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Answer:
-1/5
Step-by-step explanation:
[tex]\dfrac{1}{3z}=-\dfrac{5}{6}+\dfrac{1}{6z}\qquad\text{given}\\\\2=-5z+1\qquad\text{multiply by $6z$}\\\\1=-5z\qquad\text{subtract 1}\\\\\boxed{-\dfrac{1}{5}=z}\qquad\text{divide by $-5$}[/tex]
17. A hospital trauma center is going to be built equidistant from three cities. Positioned on a grid, the cities would be located at (1, 5), (2, -2), and (-6, -2). What are the coordinates of the location where the trauma center should be built? A (-2, -1) C (2, -1) B (-2, 1) D (2.1)
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Answer:
B (-2, 1)
Step-by-step explanation:
The trauma center will be located at the circumcenter of the triangle. That is the point of intersection of the perpendicular bisectors of the sides. Once the points are graphed, it is pretty easy to see where that will be. It is on the line x=-2, above the x-axis. Only one answer choice is appropriate:
(-2, 1)
_____
Line AC has a slope of 1. Those points are separated by 7 units horizontally and vertically, so the midpoint is 3.5 units horizontally and vertically from either point, at (-2.5, 1.5). The perpendicular line with slope -1 through that point will intersect x=2 at y=1.
Which is the graph of Y = log(-x)?
5
4
3
3
N
1
1
A++
-4 -3 -2 -11
1 2 3 4 5 6 7 8 9
-2
-3
-4
ASAP
Exercise 6.2
1.
a.
The total cost function is given by C = 100 - 5x + 7x2, find
the average cost and marginal cost.
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Answer:
average cost = 7x -5 +100/xmarginal cost = 14x -5Step-by-step explanation:
The average cost is the total cost divided by the number of units produced:
average cost = C/x = 100/x -5 +7x
__
The marginal cost is the derivative of the total cost function.
marginal cost = -5 +14x
Some friends are sharing a pizza. If each person gets 1/8 of the pizza, what percent of the pizza does each person get?
Answer:
1/8=12.50%
Step-by-step explanation:
Take the pizza as a whole = 100
Then consider 1/8 of 100
or 1/8 * 100
= 1/4 * 50
= 1/2 * 25
= 12.50
Therefore it is 12.50%
Find the range of the function represented by the list of ordered pairs below.
{(−9,4),(−6,3),(−3,0),(−2,−4)}
Answer:
(4,3,0,-4)
May this
help you
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!! Part 2.
2. What is a determinant and what role does it play with matrices (Hint: What does a determinant of 0 mean)? How can this be used when solving systems of equations?
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Explanation:
Definition
The determinant of a square matrix is a single number that is computed (recursively) as the sum of products of the elements of a row or column and the determinants of their cofactors. The determinant of a single element is the value of that element.
The cofactor of an element in an n by n matrix is the (n-1) by (n-1) matrix that results when the row and column of that element are deleted. The "appropriate sign" of the element is applied to the cofactor matrix. The "appropriate sign" of an element is positive if the sum of its row and column numbers is even, negative otherwise. (Rows and columns are considered to be numbered 1 to n in an n by n matrix.)
Uses
The inverse of a square matrix is the transpose of the cofactor matrix, divided by the determinant. Hence if the determinant is zero, the inverse matrix is undefined. This means any system of equations the matrix might represent will have no distinct solution. (There may be zero solutions, or there may be an infinite number of solutions. The determinant by itself cannot tell you which.)
Cramer's Rule for the solution of linear systems of equations specifies that the value of any given variable is the ratio of the determinants of two matrices. The numerator matrix is the original matrix with the coefficients of the variable replaced by the constants in the standard-form equations; the denominator matrix is the original coefficient matrix. This rule lets you solve a system of 3 equations in 3 variables by computing 3+1 = 4 determinants, for example.
Let's look at an example.
If we wanted to solve this system of equations
[tex]\begin{cases}2x-y = 2\\x+y = 7\end{cases}[/tex]
Then it's equivalent to solving this matrix equation
[tex]\begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}2\\7\end{bmatrix}[/tex]
We can then further condense that into the form
[tex]Aw = B[/tex]
Where,
[tex]A = \begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\\\\w = \begin{bmatrix}x\\y\end{bmatrix}\\\\B = \begin{bmatrix}2\\7\end{bmatrix}[/tex]
------------------------------------------
To solve the matrix equation Aw = B, we could compute the inverse matrix [tex]A^{-1}[/tex] and left-multiply both sides by this to isolate w.
So we'd go from [tex]Aw=B[/tex] to [tex]w = A^{-1}*B[/tex]. The order of multiplication is important.
For any 2x2 matrix of the form
[tex]P = \begin{bmatrix}a & b\\c & d\end{bmatrix}[/tex]
its inverse is
[tex]P^{-1} = \frac{1}{ad-bc}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}[/tex]
Notice the expression ad-bc in the denominator of that fractional term outside. This [tex]ad-bc[/tex] expression represents the determinant of matrix P. Some books may use the notation "det" to mean "determinant"
[tex]P^{-1} = \frac{1}{\det(P)}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}[/tex]
or you may see it written as
[tex]P^{-1} = \frac{1}{|P|}\begin{bmatrix}d & -b\\-c & a\end{bmatrix}[/tex]
Those aren't absolute value bars, even if they may look like it.
Based on that, we can see that the determinant must be nonzero in order to compute the inverse of the matrix. Consequently, the determinant must be nonzero in order for Aw = B to have one solution.
If the determinant is 0, then we have two possibilities:
There are infinitely many solutions (aka the system is dependent)There are no solutions (the system is inconsistent)So a zero determinant would have to be investigated further as to which outcome would occur.
------------------------------------------
Let's return to the example and compute the inverse (if possible).
[tex]A = \begin{bmatrix}2 & -1\\1 & 1\end{bmatrix}\\\\A^{-1} = \frac{1}{2*1 - (-1)*1}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}\\\\A^{-1} = \frac{1}{3}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}\\\\[/tex]
In this case, the inverse does exist.
This further leads to
[tex]w = A^{-1}*B\\\\w = \frac{1}{3}\begin{bmatrix}1 & 1\\-1 & 2\end{bmatrix}*\begin{bmatrix}2\\7\end{bmatrix}\\\\w = \frac{1}{3}\begin{bmatrix}1*2+1*7\\-1*2+2*7\end{bmatrix}\\\\w = \frac{1}{3}\begin{bmatrix}9\\12\end{bmatrix}\\\\w = \begin{bmatrix}(1/3)*9\\(1/3)*12\end{bmatrix}\\\\w = \begin{bmatrix}3\\4\end{bmatrix}\\\\\begin{bmatrix}x\\y\end{bmatrix} = \begin{bmatrix}3\\4\end{bmatrix}\\\\[/tex]
This shows that the solution is (x,y) = (3,4).
As the other person pointed out, you could use Cramer's Rule to solve this system. Cramer's Rule will involve using determinants and you'll be dividing over determinants. So this is another reason why we cannot have a zero determinant.
a playing card is chosen at random from a standard deck of cards. what is the probability of choosing 5 of diamonds or one jack
Answer:
1/52
Step-by-step explanation:
Measure and record the lengths of the sides of ABC and FGH.
Answer:
can you please send the picture of the diagram.
Step-by-step explanation:
Answer:
ABC:
AB-5 units
BC-12.65 units
AC-15 units
FGH:
FG-5 units
GH-12.65 units
FH-15 units
Step-by-step explanation:
PLATO SAMPLE ANSWER
how to solve the matrix equation for matrix Y.simplify all elements
[tex]Y\left[\begin{array}{ccc}-1&-4\\0&-5\\\end{array}\right] = \left[\begin{array}{ccc}5&-5\\8&8\\\end{array}\right][/tex]
Given YA = B, you can solve for Y by multiplying by A ⁻¹ on the right (on both sides of the equation). So we have
YA = B ==> (YA) A ⁻¹ = BA ⁻¹ ==> Y (AA ⁻¹) = BA ⁻¹ ==> Y = BA ⁻¹
provided that the inverse of A exists. In this case, det(A) = 5 ≠ 0, so the inverse does exist, and
[tex]A=\begin{bmatrix}-1&-4\\0&-5\end{bmatrix} \implies A^{-1}=\dfrac1{\det(A)}\begin{bmatrix}-5&0\\4&-1\end{bmatrix} = \begin{bmatrix}-1&0\\\frac45&-\frac15\end{bmatrix}[/tex]
Then
[tex]Y=\begin{bmatrix}5&-5\\8&-8\end{bmatrix}A^{-1} = \begin{bmatrix}-5&5\\-8&\frac{24}5\end{bmatrix}[/tex]
Find the equation of the line passing through the point (-1,2)
and the points of intersections of the line 2x - 3y + 11 = 0 and
5x + y + 3 = 0
Answer:
[tex]y=-5x-3[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).
To solve for the equation of the line, we would need to:
Find the point of intersection between the two given linesUse the point of intersection and the given point (-1,2) to solve for the slope of the lineUse a point and the slope in [tex]y=mx+b[/tex] to solve for the y-interceptPlug the slope and the y-intercept back into [tex]y=mx+b[/tex] to achieve the final equation1) Find the point of intersection between the two given lines
[tex]2x - 3y + 11 = 0[/tex]
[tex]5x + y + 3 = 0[/tex]
Isolate y in the second equation:
[tex]y=-5x-3[/tex]
Plug y into the first equation:
[tex]2x - 3(-5x-3) + 11 = 0\\2x +15x+9 + 11 = 0\\17x+20 = 0\\17x =-20\\\\x=\displaystyle-\frac{20}{17}[/tex]
Plug x into the second equation to solve for y:
[tex]5x + y + 3 = 0\\\\5(\displaystyle-\frac{20}{17}) + y + 3 = 0\\\\\displaystyle-\frac{100}{17} + y + 3 = 0[/tex]
Isolate y:
[tex]y = -3+\displaystyle\frac{100}{17}\\y = \frac{49}{17}[/tex]
Therefore, the point of intersection between the two given lines is [tex](\displaystyle-\frac{20}{17},\frac{49}{17})[/tex].
2) Determine the slope (m)
[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the two points [tex](\displaystyle-\frac{20}{17},\frac{49}{17})[/tex] and (-1,2):
[tex]m=\displaystyle \frac{\displaystyle\frac{49}{17}-2}{\displaystyle-\frac{20}{17}-(-1)}\\\\\\m=\displaystyle \frac{\displaystyle\frac{15}{17} }{\displaystyle-\frac{20}{17}+1}\\\\\\m=\displaystyle \frac{\displaystyle\frac{15}{17} }{\displaystyle-\frac{3}{17} }\\\\\\m=-5[/tex]
Therefore, the slope of the line is -5. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-5x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-5x+b[/tex]
Plug in the point (-1,2) and solve for b:
[tex]2=-5(-1)+b\\2=5+b\\-3=b[/tex]
Therefore, the y-intercept is -3. Plug this back into [tex]y=-5x+b[/tex]:
[tex]y=-5x+(-3)\\y=-5x-3[/tex]
I hope this helps!
Find the arc length of the 3/4 of a circle with a radius of 5
Answer:
7.5 pi
Step-by-step explanation:
The formula for arc length of a sector is denoted as
[tex]\frac{x}{360}2\pi r[/tex], where x is the central angle of the sector.
Since the sector is 3/4 of a circle, the central angle will be 3/4 of 360 degrees.
3/4 of 360 is 270, so we have our central angle. We also have our radius which we can plug into the formula.
[tex]\frac{270}{360}2(5)\pi[/tex]
2 times 5 is equal to 10, and 270/360 simplifies to 3/4. 3/4 times 10 is equal to 7.5, so the answer is 7.5 pi
c) The exponential model A = 513.5e0.009t describes the population, A, of a
country in millions, t years after 2005. Use the model to determine when the
population of the country will be 602 million.
Answer:
zotfnKhxitfupoydkfslfndckv
x^{2} +y^{2} =?
cho mình hỏi với
Answer:
[tex]{ \sf{ {x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy }}[/tex]
Step-by-step explanation:
[tex]{ \tt{ {(x + y)}^{2} = (x + y)(x + y) }} \\ { \tt{ {(x + y)}^{2} = ( {x}^{2} + 2xy + {y}^{2}) }} \\ { \tt{( {x}^{2} + {y}^{2} ) = {(x + y)}^{2} - 2xy}}[/tex]
The side-by-side stemplot below displays the arm spans, in centimeters, for two classes.
A stemplot titled Arm Span (centimeters). For Class A, the values are 148, 151, 153, 155, 156, 159, 161, 162, 164, 165, 169, 169, 170, 171, 175, 176, 179, 179, 180, 182, 183, 186, 186, 190. For Class B, the values are 153, 155, 16, 160, 162, 162, 162, 163, 163, 165, 166, 167, 170, 173, 180, 181, 182, 189, 192, 202.
Which statement correctly compares the variability of the arm spans for Class A to that of Class B?
The arm spans for Class A have more variability than the arm spans for Class B.
The arm spans for Class B have less variability than the arm spans for Class A.
The arm spans for Class A have less variability than the arm spans for Class B.
The arm spans for Class B have about the same variability as the arm spans for Class A.
Answer:
The answer is in the picture below
Step-by-step explanation:
Sorry just realised the answers were different ;-;
Answer:
The arm spans for Class A are roughly symmetric, while those for Class B are skewed left.
Step-by-step explanation:
write the equation of the graph, y=? SOMEBODY PLEASE HELP
Answer:
[tex]y=\left(6\right)^{x}\ -3[/tex]
Step-by-step explanation:
slope of (30, 600) (75, 1050)
Answer:
y2-y1/x2-x1
y2: 1050
y1:600
x2:75
x1:30
1050-600=450
75-30=45
450/45=10
slope is 10
Answer:
let:
A(30, 600)=(x1,y1)
B((75, 1050)=(x2,y2)
now,
[tex]slope(m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] = \frac{1050 - 600}{75 - 30} [/tex]
[tex] = \frac{450}{ 45} [/tex]
[tex] = \frac{10}{1} [/tex]
John borrowed a certain amount of money from Tebogo at a simple interest rate of 8,7% per year. After five years John owes Tebogo R10 000.Calculate how much money John initially borrowed
Both before and after a recent earthquake, surveys were conducted asking voters which of the three candidates they planned on voting for in the upcoming city council election. Has there been a change since the earthquake? Use a level of significance of 0.05. Table shows the results of the survey. Has there been a change in the distribution of voter preferences since the earthquake?
Peter Alan Sui
Before 1838 418 1475
After 1420 329 1140
What is the chi-square test-statistic for this data?
χ2=_____.
Answer:
0.05547
Step-by-step explanation:
Given :
_____Peter __ Alan __ Sui__total
Before 1838 __ 418 ___1475 _3731
After _ 1420 __ 329 ___1140_2889
Total _3258 __ 747 __ 2615 _6620
The expected frequency = (Row total * column total) / N
N = grand total = 6620
Using calculator :
Expected values are :
1836.19 __ 421.006 __ 1473.8
1421.81 ___325.994__ 1141.2
χ² = Σ(Observed - Expected)² / Expected
χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)
χ² = 0.05547
-1/5y+7=7
What is the value of y?
4. A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution. How many liters of the 60% solution must be used?
SHOW YOUR WORK
Given:
A solution of 60% fertilizer is to be mixed with a solution of 21% fertilizer to form 234 liters of a 43% solution.
To find:
The quantity of the 60% solution in the mixture.
Solution:
Let x be the quantity of the 60% solution and y be the quantity of the 21% solution.
Quantity of mixture is 234. So,
[tex]x+y=234[/tex]
[tex]x=234-y[/tex] ...(i)
The mixture has 43% fertilizer. So,
[tex]\dfrac{60}{100}x+\dfrac{21}{100}y=\dfrac{43}{100}\times 234[/tex]
Multiply both sides by 100.
[tex]60x+21y=10062[/tex] ...(ii)
Using (i) and (ii), we get
[tex]60(234-y)+21y=10062[/tex]
[tex]14040-60y+21y=10062[/tex]
[tex]-39y=10062-14040[/tex]
[tex]-39y=-3978[/tex]
Divide both sides by -39.
[tex]\dfrac{-39y}{-39}=\dfrac{-3978}{-39}[/tex]
[tex]y=102[/tex]
Putting this value in (i), we get
[tex]x=234-102[/tex]
[tex]x=132[/tex]
Therefore, 132 liters of the 60% solution must be used.
Help please, but more importantly, I am really trying hard to figure out how, you arrive at the answer. Thanks in advance!
A recent social survey asked respondents whether they like Apple or Microsoft. The responses were recorded in the following table.
Male Female Total
Apple 152 194 346
Microsoft 168 126 294
Total 320 320 640
a. A respondent is randomly selected among those that prefer Apple, what is the probability that the respondent will be female?
b. A respondent is randomly selected among those that are Male, what is the probability that the respondent prefers Apple?
c. What is the relative frequency of a female who prefers Microsoft?ocial survey asked respondents whether they like Apple or Microsoft. The responses were recorded in the following table.
Male Female Total
Apple 152 194 346
Microsoft 168 126 294
Total 320 320 640
a. A respondent is randomly selected among those that prefer Apple, what is the probability that the respondent will be female?
b. A respondent is randomly selected among those that are Male, what is the probability that the respondent prefers Apple?
c. What is the relative frequency of a female who prefers Microsoft?
Answer:
Step-by-step explanation:
#1
A) P(FEMALE|APPLE)
apple total = 346
apple/female = 194
194/346 = .56 = 56 %
B) P(APPLE|MALE)
male total = 320
apple male = 152
152/320 = .475 = 47.5%
C) female prefer Microsoft
152:168 = 76:84 = 38:42 = 19:21
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I need help
With these
Answer:
"A"
Step-by-step explanation:
a+b >c
a+c>b
b+c>a
~~~~~~~~~~~~
A. T,T,T
B. T,T,F
C. T,F,T
GIVING 25 POINTS AND BRAINIER IF ANSWERED!
What is one thing you would not do when finding the question in a word problem?
A. Look for a problem similar to the word problem you are trying to solve.
B. The question may not be directly stated.
C. So you can understand what the facts are in the word problem.
D. To define your strategy or game plan to solve the word problem.
Answer:
B. The question may not be directly stated.
Find the value of each determinant
Answer:
−4304
Step-by-step explanation:
1. The given determinant is :
[tex]\begin{vmatrix}7 &31 \\ 142& 14\end{vmatrix}[/tex]
We need to find its determinant . It can be solved as follows :
[tex]\begin{vmatrix}7 &31 \\ 142& 14\end{vmatrix}=7(14)-142(31)\\\\=-4304[/tex]
So, the value of determinant is equal to −4304.
Answer:
A= -4269
B= 1768
C= 647.36
Step-by-step explanation:
Which graph shows the quadratic function y = 3x2 + 12x + 10? (5 points)
The following graph is labeled A: A four quadrant graph with a parabola opening up, passing through the points negative 3, 1, negative 2, negative 2, and negative 1, 1 with the vertex at 2, negative 2. The following graph is labeled B: A four quadrant graph with a parabola opening up, passing through the points 1, 4, 2, 1, and 3, 4 with the vertex at 2, 1. The following graph is labeled C: A four quadrant graph with a parabola opening up, passing through the points negative 3, 5, negative 2, 2, and negative 1, 5 with the vertex at negative 2, 2. The following graph is labeled D: A four quadrant graph with a parabola opening up, passing through the points 1, 1, 2, negative 2, and 3, 1 with the vertex at 2, negative 2.
Answer:
The correct graph is A.
Answer:
A i got it right
Step-by-step explanation:
Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. They randomly survey 401 drivers and find that 294 claim to always buckle up. Construct a 90% confidence interval for the population proportion that claim to always buckle up. Use interval notation, for example, [1,5].
Answer:
[0.6969, 0.7695]
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
They randomly survey 401 drivers and find that 294 claim to always buckle up.
This means that [tex]n = 401, \pi = \frac{294}{401} = 0.7332.
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7332 - 1.645\sqrt{\frac{0.7332*0.2668}{401}} = 0.6969[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.7332 + 1.645\sqrt{\frac{0.7332*0.2668}{401}} = 0.7695[/tex]
The 90% confidence interval for the population proportion that claim to always buckle up is [0.6969, 0.7695]
PLEASE HELP THIS IS DUE ASAP (answer in decimal!!!!)
The table below shows the educational attainment of a country's population, aged 25 and over. Use the data in the table, expressed in millions to find the probability that a randomly selected citizenaged 25 or over , was a man with 4 years of college (or more)
Answer:
The answer is "[tex]\bold{\frac{22}{171}}[/tex]"
Step-by-step explanation:
There are 22 million males that have completed four years of undergraduate, according to the data below: (or more). This is predicated on a population of 171 million.
The chances we're searching about [tex]\frac{(22\ million)}{(171\ million)} = \frac{22}{171}[/tex]
however
This proportion could be further reduced because 22 and 171 have no common features (other than 1).
For each kilogram of a persons weight 2.5 milligrams of a drug is to be given. what dosage should be given to a child who weighs 84 pounds? Use the fact that 1 lb = 0.45 kg
Answer:
A child who weighs 84 pounds should be given 94.5 milligrams of the drug.
Step-by-step explanation:
Givens:
1kg=2.5 milligrams of dosage
Weight of child = 84 pounds
1 pound = 0.45 kg
Solution:
Convert pounds to kilograms --> 84lbs*0.45kg = 37.8 kg
Convert weight to dosage --> 37.8kg * 2.5 mg = 94.5 mg of dosage.
here's a graph of a linear function write the equation that describes the function express it in slope-intercept form
Answer:
y = 3/4 x - 3
Step-by-step explanation:
the slope of a line is the factor of x in the equation and is expressed as ratio of y/x : defining how many units y changes, when x changes a certain number of units.
in our graph here we can see that when increasing x from e.g. 0 to 4 (the x-axis intercept point, a change of +4), y changes from -3 to 0 (a change of +3).
so, the slope and factor of x is y/x = 3/4
and for x=0 we get y=-3 as y-axis intercept point.
so, the line equation is
y = 3/4 x - 3
