The square root of a number can also be negative number so x could also be -9
Taking square root of a numberSquare root of a number is the number such that if it is multiplied by itself we get the square. The opposite of squaring an integer is finding its square root. As we know multiplication of two negative numbers produce a positive number. this is the reason why square of both positive and negative numbers are both positive. therefore, square root of a number can also be positive or neegative both. That is why we can't take square root of negative numbers.
To learn more about square root visit:
https://brainly.com/question/1387049
#SPJ13
Which of the following equations have infinitely many solutions?
Choose all answers that apply:
A. −76x+76=76x+76
B. −76x+76=−76x+76
C. 76x+76=76x+76
D. 76x+76=−76x+76
The two equations with infinitely many solutions are the ones in options B and C.
−76x+76=−76x+7676x+76=76x+76Which of the given equations has infinitely many solutions?An equation only has infinitely many solutions if we have a true equation that does not depend of x.
For example, if you look at option B, we have:
-76x + 76 = -76x + 76
We have the same expression in both sides, if we subtract it in both sides we get:
0 = 0
This is true, and does not depend of x, so this equation has infinitely many solutions.
The same thing happens for equation C.
76x+76=76x+76
Where we have the same thing in both sides.
Learn more about equations:
https://brainly.com/question/13763238
#SPJ1
One fourth the sum of r and ten is identical to r minus 4.
⇒Mathematically this means
[tex]\frac{1}{4} (r+10)= r-4\\\frac{r}{4} +\frac{10}{4} =r-4\\\frac{r}{4}(4) +\frac{10}{4} (4)=r(4)-4(4)\\r+10=4r-16\\r-4r=-16-10\\-3r=-26\\\frac{-3r}{-3} =\frac{-26}{-3} \\r=\frac{26}{3}[/tex]
Attached is the solution.
solve the system by graphing; y= -5/3x + 3 y= 1/3x - 3
Answer:
The solution to the given system is:
x = 3
y = -3
Explanation:
Given the following system of equation:
[tex]\begin{gathered} y=-\frac{5}{3}x+3 \\ \\ y=\frac{1}{3}x-3 \end{gathered}[/tex]The solution to these is the point where the lines intersect.
The graph is shown below:
The solution is x = 3, y = -3
describe the transformation of f represented by G then graph each function
Transfomation 1: the function will undergo vertical shrinking( by a factor of 0.
5)
Transformation 2: the function is shifted 2 units up
Explanation
[tex]f(x)=x^4[/tex]Step 1
the first transformation is the function multiplied by a constant ( 1/2)
If the function is multiplied by a value less than one, all the values of the equation will decrease, leading to a “shrunken” appearance in the vertical direction
so
[tex]\begin{gathered} f(x)=x^4\Rightarrow\frac{1}{2}x^4 \\ \frac{1}{2}is\text{ smaller than 1, so} \end{gathered}[/tex]Transfomation 1: the function will undergo vertical shrinking( by a factor of 0.
5)
Step 2
the second transformation is add 5
[tex]f(x)=x^4\Rightarrow\frac{1}{2}x^4\Rightarrow g(x)=\frac{1}{2}x^4+5[/tex]If a positive number is added, the function shifts up the y-axis by the amount added.
so,
Transformation 2: the function is shifted 2 units up
I hope this helps you
help battery 10% pls hurry
The solution to the simultaneous equation is y = 5.5 and x = 1.5
How to solve for the simultaneous equation'Simultaneous equations are the types of equations in mathematics that is made up of two equations where the equations would have to share variables.
we have
y = 3x + 1 - - - - 1
x + y = 7 - - - - 2
we have to put the value of y in equation 1 into equation 2
we would have
x + 3x + 1 = 7
4x + 1 = 7
4x = 7 - 1
4x = 6
x = 6 / 4
x = 1.5
put the value of x in equation 2 to get y
1. 5 + y = 7
y = 7 - 1.5
y = 5.5
Therefore the values of y is 5.5 while the value of x is 1.5
Read more on simultaneous equations here:
https://brainly.com/question/16863577
#SPJ1
The required solution of the given simultaneous equation is x = 1.5 and y = 5.5.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
y = 3x + 1 _ _ _ _ _ _ (1)
x + y = 7 _ _ _ _ _ _ (2)
From equation 2
y = 7 - x substitute this in equation 1
7 - x = 3x + 1
4x = 6
x = 6 / 4
x = 3 / 2
Now put this x in equation 2
3/2 + y = 7
y = 7 - 3/2
y = 11 / 2
Thus, the required solution of the given simultaneous equation is x = 1.5 and y = 5.5.
Learn more about simultaneous equations here:
https://brainly.com/question/15165519
#SPJ1
Kayla gave 13 of a pan of brownies to Ella and 16 of the pan to Eli. Which choice is the MOST reasonable for the part of the pan of brownies Kayla gave away?
The reasonable fraction for the part of the pan of brownies Kayla gave away is 1/2.
How to illustrate the information?Kayla gave 1/3 of a pan of brownies to Ella and 1/6 of the pan to Eli.
Therefore, the part given away will be the addition of the fractions. This will be:
= 1/3 + 1/6
= 2/6 + 1/6
= 3/6
= 1/2
Therefore, 1/2 of the brownies were given away.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
what is the arithmetic mean of all of the positive two-digit integers with the property that the integer is equal to the sum of its first digit plus its second digit plus the product of its two digits?
The arithmetic mean is 59.
What is arithmetic mean?
It is the sum of collection of numbers divided by the count of the numbers.
Conider AB is the nuber satisfying the condition. Hence,
[tex]10A+B=A+B+A\times B\\9A=A\times B\\[/tex]
Since AB is a two digit number hence, [tex]A\neq 0\\[/tex]. Hence, divide both sides by [tex]A[/tex].
[tex]9=B[/tex]
Hence, B is 9 and A can take any value from 1 to 9.
Hence, numbers are 19, 29, 39, 49, 59, 69, 79, 89,99.
Now, calculate arithmetic mean as follows:
[tex]AM=\frac{Sum \ of \ numbes}{Count \ of \ numbers}\\=\frac{19+29+39+49+59+69+79+89+99}{9}\\=59[/tex]
Hence, arithmetic mean of numbers is 59.
Learn more about arithmetic means from the following link:
https://brainly.com/question/20118982
#SPJ4
If α and β are the roots of the equation ax2+bx+c=0,αβ=4ax2+bx+c=0,αβ=4 and a,b,,c are in A. P then α+β=
Considering the sum and the product of the roots of the quadratic equation, it is found that the numeric value of the expression is given as follows:
[tex]\alpha + \beta = -2.5[/tex]
What are the sum and the product of the roots of a quadratic equation?A quadratic equation is defined as follows:
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
The roots of the equation are given as follows:
[tex]\alpha, \beta[/tex]
The sum of the roots is given as follows:
[tex]\alpha + \beta = -\frac{b}{a}[/tex]
The product of the roots is given as follows:
[tex]\alpha\beta = \frac{c}{a}[/tex]
In the context of this problem, the product is of 4, as [tex]\alpha\beta = 4[/tex] hence:
c/a = 4
c = 4a.
The coefficients are in an arithmetic progression, hence:
b = a + d. (d is the common difference of the sequence).c = a + 2d.We have that c = 4a, hence:
4a = a + 2d
2d = 3a
d = 1.5a.
Hence coefficient b is calculated as follows:
b = a + d = a + 1.5a = 2.5a.
Then the sum of the roots is given as follows:
[tex]\alpha + \beta = -\frac{b}{a} = -\frac{2.5a}{a} = -2.5[/tex]
More can be learned about quadratic equations at https://brainly.com/question/24737967
#SPJ1
Use the associate property to write an expression equivalent to (w+9)+3
W+(9+3) is the equivalent expression of (w+9)+3 by using associate property
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (w+9)+3
The operator in given expression is plus and variable is W.
The associative property of addition states that Changing the grouping of addends does not change the sum.
(x+y)+z=x+(y+z)
Similarly (W+9)+3=W+(9+3)
W+(9+3) is the equivalent expression of (w+9)+3 by using associate property
To learn more on Expression click:
https://brainly.com/question/14083225
#SPJ1
Solve. (−7x−14)−(x−5)
Step-by-step explanation:
-7x(x-5)-(-14)(x-5)
-7x²+35+14x-70
-7x²-14x-35
Hope this is correct
Have a good day
What is the length of the dotted line in the
diagram below? Round to the nearest
tenth.
Answer: Length = 10√2
Step-by-step explanation: You have to use the pythagorean theorem
What’s the answer plss
Opposite Q is length PR
Adjacent is 7
Hypotenuse is 19
We got AH - which is CAH or cos
Cos-1( 7/19) = 68.38....
It's 68.4 degrees
The closest answer to this is B. So, choose that because it maybe due to a typing error.
Hope this helps!
Help da brother out.
Answer:
top: y=f(x)=-2x+5
middle: y=4x
last: y=(9/2)x-3
Write an equation of the line through (-3,- 6) having slope17/16Give the answer in standard form.The equation of the line is
The equation of a line in Standard form is:
[tex]Ax+By=C[/tex]Where "A", "B" and "C" are Integers ("A" is positive).
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
In this case you know that:
[tex]m=\frac{17}{16}[/tex]And knowing that the line passes through the point
[tex]\mleft(-3,-6\mright)[/tex]You can substitute values and solve for "b":
[tex]\begin{gathered} y=mx+b \\ -6=(\frac{17}{16})(-3)+b \\ \\ \\ -6=-\frac{51}{16}+b \\ \\ -6=-\frac{51}{16}+b \\ \\ -6+\frac{51}{16}=b \\ \\ b=-\frac{45}{16} \end{gathered}[/tex]Then, the equation of this line in Slope-Intercept form is:
[tex]y=\frac{17}{16}x-\frac{45}{16}[/tex]Now that you have this equation, you can write it in Standard form as following:
[tex]\begin{gathered} y+\frac{45}{16}=\frac{17}{16}x \\ \\ \frac{45}{16}=\frac{17}{16}x-y \\ \\ \frac{17}{16}x-y=\frac{45}{16} \end{gathered}[/tex]The answer is:
[tex]\frac{17}{16}x-y=\frac{45}{16}[/tex]I need help with my mathWrite the slope-intercept form of the equation of each line
Answer:
y = -1
Explanation:
The slope-intercept form of the equation of a line has the form:
y = mx + b
Where m is the slope and b is the y-intercept.
The slope can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are the coordinates of two points in the line.
So, replacing (x1, y1) by (1, -1) and (x2, y2) by (2, -1), we get:
[tex]m=\frac{-1-(-1)}{2-1}=\frac{-1+1}{1}=\frac{0}{1}=0[/tex]On the other hand, the y-intercept is the point where the line crosses the y-axis. So, the y-intercept is -1.
Finally, the equation of the line in the slope-intercept form is:
y = 0x - 1
y = -1
So, the answer is y = -1
the average number of miles driven on a full tank of gas for a hyundai veracruz before its low fuel light comes on is 320. assume this mileage follows the normal distribution with a standard deviation of 30 miles. what is the probability that, before the low fuel light comes on, the car will travel
The probability that, before the low fuel light comes on the car will travel is 0.2576
Given,
The average number of miles driven on a full tank of gas before its low fuel light comes on is ( μ )= 320
It follows the standard deviation of ( δ ) = 30
For the normal distribution,
P(X < x) = P( Z < x - μ / δ)
a)
P( X < 330) = P( Z < 330 - 320 / 30)
= P( Z < 0.3333)
= 0.6306
b)
P( X > 308) = P( Z > 308 - 320 / 30)
= P( Z > -0.4)
= P( Z < 0.4)
= 0.6554
c)
P( 305 < X < 325) = P( X < 325) - P( X < 305)
= P( Z < 325 - 320 / 30) - P( Z < 305 - 320 / 30)
= P( Z < 0.1667) - P( Z < -0.5)
= 0.5662 - ( 1 - 0.6915)
= 0.2576
d) P(X = 340) = 0
Since X is a continuous random variable (For normal distribution).
To learn more about standard deviation click here:
https://brainly.com/question/12402189
#SPJ4
Explain if the triangles below are congruent or not and explain why you think that.
In this picture, we have the triangles with two common sides and one common angle. However, they are not congruent, as they do not follow any of the congruence theorems. The congruence theorem with two sides and an angle is the SAS(Side-Angle-Side). However, the angle has to be the angle between the two sides, which does not happen in this case.
The marked price of an article is Rs.2080. After allowing d% discount and levying(d-2)% VAT,the cost of the article becomes Rs 1997.84. find the discount amount and VAT amount
The discount rate is 15% and the VAT rate is 13%
What is the value of the discount?The following can be deduced:
MP = 2080
Discount = d%
VAT = (d-2)%
Cost = 1997.84
Apply discount:
2080 - d% = 2080*(1 - 0.01d)
Add VAT:
2080*(1 - 0.01d) + (d - 2)%
2080*(1 - 0.01d) * (1 + (d -2)/100)
2080*(1 - 0.01d) * (0.98 + 0.01d)
= 1997.84
(1 - 0.01d)(0.98 + 0.01d) = 1997.84/2080
0.98 + 0.01d - 0.0098d - 0.0001d²
= 0.9605
- 0.0001d² + 0.0002d + 0.98- 0.9605 = 0
0.0001d²- 0.0002d - 0.0195 = 0
d² - 2d + 195 = 0
Solving the quadratic equation we get:
d = 15
Therefore discount is 15%
VAT rate = d - 2 = 15% - 2% = 13%
The concept shown above is the calculation for the discount and the amount of the value added tax.
Learn more about discount on:
https://brainly.com/question/14883253
#SPJ1
Water flows through a pipe at a rate of 7 liters every 9.5 hours. Express this rate of
flow in pints per week. Round your answer to the nearest whole number.
The rate of water flow per week is 124 liters.
What is the of water flow?
Running water naturally travels along the slope in a direction determined by gravity. This is referred to as a water flow.
Given is, the water flows through a pipe at a rate of 7 liters every 9.5 hours.
So,
water flows per hour = [tex]\frac{7}{9.5}[/tex]
Hours in a week = 7 x 24 = 168 hours
Water flow per week = hours in a week x water flow per hour.
[tex]= 168 x \frac{7}{9.5} \\= 123.7894[/tex]
Water flow per week = 124 liters.
Therefore, the water flow per week is 124 liters.
To know more about the water flow, click on the link
https://brainly.com/question/17278515
#SPJ13
formula p*r*t=I 4350 * 4 * x = I
As per the concept of Simple interest, the value of x that refers the time is 0.000057.
Simple interest:
Simple interest is obtained by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
Give,
Here we have the expression like the following:
p*r*t=I
4350 * 4 * x =1
Here we need to find the value of x.
While we looking into the expression, we have identified that the value of
Principal amount (p) = 4350
rate of interest (r) = 4
Time = x
Interest amount (I) = 1
So, while we execute this expression then we get the value of times as,
=> 4350 x 4 x x = 1
Here we need the value of x so, we have to move the other to the right hand side, then we get,
=> x = 1/(4350 x4)
=> x = 1/17400
=> x = 0.000057
Therefore, the value of x is 0.000057.
To know more about Simple interest here.
https://brainly.com/question/25845758
#SPJ1
Please solve this quickly. Thanks!
Applying the trapezoid midsegment theorem, the diameter of the bottom layer of the cake = KS = 26 inches.
What is the Diameter of a Circular Shape?The diameter of any circular shape is the length of the line segment that divides the shape into two equal halves and runs through its center.
What is the Trapezoid Midsegment Theorem?The trapezoid midsegment theorem states that the length of the midsegment of a trapezoid that is parallel to its bases is equal to half of the sum of the bases.
Using the trapezoid midsegment theorem we have:
MQ = 1/2(NP + LR)
Substitute
MQ = 1/2(8 + 20)
MQ = 1/2(28)
MQ = 14 inches
Also, we would also have:
LR = 1/2(MQ + KS) [trapezoid midsegment theorem]
Substitute
20 = 1/2(14 + KS)
40 = 14 + KS
40 - 14 = KS
26 = KS
KS = 26
The diameter = KS = 26 inches.
Learn more about diameter on:
https://brainly.com/question/390660
#SPJ1
The diameter(KS) of the cake's bottom layer is calculated using the trapezoid midsegment theorem is 26 inches.
What is a Diameter?The diameter of a circle is equal to the length of the line segment running through its center and dividing it into two equal halves.
According to the trapezoid midsegment theorem the length of a trapezoid's midsegment that is parallel to its bases is equal to half of the sum of the bases.
MQ = 1/2(NP + LR)
MQ = 1/2(8 + 20)
MQ = 1/2(28)
MQ = 14 inches.
And,
LR = 1/2(MQ + KS).
20 = 1/2(14 + KS)
40 = 14 + KS
40 - 14 = KS
26 = KS
KS = 26
The diameter(KS) is 26 inches.
Learn more about trapezium here :
https://brainly.com/question/22607187
#SPJ1
In the figure below, N lies between M and P.
Find the location of N so that the ratio of MN to NP is 7 to 2.
M
- 27
Location of N
N
?
X
→→
Ś
P
-9
The position of N on the line segment is at the -14 mark
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
How to determine the location of N?The complete question is added as an attachment
From the attachment, we have
The ratio is given as:
MN : NP = 7 : 2
Also, we have
Location of M = -27
Location of P = -9
The location of N is then calculated as
N = MN/(MN + NP) * (M - P)
Substitute the known values
N = 7/(7 + 2) * (-27 + 9)
Evaluate the sum
N = 7/9 * -18
Evaluate the product
N = -14
Hence, the location of point N is -14
Read more about line segment ratio at
https://brainly.com/question/17374569
#SPJ1
The dial on a combination lock contains markings which represent the numbers from 0 to 39. How many 3- number combinations are possible if the first and the second must be different odd numbers, while the third number must not be an odd number?.
There are 64000 distinct combinations .
The dial for the standard combination lock is fastened to a spindle. The spindle travels through many wheels and a drive cam inside the lock. Every number has one wheel, hence the number of wheels in a wheel pack depends on how many numbers are in the combination.
The lock uses the numbers 0 to 39 and has 64,000 distinct combinations.
How many possible three-number combinations are there?
You have 10 options for the first digit, 9 options for the second digit, and 8 options for the third digit, giving you 10x9x8 = 720 if you want all three possible numbers with no duplication of the digits.
Learn more about Three-number combination here:
brainly.com/question/27242731
#SPJ1
find the area of this shape. 100pts
Answer:
A = 540 m²
Step-by-step explanation:
consider the shape split into 3 rectangles
the length is divided into 3 congruent sections
single dash = 30 m ÷ 3 = 10 m
the width is divided into 3 congruent sections
double dash = 27 m ÷ 3 = 9 m
then area (A) is the total of the 3 rectangular areas
A of left rectangle = 10 × 9 = 90 m²
A of middle rectangle = 10 × (9 + 9) = 10 × 18 = 180 m²
A of right rectangle = 10 × 27 = 270 m²
total area = 90 + 180 + 270 = 540 m²
How do you write out the sum of 2 consecutive even intergers
Let's call x to an unknown even integer. The next (consecutive) even integer will be x + 2. For instance, if x = 6, then the next even integer will be 6 + 2 = 8.
In consequence, the sum of two consecutive even integers is:
x + (x + 2)
a binomial experiment with probability of success and trials is conducted. what is the probability that the experiment results in fewer than successes? do not round your intermediate computations, and round your answer to three decimal places. (if necessary, consult a list of formulas.)
One of the two outcomes, known as success or failure, arises from every try. From trial to trial, the chance of success, indicated by the symbol p, stays constant. There are n independent trials.
How to find the number of success in a binomial distribution?The likelihood of success is constant from trial to trial, and subsequent trials are independent. A binomial distribution, which derives from counting successes across a series of trials, has just two possible outcomes on each trial.
One of the two outcomes, known as success or failure, arises from every try. From trial to trial, the chance of success, indicated by the symbol p, stays constant. There are n independent trials. In other words, the results of one trial do not influence those of the others.
An experiment with a fixed number of independent trials and just two results is referred to as a binomial experiment.
To learn more about binomial distribution refer to:
https://brainly.com/question/9325204
#SPJ4
The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is 18 inches in diameter.
Suppose a standard dartboard is hung at standard height so that the bull's-eye is 12 feet from a wall to its left.
Brian throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5 feet above the floor.
Does Brian's dart land on the dartboard?
Drag the choices into the boxes to correctly complete the statements.
Considering the equation of a circle, it is found that:
The equation of the circle that represents the dartboard is [tex](x - 12)^2 + \left(y - \frac{17}{3}\right)^2 = 81[/tex], where the origin is the lower left corner of the room and the unit of the radius is in inches;The position of Brian's dart is represented by the coordinates (11.5, 5). Brian's dart does land on the dartboard.What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given as follows:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In the context of this problem, we have that:
The radius of the circle is of 9 inches, as the diameter is of 18 inches and the radius is half the diameter.The height is of 5 feet 8 inches = 5 feet and 2/3 feet = 17/3 feet, which is the y-coordinate of the center.The bull's-eye is 12 feet from a wall to its left, hence the x-coordinate of the center is of 12.Hence the equation of the circle is given by:
[tex](x - 12)^2 + \left(y - \frac{17}{3}\right)^2 = 81[/tex]
Brian's dart lands at the following position:
(11.5, 5)
All the points that land on the dartboard respect the following equation:
[tex](x - 12)^2 + \left(y - \frac{17}{3}\right)^2 \leq 81[/tex]
For the coordinate where the dart landed, we have that:
(11.5 - 12)² + (5 - 17/3)² = 0.7 < 81, meaning that Brian's dart lands on the dartboard.
More can be learned about the equation of a circle at https://brainly.com/question/24307696
#SPJ1
1. In polynomial x - 12; 12 is a ______
Answer :- Constant term
In p(x) = x - 12, 1 is the coefficient of x and -12 is the constant term.
The coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4). What are the coordinates of the image if the quadrilateral is translated 4 units down and 3 units right
If the coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4) and it is translated 4 units down and 3 units right, then the coordinates of the image is A'(-3,-2), B'(-2,-1), C'(10,-1) and D'(3,0)
The coordinates of the quadrilateral ABCD is
A (-6,2) , B(-5,3), C(7,3) and D(0,4)
The quadrilateral is translated 4 units down and 3 units right
After translation
A(x, y)⇒ A(x + a, y +b)
The value of a and b will be positive if the shift is right and up.
The value of a and b will be negative if the shift is left and down.
Therefore
a = 3, b = -4
The coordinates of A' =(-6+3,2-4)=(-3,-2)
The coordinates of B' =(-5+3,3-4)=(-2,-1)
The coordinates of C' =(7+3,3-4)=(10,-1)
The coordinates of D' =(0+3,4-4)=(3,0)
Hence, If the coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4) and it is translated 4 units down and 3 units right, then the coordinates of the image is A'(-3, -2), B'(-2, -1), C'(10, -1) and D'(3, 0)
Learn more about translation here
brainly.com/question/11805053
#SPJ1
Can you please help me out with a question
Formular for total surface area of a cylinder
[tex]TSAofacylinder=2nr^2\text{ + 2nrh}[/tex][tex]\begin{gathered} T\mathrm{}S\mathrm{}A\text{ = 2 }\times\text{ }\pi\text{ }\times7^2\text{ + 2 }\times\pi\times7\times21ft^2^{} \\ \text{ = 307.876 + }923.628 \\ \text{ = 1231.504 ft}^2 \\ =1231.5ft^2\text{ (nearest tenth)} \end{gathered}[/tex]S = 1231.5 sq ft
