Answer:
f(x) = (x - 2)²
Step-by-step explanation:
f(x) = x² - 4x + 4 is a perfect trinomial.
You know a trinomial is perfect when double the square root of the first term multiplied by the square root of the last term equals the middle term.
As an equation, a trinomial in the form ax² + bx + c = 0:
2√a√c = b is a perfect trinomial.
Perfect trinomial are factored in this form:
(√a ± √c )(√a ± √c ) = (√a ± √c )²
Whether the sign is + or - depends on if the middle term is positive or negative.
In f(x) = x²-4x+4, the middle term is a negative.
The square root of the first term is 1.
The square root of the second term is 2.
The factored form is (x - 2)²
Level D:
Rollie was successful in losing weight. He had a goal
weight in mind. He went on a diet for three months. Each
month, he would lose one-third of the difference between
his current weight and his goal weight and an additional
three pounds. At the end of three months, he was just 3
pounds over his goal weight. How many pounds did he
lose in those three months?
Explain how you arrived at your solution.
Answer:
If X is the starting weight, total pounds lost in three months is
(0.132X + 2.37)lbs
Step-by-step explanation:
Let the starting weight be X(lb)
Let the target ending weight be Y(lb)
Since Rollie ended with 3(lbs) above goal weight, final weight is Y+3(lb)
Each month, Rollie lost 1/3 of the difference between current weight and goal weight, hence
In the first month, Rollie lost 1/3 of (X - Y)
but since Rollie ended up with 3lbs above target ending weight, the actual weight loss is 1/3(X - Y) + 3
Hence by the end of the first month, Rollie's new weight is X - (1/3(X - Y)) + 3
which is equal to
X - 1/3X + 1/3Y - 3.
= 2/3X + 1/3Y - 3
By the second month, Rollie's starting weight is 2/3X + 1/3Y - 3(lb)
while her target ending weight still remains (Y)
but the actual ending weight is Y + 3
hence in the second month, Rollie lost 1/3(2/3X + 1/3Y - 3 - Y) + 3
= 2/9X + 1/9Y - 1 - 1/3Y + 3
= 2/9X - 2/9Y + 2
hence by the end of the second month, Rollie's new weight is
(2/3X + 1/3Y - 3) - (2/9X - 2/9Y + 2)
= 2/3X - 2/9X + 1/3Y + 2/9Y - 3 - 2
= 4/9X + 5/9Y - 5
By the third month, Rollie's starting weight is 4/9X + 5/9Y - 5(lb)
while her target ending weight still remains (Y)
but the actual ending weight is Y + 3
hence in the third month, Rollie lost 1/3(4/9X + 5/9Y - 5 - Y) + 3
= 4/27X + 5/27Y - 5/3 - 1/3Y + 3
= 4/27X - 4/27Y + 4/3 ------------------------- eqn (*)
hence by the end of the third month, Rollie's new weight is
(4/9X + 5/9Y - 5) - (4/27X - 4/27Y + 4/3)
= 4/9X - 4/27X + 5/9Y + 4/27Y - 5 - 4/3
= 8/27X - 19/27Y - 19/3
Hence in three months, Rollie's new weight is 8/27X - 19/27Y - 19/3
To ascertain how much weight Rollie lost in three months, there is need to equate the estimated ending weight to the final weight (Y + 3)
Therefore:
8/27X - 19/27Y - 19/3 = Y + 3
this implies that
8/27X - 19/27Y - Y - 19/3 - 3 = 0
8/27X - 36/27Y -28/3 = 0
Since Y is the target ending weight
the ending weight is generated by solving the equation with respect to Y
36/27Y = 8/27X - 28/3
multiply through by 27/36
Y = 2/9X - 7
Hence weight lost in three months is generated by substituting for Y = 2/9X - 7 in eqn (*)
Since eqn * is 4/27X - 4/27Y + 4/3
the lbs lost in three months is
4/27X - 4/27(2/9X - 7 ) + 4/3
= 4/27X - 8/243X + 28/27 + 4/3
= (32/243)X + 64/27
which in decimal is
(0.132X + 2.37)lbs
The total pounds of weight that will be lost in three months will be (0.132x + 2.37)lbs.
How to compute the weight?The starting weight is illustrated by x. The target ending weight is illustrated by y.
In the first month, the weight list by Rollie will be 1/3 × (x - y) and her new weight will be:
= 2/3x + 1/3y - 3
In the second month, the starting weight will be 2/3x + 1/3y - 3. The weight lost by the end of the second month will be:
= 1/3 × (2/3x + 1/3y - 3) + 3
= 2/9x - 2/9y + 2
The new weight will be:
= (2/3x + 1/3y - 3) - (2/9x - 2/9y + 2)
= 4/9x + 5/9y - 5
In conclusion, the weight lost in three months will be:
= 4/27x - 4/27(2/9x - 7) + 4/3
= 4/27x - 8/243x + 28/27 + 4/3
= 32/343x + 64/27
= 0.132x + 2.37
In conclusion, the total pounds of weight that will be lost in three months will be (0.132x + 2.37)lbs.
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Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality:
y > one half x + 2 (5 points)
The origin is not included in the shaded region and the shaded area is above the line.
The origin is not included in the shaded region and the shaded area is below the line.
The origin is included in the shaded region and the shaded area is above the line.
The origin is included in the shaded region and the shaded area is below the line.
Answer:
The correct option is
The origin is included in the shaded region and the shaded area is below the line.
Step-by-step explanation:
Y>3/2x + 2
Put x=0
Y= 2
(0,2)
Put y=0
X= -4/3
(-4/3,0)
See attached picture for the sketch
Answer:
The origin is included in the shaded region and the shaded area is below the line.
PLEASE HELP!!!
Nivyana and Ana are selling their apparel to earn money for a cruise. Knitted scarves are $50, and mittens are $25 per pair. They cannot make more than 30 scarves and mittens combined. They need to earn at least $1000 to pay for the cruise and souvenirs.
Part A:Write the inequalities that would represent the situation
Part B: GRAPH the system of linear inequalities and shade where the solutions are.
Part C: Identify two possible solutions to Nivyana and Ana's situation
--------- scarves ------------scarves
---------------mittens -----------mittens
Step-by-step explanation:
Part A:
Let [tex]m[/tex] be the number of mittens and [tex]s[/tex] be the number of scarves. Then we have the inequalities:
[tex]s+m\leq 30.[/tex] This says Nivyana and Ana cannot make more than 30 scarves
[tex]50s+25m\geq 1000.[/tex] This says that Nivyana and Ana have to earn at least $1000.
Part B:
The graph is attached.
Notice that the graphs of the inequalities are solid lines, this just means that the points on these lines included to the solutions of each inequality.
The darker shaded region and the solid lines bounding it, are the solutions to the inequalities because that's where the values common to both inequalities are found.
Part C:
From the graph we get two possible solutions:
15 scarves & 10 mittens
25 scarves & 5 mittens.
These two points lie on the solid lines that bound the darker shaded region (I picked those points to stress that the lines bounding the dark region are also solutions.)
Seth goes to the farmers' market every month to buy some of Ms. Wells's homemade jam. The jam costs $5 per jar. Last weekend, Ms. Wells gave a 20% discount for buying at least two flavors. So, Seth bought b jars of blackberry jam and s jars of strawberry jam.
Pick all the expressions that represent how much Seth spent on jam last weekend.
Seth's spending on jam can be represented by two expressions: 0.80*J*(b + s) and 4*(b + s). The calculations involve finding the total cost without the discount, finding the amount of the discount, and then subtracting the discount from the total cost.
Explanation:Let's denote the price of one jar of jam as J, which is $5. The number of jars of blackberry jam that Seth bought is denoted as b, and the number of jars of strawberry jam as s. Without the discount, the total cost for all the jam he bought would be J*(b + s). Given that Ms. Wells offers a 20% discount for purchasing at least two jars of jam, Seth's actual spending would be
Calculate the total cost without the discount: J*(b + s), Calculate the amount of the discount: 0.20*J*(b + s), Subtract the discount from the total cost: J*(b + s) - 0.20*J*(b + s).
So, Seth's spending is represented by the expression 0.80*J*(b + s) or, substituting J = $5, by 4*(b + s).
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If x =− 2 and x^2+y^2+3xy =-5 , then find y
Answer:
y = 3
Step-by-step explanation:
Given:
x²+y²+3xy =-5 and x = -2
Substituting x=-2 into the equation:
(-2)² + y² + 3y(-2) = -5
4 + y² - 6y = -5
y² - 6y +4 + 5 = 0
y² - 6y +9 = 0 (solve by factorization)
(y-3) (y-3) = 0
y = 3
The selling price of a box of crackers is $1.75 You mark the crackers up to $2.54 . What is the markup percentage?
The markup percentage is 45.14%
Step-by-step explanation:
The given is:
The selling price of a box of crackers is $1.75You mark the crackers up to $2.54We need to find the markup percentage
The markup percentage = [tex]\frac{New-Old}{old}[/tex] × 100%
∵ The selling price of a box of crackers is $1.75
∴ Old = 1.75
∵ You mark the crackers up to $2.54
∴ New = 2.54
- Substitute these values in the rule above
∵ The markup percentage = [tex]\frac{2.54-1.75}{1.75}[/tex] × 100%
∴ The markup percentage = [tex]\frac{0.79}{1.75}[/tex] × 100%
∴ The markup percentage = 0.4514 × 100%
∴ The markup percentage = 45.14%
The markup percentage is 45.14%
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Answer:
The markup percentage is 45%.
Step-by-step explanation:
#18 i can't figure this out
Answer:
∠Q = 75 °
Step-by-step explanation:
Since PR = PQ then Δ PQR is isosceles and the base angles are congruent, that is
∠R = ∠Q = 2x + 15
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180
2x + 15 + 2x + 15 + x = 180, that is
5x + 30 = 180 ( subtract 30 from both sides )
5x = 150 ( divide both sides by 5 )
x = 30
Hence
∠Q = 2x + 15 = (2 × 30) + 15 = 60 + 15 = 75°
answer and explanation???
Answer:
Step-by-step explanation:
x = 60 + 60 = 120
Exterior angle equals the sum of opposite interior angles.
What point is interected between 10x-3y=19 and 5x+4y=-7
Answer:
(1, -3)
Step-by-step explanation:
Solve the system of equations of the two lines:
10x-3y=19 ------> eq 1
5x+4y=-7 --------> eq 2
Solve by elimination:
eq 2 x 2
2( 5x+4y) = 2(-7 )
10x + 8y = - 14 ------> eq 3
eq3 - eq 1:
(10x + 8y) - (10x-3y) = - 14 - 19
10x + 8y - 10x + 3y = -33
8y + 3y = -33
11y = -33
y = -3 (substitute back into eq 1)
10x - 3y = 19
10x - 3(-3) = 19
10x + 9 = 19
10x = 19 - 9
10x = 10
x = 1
Hence the intersection point is (1, -3)
what is the solution of the systrem 2x - y = -7 4x - y = -4
Answer:
x=3/2, y=10. (3/2, 10).
Step-by-step explanation:
2x-y=-7
4x-y=-4
--------------
-2(2x-y)=-2(-7)
4x-y=-4
---------------------
-4x+2y=14
4x-y=-4
-----------------
y=10
2x-10=-7
2x=-7+10
2x=3
x=3/2
A professor wants to randomly select 4 students to go to the board. She decides to randomly select the fourth student who enters the classroom and every ninth student after that. Determine the students who will be going to the board. Write down the student numbers.
To determine the students selected to go to the board, start with the fourth student and then select every ninth student thereafter. Thus, the students chosen are the 4th, 13th, 22nd, and 31st students who enter the classroom.
Explanation:The question involves determining which students a professor will select to go to the board based on a specific selection process. The professor decides to randomly select the fourth student who enters the classroom and every ninth student after that. To find out who these students are, we begin by identifying the fourth student initially. After the fourth student, every ninth student subsequently means we add 9 to the initial student's number to find the next student.
The fourth student who enters
The fourth student + 9 = the 13th student
The 13th student + 9 = the 22nd student
The 22nd student + 9 = the 31st student
Therefore, the students selected to go to the board are the 4th, 13th, 22nd, and 31st students who enter the classroom.
The students who will be going to the board are students 4, 9, 18, and 27.
Let’s determine the students who will be going to the board based on the professor’s selection criteria:
1. The fourth student who enters the classroom.
2. Every ninth student after that.
Let’s find the student numbers:
1. The fourth student corresponds to the 4th position.
2. The ninth student corresponds to the 9th position.
3. The 18th student corresponds to the ninth student after that (since 9 + 9 = 18).
4. The 27th student corresponds to the ninth student after the 18th student (since 18 + 9 = 27).
Therefore, the students who will be going to the board are students 4, 9, 18, and 27.
There are 128128128 ounces in a gallon. There are 444 quarts in a gallon.
How many ounces are in a quart?
Answer:
32 ounces
Step-by-step explanation:
128oz=1gal
4quarts=1gal
128÷4=32
32oz=1 quart
Answer:
1
Step-by-step explanation:
hope this helps some one
stay safe and pease still were a mask
PLS NEED ASAP
FIRST WILL BE AWARDED
find the value of x in each case.
1. Use the exterior angle theorem that states that an exterior angle in a triangle is equal to its two remote interior angles.
x+46=84
x=38 degrees
2. There are two parallel lines cut by transversal. We can see a same side interior relationship.
3x-5+90+2x=180
5x=95
x=19 degrees
3. Use exterior angle theorem again.
90+34=x+72
x=52 degrees
Find the unit rate please and thank you...
Answer:
the unit rate is 1/10.
Step-by-step explanation:
4/40 divided by 4 equals 1/10
unit rate is 0.1 tickets per dollar
How many inches are in 15% of 1.2 feet?
Answer:
2.16 inches so ya
The number of inches in 15 percent of 1.2 foot is obtained as 216.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The number of inches in 1 feet = 12.
Then, in 1.2 foot the inches are 1.2 × 12 = 14.4.
Now, the percent value 15% of 1.2 foot is given as below,
15% × 1.2 foot
⇒ 15/100 × 14.4 inch
⇒ 216 inch
Hence, the number of inches are given as 216.
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Elijah made 100 brownies this week. He baked 4 more than three times the total he made last week. How many brownies did he bake last week?
Answer:
32
Step-by-step explanation:
Subtract 4 from 100
96
Divide by 3
32
The solution to the equation is x = 32, so Elijah baked 32 brownies last week.
Explanation:To find out how many brownies Elijah baked last week, we need to solve the equation 100 = 4 + 3x, where x is the number of brownies he made last week. Here are the steps to solve the equation:
Subtract 4 from both sides of the equation: 100 - 4 = 3xSimplify: 96 = 3xDivide both sides of the equation by 3: 96 ÷ 3 = xCalculate the result: x = 32Therefore, Elijah baked 32 brownies last week.
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10 POINTS!! Brainliest!
Find the volume of the prism. Round to the nearest tenth if necessary.
Answer:
308 cm³
Step-by-step explanation:
The volume (V) of a rectangular prism ( cuboid ) is
V = lbh ( l is the length, b the breadth and h the height )
Here l = 11, b = 7 and h = 4, thus
V = 11 × 7 × 4 = 308 cm³
CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION ASAP 30 points
Answer:
What question? I mean all you said was 'this question' so I don't know ;-;
Step-by-step explanation:
What is 10+10 Please help meeee
Answer:
20
Step-by-step explanation:
10 + 10 = 20
Hope this helps :)
-18g+14g+14g=-10 solve for g
Answer:
-1
Step-by-step explanation:
add the 3 numbers together and then you get 10 so then you divide -10 by 10 and you -1
Answer:
g=5/23
Step-by-step explanation:
46g=1046/46g=g10/46=5/23g=5/23What is the product?
(7x²)(2x + 5)(x² - 4x-9)
14x5 – x4 - 46x3 - 58x2 – 20x-45
14x6 – 56x5 – 91x4 - 140x2 - 315x2
14x? - 56x6 – 126x + 35x4 – 140X2-315x2
14x12 – 182x® + 35x4 – 455x2
Final answer:
To find the product of the given expression (7x²)(2x + 5)(x² - 4x-9), we can use the distributive property to multiply each term.
Explanation:
To find the product of the given expression (7x²)(2x + 5)(x² - 4x-9), we can use the distributive property to multiply each term.
First, multiply (2x + 5) with (x² - 4x-9) using the distributive property.
(2x + 5)(x² - 4x-9) = 2x*(x² - 4x-9) + 5*(x² - 4x-9)
= 2x³ - 8x² - 18x + 5x² - 20x-45
= 2x³ - 3x² - 38x - 45
At midnight, the temperature was 34°F. By 6:00 a.m. it had dropped 8°, and by noon it had increased by 11°. What was the temperature at noon?
Answer:
The temperature at noon was 37 °F.
Step-by-step explanation:
Given:
Temperature at midnight is 34 °F.
Reduction in temperature by 6:00 a.m. is 8°. So, temperature after reduction is given as the difference in temperature at midnight and morning.
Therefore, temperature by 6:00 a.m. in the morning is given as:
Reduced temperature = Midnight temperature - Reduction in temperature.
Reduced temperature = 34 °F - 8 °F = 26 °F.
Now, by noon, the temperature is increased by 11 °F. Therefore, the final temperature by noon is addition of 11 degree to the temperature that was in the morning. Therefore,
Temperature at noon = Temperature in morning + Increase in temperature.
Temperature at noon = 26 °F + 11 °F = 37 °F.
So, the temperature at noon is a 3 °F increase to the temperature at midnight and is equal to 37 °F.
37 boiiiiiiiiiiiiiiiii
When lines the bottom of her first pan with aluminum foil. The area of the rectangle piece of foil is 11 1/4 in.². Its length is 4 1/2 inches. What is the width of the foil
Answer:
2.5 or 2 1/2 in
Step-by-step explanation:
Area = width x length
width = area / length = 11.25 / 4.5 = 2.5
Use a paragraph, flow chart, or two-column proof to prove the angle congruence. Given: CXY ≅ BXY CAX ≅ BAX AC≅ AB Prove: XCY ≅ XBY
The Question is Incomplete with the Figure,So the complete Question with Diagram is below.
Answer:
The Proof is given Below.
Step-by-step explanation:
Given:
∠CXY ≅ ∠BXY
∠CAX ≅ ∠BAX
AC≅ AB
To Prove:
∠XCY ≅ ∠XBY
Proof:
In Δ AXC and Δ AXB
STATEMENT REASONS
1. AC ≅ AB 1. Given
2. ∠CAX ≅ ∠BAX 2. Given
3. AX ≅ AX 3. Reflexive Property
4. ΔAXC ≅ ΔAXB 4. Side-Angle-Side congruence test
5. ∴ CX ≅ BX 5.corresponding parts of congruent triangles........( 1 )
Now ,
In Δ XYC and Δ XYB
STATEMENT REASONS
1. CX ≅ BX 1. Proved above from ( 1 )
2. ∠CXY ≅ ∠BXY 2. Given
3. XY ≅ XY 3. Reflexive Property
4. ΔAXC ≅ ΔAXB 4. Side-Angle-Side congruence test
5. ∴ ∠XCY ≅ ∠XBY 5. Corresponding parts of congruent triangles...........Proved
Answer:
See attached image
Step-by-step explanation:
Hope this helps!
AN EASY PERCENTAGE PROBLEM. In a semiconductor companies quality control test machine found that 22 out of a sample of us 600 computer chips were defective how many of the 36,000 computer chips the company makes each year would you expect to be defective???
Answer:
1320
Step-by-step explanation:
Write a proportion.
22 / 600 = x / 36,000
Cross multiply.
600x = 22 × 36,000
Solve for x.
x = 1320
Answer:
Step-by-step explanation:
1320
What is the equation of the line graphed below?
Answer:
C
Step-by-step explanation:
The slope is 4/1, written as 4
The y int is 4
Write the equation in y = mx + b form
y = 4x + 4
what is a squar plus b squiar
Answer:
The theorem states that if a right triangle has two sides equal to a and b, and a hypotenuse equal to c, then a squared plus b squared equals c squared. The hypotenuse of a right triangle is the side opposite the right angle.
Step-by-step explanation:
A flour mill produces the same amount of flour every hour. At the end of 16 hours , the mill has produced 48,000 pounds of flour . How many pounds of flour does the mill produce in 1 hour ?
Answer: 3,000
Step-by-step explanation:
Divide 48,000 by 16
48,000 ÷ 16 = 3,000
Answer:
3000
Step-by-step explanation:
If they produce 48,000 in 16 hours, that means in one hour they produce 48,000 divided by 16.
48000 ÷ 16 = 3000
evaluate 8 7/8+(7 5/6-2 1/3)
Answer:
[tex]14 \frac{3}{8}[/tex]
Step-by-step explanation:
I assume you mean this:
[tex]8 \frac{7}{8} +(7 \frac{5}{6} -2\frac{1}{3} )[/tex]
Lets begin with the parentheses. When operating with fractions, we need them to have the same denominator. Looking at the expression in the parenthesis, we can see that the denominator of 5/6, that being 6, is twice that of 1/3, that being 3. Thus, if we multiply the numerator and denominator of 1/3 by 2, the result will be a fraction of same value, but with denominator 6, which we can work with.
[tex]\frac{1*2}{3*2}[/tex]
[tex]\frac{2}{6}[/tex]
Now we can replace this in the original parenthesis
[tex](7 \frac{5}{6} -2\frac{2}{6})[/tex]
We can now evaluate the parenthesis. 7-2=5, which leaves us with 5 5/6 - 2/6. Since the two fractions have the same denominator, we can subtract the numerator of 2/6 from 5/6. This gives us with 3/6, which we add to the 5 from before.
[tex]5\frac{3}{6}[/tex]
The numerator and denominator of 3/6 are both divisible by three, so we can simply the fraction.
[tex]5\frac{1}{2}[/tex]
Now that we have solved the parenthesis, we can plug our solution back into the original expression.
[tex]8 \frac{7}{8} +5\frac{1}{2}[/tex]
We now have a similar problem to the parenthesis, where our fractions have different denominators. However, you may notice that the denominator of 7/8 (8) is four times larger than the denominator of 1/2 (2). Thus, if we multiply the numerator and denominator of 1/2 by four, we will have a new fraction of equal value, but with denominator 8.
[tex]\frac{1*4}{2*4}[/tex]
[tex]\frac{4}{8}[/tex]
Now lets update our expression with this information.
[tex]8 \frac{7}{8} +5 \frac{4}{8}[/tex]
8+5=13[tex]13\frac{7}{8} +\frac{4}{8}[/tex], so we can further simplify the expression.
Since the denominators of the fractions are the same, we can combine the numerators. 7+4=11
[tex]13 \frac{11}{8}[/tex]
We can simplify the fraction by taking one whole out of it (8/8) and adding it as 1 instead. 11-8=3, thus the fraction that remains is 3/8.
[tex]14 \frac{3}{8}[/tex]
The operation 8 7/8+(7 5/6-2 1/3) evaluates to a final result of 14 3/8.
Explanation:To evaluate this mixed number operation, we must first convert each mixed number into an improper fraction.
8 7/8 is the same as 71/8 and 7 5/6 as 47/6 and 2 1/3 as 7/3.
Now, conduct the operation inside the parenthesis, which is subtraction: 47/6 - 7/3.
To subtract fractions, they must have the same denominator. Here, the least common multiple of 3 and 6 is 6. So you have 47/6 - 14/6 equals 33/6 reduced to 5 1/2.
Then add this quantity to 8 7/8 which equals to 14 3/8 when converted to a mixed number.
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A state park is designed in a circular pattern as shown. Martha rides her bike along the circular path from the ranger station to the pool. How far does she ride to the nearest hundredth of a mile?
A) .79 miles
B) 1.6 miles
C) 2.3 miles
D) 3.7 miles
C. 2.3 miles
Step-by-step explanation:
The details of the image are as follows;
Ranger station to Nature Center = 90°
Nature center to petting zoo= 40°
Petting zoo to Tennis court =120°
Tennis court to Pool = 65°
Pool to Ranger station= 45°
The radius of the circular pattern = 1 mile
The formula to apply is;
Arc length = 2πr angle / 360° where r is radius and π=3.14
Finding arc length from Ranger Station to Nature Center will be;
Arc length = 2×3.14×1×90°/360°
Arc length=2×3.14×1×1/4 =1.57 miles
Finding distance from Nature Center to Petting Zoo
Arc length= 2×3.14×1×40°/360°
Arc length= 2×3.14×1×1/9 = 0.70 miles
Total =1.57+0.70 =2.27 miles
Answer to the nearest hundredth = 2.3 miles
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