Answer:
[tex]4\sqrt{2}[/tex] which is none of your choices....
Did you mean (8,-3) and (4,-7)?
Step-by-step explanation:
We need to first find the distance between the x's.
Then the distance between the y's.
The distance between the x's is 8-4=4.
The distance between the y's is -3-(-7)=4.
So the distance between two points [tex](x_1,y1)\text{ and }(x_2,y_2)[/tex] is [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex].
So we already found x1-x2 and y1-y2 so now we have:
[tex]\sqrt{(4)^2+(4)^2}[/tex]
[tex]\sqrt{16+16}[/tex]
[tex]\sqrt{2(16)[/tex]
[tex]\sqrt{16}\sqrt{2}[/tex]
[tex]4\sqrt{2}[/tex]
what is the vertex of the graph y=x^2+4x-1
a. (1,4)
b. (0,-1)
c. (-1,-4)
d. (-2,-5)
Answer:
Option d. (-2,-5)
Step-by-step explanation:
we know that
The equation of a vertical parabola in vertex form is equal to
[tex]y=a(x-h)^{2} +k[/tex]
where
a is a coefficient
(h,k) is the vertex of the parabola
In this problem we have
[tex]y=x^{2} +4x-1[/tex]
This is the equation of a vertical parabola open up
The vertex is minimum
Convert the equation in vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y+1=x^{2} +4x[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]y+1+4=x^{2} +4x+4[/tex]
[tex]y+5=x^{2}+4x+4[/tex]
Rewrite as perfect squares
[tex]y+5=(x+2)^{2}[/tex]
[tex]y=(x+2)^{2}-5[/tex] -----> equation in vertex form
therefore
The vertex is (-2,-5)
Given the following absolute value function find the range.
f(x) = |x+5| - 8
Answer:
{f ∈ R : f≥-8}
Step-by-step explanation:
The range is the output values
f(x) = |x+5| - 8
The smallest value the absolute value part can take is 0
f (min) = 0-8
The largest value is infinity
f(max) = infinity -8 = infinity
The range is -8 to infinity
Multiply. Write the product as one power. A^8 • A^5
Answer:
a^ (13)
Step-by-step explanation:
We know x^b* x^c = x^ (b+c)
a^8 * a^5 = a^ (8+5) = a^ (13)
Answer:
Step-by-step explanation:
The answer would be A^13, because when multiplying exponents with the same base, you just have to adfd the exponents.
Please help 50 Points. im desperate
Please explain the line of best fit and give at least one real world example that demonstrates the line of best fit
Answer:
A line of best fit is a straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points. A real world example would be a scatter plot of the number if balloons bought each year and a straight line going diagonally representing the average or goal of the number of balloons bought. The points may be above (signaling that the number of balloons purchased was higher than normal or exceeded the goal) or they may be below (signaling that balloon sales are lower than normal or didnt meet there goals). I hope this helps, if not then I apologize
Answer with explanation:
Line of best fit is the line which describes the relationship between two variables with the help of Linear Equation in two variables.
The equation of line of best fit is:
y= a x + b
Where, y and x are related with each other,that is with increase in one other may decrease or with decrease in one other may increase or Both increases in same way.
Real life Example
There are ten bulbs which have to be arranged in a rectangular room.Switch off all the Bulbs.Now you have to arrange the bulbs in the room in such a way that room has maximum intensity of light.
As ceiling of room is like two dimensional coordinate plane.Now you have arranged the bulb.You have to draw a line which is called line of best fit such that as the number of bulbs increases intensity of room increases.The line of best fit may pass all the points where bulb is located or none of the points where bulb is located or may be single or two or three or more than these points where bulb is located.
segment SW is the diameter of circle C. Point S is located at (6,-1) and point W is located at (10,-7). What are the coordinates of the center of this circle?
A. (8, -3)
B. (7, -5)
C. (9, -3)
D. (8, -4)
From the equation, find the axis of symmetry of the parabola. y=-3x^2+3x-13 a. x=1/2 b. x=3 c. x=-1/2 d. x=1
The axis of symmetry of the parabola [tex]y = -3x^2 + 3x - 13[/tex] is x = 1/2.
The axis of symmetry of a parabola in the form [tex]y = ax^2 + bx + c[/tex] is given by the formula x = -b/2a.
In the given equation [tex]y = -3x^2 + 3x - 13[/tex],
we can identify a = -3, b = 3, and c = -13.
The axis of symmetry is then calculated as x = -b/2a:
x = -3/(2*-3) = -3/-6 = 1/2
So, the correct answer is a. x = 1/2.
A student is attempting to solve a multi-step equation. Sample mathematical work is shown below. Which statement best applies to the sample mathematical work? Given the equation 35x – 10 = 5, I must solve for x. I first divide both sides by 35, which results in the equation x-10=1/7 I then add 10 to both sides, which gives me my final answer of x=71/70 A. The student incorrectly divided both sides by 35. B. The student incorrectly added 10 to both sides. C. The final answer is not reduced or simplified. D. The mathematical work shown is correct.
Answer:
A
Step-by-step explanation:
A: The student incorrectly divided both sides by 35. The student should first add 10 to both sides, obtaining 35x = 15, and then divide 15 by 35, obtaining the final answer 3/7.
factor completely
1. 7x^3y+14x^2y^3-7x^2y^2
a - 7x^2(xy+2y^3-y^2)
b - 7x^2y(x+2y^2-y)
c - 7(x^3y+2x^2y^3-x^2y^2
d - prime
2. 5x(x+3)+6(x+3)
a - (x+3)(30x)
b - (x+3)(5x+6)
c - (x+3)(11x)
d - prime
3. 8x^5+2x^4+4x^2
a - prime
b- 2(4x^5+x^4+2x^2)
c - 2x(4x^4+x^3+2x)
d - 2x^2(4x^3+x^2+2)
Answer:
B)
B)
D)
Step-by-step explanation:
1. [tex]7x^3y+14x^2y^3-7x^2y^2[/tex]
The GCF of all the term of the above polynomial is [tex]7x^2y[/tex] , hence we take it outside and form a bracket
[tex]7x^2y(x+2y^2-y)[/tex]
The polynomial within the bracket can not be factorized further hence this is our final answer. Option (B) is the right answer
2. [tex]5x(x+3)+6(x+3)[/tex]
The GCF of all the term of the above polynomial is [tex](x+3)[/tex] , hence we take it outside and form a bracket
[tex](x+3)(5x+6)[/tex]
The polynomial within the bracket can not be factorized further hence this is our final answer. Option (B) is the right answer
3. [tex]8x^5+2x^4+4x^2[/tex]
The GCF of all the term of the above polynomial is [tex]2x^2[/tex] , hence we take it outside and form a bracket
[tex]2x^2(4x^3+x^2+2)[/tex]
The polynomial within the bracket can not be factorized further hence this is our final answer. Option (D) is the right answer
Use the quadratic formula to determine the exact solutions to the equation x^2-4x-8=0
The answer is 2+2√3 or 2-2√3
Answer:
[tex]x = 2[/tex]±[tex]\sqrt{12}[/tex]
Step-by-step explanation:
Given the following equation ax^2 + bx + c = 0, the quadratic formula states that the solution to that equation is going to be given by:
[tex]x1 = \frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]
[tex]x1 = \frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
In this case, a=1, b=-4 and c=-8. Therefore:
[tex]x1 = \frac{4+\sqrt{(-4)^{2}-4(1)(-8)} }{2}[/tex]
[tex]x1 = \frac{4+\sqrt{48}}{2}[/tex]
[tex]x1 = 2+\sqrt{12}[/tex]
[tex]x2 = \frac{4-\sqrt{(-4)^{2}-4(1)(-8)} }{2}[/tex]
[tex]x2 = \frac{4-\sqrt{48}}{2}[/tex]
[tex]x2 = 2-\sqrt{12}[/tex]
Therefore the solutions are:
[tex]x = 2[/tex]±[tex]\sqrt{12}[/tex]
which of the following is not part of polyhedron.
a. Face
b. Vertex
c. Oblique
d. Edge
Answer:
C
Step-by-step explanation:
Oblique. The other three are used to describe a polyhedron. They are related by the following formula
V + F - E = 2.
Where
V = number of vertexesF = the number of facesE = edgesFor example consider a common cube, like a sugar cube.
It has 6 faces (f)
It has 8 vertexes (V)
It has 12 edges. E
6 + 8 - 12 = 14 - 12 = 2
Write an expression that gives the area of the shaded region in the figure.
Answer:
The mathematical expression is : (15 - 4) x (14 - 6) square feet.
The evaluation of this expression gives 88 sq ft.
Step-by-step explanation:
The length of the shaded region is (15 - 4) feet
The width of the shaded region is (14 - 6) feet
hence the expression for area is
(15 - 4) x (14 - 6) square feet.
fyi, if you work this out, you will get
(15 - 4) x (14 - 6)
=11 x 8
= 88 square feet.
Answer:
(15 ft - 4 ft) * (14 ft - 6 ft)
Step-by-step explanation:
The shaded area is a rectangle.
area of rectangle = length * width
Length of outer rectangle = 15 ft
Length of shaded rectangle = 15 ft - 4 ft
Width of outer rectangle = 14 ft
Width of shaded rectangle = 14 ft - 6 ft
Area of shaded rectangle = length * width = (15 ft - 4 ft) * (14 ft - 6 ft)
If 47400 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
(a) Annual: $ _____.
(b) Semiannual: $ _____.
(c) Monthly: $ _____.
(d) Daily: $______.
Answer:
Part A) Annual [tex]\$66,480.95[/tex]
Part B) Semiannual [tex]\$66,862.38[/tex]
Part C) Monthly [tex]\$67,195.44[/tex]
Part D) Daily [tex]\$67,261.54[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
Part A)
Annual
in this problem we have
[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=1[/tex]
substitute in the formula above
[tex]A=47,400(1+\frac{0.07}{1})^{1*5}\\A=47,400(1.07)^{5}\\A=\$66,480.95[/tex]
Part B)
Semiannual
in this problem we have
[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=2[/tex]
substitute in the formula above
[tex]A=47,400(1+\frac{0.07}{2})^{2*5}\\A=47,400(1.035)^{10}\\A=\$66,862.38[/tex]
Part C)
Monthly
in this problem we have
[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=12[/tex]
substitute in the formula above
[tex]A=47,400(1+\frac{0.07}{12})^{12*5} \\A=47,400(1.0058)^{60}\\A=\$67,195.44[/tex]
Part D)
Daily
in this problem we have
[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=365[/tex]
substitute in the formula above
[tex]A=47,400(1+\frac{0.07}{365})^{365*5}\\A=47,400(1.0002)^{1,825}\\A=\$67,261.54[/tex]
I need help please.
Answer:
Step-by-step explanation:
(x²-6x-3)(7x²-4x+7)= ?
Multiply each term of 2nd bracket with the 1st bracket:
=7x²(x²-6x-3) -4x(x²-6x-3) +7(x²-6x-3)
=7x^4-42x^3-21x^2-4x^3+24x^2+12x+7x^2-42x-21
Now solve the like terms:
=7x^4-46x^3+10x^2-30x-21
Therefore the answer is (x²-6x-3)(7x²-4x+7)=7x^4-46x^3+10x^2-30x-21 ....
The area of the regular hexagon is 10.4 in.2. What is the measure of the apothem, rounded to the nearest tenth of an inch? 1.3 in. 1.7 in. 2.0 in. 3.4 in.
Answer:
1.7
Step-by-step explanation:
Given:
Area of polygon=10.4
sides of polygon=2
Formula for area of a regular polygon= 1/2 (apothem x perimeter )
Putting value, we get
10.4= 1/2 ( a x 12 )
10.4=6a
a=10.4/6
a=1.73
the measure of the apothem, rounded to the nearest tenth of an inch=1.7!
Answer:
1.7 inches
Step-by-step explanation:
If the area of the regular hexagon is 10.4 in.2, the measure of the apothem, rounded to the nearest tenth of an inch is 1.7 inches
The function below describes the relationship between the height H and the width w of a rectangle with area 70 sq. units. H(w)= 70/w What is the domain of the function?
Answer:
[tex]w \ne0[/tex]
Step-by-step explanation:
The area of a rectangle is given by:
[tex]Area = L \times \: W[/tex]
In this case, we have the height replacing the length.
[tex]Area=H\times w[/tex]
The area of the rectangle is 70.
[tex]H\times w = 70[/tex]
Dividing through by w gives:
[tex]H = \frac{70}{w} [/tex]
Or to show that H is dependent on w, we write
[tex]H (w)= \frac{70}{w} [/tex]
[tex]w \ne \: 0[/tex]
Domain is the set of all real numbers for which the function is defined.
Therefore the domain is all real numbers except 0.
Answer:
w>0
Step-by-step explanation:
Which inequality matches the graph?
[tex] - 2x + 3y > 7[/tex]
[tex]2x - 3y < 7[/tex]
[tex] - 3x + 2y \geqslant 7[/tex]
[tex]3x - 2y \leqslant 7[/tex]
Answer:
[tex]\large\boxed{-3x+2y\geq7}[/tex]
Step-by-step explanation:
<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded region below the line
>, ≥ - shaded region above the line
====================================
We have solid line (≤, ≥).
Shaded region is above the line (>, ≥)
Therefore, the inequality sign must be: ≥
Finally, your answer is -3x + 2y ≥ 7.
Check the equation of a line.
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we ahve the points (3, 8) and (1, 5) - look at the picture.
Substitute:
[tex]m=\dfrac{5-8}{1-3}=\dfrac{-3}{-2}=\dfrac{3}{2}[/tex]
[tex]y-8=\dfrac{3}{2}(x-3)[/tex]
Convert to the standard form [tex]Ax+By=C[/tex]:
[tex]y-8=\dfrac{3}{2}(x-3)[/tex] multiply both sides by 2
[tex]2y-16=3(x-3)[/tex] use the distributive property
[tex]2y-16=3x-9[/tex] subtract 3x from both sides
[tex]-3x+2y-16=-9[/tex] add 16 to both sides
[tex]-3x+2y=7[/tex] CORRECT :)
QP contains the points Q(-6,10) and P(-12,-2). Find the slope of a line perpendicular to QP
Answer: -2
Step-by-step explanation: Find the slope of between the two points. P is the bottom point and Q is the top point. Both x and y numbers increase, meaning that the slope is positive. The x numbers increase by 6, and the y numbers increase by 12. This means that the rise is 12, and the run is 6. The slope is 12/6 but can be simplified to 2/1. The perpendicular slope is -1/2 because the perpendicular slope of a line is opposite reciprocal. This means to make the number negative and to flip it.
Answer:
-1/2
Step-by-step explanation:
So we are asked to find the slope of a line perpendicular to the line going through Q(-6,10) and P(-12,-2).
To do this we first need to find the slope of the line going through Q(-6,10) and P(-12,-2).
We can use the slope formula for a line given two points on that line which is (y2-y1)/(x2-x1).
I like to do something I consider easier to remember and is the same thing
It is:
A) line up the points
B) subtract vertically
C) put 2nd difference over first difference
D) done unless it needs reducing
So that is exactly what I'm going to do here:
(-6, 10)
-(-12,-2)
------------
6 12
So the slope is 12/6 or 2.
Now you might prefer to write 2 as a fraction now, because I'm about to tell you to find the slope of a line that is perpendicular, you just need to take the opposite reciprocal.
Opposite means to change the sign. I'm referring to negative or positive sign.
Reciprocal means to flip the number.
Let's put 2 through that process.
Opposite of 2: -2
Reciprocal of the opposite: -1/2
I got that reciprocal there by realizing -2 is just -2/1.
Anyways the slope of a line that is perpendicular to the one that goes through P and Q is -1/2 or -0.5.
Help me on this math question
Answer:
Step-by-step explanation:
The smallest number is 0.6. A fractional amount is always less that a whole number.
6.0 is the next smallest amount in some form. 6.009 The 0.009 is very tiny compared to the other numbers
then comes 6.08 That has only 2 decimal places, but those two places are bigger than 6.009
0.009 has 3 decimal places.
========
Finally 6.24 is larger than anything else. The 2 is in the tenths place.
Which number line represents the solutions to |x+4|=2?
Answer:
Step-by-step explanation:
This is an absolute value equation.
Firstly we will remove absolute value:
Absolute value always gives the positive result. Hence to remove the absolute value we will take both positive and negative:
|x+4|=2
x+4=2
Move the constant value to the R.H.S
x=2-4
x= -2
x+4 = -2
Move 4 to the R.H.S
x= -2 -4
x= -6
Therefore x = (-2, -6)....
The point-slope form of the equation of the line that passes through (-4, -3) and (12,1) is y-1=1/4(×-12). What is the standard form of the equation for this line?
Answer:
x - 4y = 8
Step-by-step explanation:
We are given point slope form of the equation of the line that passes through the point [tex](-4, -3)[/tex] and [tex](12,1)[/tex] which is [tex]y-1=\frac{1}{4} (x-12)[/tex].
We are to write this equation in its standard form.
From the given equation, we know that the slope is [tex]\frac{1}{4}[/tex] so we will find the y intercept.
[tex]y=mx+c[/tex]
[tex]1=\frac{1}{4}\times (12) +c[/tex]
[tex]c=-2[/tex]
Substituting the given values and the y intercept in the standard form of equation.
[tex]y=mx+c[/tex]
[tex]y=\frac{1}{4} x-2[/tex]
Rearranging this to get:
x - 4y = 8
Answer:
x - 4y = 8.
Step-by-step explanation:
y - 1 = 1/4(x - 12)
y = 1/4x - 3 + 1
y = 1/4x - 2
1/4x - y - 2 = 0
1/4x - y = 2
Multiply through by 4:
x - 4y = 8 is standard form.
Noa buys 6 items that each cost $4.25 and 3 items that each cost $6.75. How much does Noa spend in total?
A$20.25
B$25.50
C$38.25
D$45.75
Answer:
Answer is D - $45.75
Step-by-step explanation:
(6 x $4.25) + (3 x $6.75) = $45.75
Answer:
D) $45.75
Step-by-step explanation:
Step One: Multiply 6 times 4.25 and get 25.5
Step Two: Multiply 3 times 6.75 and get 20.25
Step Three: Add both answers together: 25.5 + 20.25 and get 45.75 which is your answer.
SCIENCE--What is the connection between glaciers high in the Himalayan Mountains and hundreds of millions of people living in the lowlands of India, China and Bangladesh? Select one: a. The glaciers cool the region. b. There is no connection. c. The glaciers feed the great rivers of Asia and supply the lowlands with freshwater. d. The glaciers prevent people from being able to travel through the mountains.
C. Those glaciers cause large rivers and in turn large population centers to form.
Why are glaciers so important?Glaciers are the cornerstone of life on Earth. As vast freshwater reservoirs, they support the Earth's life system and affect our daily lives, including communities that live far away. But glaciers are disappearing. The disappearing glacier reveals the tallest glacier on Everest, which has lost ice for 2,000 years since the 1990s.
Even the highest mountains in the world are not safe from climate change. Even the glaciers of Everest are unsafe from climate change, new research suggests. Glacier ice turns blue because the red (long wavelength) part of white light is absorbed by the ice and the blue (short wavelength) part is transmitted and scattered. The longer the pass light travels through the ice, the bluer it looks.
Learn more about glaciers here: https://brainly.com/question/6666513
#SPJ2
Janice ran mile. She walked mile. How far did she run and walk?
Answer:
two miles
Step-by-step explanation:
Answer:
if she ran one mile....and walked one mike.....that makes...2 miles altogether
Step-by-step explanation:
1 +1=2
Solve for x given the equation Vx+9 -4=1. Extraneous or not
Answer:
x=-4/V
Step-by-step explanation:
Add 4 to both sides to cancel out the 4.
So it now the equation is Vx+9=5
Subtract 9 from both sides to cancel out the 9.
Now the equation is Vx=-4
Divide V to both sides to get x alone.
The answer being x=-4/V
For this case we must find the value of "x" of the following equation:
[tex]\sqrt {x + 9} -4 = 1[/tex]
We add 4 to both sides of the equation:
[tex]\sqrt {x + 9} = 4 + 1\\\sqrt {x + 9} = 5[/tex]
We raise both sides of the equation to the square to eliminate the radical:
[tex]x + 9 = 5 ^ 2\\x + 9 = 25[/tex]
We subtract 9 from both sides of the equation:
[tex]x = 25-9\\x = 16[/tex]
Answer:
[tex]x = 16[/tex]
When price increases, quantity supplied:
stays the same
decreases
increases
becomes zero
A bicycle is marked 40% off the original price of $150. It is then taxed at 7 1/2%.
What is the final total cost of the bicycle
Answer:
$96.75
Step-by-step explanation:
Suppose the leader of a camping trip is putting together a trail mix
raisins, and chocolate chips. The mix is to consist of equal parts raisins and chocolate. If
peanuts cost $2/lb, raisins cost $2.50/lb, and chocolate chips cost $4/lb, how much of each
should be mixed to create 20 lbs of trail mix that costs $2.75/lb?
Answer:
8 pounds of peanuts, 6 pounds of raisins and 6 pounds of chocolate chips
Step-by-step explanation:
Let x be the number of pounds of peanuts and y be the number of pounds of raisins and chocolate chips.
Peanuts cost $2 per pound, then x pounds cost $2x.
Raisins cost $2.50 per pound, then y pounds cost $2.50y.
Chocolate chips cost $4 per pound, then y pounds cost $4y.
In total, x+y+y=20 and those 20 pounds cost
2x+2.50y+4y=20·2.75.
Solve the system of two equations:
[tex]\left \{ {{x+2y=20} \\ \\ \\ \\ \\ \\ \atop {2x+6.5y=55}} \right.[/tex]
From the first equation:
[tex]x=20-2y[/tex]
Substitute x into the second equation:
[tex]2(20-2y)+6.5y=55\\ \\40-4y+6.5y=55\\ \\2.5y=15\\ \\25y=150\\ \\y=6\\ \\x=20-2\cdot 6=8[/tex]
Given: AD = BC and
Prove: DE congruent to CE
Answer:
Step-by-step explanation:
On a piece of paper, graph y+2>-3x - 3. Then determine which answer
choice matches the graph you drew.
Answer:
D.
Step-by-step explanation:
【Look at the image】
Answer:
option D
Step-by-step explanation:
[tex]y+2>-3x - 3[/tex]
Subtract 2 from both sides and solve for y
[tex]y>-3x - 5[/tex]
Now graph it using a table
Replace > symbol by == sign
[tex]y=-3x - 5[/tex]
make a table
x y=-3x-5
0 -5
-1 -2
-2 1
Graph the points (0,-5) and (-2,1)
WE have only > symbol so we use dotted line
For shading we use test point (0,0)
[tex]y>-3x - 5[/tex]
Plug in 0 for x and 0 for y
[tex]0>-3(0) - 5[/tex]
0>-5 True
So we shade the region that contains (0,0)
option D is correct
if 2x - 3 + 3x equals -28 what is the value of x
Answer:
x = -5
Step-by-step explanation:
It just is :)
For this case we must find the value of "x" of the following expression:
[tex]2x-3 + 3x = -28[/tex]
We add similar terms:
[tex]5x-3 = -28[/tex]
We add 3 to both sides of the equation:
[tex]5x = -28 + 3[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]5x = -25[/tex]
We divide between 5 on both sides of the equation:
[tex]x = \frac {-25} {5}\\x = -5[/tex]
ANswer:
[tex]x = -5[/tex]