he function y=f(x)y=f(x) is graphed below. What is the average rate of change of the function f(x)f(x) on the interval −1≤x≤0?
Answers
The estimate of the average rate of change f is -2
How to estimate the average rate of change f?The possible graph that completes the question is added as an attachment
The interval is given as
-1 ≤ x ≤ 0
This can be rewritten as
x = -1 to x = 0
This can also be represented as
(a, b) = (-1, 0)
From the attached graph, we have
f(-1) = 7
f(0) = 5
The estimate (to one decimal place) of the average rate of change f is
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(-1) - f(0)]/[-1 - 0]
So, we have
Rate = [7 - 5]/[-1 - 0]
Evaluate
Rate = -2
Hence, the average rate of change f is -22
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Related Questions
on june 10, 2010 the boston globe reported that in the six years between 2006 and 2012 boston firefighters received raises of 2%, 2.5%, 3%, 3.5%, 2.5%, and 1.5%.
Answers
on june 10, 2010 the boston globe reported that in the six years between 2006 and 2012 boston firefighters received raises of 2%, 2.5%, 3%, 3.5%, 2.5%, and 1.5%. then overall raise is 16%
on june 10, 2010 the boston globe reported that in the six years between 2006 and 2012 boston firefighters received raises of 2%, 2.5%, 3%, 3.5%, 2.5%, and 1.5%.
let us assume the amount be 100
in 2007 it increase at 2% then it become 102
in 2008 at rate 2.5% then =102+2.55=104.55
in 2009 at rate 3% then it become =3.1365+104.55= 107.68
in 2010 at rate 3.5% = 3.7690+107.68=111.44
in 2011 at rate 2.5% = 2.786+111.44=114.22
in 2012 at rate 1.5%= 1.71+114.22=115.93
Hence, overall increase is 16%
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A credit card bill for $559 was due on September 14. Purchases of $286 were made on September 19, and $15 was charged on September 28. A payment of $250 was made on
September 25. The annual interest on the average daily balance is 19.5%. Find the finance charge due (in dollars) on the October 14 bill. (Use 365 for the number of days in a year.
Round your answer to the nearest cent.)
Answers
With 19.5% annual interest on a daily basis, the finance charge due on October 14 will be $623.
What is interest?In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed). It is not the same as a fee that the borrower might pay to the lender or another party. It also differs from a dividend, which is money given to shareholders (owners) by a company from its profit or reserve but not at a set rate predetermined in advance, but rather on a pro-rata basis as a share of the reward received by risk-taking businesspeople when revenue is earned that exceeds all costs.So, the finance charge due:
(+) $ 559 due on sep 14, $ 559 * (19.5*31) / (100 * 365) = $ 9.20(+) purchase $ 289 on Sep 19, $ 289 * (19.5*26 ) / (100 * 365) = $ 2.42(+) finance charge on sep 28, $ 18 *(19.5*17 ) / (100 * 365) = $ 0.17(-) Repayment on 25 sep , $ 250 * (19.5*20 ) / (100 * 365) = (2.745)Finance charges from 14 sep to 14 oct = $ 9.7= appr. 10Amount due on 14 October = $559+$289+$15+$11.855- $250= $ 623Therefore, with 19.5% annual interest on a daily basis, the finance charge due on October 14 will be $623.
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( Please help + Will mark brainliest )
Answer the question in photo.
Answers
Answer:
length of I'J'= 4 units
length of IJ= 16 units
scale factor = 16/4 = 4
plssssss marks as brainliest
How do division properties help you evaluate expressions?
Drag a word or number to the box to correctly complete the statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
When the area of a fraction is equal to −1 and the numerator is nonzero, the value of the fraction is equal to the .
Options: numerator, opposite of the numerator, denominator, opposite of the denominator, 0
Answers
The division property of equality informs us quite simply that if we divide both sides of an equation by the same number, then the resulting equation is unaltered. This is known as the distributive property of equality.
How can we make sense of this information?It is important to keep in mind that the value of a fraction is always equivalent to the numerator of the fraction if the denominator of the fraction is 1 and the numerator of the fraction is anything other than zero.
To speak in terms of fractions is to refer to numbers that are not whole.
The value of the numerator in a fraction is determined by whether or not the numerator is nonzero and whether or not the denominator is 1.
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Find the slope of the line passing through the points (4,9) and (-6,9)
Answers
Answer:
Slope = 0
Step-by-step explanation:
[tex]\text{Slope} = m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]
where (x1, y1) and (x2, y2) are any two points on the line
Given he two points (4, 9) and (-6, 9)
m = (9 - 9)/(-6 - 4) = 0/-10 = 0
Miguel can type 448 words in 8 minutes. Jaycee can type
700 words in 25 minutes. Who types faster?
Answers
Answer:
umm i will explain
Step-by-step explanation:
miguel = 448 in 8 min
jaycee = 700 in 25 min
in 1 min miguel can type=
448/8 = 56 words
in 1 min jaycee can type=
700/25 = 28 words
so miguel can type's faster than jaycee
what equation is parallel to y=1/3x that goes through (6,0)
Answers
Considering the definition of parallel line, the equation y= 1/3x - 2 is parallel to y=1/3x and it goes through (6,0).
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts.
Equation of parallel line in this caseIn this case, the line is y=1/3x
where:
m= 1/3b= 0If two lines are parallel if they have the same slope, the parallel line has a slope of 1/3 and has a form of: y= 1/3x + b
The line passes through the point (6, 0). Replacing in the expression for parallel line:
0= 1/3× 6 + b
0= 2 + b
0 -2 = b
-2= b
Finally, the equation of parallel line is y= 1/3x - 2.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
If you have a right triangle, then you have 2 legs and 1 hypotenuse. The hypotenuse is the longest side across from the 90 degree angle. Pythagoras came up with the theorem for right triangles that states that the sum of the squares of the 2 legs is equal to the hypotenuse squared.
A line passes through the point (5,-2) and has a slope of -3
Answers
Answer: not sure
Step-by-step explanation: this: by this -
Equals this: ur mom
John buys some boxes of pencils and some packets of pens for people to use at a conference.
There are 40 pencils in a box.
There are 15 pens in a packet.
John gives one pencil and one pen to each person at the conference.
He has no pencils left.
He has no pens left.
What is the smallest number of boxes of pencils and smallest number of packets of pens that John bought?
Answers
In linear equation, He 3 boxes of pencils and 8 boxes of pens.
What are instances of linear equations?
Ax+By=C represents a two-variable linear equation in its standard form. A standard form linear equation is, for instance, 2x+3y=5.Finding both intercepts of an equation in this form is rather simple (x and y).When resolving systems of two linear equations, this form is also incredibly helpful.A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.He bought 3 boxes of pencils and 8 boxes of pens.
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120
Mulitples of 40: 40, 80, 120
This means that there are 120 people at the conference, and that he bought 3 boxes of pencils (40x3=120) and 8 boxes of pens (15x8=120)
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What is the answer to this question?
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The perimeter of the square BCDE is 8√2 cm.
How to find perimeter of a square?A square is a quadrilateral that has all its sides equal to each other. All the angles in a square are also equal.
Therefore, the perimeter of a square is the sum of the whole sides of the square.
perimeter of the square BCDE = 4l
area of triangle ABC = 2cm²
area of triangle ABC = 1 / 2 bh
2 = 1 / 2 bh
The diagonal of square bisect each other.
The base and height of the triangle ABC are the same.
bh = 4
b² = 4
b = √4
b = 2 cm
Therefore,
BC = √2² + 2²
BC = √8
BC = 2√2 cm
Hence,
perimeter of the square BCDE = 4(2√2)
perimeter of the square BCDE = 8√2 cm
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Under his cell phone plan, Julian pays a flat cost of $52 per month and $3 per gigabyte. He wants to keep his bill at $58 per month. Which tape diagram could be used to represent the context if gg represents the number of gigabytes of data Julian can use while staying within his budget?
Answers
The tape diagram to represent the context regarding the number of gigabytes of data Julian can use while staying within his budget is Tape D.
What is a tape diagram?A tape diagram simply has to do with a diagram that's used to illustrate the relationship between the numbers that are given.
In this case, Julian pays a flat cost of $52 per month and $3 per gigabyte and she wants to keep his bill at $58 per month.
This will be illustrated as:
let g = the number of gigabytes of data.
The expression will be:
52 + 3g = 58
The appropriate tape diagram is D.
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This question is not from a test. This is an extra credit MATHS assignment. Please help me if you can. If you do, thank you! :)
Answers
we have the equation
[tex]y=31sin5x+32[/tex]Find out the first derivative
[tex]\begin{gathered} y^{\prime}=(5)(31)c0s5x \\ y^{\prime}=155cos5x \end{gathered}[/tex]equate to zero the derivative, to find out the critical points
[tex]\begin{gathered} 155cos5x=0 \\ cos5x=0 \end{gathered}[/tex]The value of cosine is zero when the angle is 90, 270 degrees (pi/2 and 3pi/2)
so
[tex]\begin{gathered} 5x=\frac{\pi}{2} \\ \\ x=\frac{\pi}{10} \end{gathered}[/tex][tex]\begin{gathered} 5x=\frac{3\pi}{2} \\ \\ x=\frac{3\pi}{10} \end{gathered}[/tex]For x=pi/10
Find out the y-coordinate
[tex]\begin{gathered} y=31s\imaginaryI n\frac{5\pi}{10}+32 \\ \\ y=31sin\frac{\pi}{2}+32 \\ \\ y=31+32=63\text{ ft} \end{gathered}[/tex]Verify for x=3pi/10
[tex]\begin{gathered} y=31s\imaginaryI n5(\frac{3\pi}{10})+32 \\ \\ y=31s\imaginaryI n(\frac{3\pi}{2})+32 \\ y=-31+32=1\text{ ft} \end{gathered}[/tex]The maximum height is 63 fthoang has worked as a nurse at springfield general hospital for 6 years longer than her friend bill. four years ago, she had been at the hospital for twice as long. how long has each been at the hospital?
Answers
By solving the equation we can conclude that Bill worked 4 years and Hoang worked 10 years in the hospital.
What do we mean by equations?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, Hoang worked for 6 years longer than her friend.
Let, the time Bill worked in the hospital be 'x'.So, Hoang worked in the hospital will be 'x + 6'.She spent twice as much time in the hospital two years ago. Then:
x + 6 - 2 = 2x4 = xx = 4Hence, Bill worked for 4 years and Hoang worked (4+6) for 10 years in the hospital.
Therefore, by solving the equation we can conclude that Bill worked for 4 years and Hoang worked for 10 years in the hospital.
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a woman's boxing match consists of four 2-minute rounds, there is a 1-minute rest interval between each round. what information do you know that will help you find how long a boxing match lasts?
Answers
The total time for the boxing match will be 9 minutes.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a woman's boxing match consists of four 2-minute rounds, there is a 1-minute rest interval between each round.
The time of the match will be calculated as:-
Time = 2 x Total rounds + 1
Time = ( 2 x 4 ) + 1
Time = 8 + 1 = 9 minutes
Therefore, the total time for the boxing match will be 9 minutes.
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Find the inverse function in slope-intercept form f(x)=x-5
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:f{}^{-1}(x) = x +5 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
We need to find the inverse of given function; f(x) = x - 5
[tex]\qquad \tt \rightarrow \: y = x - 5[/tex]
here, write x in terms of y.
[tex]\qquad \tt \rightarrow \: x = y + 5[/tex]
replace x with [tex]{\tt{{f}^{-1} (x)} } [/tex] and y with x, you will get your required inverse function.
[tex]\qquad \tt \rightarrow \: f {}^{ - 1} (x) = x + 5[/tex]
And it's already in slope intercept form
[tex]\qquad \tt \rightarrow \: y = mx + c[/tex]
where, slope (m) = 1 and y intercept (c) = 5
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Please help for 100 points.
Answers
By using matrix operations, the resulting matrix is [tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex].
How to simplify a combination of matrices
In this problem we must simplify a combination of two matrices, this can be done by using properly the fundamental operations for matrices. Matrices are algebraic constructions characterized by a number of row and a number of columns. For instance, there is a matrix with two rows and three columns:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right][/tex]
There are two fundamental operations for matrices:
Sum - The respective elements of the same row and the same column of the matrix are summed:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] + \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right][/tex]
Where C(i, j) = A(i, j) + B(i, j), i is the row index and j is the column index.
Scalar mutiplication - Every element of the matrix is multiplied by a scalar:
[tex]2 \cdot \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right][/tex]
Where B(i, j) = k · A(i, j), k is the scalar.
Now we show the complete procedure to find the simplified expression:
[tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] Given
[tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] + (- 1) \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] Definition of subtraction
[tex]\left[\begin{array}{cc}4&8\\16&20\end{array}\right] + \left[\begin{array}{cc}- 1&- 2\\- 4&- 5\end{array}\right][/tex] Scalar multiplication
[tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex] Sum of matrices / Result
The simplifed form of the matrix is [tex]4 \cdot \left[\begin{array}{cc}1&2\\4&5\end{array}\right] - \left[\begin{array}{cc}1&2\\4&5\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}3&6\\12&15\end{array}\right][/tex].
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A penguin walks south. it completes the first 1/3 mile in 1/5 hour and continues walking at the same rate. what is the penguin's speed in miles per hour?
Answers
In distance, the penguin speed in mi/hr is 1.67mi/hr.
What is distance in math?
A measurement of the distance between two places along a line or line segment.the length or width between two objects, points, lines, etc. remoteness is the state or fact of something or someone being physically distant from another. A straight line in space It would take too long to walk seven miles in one hour. a distance; a space: The ship was encircled by a sizable body of water.Distance = 1/3 mile
Time = 1/5 hour
Speed of the penguin = Distance/Time taken
Substitute the given data into the speed formula;
Speed = (1/3)/(1/5)
Speed = 1/3 * 5/1
Speed = 5/3
Speed = 1.67miles/hour
Hence the penguin speed in mi/hr is 1.67mi/hr
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Estimate the quotient of 56.6 ÷ 7.21.
6
7
8
9
Answers
Answer:
56.6 estimated= 56
7.21 estimated=7
56/7= 8
pls mark as brainliest
Answer:
56.6 estimated= 56
7.21 estimated=7
56/7= 8
Step-by-step explanation:
the probability that it will rain is 0.42 what is the probability that it will not rain
Answers
Answer:
99.58
Step-by-step explanation:
Im not sure if its correct but the way I got the answer is 100-0.42
Lucy wants to drink 2L of water.
She has poured this amount into a jug. Between breakfast and lunch she pours 2 glasses of water each measuring 250ml.
Between lunch and her dinner she pours 3 glasses also measuring 250 ml.
How much water does she need to drink before going to bed?
Answers
The amount of water that Lucy should drink more is 750 ml.
How to calculate the value?From the information, Lucy between breakfast and lunch she pours 2 glasses of water each measuring 250ml. This will be:
= 250ml × 2
= 500ml
Between lunch and her dinner she pours 3 glasses also measuring 250 ml. This will be:
= 3 × 250ml
= 750 ml
Since Lucy wants to drink 2L of water, the amount needed to drink more will be:
= 2L - (750 + 500)
= 2000ml - 1250ml
= 750ml
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please help asap! i dont understand this
Answers
Answer:
y = -2x + 11
Step-by-step explanation:
When two lines are parallel, their gradients are the same. So the gradient of the line parallel to this equation will be -2 as well.
Now we substitute values from this point to find the rest of the equation :
y = -2x + c
3 = -2(4) + c
3 = -8 + c
c = 11
So the equation of the line parallel will be y = -2x + 11
Hope this helped and have a good day
Write an algebraic equation for the following problem and then solve it.
The population of a country in 2015 was estimated to be 321.4 million people. This was an increase of 17% from the population in 1990. What was the population of the country in 1990?
The algebraic equation is _=321.4
Answers
The population of the country in 1990 will be 274.7 million.
How to illustrate the information?From the information given, the population of a country in 2015 was estimated to be 321.4 million people and this was an increase of 17% from the population in 1990.
Therefore,since let the population on 1990 be x. Therefore, this will be illustrated as:
x + (17% × x) = 321.4
x + 0.17x = 321.4
1.17x = 321.4
Divide
x = 321.4 / 1.17
x = 274.7
The population is 274.7 million.
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Show all work. Round all percentages to the nearest tenth of a percent. Mr. McCullough paid 80 people to say they were his friends. After he paid them, 26 of them still did not claim to be his friend. What percent of the people he paid claimed to be his friends?
Answers
The percent of the people he paid claimed to be his friends is 67.5%
Given,
Mr. McCullough paid 80 people to say they were his friends.
and, After he paid them, 26 of them still did not claim to be his friend.
To find the percent of the people he paid claimed to be his friends
Now, According to the question:
Based on the given condition,
Formulate :
(80- 26) ÷ 80
Calculate:
(80- 26) / 80
= 54/80
Simplify
= 27/40
=0.675
Convert to percentage;
Multiply a number to both the numerator and the denominator
0.675 × 100/100
Calculate
67.5 / 100
= 67.5%
Hence, The percent of the people he paid claimed to be his friends is 67.5%.
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What is the pressure when 650N is applied over 40m2?
Answers
Answer:
16.25 pascal
Step-by-step explanation:
pressure=force/area
pressure=650/40
pressure=16.25 pascal
need to show my work and find the surface area
Answers
4) The surface area of the square pyramid is; 145 ft²
5) The surface area of the rectangular prism is; 948 ft²
How to find the surface area of regular shapes?
4) For the square pyramid, we see that the faces have been broken down into 4 equal rectangles and one square base.
We know that;
Area of triangle = 1/2 * base * height
Thus
Area of 4 triangles = 4(1/2 * 5 * 12) = 120 ft²
Area of square = 5 * 5 = 25 ft²
Total surface area = 120 + 25 = 145 ft²
5) The surface area of a rectangular prism is;
A = 2(wl + hl + hw)
Thus, Area = 2((20 * 3) + (20 * 18) + (18 * 3))
Area = 2(474)
Surface area = 948 ft²
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Which expressions are equivalent to 25? Choose ALL that apply.
6-6-6-6-6-6
2-6
12-12
2-2-2-2-2-2
4-16
8-8
Answers
None of the given expressions are equivalent to 25.
What is an expression?
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (operands), variable, operations, units, brackets, punctuation, and groups can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's sequence of operations and other features.
Many writers make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects. However, in contemporary mathematics, and particularly in computer algebra, formulae are seen as expressions that, depending on the values supplied to the variables present in the expressions, can be evaluated to true or false.
The expressions are solved as follows
6-6-6-6-6-6 = -24
2-6 = -4
12-12 = 0
2-2-2-2-2-2 = -8
4-16 = -12
8-8 = 0
Hence, none of the expressions are equivalent to 25.
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please help asap! i dont know what to do
Answers
rise over run to find the slope
y = mx+b
we rose 1 and went over by 2
which means the equation is 1/2 x or 0.5x
Factorise 5x^2-28x+23=0
Answers
[tex]5 {x}^{2} - 28x + 23 = 0 \\ \\ 5 {x}^{2} - 23x - 5x + 23 = 0 \\ (5 {x}^{2} - 23x) - (5x - 23) = 0 \\ x(5x - 23) - (5x - 23) = 0 \\ (x - 1)(5x - 23) = 0 \\ \\ x - 1 = 0 \\ \\ or \\ \\ 5x - 23 = 0 \\ \\ \\ x = 1 \\ \\ or \\ \\ x = \frac{23}{5} [/tex]
ATTACHED IS THE SOLUTION
3/4 divided by 2/x simplified
Answers
Answer:3
Step-by-step explanation:
(-3/4)/(-2/8)=(-3/4)(-8/2)=(-3/4)(-4)=3