Multiply the numerator and denominator by the conjugate.
Exact Form:
−10−5√3
Decimal Form:
−18.66025403...
How to solve x3 6x2 11x 6 0?
The solutions of the cubic equation x³ + 6x² + 11x + 6 = 0 will be -1, -2, and -3.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The equation is given below.
x³ + 6x² + 11x + 6 = 0
Factorize the equation, then we have
x³ + 6x² + 11x + 6 = 0
x³ + x² + 5x² + 5x + 6x + 6 = 0
x²(x + 1) + 5x(x + 1) + 6(x + 1) = 0
(x + 1)(x² + 5x + 6) = 0
(x + 1)[x² + 3x + 2x + 6] = 0
(x + 1)(x + 3)(x + 2) = 0
x = -1, -2, -3
The solutions of the cubic equation x³ + 6x² + 11x + 6 = 0 will be -1, -2, and -3.
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A man i four time a old a hi on. In 5 year’ time he will be three time a old a hi on. What i the preent age of the on in year?
The present age of the Son will be 10 years and Father's present age will be 40 years.
We will solve this problem with the concept of age.
Age is referred to as the length of time that a person or item has been alive. Problems based on age generally consist of information about the ages of two or more people and a relation between their ages in the present or future or past. Using this information it is asked to calculate the ages of one or more people in the present past or future.
The important thing to keep in mind while solving problems of ages.
If the present age is y, then n times the present age = ny.
If the present age is x, then age n years later/hence = x + n.
If the present age is x, then the age n years ago = x – n.
The ages in a ratio a: b will be ax and bx.
If the current age is y, then 1/n of the age is y/n.
According to our problem:
Let the present age of the son = x
The present age of the father = 4x
After 5 years
Son age = x+5.
Father age = 4x+5
According to the condition =
4x+5 = 3(x+5)
4x+5 = 3x + 15
x = 10
Therefore the present age of the son will be x = 10 years and the father will be 4x= 40 years.
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4 of 64 of 6 Questions
Question
A new doughnut shop lost $624 during its first 13 days of business. If it lost the same amount of money each day, what was the loss each day?
Which choice shows the correct quotient and answer?
(−624)÷13=−48; The doughnut shop lost $48 each day.
(−624)÷13=8,112; The doughnut shop made a profit of $8,112 each day.
(−624)÷13=48; The doughnut shop made a profit of $48 each day.
(−624)÷13=−611; The doughnut shop lost $611 each day.
If a new doughnut shop lost $624 during its first 13 days of business. If it lost the same amount of money each day, the loss each day is: A. (−624)÷13=−48; The doughnut shop lost $48 each day.
How to find the loss per day?Given data:
Amount lost = $624
Days of business = 13 days
Now let determine the amount that the doughnut shop lost per day
Loss per day = Amount lost / Days of business
Loss per day = - $624/13 days
Loss per day = -$48
Therefore we can conclude that the correct option is A
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At which roots does the graph cross the x axis 0?
the root is zero when the graph crosses the X-axis.
what is root?The word root used in mathematics to express a solution of equation.
The root is written in a number or algebraic form.
What happens when graph cross the x axis?When graph crosses the x axis the root of an equation become zero.
hence, we get zero value while crossing the X-axis
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Tonya and Jill each opened savings accounts. Tonya started with $60 and deposited $20 each month.Jill started with $20 and deposited $40 each month. If they each continue to make deposits at the same rate when will they have the same amount of money
Two months would pass before they received the same sum of money.
What does same rate mean in math?In mathematics, equivalence is a relationship that states that two quantities have the same value or that two mathematical expressions reflect the same mathematical object. A = B is the symbol for the equality of A and B, and it is also pronounced as A = B.
Briefing:Total amount saved = amount started with + (amount deposited per month x number of months)
Amount saved by Tonya = $60 + $20m
Amount saved by Jull = $20 + $40m
The two aforementioned equations would be equivalent if they both saved the same amount of money:
60 + 20m = 20 + 40m
Take the below actions to find the value of m:
60 - 20 = 40m - 20m
40 = 20m
m = 40 / 20
m = 2
In the calculation that shows how much money Tonya has overall saved, replace m with:
$60 + $20(2)
$60 + $40 = $100
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24) Use approximation to find the square root of the given number to the nearest hundredth.
√20
Answer:
The square root of 20 is 4.472.
Step-by-step explanation:
y varies jointly as x and z. If y = -40 when x = -2 and z = -1, what is the variation equation?
Answer:
-20
Step-by-step explanation:
if y varies jointly as x and z, then y = k * x * z
where k is the variation constant.
-40 = k * -2 * -1
-40 =2k
k = -20
How do you tell if a limit is coming from the right or left?
To tell if a limit is coming from the right or left, you need to look at the sign of the x-value in the limit equation. If the x-value is positive, the limit is coming from the right. If the x-value is negative, the limit is coming from the left.
To determine which side a limit is coming from, you must first examine the x-value in the limit equation. If the x-value is positive, then the limit is coming from the right side. This is because when the x-value is positive, it is approaching from the positive side of the number line. On the other hand, if the x-value in the limit equation is negative, then the limit is coming from the left side. This is because when the x-value is negative, it is approaching from the negative side of the number line. It is important to note that the sign of the x-value in the limit equation indicates which side the limit is coming from.
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The length of segment ef is 8 units and the length of segment ed is 10 units. Find the length of segment fa. Explain or show your reasoning.
If the length of segment ef is 8 units and the length of segment ed is 10 units. The length of segment fa is 6 units.
How to find the length of segment?Using Pythagoreans theorem formula to find the length of segment
c² = √a² + b²
Where:
c = Length
a = 10 units
b = 8 units
Let plug in the formula
c² = √10² - 8²
c² = √100 - 64
c² = √36
c = 6 units
Therefore we can conclude that the length is 6 units.
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What is example of distributive?
An example of distributive property is 3 × (4 + 7) = (3 × 4) + (3 × 7).
Distributive Property is a property of multiplication and it is related with the distribution of numbers.
It states that the product of three numbers do not change even if the distribution of numbers are changed.
The distributive property of multiplication states that:
a × (b + c) = (a × b) + (a × c).
Let us verify it with help of an example.
3 × (4 + 7) = (3 × 4) + (3 × 7)
Taking L.H.S
3 × (4 + 7) = 3 × 11 = 33
Taking R.H.S
(3 × 4) + (3 × 7) = 12 + 21 = 33
Therefore, L.H.S = R.H.S
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it takes 8 minutes for byron to fill the kiddie pool in the backyard using only a handheld hose. when his younger sister is impatient, byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. if the hose and sprinkler are used together, it takes 5 minutes to fill the pool. which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?startfraction 5 over 8 endfraction plus 5 r equals 8. 5r
The equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone is 5(8) + 5r = 1.
Simplify surely approach to make it simple. In mathematics, surely or simplification is lowering the expression/fraction/trouble in a less difficult form. It makes the trouble clean with calculations and solving.
Let r be the rate in parts per minute at which the lawn sprinkler would fill the pool if use alone then. If the handheld hose and the lawn sprinkler are used together, we have this equation:
5/r + 5/8 = 1
Simplifying this expression,
5(8) + 5r = 1
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Are these parallel, perpendicular, or neither y= --2x+4 and -5x+10y=5
NEED HELP ASAP!!!!
need a quick answer
Answer:
-14
Step-by-step explanation:
Mel slides down waterslide A,
and Victor slides down waterslide B. After 2 seconds, Mel was 50 feet in
the air, and after 5 seconds, she was 35 feet in the air. After 1 second, Victor was 60 feet in the air, and
after 4 seconds, he was 50 feet in the air. Who was descending at a
faster rate?
Mel: (2, 50) and (5, 35)
Victor: (1, 60) and (4, 50)
Mel's rate of change is
second.
That means that her height in the air decreases
feet every
Victor's rate of change is
second.
That means that his height in the air decreases _
feet every
DONE
Intro
0 000
Answer:
Step-by-step explanation:
answer:
Mel was descending at a faster rate
Mel's rate of change is negative. That means that your height in the air decreases 5 feet every second.
Victor's rate of change is negative. That means that his height in the air decreases 3.33 feet every second.
Answer:
Mel (2, 50) and (5, 35)Victor (1, 60) and (4, 50)
Step-by-step explanation:
Edge 2020.
Simplify quantity 9 x squared plus 12 end quantity over 6 (5 points)
By distributing the division, we will get the simplified expression:
(3/2)*x² + 2
How to simplify the quantity?Here we have the following quadratic expression:
(9x² + 12)/6
Remember that the division is distributive, then we can rewrite:
(9x² + 12)/6 = 9x²/6 + 12/6
Now we can just simplify the two fractions.
(9x² + 12)/6 = (9/6)*x² + 2
= (3/2)*x² + 2
This is the most we can simplify the given expression.
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How do you tell if the function is increasing or decreasing?
A function is increasing if the function value increases on increasing the input value and the function is decreasing if the function value decreases on increasing the input value.
We know that a function is a relation between input and output values where each input has exactly one output.
Consider a function y = f(x)
For a given function if the value of y increases on increasing the value of x, then the function is called as an increasing function
If the y-value decreases on increasing the value of x, then the function is called as a decreasing function.
Another method is that if a function f(x) is differentiable on an open interval, we calculate the derivative of function f(x)
If the derivative f′(x) > 0 on an open interval, then function f(x) is increasing on that interval.
If the derivative f′(x) < 0 on an open interval, then function f(x) is decreasing on that interval.
Therefore, if the output value of function increases on increasing the input value then the function is an increasing function and if the output value of function decreases on increasing the input value then the function is an decreasing function.
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A guidance counselor wants to determine if there is a relationship between a student’s number of absences, x, and their grade point average (gpa), y. the given data list the number of absences and gpas for 15 randomly selected students. using technology, what is the value of r2? a. –0.56
b. –0.32
c. 0. 32
d. 0.56
Linear regression is used to model the linear relationship between two variables and r2 measures the strength of this relationship. It is calculated by squaring the correlation coefficient, which is a measure of the strength and direction of the relationship.
To determine the value of r2, you can use technology to perform a linear regression analysis on the given data. Linear regression is a statistical method used to model the linear relationship between two variables, x and y. The value of r2, also known as the coefficient of determination, measures the strength of the relationship between x and y and indicates how well the model fits the data.
The value of r2 is calculated using the following formula:
r2 = (Correlation coefficient)2
The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the relationship between two variables. It is calculated using the following formula:
r = ∑(x - x')(y - y') / √[∑(x - x')2 ∑(y - y')2]
where x' and y' are the means of the x and y variables, respectively, and ∑ indicates the sum of the values.
To determine the value of r2, you would first need to calculate the correlation coefficient using the given data. Once you have calculated the correlation coefficient, you can then square it to get the value of r2.
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You can use technology to do a linear regression analysis on the supplied data to find the value of r2. A statistical technique called linear regression is used to simulate the linear relationship between two variables, x and y. The strength of the link between x and y is measured by the coefficient of determination, or r2, which also serves as a measure of how well the model fits the data.
The value of r2 is calculated using the following formula:
r2 = (Correlation coefficient)2
The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the relationship between two variables. It is calculated using the following formula:
r = ∑(x - x')(y - y') / √[∑(x - x')2 ∑(y - y')2]
where x' and y' are the means of the x and y variables, respectively, and ∑ indicates the sum of the values.
You must first compute the correlation coefficient using the provided data in order to obtain the value of r2. Once the correlation coefficient has been determined, you can square it to obtain the value of r2.
if 4x ≤ g(x) ≤ 2x4 − 2x2 + 4 for all x, evaluate lim x→1 g(x).
The value of expression lim x→1 g(x) is 4.
In mathematics, a limit is a point at which a function becomes close to producing the desired result for the given input values. Limits are necessary for calculus and mathematical analysis and are also needed to establish integrals, derivatives, and continuity. It is used during the analysis process and continually thinks about how the function will act in a particular situation. The idea of the limit of a topological net broadens the definition of the limit of a sequence and relates it to the limit and direct limit in the theory category.
Given expression,
[tex]4x\leq g(x)\leq2x^{4}-2x^{2} +4[/tex]
For x → 1
4x = 4(1)
= 4
[tex]2x^{4}-2x^{2} +4[/tex] = 2(1)-2(1)+4
= 4
Hence, the value of lim x→1 g(x) is 4.
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Which of the following equations has no real roots a X² 4x 3 √ 2?
The equation that has no real roots is 3x² + 4√3x + 4.
Option D is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
If the discriminant of the equation is less than zero the equation has no real roots.
Discriminant < 0
D < 0
D = b² - 4ac
Now,
The equation is in the form of ax² + bx + c
x² - 4x + 3√2 = 0
D = (-4)² - 4 x 1 x 3√2 = 16 - 12√2 > 0
x² + 4x - 3√2 = 0
D = 16 + 12√2 > 0
x² - 4x - 3√2 = 0
D = 16 + 12√2 > 0
3x² + 4√3x + 4 = 0
D = 16 - 48 = 32 < 0
Thus,
The equation 3x² + 4√3x + 4 has no real roots.
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The complete question is:
Which of the following equations has no real roots
a. x² - 4x + 3√2 = 0
b. x² + 4x - 3√2 = 0
c. x² - 4x - 3√2 = 0
d. 3x² + 4√3x + 4 = 0
How do you know what method SSS SAS ASA AAS to use when proving triangle congruence?
The method to use when proving triangle congruence depends on the information given about the triangles.
What is triangle congruence?Triangle congruence is a doctrine of mathematics which states that two triangles are congruent when all the corresponding sides and angles of both triangles have the same measure. This means that the two triangles are of the same size and shape, and each of their sides and angles correspond to each other in terms of size and measure. Triangle congruence is an important theorem in geometry, and is often used for solving various problems in mathematics.
If two triangles have three pairs of corresponding congruent sides, then the Side-Side-Side (SSS) method can be used. If two triangles have two pairs of corresponding congruent angles and a pair of corresponding congruent sides, then the Angle-Side-Angle (ASA) method can be used. If two triangles have two pairs of corresponding congruent sides and a pair of corresponding congruent angles, then the Side-Angle-Side (SAS) method can be used. If two triangles have three pairs of corresponding congruent angles, then the Angle-Angle-Side (AAS) method can be used.
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What is the nature of the roots of the quadratic equation 4x² 4 √ 3x 3 0?
The roots of the quadratic equation 4x² + 4√3x - 3 = 0 are two distinct imaginary roots.
To find the roots of a quadratic equation, we have to use the quadratic formula. The formula is x = [-b ± √(b² - 4ac)]/2a. In this case, a = 4, b = 4√3, and c = -3. Plugging in the values, we get x = [-4√3 ± √(4√3² - 4*4*(-3))]/8. Simplifying and solving, we get x = [-2i ± √12]/4. Since both solutions contain an imaginary component, this means that the roots of the equation are two distinct imaginary roots.
x = [-4√3 ± √(4√3² - 4*4*(-3))]/8
x = [-4√3 ± √(48)]/8
x = [-2i ± √12]/4
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What is (2x^2 + 6x − 1) subtracted
from (2x^3 − 3x + 2)?
Answer:
2x^3 - 2x^2 - 9x + 3
Step-by-step explanation:
(2x^3 − 3x + 2) - (2x^2 + 6x − 1) =
2x^3 − 3x + 2 - 2x^2 + (-6x) − (-1) = ==> distribute the negative sign to 2x^2,
6x, and -1 in (2x^2 + 6x − 1)
Adding a negative number is equivalent to subtracting by a positive number.
Subtracting a negative number is equivalent to adding by a positive number.
Hence:
2x^3 − 3x + 2 - 2x^2 - 6x + 1 =
2x^3 - 2x^2 - 3x - 6x + 2 + 1 = ==> rearrange the expression in which like
terms are matching
2x^3 - 2x^2 - 9x + 3 ==> simplify
What is negative infinity?
The negative infinity, which is smaller than any real number, is the idea of infinity. For the representation of negative infinity, use the sign "-∞".
Given that,
We have to find what is negative infinity.
We know that,
The negative infinity, which is smaller than any real number, is the idea of infinity. For the representation of negative infinity, use the sign "-∞".
Look closely at this representation of infinity: opposite-pointing zip lines that travel along positive and negative infinity. To get closer to negative infinity on the zip line, they must turn left. On a number line, numbers move closer to positive infinity as they advance to the left and negative infinity as they move to the right. Positive infinity is always larger than any number, while negative infinity is always smaller.
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What are the slope and y value at the y-intercept of the line y 3x 5?
The slope is 3 and the y-intercept is −5 of the equation y = 3x - 5.
The line with m as the slope, m, and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope.
Slope-intercept form,
y = mx + c
Given equation,
y = 3x-5
Slope, m = 3
y-intercept, c = -5
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PLS HELP QUICK PLS
The two figures below are similar.
30 in
???
inches
12 in
16 in
What is the length of the missing side?
Answer:
40 inches
Step-by-step explanation:
Similar Triangles
In similar triangles, corresponding sides are always in the same ratio.
Let x be the length of the missing side.
Therefore:
[tex]\implies \sf x:16=30:12[/tex]
[tex]\implies \sf \dfrac{x}{16}=\dfrac{30}{12}[/tex]
[tex]\implies \sf 16 \cdot \dfrac{x}{16}=16 \cdot \dfrac{30}{12}[/tex]
[tex]\implies \sf x=\dfrac{480}{12}[/tex]
[tex]\implies \sf x=\dfrac{40 \cdot 12}{12}[/tex]
[tex]\implies \sf x=40[/tex]
Therefore, the length of the missing side is 40 inches.
What is the slope of the line that passes through the points (2, 8)(2,8) and (12, 20)(12,20)? Write your answer in simplest form.
The slope of the line that passes through the points (2,8) and (12, 20) is 6/5.
What is the Slope of a Line?The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of approaches.Given the coordinates of two points on the line, use the slope formula to determine the slope of the line. The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1).given :
points (2,8) and (12, 20)
slope = m=(y2-y1)/(x2-x1).
= 20-8 / 12-2
= 12/10 =6/5
the slope of the line that passes through the points (2,8) and (12, 20) is 6/5.
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Answer:
6/5
Step-by-step explanation:
What is nature of root equation?
The nature of root equation is depends of their types.
(1) When D=0, the roots in this situation are x = -b/2a.
(2) When D>0, the roots are real and unequal.
(3) When D<0, the roots are imaginary and unequal.
The type of roots depends on the discriminator:
We will talk about the following scenarios involving the nature of roots in accordance with the discriminates value.
Case: D=0
The roots of the quadratic equation ax^2 + bx + c = 0 are real and equivalent if the discriminate is equal to zero (b^2 - 4ac = 0), a, b, and c are real values, and a(0) . The roots in this situation are x = -b/2a. The X axis is the only location at which the equation's graph meets it.
Case: D>0
The roots of the quadratic equation ax2 + bx + c = 0 are real and unequal if the discriminate is bigger than zero (b2 - 4ac > 0), a, b, and c are real integers, and a0. The X-axis is intersected by the equation's graph twice.
Case: D<0
When a, b, and c are real numbers and the discriminate is smaller than zero (b2 - 4ac 0), the roots of the quadratic equation ax2 + bx + c = 0 are imaginary and unequal. There are conjugate pairings of roots. The equation's graph does not extend to the X-axis.
Case: D > 0 and perfect square
The roots of the quadratic equation are real, unequal, and rational if D > 0 and a perfect square.
Case: D < 0 and perfect square
The roots of the quadratic equation are real, unequal, and irrational if D > 0 and not a perfect square.
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You want to construct an open-top box that is 6 inches deep, with a square base. It must have a volume of 864 cubic inches. You have one big piece of cardboard. You will start by cutting it down to a square, and then you will cut smaller squares out of each corner and fold up the sides.
The statements that are true are the volume of the box is v = lwh = 864 in³ and the volume can be expressed in an equation as v = 6x² = 864in³
Volume of a SquareThe volume of a square box is equal to the cube of the length of the side of the square box. The formula for the volume is V = l³, where "l" is the length of the side of the square box.
In the given problem, the volume of the box is 864 cubic inches.
However, we have to remember that the box isn't a square, but rather the base has a square shape.
The volume of the figure is
v = l * w * h
l = lengthw = widthh = heightIf we divide the volume by the height, we will have the area of the figure
Area = volume / height
Area = 864 / 6
Area = 144 square inches
Since the base has a square shape;
A = l²
144 = l²
l = √144
l = 12 in
The side length is 12 inches.
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What is the median of the following set of scores 18 16 12 14?
The median of the set of numbers 18, 16, 12, and 14 is 15. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.
The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 18, 16, 12, and 14. When we order this set from least to greatest, we get 12, 14, 16, and 18. There are four numbers in this set, so the median is the average of the two middle numbers. The two middle numbers in this set are 14 and 16, so the median is (14 + 16) / 2 = 15.
To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are four numbers in the set, so the median is the average of the two middle numbers.
In summary, the median of the set of numbers 18, 16, 12, and 14 is 15. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.
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What is an expression 6th grade?
Answer:
An expression is a group of terms with an operation performed on them.
TL;DR:
An expression is an equation without an equal sign (=).
Examples:
[tex]\frac{(4x+2y)}{10}[/tex]
[tex]2y-5[/tex]
[tex]3x+2y+z[/tex]