The weight of each fountain pen manufactured in a factory must be 10g with a tolerance of 2g. Pens that are not within the tolerated weight must be thrown away. Write an inequality that can be used to assess which pens are tolerable (w is the weight of the pen)?
According to the information given, the absolute value inequality that can be used to assess which pens are tolerable is:
[tex]|w - 10| \leq 2[/tex]
The absolute value function measures the distance of a point to the origin, and is defined by:
[tex]|x| = x, x \geq 0[/tex][tex]|x| = -x, x < 0[/tex]The weight must be of 10g, with a tolerance of 2g, which means that the absolute value of the difference between the weight w and 10g must be of at most 2g, hence the inequality is:
[tex]|w - 10| \leq 2[/tex]
To learn more about absolute value inequalities, you can take a look at https://brainly.com/question/24005819
the sum of the interior angle in a polygon is 40,500° what is the number of sides in the regular polygon
Answer:
227 sides
Step-by-step explanation:
The sum of the interior angles of a convex polygon is S=180(n-2) where n is the number of sides. If S=40500, then we have our equation 40500=180(n-2) and we can solve for n:
40500 = 180(n-2)
225 = n-2
227 = n
Therefore, the number of sides in the regular polygon is 227.
2. A high school wants to double the size of its parking lot by expanding the existing lot as
shown below. By what distance should the lot be expanded?
x ft
kin
75ft
old parking lot
165ft
school
300 Ft
75 ft xft
The parking lot is located along the front and one side of the school
building.
The distance x with which the lot should be expanded is 60 feet.Reasons:
The given dimensions in the compound are;
Length of the school and the old parking lot = 300 + 75
Width of the school and the old parking lot = 165 + 75
Length of the school, the old and new parking lot = 300 + 75 + x
Width of the school and the old and new parking lot = 165 + 75 + x
Area of the new parking lot the school wants = Double the old parking lot
In terms of areas, we have;
New compound - School = 2 × (old compound - school)
Which gives;
(300 + 75 + x) × (165 + 75 + x) - 300 × 165 = 2 × ((300 + 75) × (165 + 75) - 300 × 165)
2 × (375 × 240 - 49,500) = (375 + x) × (240 + x) - 49,500
Simplifying gives;
81,000 = x² + 615·x + 40,500
x² + 615·x + 40,500 - 81,000 = 0
x² + 615·x - 40,500 = 0
Factorizing with a graphing calculator gives;
(x - 60)·(x + 675) = 0
Therefore;
x = 60 or x = -675
Given that x is a natural number, we have, the correct value is; x = 60;
The distance with which the lot should be expanded, x = 60 feet.
Learn more about writing equations here:
https://brainly.com/question/20475360
https://brainly.com/question/7107994
what value is equivalent to 5^2 x 5^2 A20 B425 C625 D80
Im doing an extra credit assignment and I need someone to help me solve by substitution method
y=x+3
y=2x+5
Answer:
(-2,1)
Step-by-step explanation:
that is where the two graphs intersect
I willl mark brainiest plz answer send right answer get points
Answer: Option D
Step-by-step explanation:
Soup : 15/5 is 3 x 7 is 21
Peanut: 35/7 is 5 x 5 is 25
what's the answer of 7 1/2
Answer: 7.5
Step-by-step explanation: hope this help :)
Answer:
7.5
Step-by-step explanation:
hope this help you guys to answer the question
x varies directly with y. If x is 108 when y is 180, find x when y is 150.
Answer:
X=90
Step-by-step explanation:
k=3/5
X=3/5×150
X=90
What fraction goes in the box to make it correct? 5/12×□=1
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\large\boxed{\mathbf {Your\ equation} :\mathsf{\dfrac{5}{12}\times\boxed{} = 1}}[/tex]
[tex]\large\textbf{We don't know the unknown number yet so we will}\\\large\textbf{label it as \boxed{f}}[/tex]
[tex]\large\boxed{\mathsf{\dfrac{5}{12}\times f = 1}}[/tex]
[tex]\large\boxed{\rightarrow\mathsf{\dfrac{5}{12}(f)= 1}}[/tex]
[tex]\large\textbf{MULTIPLY by }\mathbf{\dfrac{12}{5}}\large\textbf{ to BOTH SIDES}[/tex]
[tex]\large\boxed{\mathsf{\dfrac{12}{5}\times\dfrac{5}{12}f = \dfrac{12}{5}\times1}}[/tex]
[tex]\large\textbf{CANCEL out: }\mathbf{\dfrac{12}{5}\times\dfrac{5}{12}}\large\textbf{ because it gives you 1.}[/tex]
[tex]\large\textbf{KEEP: }\mathbf{\dfrac{12}{5}\times1}\large\textbf{ because it helps solve for the f-value.}[/tex]
[tex]\large\boxed{\mathbf{NEW \ EQUATION: }\mathsf{f = 1\times \dfrac{12}{5}}}[/tex]
[tex]\large\textbf{SIMPLIFY IT!}[/tex]
[tex]\huge\boxed{\textbf{Therefore, your answer: \boxed{\mathsf{f = \dfrac{12}{5}}}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \&}\\\huge\textbf{enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Write 72,658 in expanded form using
exponents to write powers of 10.
ayo how do answer these
Step-by-step explanation:
7 x 10^4
+ 2 x 10^3
+ 6 × 10^2
+ 5 × 10^1
+ 8 X 10^0
solve this
(below, in picture)
Divide 75 by -25.
12
Answer: 6.25
Step-by-step explanation:
D(3, 6), E(-4,-3), F(6, 1) and
D'(1, 6), E'(8, -3), F(-2, 1)
Answer:
d
Step-by-step explanation:
Can someone please give me the (Answers) to this? ... please ...
Answer:please correct me if I’m wrong but I believe Part A for the slopes are…
1.3/1 or 3
2.-3
3.9/5
4.4/3
Step-by-step explanation:
It’s going up 3 and “running” 1 and it’s positive since the line is going up.
Y2-y1. -16-2
————= ————=-18/6=-3
X2-x1. 8-2
You’re just finding the slope
Solve for it. If further explanation is needed please tell me.
A.
1. 9/5
2. -1/5
3. ? (no question)
4. 4 or 4/1
B.
5. y = 1x + 4
6. -2x + 3
7. -1/5x + 2
8. -4x + 2
I'm not sure about 5-8 the wording of the questions are confusing.
is the change of rate always constant
In mathematics, a constant rate of change is a rate of change that stays the same and does not change.
Check image for question
[tex]\dfrac{0.8\times 0.04}{0.5}\\\\\\=\dfrac{\tfrac 8{10} \times \tfrac 4{100}}{\tfrac 5{10}}\\\\\\=\dfrac{\tfrac 45 \times \tfrac 1{25}}{\tfrac 12}\\\\\\= \dfrac 4{125} \times 2\\\\\\=\dfrac 8{125}[/tex]
HELP ME PLEASE REALLY NEED DONE INE the NEXT 3 MINUTES
7.
Quentin takes piano lessons
each month. Last month, he
took 4 piano lessons and paid
$104. This month, he plans to
take 2 piano lessons. How much
will Quentin pay this month?
Answer:
52$
Step-by-step explanation:
104 / 4 = 26$ per lesson
2 piano lessons = 26 x 2 = 52$
Haynes High School chartered buses for 60 students to go on a field trip. Valley High School chartered buses for 80 students.
*The total cost of the buses was the same for the two schools
*Students from Valley High School paid $5 less than students from Haynes High School.
What was the cost per student for Haynes High School?
A. $5 B. $15 C. $20 D. $40
Answer: $20
Step-by-step explanation:
Let 'x' be the cost of a ticket at Haynes
Let 'y' be the cost of a ticket at Valley
Since the total cost from both schools are the same, we can write it as:
[tex]60x=80y[/tex]
Since the cost of tickets at Valley was $5 less than Haynes, we can write it as:
[tex]y=x-5[/tex]
Now we have two equations, we can use to substitute into the other expression:
[tex]60x=80y[/tex]
[tex]60x=80(x-5)[/tex] we substitute y in this equation with the other equation
[tex]60x=80x-400[/tex]
[tex]-20x =-400[/tex]
[tex]x = 20[/tex]
Therefore the cost of the ticket at Haynes is $20 and the cost of the ticket at Valley is $15.
PLEASE HELP. I'LL GIVE BRAINLIEST!!!
Mike purchased a car worth $18,000 in the year 2008. It loses its value by 6% per year. What is the value of the car in 2020? Round your answer to the nearest whole dollar, and do not enter any decimals or commas.
Answer:
8762
Step-by-step explanation:
Exponential decay equation
Initial = 18000
Rate 6% = 0.06
Time = 12
Answer:
$8567
Step-by-step explanation:
In the image the answer is given.
Formula of depreciation is used in the answer.
I watch television from 5 o clock until half past. How long do I watch for?I watch television from 5 o clock until half past. How long do I watch for?
Answer:
30 minutes
Step-by-step explanation:
Billy kicks a soccer ball off the ground after taking a quick running start. The graph below shows the height of the ball. What do(es) the solution(s) to the function represent?
From the graph, the solutions of the function represents the instants in which the ball hits the ground.
In the graph, we have that:
The x-axis is the time, ins seconds.The y-axis is the height of the ball, in feet.The solutions are x = 1 and x = 5, which represents the instants in which the ball is in the ground.
For a similar problem, in which we find the times in which an object hits the ground, you can check https://brainly.com/question/16840613
Ben bowled 153 and 192 in his first two games. What must he bowl in his third
game to have an average of at least 170?
in his third game in order to have an average of at
Ben must bowl at least
least 170.
convert the following equation into standard form. y= -5x/6+2
Answer:
5x + 6y = 12
Step-by-step explanation:
The standard form of a linear equation is Ax + By = C.
Multiply both sides by 6
6y = 6(-5x/6 + 2)
Simplify the right side
Simplify
6(−5x/6+2)
Apply the distributive property = a ( b + c ) = ab + ac
6y = 6( −5x/6) + 6 ⋅ 2
Cancel the common factor of 6
Move the leading negative in −5x/6 into the numerator
6y = 6 −5x/6 + 6 ⋅ 2
Cancel the common factor 6
Rewrite the expression
6y = −5x + 6 ⋅ 2
Multiply 6 by 2
6y = -5x + 12
Move all terms containing variables to the left side of the equation
Add 5x to both sides of the equation.
6y + 5x = 12
Reorder 6y and 5x
5x + 6y = 12
FOOTBALL Tyrell plays running back
and kicks field goals for his team. He
scores 6 points for a touchdown and
3 points for a field goal. In his last
game, he scored 24 points. This can be
represented by the function
6x + 3y = 24. Find the x- and
y-intercepts. Interpret the x- and
y-intercepts.
=
Answer:
x-intercept(s):
4,0
y-intercept(s):
0,8
Step-by-step explanation:
The average 8- to 18-year-old spends____ per day on average in front of a screen doing very little to
no physical activity.
A. O hours
B 30 minutes
0. 1 hour
D 3 hours or more
Please select the best answer from the choices provided.
Answer:
3 hours or more
Step-by-step explanation:
why because of the games and entertainment
Can someone please help me with this easy math problem?
Which of the following represents the zeros of f(x) = 6x3 − 31x2 + 4x + 5?
If any doubt leave a comment
X-2y=2 in slope intercept form
Answer:
I believe it's written y = 1/2x - 1
Hope this helps :)
3. What is the area of the figure?
Answer:
981.75
Step-by-step explanation:
The area of a circle is πr^2, but this a semi circle, so you need to half it.