Marcus loves baseball and wants to create a home plate for his house. Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. Calculate the area of the polygon.
TYSM
Answers
Answer:
Area of the polygon = 59 in²
Explanation:
From the given diagram, we can note that the given polygon is composed of an upper triangle, a side triangle and a rectangle
Therefore:
Area of polygon =
area of upper triangle + area of side triangle + area of rectangle
1- getting the area of the upper triangle:
We have:
base of triangle = 7 in
height of triangle = 6 in
Therefore:
Area of upper triangle = [tex]\frac{1}{2}*base*height = \frac{1}{2}*7*6=21[/tex] in²
2- getting the area of the side triangle:
We have:
base of triangle = 4 in
height of triangle = 5 in
Therefore:
Area of upper triangle = [tex]\frac{1}{2}*base*height = \frac{1}{2}*4*5=10[/tex] in²
3- getting the area of the rectangle:
We have:
length of rectangle = 7 in
width of rectangle = 4 in
Therefore:
Area of rectangle = length x width = 7 x 4 = 28 in²
4- getting the total area of the polygon:
Area of polygon =
area of upper triangle + area of side triangle + area of rectangle
Therefore:
Area of polygon = 21 + 10 + 28 = 59 in²
Hope this helps :)
Related Questions
Lexi and Maria had $250 altogether. After Lexi spent 2/5 of her money and Maria spent $40 they had the same amount of money left. How much more money did Lexi have in the beginning.
Answers
Answer:
The amount of money that Lexi had at the beginning was $131.25
Step-by-step explanation:
Let
x -----> amount of money that Lexi had at the beginning
y -----> amount of money that Maria had at the beginning
we know that
x+y=250 -----> equation A
(1-2/5)x=y-40
(3/5)x=y-40
y=(3/5)x+40 ----> equation B
substitute equation B in equation A and solve for x
x+(3/5)x+40=250
(8/5)x=250-40
(8/5)x=210
x=210*5/8
x=$131.25
Evaluate the function.
a. f(x) = 3x+5 {-2,0,2}
b. g(x) = x-9 find g(5)
c. f(n) = (3-n) + 4 {-1,-2,3}
Answers
Answer:
Part a) The values of the function f(x) are {-1,5,11}
Part b) The value of g(5) is -4
Part c) The values of the function f(n) are {8,9,4}
Step-by-step explanation:
Part a) we have
f(x)=3x+5
Evaluate for {-2,0,2}
1) For x=-2
substitute the value of x in the function
f(-2)=3(-2)+5=-1
2) For x=0
substitute the value of x in the function
f(0)=3(0)+5=5
3) For x=2
substitute the value of x in the function
f(2)=3(2)+5=11
Part b) we have
g(x)=x-9
Evaluate for x=5
substitute the value of x in the function
g(5)=5-9=-4
Part c) we have
f(n)=(3-n)+4
Evaluate for {-1,-2,3}
1) For n=-1
substitute the value of n in the function
f(-1)=(3-(-1))+4=8
2) For n=-2
substitute the value of n in the function
f(-2)=(3-(-2))+4=9
3) For n=3
substitute the value of n in the function
f(3)=(3-(3))+4=4
Factor completely 3x² − x − 4.
20 for the top answer
Answers
Answer:
[tex](3x-4)(x+1)[/tex]
Step-by-step explanation:
This is in the form [tex]ax^2+bx+c[/tex].
If your wish is to factor by grouping, then you goal is too look for two numbers that multiply to be [tex]ac[/tex] and adds up to be [tex]b[/tex].
Then once you find those numbers you replace b with those numbers. Then the factor by grouping can be done.
So you have [tex]a=3,b=-1,c=-4[/tex]
[tex]ac=3(-4)[/tex]
[tex]b=-1[/tex]
The numbers that we need are already present since -4+3 is -1.
So replace -1 in
[tex]3x^2-1x-4[/tex]
with (-4+3)
[tex]3x^2-4x+3x-4[/tex]
Now group the first two terms together and group the last two terms together:
[tex](3x^2-4x)+(3x-4)[/tex]
Factor what you can from both pairs:
[tex]x(3x-4)+1(3x-4)[/tex]
Notice you have two terms: x(3x-4) and 1(3x-4). These terms have a common factor of (3x-4) so factor that out of our expression like so:
[tex](3x-4)(x+1)[/tex]
Check with foil if you like:
First: 3x(x)=3x^2
Outer: 3x(1)=3x
Inner: -4(x)=-4x
Last: -4(1)=-4
----------------------Add together:
3x^2-x-4
Answer: [tex]=(3x-4)(x+1)[/tex]
Step-by-step explanation:
Given the polynomial [tex]3x^2- x -4[/tex]
We can observe that it is written in this form:
[tex]ax^2+bx+c[/tex]
To factor completely, we need to follow these steps:
- Rewrite the term "b" as the sum of two terms whose product be [tex](3)(-4)=-12[/tex] and whose sum be -1:
[tex]=3x^2+(-4+3)x-4[/tex]
- Applying Distributive property, we get:
[tex]=3x^2-4x+3x-4[/tex]
- Make two groups of two terms each:
[tex]=(3x^2-4x)+(3x-4)[/tex]
- Factor out "x" from the first group and 1 from the second group:
[tex]=x(3x-4)+1(3x-4)[/tex]
- Factoring out [tex](3x-4)[/tex], we get:
[tex]=(3x-4)(x+1)[/tex]
Which point below is not on the graph of p(x) = +36- X?
(-13,7)
• (-35, 1)
O (11,5)
o (27,3)
SUBMIT ANSWER
ASK FOR HELD
Answers
Answer:
We have the following equation: y = 36 - x. And we need to find which of the following points belong to the graph:
(-13,7) (-35, 1) (11,5) (27,3)If any of the points belong to the equation, then the equality will be met.
Then:
(-13,7) :7 = 36 - (-13)
7 = 36 + 13
7 = 49 ❌
(-35, 1) :1 = 36 - (-35)
1 = 71❌
(11, 5) :5 = 36 - 11
5 = 25 ❌
(27,3)3 = 36 - 27
3 = 9 ❌
None of the points belong to the graph. Therefore, all points are NOT on the grah of p(x) = 36 - x.
Answer:
ANSWER IS (-35,1)
Step-by-step explanation:
I got it because I am looking at the answer right now
5xy-25x square+50x-10y
Answers
Answer:
the answer is 5(y-5x) (x-2)
Step-by-step explanation:
Answer:
[tex]5(x - 2)(y - 5x)[/tex]
Explanation
We want to factorize:
[tex]5xy - 25 {x}^{2} + 50x - 10y[/tex]
The factors have been grouped already. We now factor the GCF from each group to get:
[tex]5x(x- 5x) - 10(y - 5x)[/tex]
We factor further to obtain:
[tex](5x- 10)(y - 5x)[/tex]
We can still factor 5 to obtain:
[tex]5(x - 2)(y - 5x)[/tex]
Simplify the following expression: square root of -36 + square root of -100 +7
Answers
Answer:
[tex]\large\boxed{\sqrt{-36}+\sqrt{-100}+7=7+16i}[/tex]
Step-by-step explanation:
[tex]\sqrt{-1}=i\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\=====================\\\\\sqrt{-36}=\sqrt{(36)(-1)}=\sqrt{36}\cdot\sqrT{-1}=6i\\\sqrt{-100}=\sqrt{(100)(-1)}=\sqrt{100}\cdot\sqrt{-1}=10i\\\\\sqrt{-36}+\sqrt{-100}+7=6i+10i+7=7+16i[/tex]
Answer:
The answer is [tex]16i+7[/tex]
Step-by-step explanation:
In order to determine the answer, we have to know about imaginary numbers.
The imaginary numbers are different to real numbers because they use a new unit called "imaginary unit":
[tex]i=\sqrt{-1}[/tex]
i: imaginary unit
This new unit is applied like a factor when we have even roots with negative numbers inside.
In this case:
[tex]\sqrt{-36}=\sqrt{-1}*\sqrt{36}=6i\\\sqrt{-100}=\sqrt{-1}*\sqrt{100}=10i\\ \\\sqrt{-36}+\sqrt{-100}+7\\ 6i+10i+7\\16i+7[/tex]
Finally, the answer is [tex]16i+7[/tex]
please help , 1-10 , thanks !
Answers
Answers:
22
9
20
17
20
35
26
32
23
9
simplify the square root of 6 * the square root of 8
Answers
Answer:
4√3
Step-by-step explanation:
The question is to simplify √6 × √8
Applying surds
√6 can be written as √2 ×√3
and
√8 can be written as √2 × √4
but √4=2
so;
√8 is 2√2
Write the whole question as
√2×√3×2√2
This can be written as
2√2×√2×√3
But you know √2×√2 = √4 =2
So, write as
2×2×√3 = 4√3
4√3 is the simplified form
Simplified form of expression √6 × √8 is,
⇒ 4√3
We have to given that,
An expression to simplify,
⇒ √6 × √8
Simplify as,
⇒ √6 × √8
Since, √6 = √2 × √3
√8 = √2 × √2 × √2
Hence, We can write as,
⇒ √6 × √8
⇒ √2 × √3 × √2 × √2 × √2
⇒ 4√3
Therefore, Simplified form of expression √6 × √8 is,
⇒ 4√3
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which equation represents a line that passes through (0,-8) and (-5,23)
Answers
Answer:
[tex]\large\boxed{y=-\dfrac{31}{5}x-8}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept - (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
====================================
We have the points (0, -8) → b = -8, and (-5, 23).
Substitute:
[tex]m=\dfrac{23-(-8)}{-5-0}=\dfrac{31}{-5}=-\dfrac{31}{5}[/tex]
Put the value of the slope and of the y-intercept to the equation of a line:
[tex]y=-\dfrac{31}{5}x-8[/tex]
The diagonal of a square is x units. What is the area of the square in terms of x?
Answers
Answer:
[tex]\frac{1}{2}[/tex] x²
Step-by-step explanation:
let the length of the side be l
Then using Pythagoras' identity on the right triangle formed by the diagonal ( hypotenuse ) and the 2 sides
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
l² + l² = x²
2l² = x² ( divide both sides by 2 )
l² = [tex]\frac{1}{2}[/tex] x² ( since A of square = l² )
without actually performing the long division state whether 17 / 3125 will have a terminating decimal expansion or a non-terminating decimal expansion
Answers
Answer:
It is terminating decimal expansion.
Step-by-step explanation:
17/3125 is a terminating decimal expansion.
REASON:
If the factors of the denominator are in the form of 2^n 5^m then the rational number is a terminating decimal expansion otherwise it is recurring. Here n and m are non negative integers.
Proof:
Lets have a look on the solution of the given term.
17/1325
We will break the denominator in the factors:
If we multiply 5 five times than it will give us 1325.
17/1325 = 17/5^5 * 2^0 = 17/2^0 * 5^5
We know that any number with exponent zero = 1
∴ 2^0 = 1
So it satisfies our explanation that the factors of the denominator are in the form of 2^n * 5^m and n and m are non negative integers.
Thus this term has a terminating decimal expansion....
Answer:
Two of the most important characteristics of seawater are temperature and salinity – together they control its density, which is the major factor governing the vertical movement of ocean waters. The temperature of seawater is fixed at the sea surface by heat exchange with the atmosphere.
Step-by-step explanation:
plz mark as brainliest..
WILL MARK BRAINLEST PLEASE HELP!!!!!
Answers
Answer:
C
Step-by-step explanation:
your answer will be option number
(3) {(1,1),(2,9),(4,8)}
I hopes its help's u
please follow me..!!
@Abhi.❤❤
Solve for x in the equation x^2+ 4x-4=8.
X = -6 or x = 2
X=-2+or-2sqrt2
x = -2 or x = 6
x=2+or-2sqrt2
Answers
Answer:
x = -6 or x = 2
Step-by-step explanation:
The given equation is:
[tex]x^{2}+4x-4=8\\\\ x^2+4x-4-8=0\\\\ x^2+4x-12=0\\\\[/tex]
This is quadratic equation, so we can use the quadratic formula to find the roots of the equation i.e. the value of x that satisfy the given equation.
According to the quadratic formula, the two roots will be:
[tex]x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}[/tex]
Here,
a = coefficient of x² = 1
b = coefficient of x = 4
c = constant term = -12
Using these values, we get:
[tex]x=\frac{-4 \pm \sqrt{(4)^2-4(1)(-12)}}{2(1)}\\\\ x=\frac{-4 \pm \sqrt{64}}{2}\\\\ x=\frac{-4 \pm 8}{2}\\\\ x = \frac{-4-8}{2} , x = \frac{-4+8}{2}\\\\ x=-6, x = 2[/tex]
Thus, the two values of x that satisfy the given equation are: -6 and 2. So 1st option gives the correct answer.
A rectangular flower bed is to be 8 m longer than it is wide. The flower bed will have an area of 84 m squared
What will it's dimensions be?
Answers
Answer:
6m wide
14m long
Step-by-step explanation:
Let the length be represented by L.
Let the width be represented by W.
We are given we want the length to be 8 m longer than it's width.
So we want L=8+W.
The area of the rectangle is 84 m squared, this means that LW=84.
So I'm going to substitute L=8+W into LW=84.
LW=84
(8+W)W=84 (L=8W)
So we are going to solve (8+W)W=84 for W.
(8+W)W=84
Distribute:
8W+W^2=84
Rearrange left hand side using commutative property:
W^2+8W=84
Subtract 84 on both sides:
W^2+8W-84=0
Now to factor a quadratic with leading coefficient 1 (assuming it isn't prime) is to find two numbers that multiply to be c=-84 and add up to be b=8.
I'm going to play with factor pairs that multiply to be -84
c=-84=4(-21)=12(-7)=6(-14)
So the number we are looking for is -6 and 14 since -6(14)=-84 and -6+14=8.
The factored form of our equation is:
(W+14)(W-6)=0
This means we need to solve both W+14=0 and W-6=0.
W+14=0
W=-14 (I subtracted 14 on both sides)
W-6=0
W=6 (I added 6 on both sides)
The solution W=-14 makes no sense.
W=6 is the solution for the width. That is the width is 6 m long.
Now the length is 8 more than the width so the length is 14 m long.
Answer:
6m wide and 14m long
Step-by-step explanation:
If a rectangular flower bed is to be 8 m longer than it is wide and the flower bed will have an area of 84 m squared, its dimensions will be 6m wide by 14m long.
L = length
W = Width
help asap!! interpret the meaning of the expression
Answers
Answer:
D
Step-by-step explanation:
This is exponential growth, and to my understanding, the format goes:
initial amount (percent growth/ decay)^time
percent growth = (decimal percent + 1)
percent decay = (1 - decimal percent)
Your equation:
1500(1.02)^t
Using the above format, 1500 appears to be the initial amount, which increases by 2% per annum.
i think
Solve the following addition and subtraction problems. 72km95hm+7g12cg18mg= 12dag5g−7g= 4kg2hg14kg+5kg17hg= 8kg−9g−−−−−−−−−−
Answers
Answer:
a. 8g 1dg 3cg 3mg
b. 11dag 8g
c. 24kg 9hg
d. 7kg 1hg
Step-by-step explanation:
Answer:
a. 8g 1dg 3cg 3mg
b. 11dag 8g
c. 24kg 9hg
d. 7kg 1hg
Step-by-step explanation:
got it from the other person
Help meeeeeeeeeeeeee
Answers
Answer: Second Option
[tex]f (x)=\frac{2}{x}[/tex] and [tex]g(x)=\frac{2}{x}[/tex]
Step-by-step explanation:
If we have a function f(x) and its inverse function [tex]f ^ {- 1} (x) = g (x)[/tex]
Then by definition:
[tex](fog) (x) = (gof) (x) = x[/tex]
Notice that the inverse of the function [tex]f (x)=\frac{2}{x}[/tex] is [tex]f ^ {- 1}(x)=\frac{2}{x}[/tex]
then:
If [tex]f (x)=\frac{2}{x}[/tex] and [tex]g(x)=\frac{2}{x}[/tex]
Then:
[tex](fog) (x) =\frac{2}{\frac{2}{x}}[/tex]
[tex](fog) (x) =\frac{2x}{2}[/tex]
[tex](fog) (x) =x[/tex]
The answer is the second option
A miner dug to a point 1680 feet below sea level.
Write a signed number to represent this elevation.
Answers
Answer:
-1680
Step-by-step explanation:
Above would be positive.
Below would be negative.
You have 1680 below, so the answer as a signed number for the elevation would be -1680.
The signed number - 1680 feet addresses the excavator's exhuming point 1680 feet underneath ocean level (negative worth demonstrates beneath ocean level).
How to write a signed number to represent this elevation.The signed number addressing the height of the point 1680 feet beneath ocean level is - 1680 feet. The negative sign demonstrates that the worth is beneath the reference point, which for this situation is ocean level.
With regard to heights, we utilize positive numbers to address positions over the reference point (ocean level) and negative numbers to address positions beneath it.
The miner dug downward in this scenario, lowering the elevation above sea level. Since it is below the reference point, the elevation is negative.
The greatness of - 1680 feet shows the separation from ocean level to the place of removal, and the negative sign demonstrates the bearing beneath ocean level.
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(03.02)
If g(x) = 2(x - 4), find the value of x if g(x) = 20. (2 points)
Answers
Answer:
14
Step-by-step explanation:
20=2(x-4)
therefore, x=14
Answer:
2(x -4) = 20
2x - 8 = 20
2x = 28
x = 14
Evaluate the expression for the given values. (5 x - 4 y) 2 given x = 1 and y = -1.
Answers
[tex]((5 \times 1) - (4 \times - 1) = \\ 5 - ( - 4) = \\ 5 + 4 = \\ 9[/tex]
Solve -2 (t- 1) = 18
Answers
Answer:
t=-8
Step-by-step explanation:
-2 (t- 1) = 18
Divide each side by -2
-2 (t- 1)/-2 = 18/-2
t-1 = -9
Add 1 to each side
t-1+1 = -9+1
t = -8
Answer:
t = -8
Step-by-step explanation:
Isolate the variable, t. Note the equal sign, what you do to one side, you do to the other.
First, Divide -2 from both sides:
(-2(t - 1))/-2 = (18)/-2
t - 1 = 18/-2
t - 1 = -9
Isolate the variable t. Add 1 to both sides:
t - 1 (+1) = -9 (+1)
t = -9 + 1
t = -8
t = -8 is your answer.
~
The graph shows the relationship between the volume of a rectangular prism and the volume of a square pyramid with an identical bas and height what is the slope of the line
Answers
Answer:
what graph? there is no graph?
a line of best fit predicts that when x equals 32
, y will equal 34.215 but y actually equals 30. what is the residual in this case
Answers
Answer:
Residual in this case is -4.215
Step-by-step explanation:
A residual can be defined by
Residual = Actual value - Predicted value
We are given:
Predicted value of y = 34.215
Actual value of y = 30
Putting values in the formula:
Residual = Actual value - Predicted value
Residual = 30 - 34.215
Residual = -4.215
So, residual in this case is -4.215
Which normal distribution has the greatest standard deviation?
Answers
Answer with explanation:
Both the normal distribution curves have sample mean equal to 16.
Normal distribution curve 1 is more wider than Curve 2, resulting in greater standard deviation.
So, Curve 1 has the greatest standard deviation.
The first normal distribution curve has the greatest standard deviation.
Standard deviation describes how far from the mean the given data set spread out.
A normal distribution that is widely spread out has a high standard deviation while a normal distribution that is close to the mean has low standard deviation.From the given normal distribution curves, the first curve is widely distributed than the second which is clustered around the mean.Thus, we can conclude that the first normal distribution curve has the greatest standard deviation.
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if f(x) = x + 7 and g(x) = 1/x -13, what is the domain of (f O g)(x)
Answers
Answer:
domain of (f O g)(x) is {x|x≠0}
Step-by-step explanation:
Given:
f(x) = x + 7
g(x) = 1/x -13
Putting g(x) in f(x) i.e f(g(x))
(fog)(x)= 1/x -13 +7
= 1/x-6
Domain of 1/x-6 is {x|x≠0} !
For this case we have the following functions:
[tex]f (x) = x + 7\\g (x) = \frac {1} {x} -13[/tex]
We must find [tex](f_ {0} g) (x).[/tex] By definition we have to:
[tex](f_ {0} g) (x) = f (g (x))[/tex]
So:
[tex](f_ {0} g) (x) = \frac {1} {x} -13 + 7 = \frac {1} {x} -6[/tex]
By definition, the domain of a function is given by all the values for which the function is defined.
The function [tex](f_ {0} g) (x) = \frac {1} {x} -6[/tex] is no longer defined when x = 0.
Thus, the domain is given by all real numbers except zero.
Answer:
x nonzero
please answer also if you answer this one please answer my other one it basically the same
Answers
Answer:
D is the correct answer.
Step-by-step explanation:
Step 1: Write the data
Total number of songs = 100
Total ratio = 1
Total percentage = 100%
Ratio of jazz songs = 1/4
Percentage of jazz songs = 1/4 x 100 = 25%
Ratio of pop songs = 1 - 1/4 = 3/4
Percentage of pop songs = 3/4 x 100 = 75%
Step 2: Match the statement.
The correct statement is D; 25% are Julian's songs are jazz because 1/4 = 25/100 and 75% are pop because 3/4 = 75/100.
!!
Which function represents the following graph?
00
Answers
Answer:
[tex]\large\boxed{y=\sqrt[3]{x+3}+3}[/tex]
Step-by-step explanation:
f(x) + n - shift the graph n units up
f(x) - n - shift the graph n units down
f(x + n) - shift the graph n units to the left
f(x - n) - shift the graph n units to the right
===========================================
The original graph ( y = ∛x) shifted 3 units to the left and 3 units up.
Therefore, the new equation is:
y = ∛(x + 3) + 3
Given the Arithmetic sequence A1,A2,A3,A4 45, 51, 57, 63 What is the value of A34?
Answers
Answer:
Value of A(34) = 219
Step-by-step explanation:
A1, A2,A3,A4,45,51,57,63 are in Arithmetic sequence
Common difference in this Arithmetic sequence = 63 - 57 = 06
so, A4 = 45 - 6 = 39
A3 = 39 - 6 = 33
A2 = 33 - 6 = 27
A1 = 27 - 6 = 21
First term of Arithmetic sequence = 21
Common difference = 06
Using general term of Arithmetic sequence,
A(n) = First term + (n - 1) common difference
A(34) = 21 + (34 - 1) 6
A(34) = 21 + 33 × 6
A(34) = 21 + 198
A(34) = 219
Value of A(34) = 219
Which equivalent expression will be generated by applying the Distributive Property and combining like terms in the expression 11 + 4(x + 2y + 4)?
Answers
Answer:
27+4x+8y
or
4x+8y+27 ( I can reorder this a few different ways. I don't know what your choices are)
Step-by-step explanation:
11+4(x+2y+4)
We can apply distributive property to the 4(x+2y+4), this will give us 4x+8y+16.
Bring down the 11+ and we have 11+4x+8y+16.
The only like terms we have is 11 and 16. So reorder using commutative property and get 11+16+4x+8y.
I'm going to simplify the 11+16 part which gives us 27.
In the end we have 27+4x+8y.
Let me line up so it is all nice and neat:
11+4(x+2y+4)
11+4x+8y+16
11+16+4x+8y
27+4x+8y
Which expression is equivalent sqrt10/4sqrt8
Answers
Answer:
The correct option is A
Step-by-step explanation:
The given expression is:
√10/4√8
We have to eliminate the √ from the denominator
4√8 = (2^3)^1/4
Multiply the whole expression by (2)^1/4
=(2)^1/4 * √10/ 2^(1/4)*(2^3)^(1/4)
= 2^(1/4) · 10^(2/4) / 2^1/4+3/4
=2^(1/4) · 10^(2/4) / 2^1+3/4
=2^(1/4) · 10^(2/4) / 2^4/4
=2^(1/4) · 10^(2/4) /2
=2^(1/4) · 100^(1/4) /2
=200^1/4 /2
= 4√200 /2
Thus the correct option is A....
Answer:
correct answer is a
Step-by-step explanation: