A cube is a three-dimensional geometric shape that has six square faces of equal size, 12 straight edges, and eight vertices or corners. I
The statement to be proven is:
min(a^3) = (min(a))^3
To prove this statement, we need to show that the minimum value of the cube of any number in a set is equal to the cube of the minimum value in the same set.
Let's assume that the set A contains n numbers, a1, a2, ..., an. The minimum value in this set is min(a1, a2, ..., an) = m.
We need to show that the minimum value of the cube of any number in the set A is (min(a1^3, a2^3, ..., an^3)) = m^3.
First, we can observe that if x and y are two non-negative numbers, then x^3 ≤ y^3 if and only if x ≤ y. This is because the cube function is monotonically increasing on the non-negative real numbers.
Now, let's consider any number in the set A, say ai. We have:
ai ≤ m (since m is the minimum value of the set A)
Cubing both sides, we get:
ai^3 ≤ m^3
Thus, we have shown that ai^3 cannot be smaller than m^3 for any i, since ai^3 is non-negative. Therefore, we can conclude that the minimum value of the cube of any number in the set A is m^3, or:
min(a^3) = (min(a))^3
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how many minutes would it take rachel to jog 3 miles if she jogs 1/15 mile every minute
Answer:
3 mi * 15 min/mi = 45 min
Step-by-step explanation:
i need help with these two due today plssss help me
Answer:
10. 264
11. 13
Step-by-step explanation:
10- When we are doing perimeter we add all the sides together. Since it's a square this time, we know all the sides are even at 66ft.
66+66+66+66= 264
I added 4 times for each side we have and we get the perimeter of 264
11- When dealing with area, all we need is two numbers. To get area we multiply the length and width. If we have the area and want either length or width, we can still easily do that. All we have to do is divide the area from your given number.
65 divided by 5 is 13
Area divided by Length is Width
Answer:
#10= 264
#11= 13
Step-by-step explanation:
#10: We can see that this is a square because it says so in the question so we can assume that if it is a square then all the lengths and widths are 66 feet. 4(66) = 264 or 66+66+66+66 = 264
#11: 65/5 = 13 because it is dealing with area, simply just divide the total of area by the known length to get the width.
What is the GCF of 45x^5
and
36x^9
Answer:
9x^5
Step-by-step explanation:
the factors of 45:
1, 3, 5, 9, 15, 45
the factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
Greatest common is 9
Answer:
The answer is 3
Step-by-step explanation:
because I said so
86, 82, 78, 74 , what is the 40th sequence
Answer:
The numbers slowly decrease by 4 so we can determine that the 40th sequence is -70.
Step-by-step explanation:
In slope-intercept form ?
Answer:
A) $5.5= 0.25(17)+0.05(n) where n = nickels
B) 25 nickels
Step-by-step explanation:
find the product of (2x^2+2x-3)(4x^2-3x+6
Answer:
=8x^4+2x^3−6x^2+21x−18
Step-by-step explanation:
(2x2+2x−3)(4x2−3x+6)
Which additional piece of information would allow you to
prove that the triangles are congruent by the HL theorem?
The additional piece of information would allow you to prove that the triangles are congruent by the HL theorem is AB ≅ DE
What is HL theorem?The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
Given that two triangles Δ ABC and Δ DEF,
To prove them congruent by HL Postulate, we need one more side to be congruent, as the hypotenuse of both are already congruent.
Therefore, the sides should be either BC ≅ FE or AB ≅ DE
In options, AB ≅ DE is given.
Hence, The additional piece of information would allow you to prove that the triangles are congruent by the HL theorem is AB ≅ DE
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3W + 2n - W + 8 + 3
how do you simplify this expression ?
3w+2n-8w+3 I think but don't get me wrong
the difference of 10 and a number is -2 what is the answer
Answer:
The answer is 8.
Step-by-step explanation:
This question can be written as the equation x-10=-2. With this equation in mind we can get straight ahead to solving. This is just a one-step equation and all we need to do to get our answer from this point is just add 10 to both sides using the addition property of equality and once we do that we have X=8.
There are 9 gallons of paint for the students to use to paint the fence outside of the schoolyard. Each student has a bucket that holds 1/3 gallon. How many buckets does the 9 gallons of paint fill?
Answer:
27 buckets.
Step-by-step explanation:
If we multiply the 9 gallons of paint by the denominator of the number of gallons that fit into one of the buckets we can discover the answer to the question.
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4. Sarah, Toby, and their mother run an online store called Unique Bracelets that sells handmade bracelets consisting of unique, individually-painted charms. Each bracelet they sell consists of 12 small charms and 5 large charms. Each order also gets 5 blank spacer charms to use to separate charms or fill in the bracelet. They do not sell charms separately and do not sell bracelets in parts. (f) Write an equation showing the number of charms, y, needed for x bracelets purchased in an order. Describe what the equation means in a real-world context.
Complete question :
Sarah, Toby, and their mother run an online store called Unique Bracelets that sells handmade bracelets consisting of unique, individually painted charms. Each bracelet they sell consists of 12 small charms and 5 large charms. Each order also gets 5 blank spacer charms to use to separate charms or fill in the bracelet. They do not sell charms separately and do not sell bracelets in parts.
(a) Write an equation showing the number of charms, y, needed for x bracelets purchased in an order. Describe what the equation means in a real-world context.
(b) Sarah’s and Toby’s mother says the order she is filling needs 158 charms. How many bracelets were purchased in this order?
(c) Toby says they don’t have enough charms to fill an order that needs 264 charms. Sarah says it’s notpossible for an order to need 264 charms. Is Sarah right? Why or why not? Justify your answer.
Answer:
y = 17x + 5 ;
9 bracelets ;
Sarah is right
Step-by-step explanation:
Contents per bracelet :
Small charms per bracelet = 12
Large charms per bracelet = 5
Blank spacer charms per order = 5
Number charms, y needed for X bracelets in an order ;
1 order ; x bracelets
12 + 5 = 17 small and large charms
5 = black spacer charms per order
y = 17x + 5
B.)
Order requiring 158 charms, number of bracelets :
y = 158
158 = 17x + 5
158 - 5 = 17x
153 = 17x
x = 153 / 17
x = 9 bracelets
Order requiring 264 charms
y = 264
264 = 17x + 5
264 - 5 = 17x
259 = 17x
x = 259 / 17
x = 15.23 bracelets
Sarah is right, the number of bracelets should be a positive integer and not a decimal.
Which of the following values is the solution to the equation
-16 + x = -30 ?
-2
-14
-46
-480
Answer:
-14
Step-by-step explanation:
so we see -30-(-16)=-30+16=(-14)
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Do the ratios 4/12 and 10/30 form a proportion? yes or no
Answer:
Yes because you can multiply the numerator and denominator by 2.5 to get 10/30 so it is proportional
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
it makes 2/3 when reduced
A shop makes £2,750 in March. It has an Easter sale and the profit for April is £3,162.50 Work out the percentage increase
Answer: 15%
Step-by-step explanation:
From the question, we are informed that a shop makes £2,750 in March while it made £3,162.50 in April. The increase will be:
= £3,162.50 - £2,750
= £412.50
Percentage increase = £412.50/ £2750 × 100
= 15%
What is 3/8 simplified and divided please show steps
Answer:
0.375
cannot be simplified more.
Step-by-step explanation:
three is prime, meaning it can only be divided by 1 and itself. When you see a prime in a fraction, you cannot simplify anymore without accidentally making it more complicated. Divided would just be the decimal form. The decimal form of 1/8 is 0.125, so if you multiply it by three you should get 3/8=0.375
show that the ratios 14/18 and 28/36 form a proportion by finding a common multiplier.
Step-by-step explanation:
divide it by 2...............
[tex]18 = -5b - 17[/tex]
Answer:
b = -7
Step-by-step explanation:
18 = -5b-17
Add 17 to each side
18+17 = -5b-17+17
35 = -5b
Divide each side by -5
35/-5 = -5b/-5
-7 = b
Find the GCF: 12,24,36
Answer:
12 is the GCF..........
Answer:
12
Step-by-step explanation:
listing the factors
12 : 1, 2, 3, 4, 6, 12
24 : 1, 2, 3, 4, 6, 8, 12, 24
36 : 1, 2, 3, 4, 6, 9, 12, 18, 36
The common factors are 1, 2, 3, 4, 6, 12
The GCF is 12
Identify the independent and dependent variables in the equation y = 3x + 5
Group of answer choices
y is independent and x is dependent
x is independent and y is dependent
both x and y are independent
both x and y are dependent
Answer:
A system of equations consists of two or more equations with two or more variables, where any solution must satisfy all of the equations in the system at the same time.
PLEASE HELP ITS DUE SOONNNNN
Answer:
1 is correct.
2 is incorrect.
3 is correct.
4 is correct.
5 is correct.
6 is incorrect.
Step-by-step explanation:
You're welcome, hope I helped.
please help me what is the answers
Answer:
What is your question. Please refer to a single question.
A sandwich store charges $20 to have 3 turkey subs delivered and $26 to have 4 delivered. How much does the store charge for the one additional turkey sub?
Answer:
Seven dollars
Step-by-step explanation:
Help please please please! WILL MARK BRAINLIST
Answer: I think it is A or B
Step-by-step explanation:
Which graph represents an exponential function?
Answer:
second which would be c for edg
Step-by-step explanation:
can somebody please help me with this I’m currently failing this class .. I’ll really appreciate it
umm so
Step-by-step explanation:
wait ill answer that just now let me work it out
A company has recently been hiring new employees. Today the company has 35% more employees than it did a year ago. If there are currently
43,200 employees, how many employees did the company have a year ago?
Answer:
28,080
Step-by-step explanation:
Turn 35% into a decimal (.35)Multiply .35 by the amount of current employees (.35 * 43200 = 15120)Subtract the current amount of employees (43200) by 15120 (the amount of employees that joined) which should be 28080. This is your answer.2x-7=8. find the value of x
Please help ❤️❤️❤️❤️❤️❤️
Answer:
[tex]\frac{-1}{7}[/tex] or 0.14
Step-by-step explanation:
To find slope you can use the formula
mx=[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
or
[tex]\frac{rise}{run}[/tex]
Rise over run:
Rise over run is the easiest of the two so we'll be using that one first for this question, but both should give you the same answer
To find rise over run, select the points and see how many points up or down you must got to make it the same level as the other point
In this case, the point (-3,1) would have a run of -1 because you have to move down one
To find run, now that you have rise start from that point and count how far you have to go to get to the next point. You should be going in a straight line.
The run would be 7.
Now you make it a fraction/division problem
[tex]\frac{rise}{run} =\frac{-1}{7}[/tex]
-0.14285714285714285714285714285714 <- decimal value
-0.14
Depending on what it means by reduce, your answer will either be -1/7 or the decimal. Use the reduced decimal value if it's asking for a decimal
I've included a picture in case my explanation was not satisfactory or you need a visual.
Slope form:
Identify the two points
First one will be (-3,1)
Second one would be (4,0)
Now label them
-3 will be x1
1 is y1
4 is x2
0 is y2
You will be using [tex]\frac{y2-y1}{x2-x1}[/tex]
Put the values into the equation
[tex]\frac{0-1}{4--3} =\frac{0-1}{4+3} =\frac{-1}{7}[/tex]
You get the same thing as the previous way.
Same answer
Visuals also included
I hope this helps and don't be afraid to reach out with further questions!
PLEASE HELP IT WOULD BE VERY MUCH APPRECIATED! Last year, James earned £1,600 per month.
This year, he's had a 2% increase in his monthly pay.
He worked 35 hours per week for 46 weeks in the year.
What is James' average pay per hour this year?
Give your answer to 2 dp.
Answer:
Your answer is
12$ per hour
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Do 4x and 15 + x have the same value when x is 5? How do you know?
Answer:
yes
Step-by-step explanation:
If x = 5,
4x=4*5=20
15+x=15+5=20
They're both the same.
Yes
Step-by-step explanation:
x = 5
4(5) = 15 + (5)
20 = 20