hmmm proofs like these can be a bit circular kinda, let's do some rigamarole on the equations and we'll see if that works for a definition
[tex]\stackrel{\theta \textit{ is always in radian unit}~\hfill }{s=r\theta\implies \cfrac{s}{\theta }=r \hspace{5em}v=\cfrac{s}{t}\implies t=\cfrac{s}{v}\hspace{5em}\omega=\frac{\theta }{t}} \\\\[-0.35em] ~\dotfill\\\\ \omega=\cfrac{\theta }{t}\implies \omega=\cfrac{\theta }{~~ \frac{ s}{v } ~~}\implies \omega=\cfrac{\theta }{1}\cdot \cfrac{v}{s}\implies \omega=\cfrac{\theta v}{s}\implies s\omega=\theta v \\\\\\ \cfrac{s\omega}{\theta }=v\implies \cfrac{s}{\theta }\cdot \omega=v\implies \boxed{r\cdot \omega=v}[/tex]
Given the following data, fill out the table for V* n and V/n
(give your answers to 3 sig figs).
The table for V* n and V/n shows the various answers as
What is multiplication and Division?Multiplication is when you take one number and add it together a number of times.
The table appears as follows
Volume(V) Moles(n) V*n V/n
3 0.145 0.435 20.7
4 0.193 0.773 20.7
5 0.242 1.210 20.7
6 0.290 1.740 20.7
These figures are gotten by the multiplication and division of the numbers in the tables as given by the formulae
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A chef made a blend of cooking oil. 1/5 of his mix was olive oil and 4/5 was corn oil. Write this blend as a ratio of corn oil to olive oil
1 :1 is the blend as a ratio of corn oil to olive oil.
Now, According to the question:
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)
"Information available from the question"
A chef made a blend of cooking oil.
1/5 of his mix was olive oil
and 4/5 was corn oil.
To find the blend as a ratio of corn oil to olive oil.
Now, Blend Ratio will be:
olive ratio + corn ratio
1/5 + 4/5
= 5/5 = 1/1
Hence, 1:1 is the blend as a ratio of corn oil to olive oil.
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The length of the minute hand of a clock i 6cm. Find the area wept by it when it move from 7:05 p.m. to 7:40 p.m.
Area swept by minute hand of a clock is 66cm².
Given that length of the minute hand of clock is 6cm.
We know that, total angle covered by the minute hand of clock is 360° in 60 minutes.
Total time interval = 7:45 PM – 7:05 PM = 35 minutes
In 60 minutes 360° angle covered
Then, in 1 minute 360/60 angle covered
So, in 35 minutes
total angle covered = 360/60 * 35 = 210°
Total area covered = sectional area of circle with radius 6cm
Total area covered = Ф/360 * πr²
= 210/360 * 22/7 * 6² = 66 cm²
Therefore, total area swept by minute hand of a clock is 66cm².
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Help please!!! (3x² - 4xy + y²)(4x + 3y)
The simplified form of the expression (3x² - 4xy + y²)(4x + 3y) is 12x³ - 7x²y + 8xy² + 3y³.
What is the simplified form of the expression?Given the expression in the question;
(3x² - 4xy + y²)(4x + 3y)
To simplify, apply distributive property by multiplying each term in the first expression by each term in the second expression.
(4x + 3y)(3x² - 4xy + y²)
4x (3x² - 4xy + y²) + 3y(3x² - 4xy + y²)
3x² × 4x - 4xy × 4x + y² × 4x + 3x² × 3y - 4xy × 3y + y² × 3y
12x³ - 16x²y + 4xy² + 9x²y - 12xy² + 3y³
Collect like terms
12x³ - 16x²y + 9x²y + 4xy² - 12xy² + 3y³
Add -16x²y and 9x²y
12x³ - 7x²y + 4xy² - 12xy² + 3y³
Add 4xy² and -12xy²
12x³ - 7x²y + 8xy² + 3y³
Therefore, the simplified form is 12x³ - 7x²y + 8xy² + 3y³.
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Willow is driving on the freeway. She just passed mile marker 325. The fastest she will drive is 75 miles per hour, though, there is a bit of traffic that might slow her down a bit, but she doesn’t know exactly how much. The mile markers are increasing on her route.
The expression 325 + 2y represents what mile marker she’s at after 2 hours, depending on traffic. Which inequality describes the mile marker she would be at this point?
The inequality describes the mile marker she would be at this point is:
325 + 2y ≤ 475
Now, According to the question:
Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have,
The fastest driving speed of Willow is 75 miles per hour,
There is a bit of traffic on her route that might slow her speed down,
So, the inequality which represents the speed of the willow is:
y ≤ 75
Hence, the inequality which represents the speed of the driving of willow is y ≤ 75.
Now, the expression 361 + 2y represents what mile marker he is at after 2 hours. We know that the fastest he will drive is 75, so we could replace y=75 in the last expression to know what mile marker he would be seeing at that point. This is:
325 + 2(75) => 325 + 150 = 475
Now, we know that the inequality would be:
325 + 2y ≤ 475
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Tell whether the two rates form a proportion.
-0. 4 kilometer for every 15 minutes
-0. 6 kilometer for every 20 minutes
As the value of the ratio of both the quantities are NOT same so the given values .
No, The two rates not form a proportion.
Now, According to the question:
Two ratios are equivalent, if the fractions corresponding to them are equivalent. Four quantities are said to be in proportion, if the ratio of the first and the second quantities is equal to the ratio of the third and the fourth quantities.
A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows:
1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)
Now,
0. 4 kilometer for every 15 minutes equals to (0.4/15) = 0.026
So for every minute they travel 0.026km.
0. 6 kilometer for every 20 minutes equals (0.6/20) = 0.03
So for every minute they travel 0.03km.
Here, as the value of the ratio of both the quantities are NOT same so the given values .
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Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their HCF is 101. Show your steps.
Please give answer immediately
Based on the information provided, the two numbers whose HCF is 101 are 1010 and 1313.
What is the HCF?The HCF is the highest common factor or in other words, the highest number by which two numbers can be divided. Let's start by listing the four digits numbers that can be the HCF related to 101.
101 x 10 = 1010
101 x 11 = 1111
101 x 12 = 1212
101 x 13 = 1313
Now, from these numbers, there are two numbers whose difference is 303.
1313 - 1010 = 303
Based on this, the two numbers are 1010 and 1313
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Multiple. Write your answer as a fraction or as a whole or mixed number.
3/4 x 8
Answer:
6
Step-by-step explanation:
3/4 x 8 = 3 x 8 / 4 x 1 = 24/4 = 6
Find the lateral area, and surface area of the figure.
Round your answers to the nearest thousandth, if necessary
Lateral Area = 108 square km
Surface Area = 120 square km
Think of the triangles as the floor and ceiling of this 3D room. The walls are three rectangular sides.
We have a 9 by 4 wall with an area of 9*4 = 36 square km
We have a 9 by 3 wall with an area of 9*3 = 27 square km
We have a 9 by 5 wall with an area of 9*5 = 45 square km
The lateral area is 36+27+45 = 108
The two triangles form the base faces of this prism.
Let's find the area of one of the triangles
area=0.5*base*height = 0.5*3*4 =6
One triangle has an area of 6, so both triangles in total have an area of 2*6 = 12 square km.
The total surface area is therefore 108+12 = 120 square km.
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Ayúdenme a encontrar el valor de los ángulos la medida de A) es 48 grados y E) es 136 grados y con eso encuentra los valores de los demás
eeeeeAnswer:
Step-by-step explanation:
a cell phone company has three different production sites. five percent of the phones from site 1, 7% from site 2, and 9% from site 3 have been recalled due to unexpected shutdown issue. suppose that 60% of the phones are produced at site 1, 30% at site 2, and 10% at site 3. if a randomly selected cell phone has been recalled, what is the probability that it came from site 3 (write it up to second decimal place)?
So, the probability that a randomly selected cell phone that has been recalled came from site 3 is 2.5 or 25%.
We can use Bayes' theorem to calculate the probability that a phone that has been recalled came from site 3. Bayes' theorem states that:
P(A|B) = P(B|A) * P(A) / P(B)
where:
P(A|B) is the probability of event A occurring given that event B has occurred (in this case, the probability that a phone came from site 3 given that it has been recalled)
P(B|A) is the probability of event B occurring given that event A has occurred (in this case, the probability that a phone has been recalled given that it came from site 3)
P(A) is the prior probability of event A occurring (in this case, the probability that a phone came from site 3)
P(B) is the prior probability of event B occurring (in this case, the probability that a phone has been recalled)
So, in this case, we have:
P(site 3 | recalled) = P(recalled | site 3) * P(site 3) / P(recalled)
We know that:
P(recalled | site 3) = 9%,
P(site 3) = 10%
We also know that:
P(recalled) = P(recalled | site 1) * P(site 1) + P(recalled | site 2) * P(site 2) + P(recalled | site 3) * P(site 3)
= (5% * 60%) + (7% * 30%) + (9% * 10%) = 3% + 2.1% + 0.9% = 6%
So, we can now calculate the probability that a phone that has been recalled came from site 3 as:
P(site 3 | recalled) = (9% * 10%) / 6% = 0.15 / 0.06 = 2.5
So the probability that a randomly selected cell phone that has been recalled came from site 3 is 2.5 or 25%.
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Simplify this to help me out
When we simplify the expression (4x⁴y⁵ / 3xy²)⁵, the result obtained is 1024x¹⁵y¹⁵ / 243
How do I simplify (4x⁴y⁵ / 3xy²)⁵?To simplify the expression (4x⁴y⁵ / 3xy²)⁵, the laws of indices must be applied as illustrated below:
(4x⁴y⁵ / 3xy²)⁵
Recall
(Aᵐ)ⁿ = Aᵐⁿ
Thus,
(4x⁴y⁵ / 3xy²)⁵ = 1024x²⁰y²⁵ / 243x⁵y¹⁰
Recall
Aᵐ / Aⁿ = Aᵐ⁻ⁿ
Thus,
1024x²⁰y²⁵ / 243x⁵y¹⁰ = (1024 / 243)x²⁰⁻⁵y²⁵⁻¹⁰
1024x²⁰y²⁵ / 243x⁵y¹⁰ = (1024 / 243)x¹⁵y¹⁵
1024x²⁰y²⁵ / 243x⁵y¹⁰ = 1024x¹⁵y¹⁵ / 243
Therefore,
(4x⁴y⁵ / 3xy²)⁵ = 1024x¹⁵y¹⁵ / 243
From the above illustration, we can conclude that the simplified form of (4x⁴y⁵ / 3xy²)⁵ is 1024x¹⁵y¹⁵ / 243
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Shirley can choose between peanut butter pretzels and caramel coated popcorn for her evening snack. According to economists, her _____ cost of consuming caramel coated popcorn would be the forgone peanut butter pretzels. Group of answer choices internal opportunity average transaction social
According to economists, her opportunity cost of consuming caramel-coated popcorn would be the forgone peanut butter pretzels.
Opportunity costs are the possible advantages that a person, investor, or company forgoes while deciding between two options. Opportunity costs are by definition invisible, making it simple to ignore them.
Better choices can be made by being aware of the opportunities that might be lost when a company or person chooses one investment over another. It is necessary to weigh the advantages and disadvantages of each choice offered in order to correctly assess opportunity costs.
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Given a rope 10 units in length, if side lengths must be in whole units, how many different triangles can be made?
A per the measurement, there is only form exactly 1 unique triangle.
The term triangle in math is known as a two-dimensional shape with three sides, three interior angles, and three vertices.
Here we have know that a rope 10 units in length, if side lengths must be in whole units.
And we need to find the number of different triangles can be made.
Here we know that length is 10 units, and the side length are whole units.
Which means that here we have 3 distinct value.
So as we all know that all of the triangles you make are the same triangle. Which means that if your three side lengths can form a triangle, then they can only form exactly 1 unique triangle.
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Joseph took a taxi from his house to the airport. The taxi company charged a pick-up
fee of $3. 10 plus $2 per mile. The total fare was $21. 10, not including the tip. Write
and solve an equation which can be used to determine m, the number of miles in the
taxi ride.
The equation is 2m + 3.10 = 21.10
And, the number of miles in the taxi ride is m = 9.
Now, According to the question:
Joseph took a taxi from his house to the airport. The taxi company charged a pick-up fee $3.10 plus $2 per mile. The total fare was $21.10.
Now,
The equation is written as,
2m + 3.10 = 21.10
Subtract 3.10 from both sides
2m = 18
Divide 2 from both sides
m = 9
Hence, The equation is 2m + 3.10 = 21.10
And, the number of miles in the taxi ride is m = 9.
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Jason is closing on a $430,000 home. He made a 13% down payment and is borrowing the rest. What is the approximate range of costs that he might expect to pay at the closing?
Answer:
$8,600 - $31,100
Step-by-step explanation:
Hope this helps :)
2. Consider this excerpt from chapter 39: "Something is discomforting about a sun that gives no
heat but keeps shining. " In this comparison, who is the sun?
O The tour guide
Maxine
Jade's mother
The symphony members
Jade's mother is the sun of Jade because she motivated Jade against race and gender, class and privilege, and fear and courage. Something is discomforting about a sun that gives no heat but keeps shining. " In this comparison, Jade's mother is the sun. So the option 3 is correct.
While expressing the complicated emotions of an aspirational, devoted girl, Jade's narrative voice offers riveting insights on the intricacies of race and gender, class and privilege, and fear and courage. Watson's story, which brims with empathy and wisdom, extols the ability of creative expression to reimagine and transform the world.
The many individuals who find themselves in the world looking for themselves are addressed in Watson's exquisitely written book. Piecing Me Together is a novel about how young people deal with the struggles and pain of daily life while remaining entire and true to themselves. It is both timely and timeless.
The reason why Jade's mother is said to as the sun of Jade is because she inspired Jade to overcome prejudices related to class, privilege, and fear.
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The complete question is:
Consider this excerpt from chapter 39:
Something is discomforting about a sun that gives no heat but keeps shining. " In this comparison, who is the sun?
1. The tour guide
2. Maxine
3. Jade's mother
4. The symphony members
relative frequency distributions are generally more useful than frequency distributions when
Relative frequency distributions are generally more useful than frequency distributions when comparing data sets of different sizes.
Frequency distributions can show the actual number of observations falling in each range or the percentage of observations. In the latter sample, the distribution is called a relative frequency distribution.
Frequency distribution tables can be utilised for both categorical and numeric variables. Continuous variables should only be used with class intervals, which will be described shortly.
A relative frequency distribution displays the proportion of the total number of observations associated with each value or class of values and is related to a probability distribution, which is extensively used in statistics.
--This question is incomplete; the complete question is
"Relative frequency distributions are generally more useful than frequency distributions when _____."--
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Please help with this problem!!!
At 11.5 hours, the red turtle pass the blue turtle. The red turtle won the race. The solution has been obtained by studying graph of the functions.
What is graph of the function?
The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. The graph of f is also known as the graph of
y = f(x).
In the graph, it is seen that from 6 to 13 hours, the blue turtle is at the same place whereas the red turtle is moving.
Therefore, at 11.5 hours the red turtle passes the blue turtle.
The red turtle won the race in 16 hours because in the graph it is observed that the blue turtle did not complete the entire km. The graph of blue turtle is a little less than that of red turtle.
Hence, at 11.5 hours, the red turtle pass the blue turtle and wins the race.
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Since there are multiple questions, so the question answered above is attached below.
what is the smallest even consecutive number such that their sum is at most 90?
SOLVE PLEASE
To find the smallest even consecutive numbers whose sum is at most 90, we can start with the smallest even number, which is 2. Then, we can add 2 to it to get the next even number, which is 4. We can keep adding 2 to get the next even numbers, and keep track of their sum. We can stop as soon as the sum exceeds 90.
The smallest even consecutive numbers whose sum is at most 90 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90
The first 20 even consecutive numbers sum 90.
the roof of a clock tower is a pentagon pyramid. each side of the base is 7ft long. the slant is 9. what is the area of the roof
The area of the roof is 157.5 .
It is given that the roof of a clock tower is a pentagonal pyramid.
Each side of the base is 7 ft long.
The slant height is 9 ft.
we know that, to find area we have,
Area=1/2 × 7 × 9 × 5
= 315/2
= 157.5
Hence, 157.5 square feet is the area of the roof.
Pentagonal pyramid
A pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point.
It is a three dimensional figure, it is a solid figure or an object or shape that has three dimensions—length, width, and height.
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Which even number is not a composite number?
A) 6
B) 4
C) 2
D) 8
Francine had six times the money Tommy had, but after Francine gave Tommy $33 to help him purchase a baseball cap, Tommy had twice as much as Francine. How much did they each start with?
For the relation of times of money , Francine and Tommy start with the amount of money equals to $18 and $3 respectively.
Let 'x' represents the amount of money with Francine .
And 'y' represents the amount of money with Tommy.
In the first condition:
x = 6y __(1)
To purchase baseball cap Francine gave $33 then the given relation is :
y - 33 = 2( x - 33 )
⇒ y - 33 = 2x - 66
⇒y = 2x -66 + 33
⇒ y = 2x -33 __(2)
Substitute the value of 'x' from (1) in (2) we get,
y = 2(6y) - 33
⇒y = 12y - 33
⇒ 12y - y = 33
⇒ 11y = 33
⇒ y = $3
⇒ x = 6(3)
⇒ x = $18
Therefore, the amount of money Francine and Tommy start with is equal to $18 and $3 respectively.
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i dont understand this
The given expression has sin A = BC/AC=36/85, cos A = AB/AC=77/85, tan A = BC/AB=36/77
How to find sin cos tan?In trigonometry, the values of sin, cos, and tan are the main functions we consider when solving trigonometric problems. Using these trigonometric values, the angles and sides of a right-angle triangle are calculated. In addition to sine, cosine, and tangent values, the other three significant values are cotangent, secant, and cosecant.
Normally, when calculating the sin, cos, and tan values for a triangle, the angles of 0°, 30°, 45°, 60°, and 90° are taken into consideration. These specific angles' values are easy to remember. What the trigonometric values are all about is knowing the standard angles for a specific triangle according to the trigonometric ratios (sine, cosine, tangent, cotangent, secant and cosecant).
We have, AB = 77 , BC = 36.and CA=85
When we consider the t-ratios of ∠A, we have
Base = AB = 77, Perpendicular = BC = 36, Hypotenuse = AC =85.
∴sin A = BC/AC=36/85 , cos A = AB/AC=77/85 , tan A = BC/AB=36/77
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:)))))))))))))))))))))))))))))
All sides of a lawn are expanded by the same amount so that it’s dimension are now 100 feet by 60 feet. If x is the same amount of length added to each side, write a function of x giving the length of each of the original sides. Use these functions to make a function for the area of the original lawn.
The function of x giving the length of each of the original sides would be [tex](x + 100) * (x + 60) = x^2 + 160x + 6000[/tex].
What is Function of x?
A function is a formula that expresses one variable in terms of another. The statement "y is a function of x" (denoted y = y(x)) states that y changes depending on the value of x.
The original length of each side of the lawn can be represented by the function x + 100, and the original width can be represented by the function x + 60.
To find the area of the original lawn, we can multiply the length and width functions.
So, the function for the area of the original lawn is:
[tex](x + 100) * (x + 60) = x^2 + 160x + 6000[/tex]
This is a quadratic function in x, whose leading coefficient is 1, and the value of x is the same amount of length added to each side of the lawn.
Hence, The function of x giving the length of each of the original sides would be [tex](x + 100) * (x + 60) = x^2 + 160x + 6000[/tex].
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fred has ten feet of wire.he decides to cut it into equal length pieces. how many pieces will he get if each piece is 4 feet long?
Answer:
I don't know
Step-by-step explanation:
A recipe states that chicken needs to be cooked for 15 minutes per kg plus an extra 40 minutes. Express the relationship between mass and cooking time using function notation, and define the domain and range.
For the given statement, the domain and range are - Domain : x ,Range : f(x) 40.
What does a notation in mathematics mean?In mathematical notation, symbols are used in expressions and formulas to represent operations, unnamed numbers, relations, and any other mathematical objects. In mathematics, science, and engineering, mathematical notation is frequently used to communicate complicated ideas and properties in a clear, unambiguous manner.
A notation is a set of clear guidelines for using symbols to describe numbers and actions.
The sum of numerous linked terms is frequently represented by the sign (capital sigma) in shorthand notation. In statistics, sigma notation is frequently employed.
For each dividend number, the extended notation division method merely repeats the division, multiplication, and subtraction operations.
Given data :
x is the mass of the chicken (in kg)
f(x) : the cooking time ( in minutes )
Domain : x
Range : f(x) 40
f(x) = 15x + 40 - 15 minutes per kg (x) plus 40 more minutes
f (1) = 15 x 1 + 40 = 55
A 1 kg chicken needs 15 min + 40 min = 55 min
f (2) = 15 x 2 + 40 = 70
A 2 kg chicken needs 30min + 40 min = 70 min
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Solve for kkk.
20-6+4k=2-2k20−6+4k=2−2k20, minus, 6, plus, 4, k, equals, 2, minus, 2, k
k =k=k, equals
The value of k is -2
Now, According to the question:
The given equation is:
20 - 6 + 4k = 2 - 2k
We have to solve for the value of k.
Now,
20 - 6 + 4k = 2 - 2k
Combine the like terms;
20 - 6 - 2 = -2k - 4k
Calculate the sum or difference:
20 - 8 = -6k
12 = -6k
Calculate the product or quotient:
k = -12/6
k = -2
Hence, The value of k is -2
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What is the solution of the system of equations
Y=1/8x-1
-5x+4y= - 13
Answer:
(2.57, -0.07)
Step-by-step explanation:
To solve the system of equations, we can substitute the expression for y in the second equation:
-5x + 4(1/8x - 1) = -13
We can then simplify and solve for x:
-5x + (1/2)x - 4 = -13
-3.5x = -9
x = 2.57
We can then substitute this value of x back into the first equation to find the value of y:
y = 1/8(2.57) - 1
y = -0.07
So the solution of the system of equations is (x, y) = (2.57, -0.07)