(8)^2\pi(17)\text{ = }1088\pi\text{ }\approx3418,05[/tex]Then, we can conclude that the volume of the cylinder would be
3418,05 in^3
What is the probability that a customer selected at random was male and purchased a SUV?
Given:
A table
Required:
The probability that a customer selected at random was male and purchased an SUV.
Explanation:
The probability of getting a male with an SUV is given by
The total number of males divided by the total number of people and multiply by the number of SUVs divided by the total number of cars
[tex]\frac{60}{240}\times\frac{21}{240}=0.021875[/tex]Final Answer:
0.021875
Find a49 of the sequence 70,63, 56, 49, .
The 49th term of the Arithmetic Progression is -266.
The given sequence is 70,63, 56, 49,..
The given sequence is in Arithmetic Progression,
Where,
a = first term = 70,
d = common difference = 63 - 70 = -7
The general term of Arithmetic Progression is given by
[tex]a_{n} = a +(n-1)d[/tex]
Now, for n =49, the term of A.P. will be
[tex]a_{49}[/tex] = 70 + (49 -1)*(-7)
= 70 + 48*(-7)
= 70 - 336
= - 266
Hence, The 49th term of the Arithmetic Progression is -266.
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The circle below has center P.The point (x, y) is on the circle as shown.12-(a) Find the following.1110-unitsRadius: 0Center: 0987Value of a:(Choose one)(x,y)351Value of b:(Choose one)4a32(b) Use the Pythagorean Theorem to write an equationrelating the side lengths of the right triangle. Writeyour answer in terms of x and y (with no otherletters)+
Given:
Center of the circle = P
Let's determine the following:
a) Radius.
Here, the radius of the circle is the hypotenuse of the triangle.
Therefore, the radius of the circle is 3 units
b) Center:
To find the point at the center of the circle, let's locate the point P on the graph.
On the graph, the point P is at (x, y) ==> (9, 4)
Therefore, the center (h, k) is (9, 4)
c) Value of a:
To find the value of a, let's first find the value of b.
Value of b = 6 - 4 = 2
Apply Pythagorean Theorem to find the value of a:
[tex]c^2=a^2+b^2[/tex]Where:
c is the hypotenuse = 3
b = 2
Thus, we have:
[tex]\begin{gathered} 3^2=a^2+2^2 \\ \\ 9=a^2+4 \\ \\ \text{Subtract 4 from both sides:} \\ 9-4=a^2+4-4 \\ \\ 5=a^2 \\ \\ \text{Take the square root of both sides:} \\ \sqrt[]{5}=\sqrt[]{a^2} \\ \\ 2.2=a \\ \\ a=2.2 \end{gathered}[/tex]Therefore, the value of a is 2.2 units
d) Value of b.
The value of b is 2 units
ANSWERS:
• Radius: , 3 units
,• Center: , (9, 4)
,• Value of a = , 2.2 units
,• Value of b = , 2 units
5g + h =g solve for g
You have the following equation:
5g + h = g
In order to solve for g, you first organize the previous equation, as follow:
5g + h = g substract g both sides and substract h both sides too
5g - g = -h
4g = -h dive by 4 both sides
g = -h/g
Then, the answer is g = -h/g
PLS HELP WILL MARK BRAINLIEST 5 QUESTIONS
The vertex form equation is y = (x-3)^2 - 14
The equation y = x^2-6x+5 is really the equation y = 1x^2-6x+5. It is in the form y = ax^2 + bx + c where
a = 1
b = -6
c = 5
We will use 'a' and 'b' in the formula below
h = -b/(2a)
h = -(-6)/(2*(1))
h = 6/(2)
h = 3
The h refers to the x coordinate of the vertex. Since we know the x coordinate of the vertex (is 3), we can use it to find the y coordinate of the vertex
Simply plug x = 3 into the original equation
y = x^2 - 6x + 5
y = -(3)^2 - 6(3) + 5
y = (9) - 6(3) + 5
y = +9-18+5
y = -4
This is the k value, so k = -4.
In summary so far, we have a = -1, h = 3 and k = -4. Plug all this into the vertex form below
y = a(x-h)^2 + k
y = 1(x-3)^2 -4
y = (x-3)^2 - 14
Therefore the vertex form equation is y = (x-3)^2 - 14
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Hello, I need help with this problem. Picture will be included . Thank youu!
Solve for the missing equivalent rational expressions
[tex]\begin{gathered} \frac{-7}{w}=\frac{\square}{4w^8} \\ \\ \text{Swap left and right side of equations} \\ \frac{\square}{4w^8}=\frac{-7}{w} \\ \\ \text{Multiply both sides by }4w^8\text{ to cancel out the denominator on the left side} \\ \frac{\square}{4w^8}=\frac{-7}{w} \\ \frac{\square}{4w^8}\cdot4w^8=\frac{-7}{w}\cdot4w^8 \\ \frac{\square}{\cancel{4w^8}}\cdot\cancel{4w^8}=\frac{-28w^8}{w} \\ \square=\frac{-28w^8}{w} \\ \\ \text{Simplify the right side of the equation} \\ \square=\frac{-28w^8}{w} \\ \square=-28w^{8-1} \\ \square=-28w^7 \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ \frac{-7}{w}=\frac{-28w^7}{4w^8} \end{gathered}[/tex]