Given:
The principal amount = $500
Interest rate = 10% quarterly
Required:
Find the deposing amount after 25 years.
Explanation:
The amount formula when the interest is compounded quarterly is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where r = interest rate
t = time period
n = The number of compounded times
The amount after 25 years is:
[tex]\begin{gathered} A=500(1+\frac{0.1}{4})^{4\times25} \\ A=500(1+.025)^{100} \\ A=500(1.025)^{100} \end{gathered}[/tex][tex]\begin{gathered} A=500\times11.81371 \\ A=5906.8581 \end{gathered}[/tex]Final Answer:
The amount after 25 years will be &5906.85
can you help me solve this in expanded form. 156 X 687 = ?
Given data:
The given expression is 156x687.
The given expression can be written as,
[tex]\begin{gathered} (100+50+6)(600+80+7)=60000+8000+700+30000+4000+350+3600+480+42 \\ =107172 \end{gathered}[/tex]Thus, the value of the given expression is 107172.
write an expression such that if you apply the distributive property to your expression it would give the same result presented. 8x + 12
Solution:
Let's find a expression such that if you apply the distributive property to your expression it would give the same result presented:
• 8x + 12 = 2 (4x + 6)
,• 8x + 12 = 4 (2x + 3)
,• 8x + 12 = 8 (x + 1.5)
Any of these expressions could be the solution to the question.
Which value of n makes the following equation true?√n=4020408O 16
Solution
- The solution steps are given below:
[tex]\begin{gathered} \sqrt{n}=4 \\ \text{ Square both sides} \\ n=4^2 \\ n=16 \end{gathered}[/tex]Final Answer
The answer is 16
A baseball card store prints a total of 15,363 cards on Tuesday and Wednesday. It printed 3,978 cards on Wednesday. How many cards did the store print from Tuesday through Thursday?
The stored printed 34,704 cards from Tuesday through Thursday.
How to find the total number of cards printed?To find the total number of cards printed through a series of n days, we add the amounts printed on each day.
In the context of this problem, from the text presented, the daily amount of cards printed on Tuesday, Wednesday and Thursday is given as follows:
Tuesday: 15,363 cards.Wednesday: 15,363 cards.Thursday: 3,978 cards.Hence the total number of cards printed by the store from Tuesday through Thursday is calculated by the addition presented as follows:
15,363 + 15,363 + 3,978 = 2 x 15,363 + 3,978 = 34,704 cards printed by the store from Tuesday through Thursday.
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find the slope that goes through the points (1, -4) and (-3, 8)
Given the points:
(x1, y1) ==> (1, -4)
(x2, y2) ==> (-3, 8)
To find the slope, use the slope formula below:
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]\begin{gathered} m\text{ = }\frac{8-(-4)}{-3-1} \\ \\ m=\frac{8+4}{-3-1} \\ \\ m=\frac{12}{-4} \\ \\ m\text{ = -3} \end{gathered}[/tex]Therefore, the slope is -3.
ANSWER:
-3
Triangle HJK has vertices at H(2, 2) J(2, 4) and K(0, 2). What is the midpoint of the longest side of the triangle?
The coordinates of the vertices of triangle are given as H(2,2), (J(2, 4), K(0,2)
We would determine the longest side by applying the formula for finding the distance between two points which is expressed as
[tex]\begin{gathered} \text{Distance = }\sqrt[]{x2-x1)^2+(y2-y1)^2} \\ \text{For HJ, x1 = 2, y1 = 2, x2 = 2, y2 = 4} \\ \text{Distance = }\sqrt[]{(2-2)^2+(4-2)^2}\text{ = }\sqrt[]{2^2}\text{ = 2} \\ \text{For JK, x1 = 2, y1 = 4, x2 = 0, y2 = 2} \\ \text{Distance = }\sqrt[]{(0-2)^2+(2-4)^2}=\sqrt[]{(4+4)}=\text{ }2.83 \\ \text{For HK, x1 = 2, y1 = 2, x2 = 0, y2 = 2} \\ \text{Distance = }\sqrt[]{0-2)^2+(2-2)^2}=\text{ }\sqrt[]{4}\text{ = 2} \end{gathered}[/tex]Thus, the longest side is JK. The formula for finding midpoint is
Midpoint = (x1 + x2)/2, (y1 + y2)/2
Midpoint = (2 + 0)/2, (4 + 2)/2
Midpoint = 2/2, 6/2
Midpoint = 1, 3
4. A teacher can only make 3000 copies in a month. If a teacher-has-made 2700 copies so far this month, what percentage of her copies has she used?
In order to determine the percentage, let x as the percentage. Then, you can write:
[tex]\frac{x}{100}\cdot3000=2700[/tex]factor x/100 is the percentage in decimal form. The product of this factor and 3000 equals 2700.
Solve for x and simplify:
[tex]x=\frac{2700}{3000}\cdot100=90[/tex]Hence, teacher has used 90% of the copies.
A local road has a grade of 5%. The grade of a road is its slope expressed as a percent. What is the slope? What is the rise? What is the run?
a) Since the grade is given by the slope, and the grade has a 5%.
We can rewrite it as a fraction, like this:
[tex]\frac{5}{100}=\frac{1}{20}[/tex]Note that we have simplified this to 1/20 by dividing the numerator and the denominator (bottom number) by 5
So, the slope is:
[tex]\frac{1}{20}[/tex]b) The "rise" is the difference between two coordinates on the y-axis and the "run" is the subtraction between two coordinates on the x-axis. Let's remember the slope formula and the Cartesian plane:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{1}{20}[/tex]So the "rise" for this grade is 1 foot and the run is 20 feet.
3) Hence, the answers are:
[tex]\begin{gathered} a)\text{ }\frac{1}{20} \\ b)\text{ }Rise\colon\text{ }1\text{ Run: 20} \end{gathered}[/tex]Circumference? (you must include units) Round to the tenthsas needed.
The circumference formula is given by:
[tex]L=2\pi r[/tex]Where r is the radius of the circle. From the problem, we have r = 10.9 ft. Then, using the formula:
[tex]\begin{gathered} L=2\pi\cdot10.9 \\ \\ \therefore L=68.5\text{ ft} \end{gathered}[/tex]The circumference is 68.5 ft
Give the point-slope form of the equation of the line that is perpendicular to y= -4x/5+10 and contains P(5,6)
You have to write the equation of a line perpendicular to
[tex]y=-\frac{4}{5}x+10[/tex]That crosses the point (5, 6)
A caracteristic of a line permendicular to another one is that its slope pf the perpendicular line is the negative inverse of the slope of the first line.
So for example if you have two lines:
1_ y=mx+b
and
2_ y=nx+c
And both lines are perpendicular, the slope of the second one will be the negative inverse of the slope of the first one, that is:
[tex]n=-\frac{1}{m}[/tex]The slope of the given line is m=-4/5
The negative inverse is
[tex]-(\frac{1}{-\frac{4}{5}})=-(-\frac{5}{4})=\frac{5}{4}[/tex]Now that you know the slope of the perpendicular line, use it along with the given point (5, 6)
in the slope-point formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-6=\frac{5}{4}(x-5) \end{gathered}[/tex]In which quadrant does 0 lie if the following statements are true:sin 0 > 0 and sec 0 < 0Quadrant IQuadrant IIQuadrant IIIQuadrant IV
Given the conditions in the question:
1. sin θ > 0, therefore, it must be positive. From that, we can conclude that y must be on the positive side, therefore, located at the top of the coordinate plane.
2. sec θ < 0, therefore, it must be negative. From that, we can conclude that x must be on the negative side, therefore, located at the left side of the coordinate plane.
Therefore, the quadrant that the θ belongs to is in the top and left of the coordinate plane and that is Quadrant II.
What is the measure of ∠N, if ∠M and ∠N are angles in a linear pair and the m∠M is 30°? *.
Given:
[tex]\angle M=30\degree[/tex]And angle M and N are angles in a linear pair.
Required:
To find the angle N.
Explanation:
The sum of angles of a linear pair is always equal to 180°.
Therefore,
[tex]\begin{gathered} \angle M+\angle N=180\degree \\ \\ 30\degree+\angle N=180\degree \\ \\ \angle N=180\degree-30\degree \\ \\ \angle N=150\degree \end{gathered}[/tex]Final Answer:
[tex]\angle N=150\degree[/tex]INT. ALGEBRA: You have a coupon for $20 off the purchase of a calculator. At the same time, the calculator is offered with a discount of 20%, and no further discounts apply. For what price on the calculator do you pay the same amount for each discount?
Thank you for your help, and please do show work! I will be looking to give the Brainliest answer to someone!
So I joined a ged class and this is apparently a “high school level” math problem, maybe for people in advanced classes but not regular. Anyway, I need help with solving this. Also the greater than sign with the problem that I’m doing has like an underline under it, which I think means greater than or equal to 3x + 9 > - x + 19
Given the inequality:
[tex]3x+9\ge-x+19[/tex]Solve for x:
[tex]\begin{gathered} 3x+x\ge19-9 \\ 4x\ge10 \\ x\ge\frac{10}{4} \\ \\ x\ge\frac{5}{2} \end{gathered}[/tex]so, the answer will be:
[tex]\begin{gathered} x\ge\frac{5}{2} \\ x\in\lbrack\frac{2}{5},\infty) \end{gathered}[/tex]3. What is the vertical shift for the absolute value function below?F(x) 9|x + 1|+ 2
Answer:
The vertical shift is of 2 units up
Step-by-step explanation:
We have a function in the following format:
F(x) = a(x+b) + c
The vertical shift is given by c.
If c > 0, the shift is up.
If c < 0, the shift is down.
In this question:
F(x) = 9|x+1| + 2
So c = 2
The vertical shift is of 2 units up
Rachel says when she ran 115 yards she went farther than beth who only ran 327 feet. Is Rachel correct?
Rachel is correct because Rachel ran farther than Beth .
In the question ,
it is given that ,
Rachel ran 115 yards and Beth ran 327 yards ,
For comparing both the distance , we need to convert both the distance in the same unit ,
So , we convert yards to feet ,
we know that,
1 yard = 3 foot ,
So, 115 yard = 3*115 = 345 feet ,
Rachel ran 345 feet and Beth ran 327 feet .
hence , we can conclude that Rachel ran 345 feet which is greater than Beth , who ran only 327 feet .
Therefore , Rachel is correct because Rachel ran farther than Beth .
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What’s is the volume and surface area of the figure shown ?
• The total surface area of a cylinder is given by:
[tex]SA=2πr\left(r+h\right)[/tex]where r = 1.75 cm
h = 3 cm
Hence:
[tex]SA=2\times\pi\times1.75\times(1.75+3)=57.7\text{ }cm^2[/tex]• The volume of a cylinder is given by:
[tex]V=πr^2h[/tex]Hence:
[tex]V=\pi\times(1.75)^2\times3=28.9\text{ }cm^3[/tex]ANSWER
surface area = 57.7 cm²
volume = 28.9 cm³
The stem-and-leaf plot shows the number of hours per semester that students in a certain school club watchtelevision. What is the greatest number of hours that were watched?
Answer:
45
Explanation:
The number on the left of the line represent the tens and the numbers on the right of the line represent the units, so data for the stem and leaf plot is:
20, 22, 22, 22, 23, 23
30, 31, 33, 35
40, 42, 42, 43, 43, 43, 45
It means that the greatest number of hours is 45.
Then, the answer is 45.
Write an expression to determine the surface area of a cube-shaped box, S A , in terms of its side length, s (in inches).
The cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
What is a cube?A three-dimensional object with six equal square faces is called a cube. The cube's six square faces all have the same dimensions.
A cube is become by joining 6 squares such that the angle between any two adjacent lines should be 90 degrees.
A cube is a symmetric 3 dimension figure in which all sides must be the same.
The cube has six equal squares.
It is known that the surface area of a square = side²
Therefore, the surface area of the given cube is 6 side².
Given cube has side length = s
So,
Surface area = 6s²
Hence the cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
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a farmer has 150 yards of fencing to place around a rectangular garden. the fence will have an opening that is 1/3 of the gardens length(see picture). write a function a(x) that describes the area of the garden.Find the dimensions of the garden if it has the maximum area, and find the maximum area.
By forming equations, we know that the garden is 37.5 yards long, and 37.5 yards wide, and it has an opening that is 12.5 yards wide.
What are equations?A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 = 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.So, the dimensions and area of the garden:
Let x and y stand for length and width, respectively.There are 150 yards of fencing available, so:
2(x + y) = 150x + y = 75y = 75 - x ...(1)The garden's area (A) is given as follows:
A = xyA = x(75 - x)A = 75x - x²At A' = 0, the area is largest.
A' = 75 - 2x75 - 2x = 0x = 37.5 yardsy = 75 - x y = 75 - 37.5 = 37.5Garden opening: 1/3 × 37.5 = 12.5 yards
Therefore, by forming equations, we know that the garden is 37.5 yards long, and 37.5 yards wide, and it has an opening that is 12.5 yards wide.
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The correct question is given below:
A farmer has 150 yards of fencing to place around a rectangular garden. The fence will have an opening that is 1/3 of the garden's length. Write a function A(x) that describes the area of the garden, where x is the length of the garden. Find the dimensions if that has a maximum area, and find the maximum area
Answer:
The length is 45 yards.
The width is 37.5 yards.
The area is 1,687.5 yards
Step-by-step explanation:
I go to RSM too lolol
The other answer posted here was incorrect. Since the length and width DID have a relatively equal factor without the -12.5 yard opening taken into account, you'd usually get 37.5 yards.
BUT, if we use the width and subtract it from the total (which we'd get 75 yards left), we can see that in the total length, a sixth (it is 1/6th since we are taking both sides) is taken from that. 75 is easily dividable by 5, so we can take 15, and multiply it by 3. We'd then get 45 yards in total for each side (minus the 12.5 yard opening).
All you need to do now is multiply the length and width to get 1,687.5 yards.
Now get a 100 on that RSM assignment and get the bragging rights for your class. You can thank me later. Your homework is more important.
Use the “complete the square” method to solve the following problemx^2 + 3x + 11 = 0
[tex]x^2+3x+11=0[/tex][tex](\frac{1}{2}\times3)^2=(+\frac{3}{2})^2[/tex][tex]\begin{gathered} x^2+3x=-11 \\ x^2+3x+(+\frac{3}{2})^2=-11+\frac{9}{4} \\ \\ (x+\frac{3}{2})^2=-\frac{35}{4} \\ \\ x+\frac{3}{2}=\sqrt{\frac{-35}{4}} \\ \\ x+\frac{3}{2}=\pm\frac{\sqrt{35}}{2}i \\ \\ x=\frac{-3}{2}\pm\frac{\sqrt{35}}{2}i \end{gathered}[/tex]
The answers are
[tex]x=\frac{-3}{2}+\frac{i\sqrt{35}}{2},\text{ }x=\frac{-3}{2}-\frac{i\sqrt{35}}{2}[/tex]Find the measurement of each side indicated and round to the nearest tenth for both triangles
a) We have a right triangle.
We have to find the value of x, which is the hypotenuse.
We can relate the angle B, the side AC and x with a trigonometric ratio as:
[tex]\begin{gathered} \sin (B)=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{AC}{AB} \\ \sin (57\degree)=\frac{10.8}{x} \\ x=\frac{10.8}{\sin (57\degree)} \\ x\approx\frac{10.8}{0.83867} \\ x\approx12.9 \end{gathered}[/tex]b) In this case, x is the adyacent side to angle A.
We can relate the sides and the angle as:
[tex]\begin{gathered} \cos (A)=\frac{\text{Adyacent}}{\text{Hypotenuse}}=\frac{AC}{AB} \\ \cos (47\degree)=\frac{x}{3} \\ x=3\cdot\cos (47\degree) \\ x\approx3\cdot0.682 \\ x\approx2.0 \end{gathered}[/tex]Answer:
a) x = 12.9
b) x = 2.0
A health club charges a one time initiation fee of $120.00 plus a membership fee of $30.00 per month. a. Write an expression for the cost function C(x) that gives the total for membership at the health club for x months. b. Draw a graph of the function in (a).c. The health club decided to give it's member an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, use a different color and draw on the same set of axes the cost graph under the plan. d. Determine after how many months the second plan is less expensive for the member. a. C(x) = _______ (Do not factor)
a.
Given that a health club charges a one-time initiation fee of $120.00 plus a membership fee of $30.00 per month.
The total cost will be equal to the fixed one-time charge plus the charge per month times the number of months.
It can be represented by the expression C(x);
[tex]C(x)=120+30x[/tex]b.
Graphing of the function, we would have;
c.
If the health club decided to give its members an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, we will have the function as;
[tex]F(x)=420+10x[/tex]graphing the above function, we have;
the first plan is represented by the blue line while the second plan is represented by the red line.
d.
The number of months after which the second plan is less expensive is the value of x when the two lines meet.
the two lines meet at point;
[tex](15,570)[/tex]The value of the x coordinate is 15.
So, The number of months after which the second plan is less expensive is
[tex]15\text{ months}[/tex]Let f(x) = 2x² + 14x – 16 and g(x) = x+8. Perform the function operation and then find the domain of the result.(x) = (simplify your answer.)
We need to find the following division of the functions f(x) and g(x):
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)}=\frac{2x^2+14x-16}{x+8}[/tex]We can note that the numerator can be rewritten as
[tex]2x^2+14x-16=2(x^2+7x-8)=2(x+8)(x-1)[/tex]Then the division can be written as:
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)}=\frac{2(x+8)(x-1)}{x+8}[/tex]From this result, we can cancel out the term (x+8) from both sides and get,
[tex]\frac{f}{g}(x)=\frac{f(x)}{g(x)}=2(x-1)[/tex]Therefore, the result of the division is:
[tex]\frac{f}{g}(x)=2(x-1)[/tex]which domain is all real numbers:
[tex]x\in(-\infty,\infty)[/tex]A rectangular prism has a legth of 5 1/4 m, a width of 4m, and a height of 12 m.How many unit cubes with edge lengths of 1/4 m will it take to fill the prism? what is the volume of the prism?
Volume of a cube with edge lengths of 1/4m:
[tex]\begin{gathered} V_{cube}=l^3 \\ \\ V_{cube}=(\frac{1}{4}m)^3=\frac{1^3}{4^3}m^3=\frac{1}{64}m^3 \end{gathered}[/tex]Volume of the rectangular prism:
[tex]\begin{gathered} V=l\cdot w\cdot h \\ \\ V=5\frac{1}{4}m\cdot4m\cdot12m \\ \\ V=\frac{21}{4}m\cdot4m\cdot12m \\ \\ V=252m^3 \end{gathered}[/tex]Divide the volume of the prism into the volume of the cubes:
[tex]\frac{252m^3}{\frac{1}{64}m^3}=252\cdot64=16128[/tex]Then, to fill the prism it will take 16,128 cubes with edge length of 1/4 mthe four faced of a rectangular pyrimid below are painted yellow. how many square feet will be painted
The number of square feet to be painted is equal to the surface area of the four face painted yellow.
Total Surface Area (TSA) =
[tex]4(\frac{1}{2}bh)[/tex]By Pythagoras Theorem,
[tex]\begin{gathered} h^2+1.5^2=5^2 \\ h^2=5^2-1.5^2 \\ h=\sqrt[]{25-2.25}\text{ =}\sqrt[]{22.75}=4.7697\text{ fe}et \end{gathered}[/tex]. . Read the problem and write your answer for each part. Make sure to label each part: , , .jasmine is tracking the growth of a specific bacteria bacteria for a science experiment. She assumes that there are bacteria () in a Perti dish at 12:00 midnight. Jamie observes that the number of bacteria increases by 25 every hour . write an equation that describes the relationship between total number of bacteria () and time () in hours, assuming there are () bacteria in the perti dish at = 0. . if Jamie starts with bacteria in the perti dish, how many bacteria will be present after 6 hours? . if Jamie starts with bacteria in the perti dish, draw a graph that displays the total number of bacteria with respect to time from 12:00 midnight ( = ) to 8:00 am. ( = ). Label each axis and label points on your graph at times = , , , .use the coordinate plane below to draw your graph.
Part A:
Let:
T(h)= Total Number of bacterias as a function of time
h = Number of hours
B = Initial number of bacterias
Since the number of bacteria increases by 25 every hour, we can defined the equation as:
[tex]T(h)=25h+B[/tex]Part B:
B = 5
h = 6
Evaluate the previous equation for those values:
[tex]\begin{gathered} T(6)=25(6)+5 \\ T(6)=150+5 \\ T(6)=155 \end{gathered}[/tex]there will be 155 baterias after 6 hours
Part C
Let's graph the equation:
[tex]T(h)=25h+5[/tex]Solve the inequality: 3x + 4 ≤ 5
Answer in interval notation.
(-∞,1/3] will be the required option in interval notation for the given inequality 3x + 4 ≤ 5 as it's definition states "a relationship between two expressions or values that are not equal to each other".
What is inequality?A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. a ≠ b says that a is not equal to b. a < b says that a is less than b. a > b says that a is greater than b. a ≤ b means that a is less than or equal to b. a ≥ b means that a is greater than or equal to b.
What is interval notation?When using interval notation, we first write the set's leftmost number, then a comma, and finally its rightmost number. Depending on whether those two numbers are a part of the set, we then enclose the pair in parentheses or square brackets (sometimes we use one parenthesis and one bracket!).
Here,
3x+4≤5
3x≤1
x≤1/3
(-∞,1/3]
As it's definition states "a relationship between two expressions or values that are not equal to each other" (-∞,1/3] will be the required option in interval notation for the given inequality 3x + 4 ≤ 5.
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help meeeeeeeeee pleaseee !!!!!
The values of the functions are;
a. (f + g)(x) = x( 2 + 3x)
b. (f - g)(x) = 2x - 3x²
c. (f. g) (x) = 6x²
d. (f/g)(x) = 2/ 3x
What is a function?A function can be defined as an expression, rule, law or theorem that explains the relationship between two variables in a given expression
These variables are called;
The independent variablesThe dependent variablesFrom the information given, we have;
f(x) = 2xg(x) = 3x²To determine the composite functions, we have;
a. (f + g)(x)
Add the functions
(f + g)(x) = 2x + 3x²
Factorize the functions
(f + g)(x) = x( 2 + 3x)
b. (f - g) (x)
Subtract the functions
(f - g)(x) = 2x - 3x²
c. (f. g) (x)
Substitute the values of x as g(x) in f(x)
(f. g) (x) = 2(3x²)
(f. g) (x) = 6x²
d. (f/g)(x) = 2x/ 3x²
(f/g)(x) = 2/ 3x
Hence, the functions are determined by substituting the values of the dependent variables.
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You have a pizza with a diameter of 6 1/3 in., and a square box that is 6.38 in. Is the box big enough to fit the pizza inside?
Pizza diameter D is given in mixed form:
[tex]\begin{gathered} D=6\frac{1}{3}\text{ in} \\ in\text{ fraction form:} \\ D=\frac{19}{3}\text{ in} \\ In\text{ decimals, } \\ D=6.33\text{ in} \end{gathered}[/tex]Now, me must compare D with the lenght of the square box.
Since the lenght of the box is L=6.38 in. Hence, the box is big enough to
fit the pizza.
[tex]\begin{gathered} \\ \\ \\ \end{gathered}[/tex]