Answers
110 inches cost $6.60 so the point (x,y) = (110, 6.60) is on the line
125 inches cost $7.50 so the point (x,y) = (125, 7.50) is on the line
We only need two points form this line. Let's find the slope
m = (y2-y1)/(x2-x1)
m = (7.50-6.60)/(125-110)
m = 0.90/15
m = 0.06
The slope is 0.06 meaning that each additional inch costs $0.06 (6 cents) extra.
In other words, the cost is 6 cents per inch.
Plug (x,y) = (110, 6.60) and m = 0.06 into the equation below to solve for b. This will get us the fixed cost
y = mx+b
6.60 = 0.06*110+b
6.60 = 6.60+b
6.60-6.60 = 6.60+b-6.60
0 = b
b = 0
So the fixed cost is 0 which makes sense. If you buy 0 inches of wire (i.e. you don't buy anything) then you don't pay anything.
Therefore the cost function is f(x) = 0.06*x which can be written as y = 0.06*x
------------------------------------------------------------------------
We're told that "Emily needs 23 feet of wire" so we need to convert that feet measurement into inches before we can use the function. The reason why is because x is length in inches (not feet).
23 feet = 23 feet * (12 inches/1 foot) = 23*12 = 276 inches
so in short, 23 feet is equivalent to 276 inches
This means x = 276 and y is...
y = 0.06*x
y = 0.06*276
y = 16.56
Emily will spend 16.56 dollars for her wire.
------------------------------------------------------------------------
Andy needs 14 yards. We'll have to convert from yards to feet
14 yards = 14 yards * (3 feet/1 yard) = 14*3 = 42 feet
14 yards = 42 feet
Then convert that feet measurement to inches
42 feet = 42 feet * (12 inches/1 foot) = 42*12 = 504 inches
So overall,
14 yards = 504 inches
Now we can use the function
y = 0.06*x
y = 0.06*504
y = 30.24
Andy will spend 30.24 dollars for his wire.
Side Note: Andy will spend 13.68 dollars extra compared to Emily (since 30.24-16.56 = 13.68). So Andy spends more. Which makes sense given how Andy needs 504 inches of wire compared to Emily's needs of 276 iches of wire.
Related Questions
he earns $7 a week for each cat he feeds and $0.20for each email he answers. Marcus answered 140 emails and earned $49 last week. create an equation that will determine the number of cats he fed
Answers
140x0.020= 28
7x3=21
28+21=49
bam hope i helped :)
how do u find the answer a simpler way
Answers
8^-4/8^-2= 8^-2
8^-2= 1/8^2
1/8^2=1/64
Final answer: 1/64
draw a 150 degree angle
Answers
what is the answer to the equation -7+x=6x-12 ?
Answers
-7 +12 = 6x - x
5 = 5x
x = 1
hope this helps
-x -x
-7=5x-12
+12 +12
5=5x
X=1
Eva would like to add paper streamer around the edge of a round table. The table covers an area of 19.5 square ft. What is the minimum length of the paper streamer Eva needs?
Answers
A=3.14 r squared
19.5 divided by 3.14 =r squared
6.21 =r squared
R=2.49
C= 3.14 (4.98)=15.64 feet of paper
Divide 28 cans of soda into two groups so the ratio is 3 to 4.
Answers
3 x 4 = 12
4 x 4 = 16
12 + 16 = 28
you will put 12 cans in one group and 16 cans in another group
hope this helps
Pls help
Simplify
6m+ 7n+ 5m - 3n
Answers
(6m + 5m) + (7n - 3n)
11m + 4n ← answer
Do the 6m and 5m first. Add them together.
6m + 5m = 11m
Now subtract -3n from 7n.
7n - 3n = 4n
11m + 4n is simplified.
567,433 to the nearest hundred thousand
Answers
first, find the number in the hundred thousand place....it is the 5...now look at the number directly to the right of it...
if that number is 5 or above, ur 5 gets rounded up to a 6
if that number is 4 or below, ur 5 stays the same
so the number to the right of 5 is 6....it is greater then 5, so u round ur 5 up to a 6...and ur answer is 600,000 <==
because 567,433 is closer to 600,000 then it is to 500,000
The number 567,433 nearest hundred thousand is 600,000 after rounding off, the answer is 600,000.
What is rounding off the number?Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.
It is given that:
The number is 567,433
600,000
Rounded to the nearest 100,000 or
the Hundred Thousands Place.
Thus, the number 567,433 nearest hundred thousand is 600,000 after rounding off, the answer is 600,000.
Learn more about the rounding off number here:
https://brainly.com/question/13391706
#SPJ2
the number 80 is increased by 50%. The result is then decreased by 25%. What is the final number?
Answers
So your awnser is 39.75
apply the rules for order of operstions to simplify 2 + 3 - 4 (5 × 4)
Answers
2+3-4 (5x4)
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction So first is Parenthesis 5x4=20 next will be Addition because there are no exponents 2+3= 5-4= 1 so now we go back to multiplication 20 x 1= 20 so 20 is your answer.
Hope I helped out ^^
Final answer:
To simplify the expression, follow the order of operations: first perform the multiplication inside the parentheses, then multiply that result, and finally subtract it from the sum of 2 and 3. The expression simplifies to -75.
Explanation:
To simplify the mathematical expression 2 + 3 - 4 (5 × 4) we must apply the rules of order of operations, commonly remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Multiplication inside the parentheses: 5 × 4 = 20
Multiply 4 by the result of the previous step: 4 × 20 = 80
Subtract this result from the sum of 2 and 3: (2 + 3) - 80 = 5 - 80 = -75
Therefore, the expression simplifies to -75.
Remember that in subtraction, you change the sign of the number being subtracted, and then follow the rules of addition: e.g., 5 - 3 becomes 5 + (-3) = 2. Similarly, when two numbers with opposite signs multiply, the result has a negative sign: e.g., (-3) × 2 = -6.
Every 4th visitor to a museum gets a free bumper sticker.Every 10th visitor to that museum gets a free key chain.Which visitor number will be the first person to get them both bumper sticker and keychain.
Answers
So the first person to get both rewards would be the 20th visitor
When you write a deposit slip, you put the cash and the checks in the same section True or False
Answers
Ally works in a shop for $18 per hour dependent
Answers
Dependent is her rate ($18) because it DEPENDS on how long she works
Final answer:
Explanation of independent and dependent variables in a linear equation
Explanation:
Independent variable: The hours worked by Ethan (x).
Dependent variable: Total amount earned (y).
Y-intercept: $25, this represents the initial charge even if no hours are worked.
Slope: $20, this represents the additional amount earned per hour of work.
The question about Ally working in a shop for $18 per hour relates to wage determination and labor economics within the field of Business. Discussions surrounding hourly wages, annual salaries, and job requirements touch upon various economic principles.
if sin q = 4/5, cos p + cos q =?
Answers
Algebra 1: Consecutive Integers
If the sum of the first two consecutive even integers is equal to three times the third what are the three integers
Answers
x+(x+2)= 3(x+4)
2x+2= 3x+12
2x= 3x+10
-x=10
x=-10
Final answer: -10, -8, -6
What is the equation of the line perpendicular to the line y=4/9x-2 that passes through the line 4,3
Answers
Given
The line equation is
[tex]y= \frac{4}{9}x-2[/tex]
passes through the line (4,3 )
Find out the equation of the perpendicular line.
To proof
given equation is
[tex]y= \frac{4}{9}x-2[/tex]
the equation of line is in the form y = mx +c
where m = slope
c is the intercept on the y axis.
compare this equation to the above equation
we get
[tex]m =\frac{4}{9}[/tex]
In perpendicular line case
The slope of a perpendicular line is the "negative reciprocal" of the slope of the original line.
thus slope of the perpendicular line
= [tex]\frac{-9}{4}[/tex]
Than equation perpendicular line becomes
[tex]y= \frac{-9}{4}x + c[/tex]
as the line passes through the point( 4,3)
put these value in the above equation
we get
[tex]3= \frac{-9}{4}\times 4 + c[/tex]
solving the above equation
3 +9 =c
12 =c
put this value in the above equation
we get
[tex]y= \frac{-9}{4}\times x + 12[/tex]
this is equation of the perpendicular line.
Hence proved
Describe how to write an equivalent ratio for 9/27 without using a multiplication table
Answers
9/27 = 1/3
Hope this helped!
a 7/16 inch bolt is used in a machine . what is the length of the bolt writtin as a decimal?
Answers
After 3.5 hours pasha had traveled to 17 miles if she travels at a constant speed how far will she have traveled after four hours
Answers
Write this number in standard form 12 ten thousands, 8 thousands, 14, 7 ones
Answers
8 thousands =8,000
14 hundreds = 140
7 ones = 7
12,000 + 8,000 + 140 + 7
Standard form = 20,147
The number composed of 12 ten thousands, 8 thousands, 14 tens, and 7 ones is written in standard form as 128,147.
To write the number consisting of 12 ten thousands, 8 thousands, 14, and 7 ones in standard form, each element must be placed according to its value in our base-ten number system. First, we note that 14 needs to be broken down into 'tens' and 'ones' as well.
12 ten thousands = 12 times 10,000
8 thousands = 8 times 1,000
14 tens = 14 times 10
7 ones = 7 times 1
Next, we translate these values into their numeral counterparts:
12 ten thousands = 120,000
8 thousands = 8,000
14 tens = 140
7 ones = 7
Now we simply add these numbers together:
120,000 + 8,000 + 140 + 7 = 128,147
The number 12 ten thousands, 8 thousands, 14 tens, and 7 ones written in standard form is 128,147.
What is 1,995298 to the nearest 1,0000
Answers
hope this helps
Evaluate A2 for A = -3.
-9
-6
6
9
Answers
A^2
-3^2 = 9
the answer is 9
why is scientific notation useful? how is scientific notation used in the real world?
Answers
It makes it easier to deal with because the long numbers are converted into smaller numbers. Like for example, 0.000000000000000000000000000000000000000000045 is converted into 4.5*10^44. Isn't that MUCH MORE simpler?!?!??!
It is also used to find masses, for example, like some metals or substances that have a really smaller mass.
if x = -6, which inequality is true, -5 - 3x > 10, -3 - 5x < -14 or 2-x < -3?
Answers
we can subtitution x to every inequality, so :
-5 - 3x > 10
-5 - 3(-6) > 10
-5 - (-18) > 10
-5 + 18 > 10
13 > 10 [true]
-3 - 5x < -14
-3 - 5(-6) < -14
-3 - (-30) < -14
-3 + 30 < -14
27 < -14 [false]
2 - x < -3
2 - (-6) < -3
2 + 6 < -3
8 < -3 [false]
So if x=-6, inequality true is -5 - 3x > 10.
how can I turn a parabola into an equation? (please be specific)
Answers
Kofi is one of the best baseball players in his league. His last three pitches have been clocked at 71.025 mph, 72.35 mph, and 71.95 mph. What is the difference between the fastest and slowest pitches that were clocked?
Answers
What’s b = 3x + 9xy ? Solving the equation for x.
Answers
Answer:
x= [tex]\frac{b}{3+9y}[/tex] .
Step-by-step explanation:
Given : b = 3x + 9xy.
To find : Solving the equation for x.
Solution : We have given
b = 3x + 9xy.
Taking common 3x from right hand side
b = 3x ( 1 + 3y).
On dividing both sides by 1 + 3y .
[tex]\frac{b}{1+3y}[/tex] = 3x
On dividing both sides by 3
[tex]\frac{b}{(3+9y)}[/tex] = x .
Therefore, x =[tex]\frac{b}{(3+9y)}[/tex] .
x = b/(3 + 9y)
Further explanation[tex]\boxed{ \ b = 3x + 9xy \ }[/tex]
In the equation, there are three variables, namely b, x, and y. The coefficients of x and xy are 3 and 9, respectively.
We need solving for x from the equation.
Let us reposition it by swapping sides. The aim is to prepare x as the subject on the left-hand side.
[tex]\boxed{ \ 3x + 9xy = b \ }[/tex]
On the left-hand side, 3x is pulled out of the brackets because it is the GCF (The Greatest Common Factor) of 3x and 9xy.
[tex]\boxed{ \ 3x(1 + 3y) = b \ }[/tex]
Both sides divided by 3(1 + 3y).
[tex]\boxed{ \ x = \frac{b}{3(1 + 3y)} \ }[/tex]
Hence, the final result is
[tex]\boxed{\boxed{ \ x = \frac{b}{3 + 9y} \ }}[/tex]
That's all the steps to get x as a subject.
Learn moreSolve one of the variables of the equation to become the subject https://brainly.com/question/6465937# The inverse of a function https://brainly.com/question/3225044What is the simplified form of 5(14 - 2)² ÷ 2 ? https://brainly.com/question/1602237Keywords: what’s b = 3x + 9xy?, solving the equation for x, solve for x, both sides, divide, GCF, subject, steps, b/(3 + 9y)
What is 855,000 in scientific notation
Answers
you want your scientific notation number in between 1 and 10 !!!
- Where’s the decimal point in 312,000,000,000? Because it’s a whole number, the decimal point is understood to be at the end of the number: 312,000,000,000.
So, N = 3.12.
Step TWO: Determine the exponent, which is the number of times you moved the decimal.
-In this example, you moved the decimal 11 times; also, because you moved the decimal to the left, the exponent is positive. Therefore, a = 11, and so you get
Step THREE: Put the number in the correct form for scientific notation
2/5 (y-40) = 5 (solve for y)
Answers
2(y-40) = 25
then, divide both sides by 2 to get rid of the 2 in the left side:
y-40 = 12.5
then, isolate the y in one side and the other terms on the other.
y = 12.5+40
y = 52.5
What is 51/8 as a mixed number?
Answers
It's 6, and the remainder is 3, then put 3 over the denominator.
It would be 6 3/8.