please helppppppppppppp ASAP. please ensure to use step by step explanation. thanks.
I'll do the first two parts to get you started.
=====================================================
Part (i)
We can show that the operation [tex]\nabla[/tex] is not commutative by picking two random and different real numbers for a,b. In other words, I'm using a counter-example.
Let's say we go for a = 1 and b = 2
[tex]a \nabla b = \frac{3a+b}{5} - 1\\\\1 \nabla 2 = \frac{3*1+2}{5} - 1\\\\1 \nabla 2 = \frac{5}{5} - 1\\\\1 \nabla 2 = 1 - 1\\\\1 \nabla 2 = 0\\\\[/tex]
Now let's swap the values. We'll try a = 2 and b = 1
[tex]a \nabla b = \frac{3a+b}{5} - 1\\\\2 \nabla 1 = \frac{3*2+1}{5} - 1\\\\2 \nabla 1 = \frac{7}{5} - 1\\\\2 \nabla 1 = 1.4 - 1\\\\2 \nabla 1 = 0.4\\\\[/tex]
We can see that [tex]1 \nabla 2[/tex] and [tex]2 \nabla 1[/tex] are not the same value. In general, [tex]a \nabla b \ne b \nabla a[/tex] Therefore, the operation [tex]\nabla[/tex] is not commutative.
The only time [tex]a \nabla b = b \nabla a\\\\[/tex] is true is when [tex]a = b[/tex], since,
[tex]\frac{3a+b}{5}-1 = \frac{3b+a}{5}-1\\\\\frac{3a+a}{5}-1 = \frac{3a+a}{5}-1\\\\\frac{4a}{5}-1 = \frac{4a}{5}-1\\\\[/tex]
It's when [tex]a \ne b[/tex] is where the operation becomes noncommutative.
Another way to arrive at the [tex]a = b[/tex] condition is to solve the original equation for either 'a' or b.
=====================================================
Part (ii)
Using the previous part as inspiration, we'll do a counter-example to show that the operation is not associative. Pick 3 random values for a,b,c. Here are the values I'll pick.
a = 1b = 2c = 3Then,
[tex]d = b \nabla c = \frac{3b+c}{5}-1 = \frac{3*2+3}{5}-1 = 0.8\\\\a \nabla (b \nabla c) = a \nabla d = \frac{3a+d}{5}-1 = \frac{3*1+0.8}{5}-1 = -0.24\\[/tex]
Next, we can say:
[tex]d = a \nabla b = \frac{3a+b}{5}-1 = \frac{3*1+2}{5}-1 = 0\\\\(a \nabla b) \nabla c = d \ \nabla c = \frac{3d+c}{5}-1 = \frac{3*0+3}{5}-1 = -0.4[/tex]
Let's compare the two outputs:
[tex]a \nabla (b \nabla c) = -0.24\\\\(a \nabla b) \nabla c = -0.4[/tex]
They don't match up, so [tex]a \nabla (b \nabla c) \ne (a \nabla b) \nabla c[/tex] when (a,b,c) = (1,2,3).
In general, the operation is not associative in R.
Help help math math math
Answer:
Yes, this is a function
Step-by-step explanation:
You know this because it passes the vertical line test.
I hope this helps!
Answer:
Function
Step-by-step explanation:
Translate the sentence into an equation using n as the unknown number. Then solve the equation for n.
5 increased by half a number is 11.
a.
5 + 0.5n = 11
n = 12
c.
5(0.5n) = 11
n = 4.4
b.
5n + 0.5 = 11
n = 2.1
d.
5n +0.5 = 11
n = 12
Please select the best answer from the choices provided
A
B
C
D
Answer:
the answer is A)5+0.5n=11
Step-by-step explanation:
5 is increased by half a number, so half of. a number(n) is added to 5
Answer:
D is correct
Step-by-step explanation:
I hope this helps
5 increased by half a number is 11.
5 increased by half a number is 11. 5 + 1/2n = 11 where n is the unknown number. 1/2n = 11 - 5 = 6 n = 6 * 2 = 12 The number is 12.
In one week, a farmer sells pumpkins to 60% of his customers.
If 720 customers purchase pumpkins, how many total customers does the farmer have?
Answer:
1,200
Step-by-step explanation
Multiply 720 and 100 = 72,000
Divide by 60 = 1,200
Answer:
The answer is 1,200
Step-by-step explanation:
First Multiply 720 and 100 which = 72,000
Then Divide 72,000 by 60 = 1,200
The question in the picture
1/27
Explanation:
You would multiply to get to the answer.
Please please help me
[tex]1)3k - 2k \\ = k(3 - 2) \\ = k(1) \\ = k[/tex]
[tex]2) {5x}^{2} - 10x - {8x}^{2} + x \\ = {5x}^{2} - {8x}^{2} - 10x + x \\ = - 3 {x}^{2} - 9x \\ = - 3x(x - 3)[/tex]
[tex]3) - (m + n) + 2(m - 3n) \\ = - m - n + 3m - 6n \\ = - m + 2m - n - 6n \\ = m - 7n [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
Rewrite the quadratic function f(2) = 5x2 + 10x – 8 in standard form, f(x) = a (x – h)? + k, and give the vertex.
Answer: [tex]f(x) = 5(x+1)^{2} - 13[/tex]
Vertex = (-1, -13)
Step-by-step explanation:
[tex]f(x) = 5x^{2} + 10x - 8\\f(x) = 5(x^{2}+2x)-8\\f(x) = 5(x^{2}+2x+1-1)-8\\f(x) = 5((x+1)^{2}-1)-8\\f(x) = 5(x+1)^{2}-5-8\\f(x) = 5(x+1)^{2}-13[/tex]
Vertex = (h, k) = (-1, -13)
Ratio. Proportion and many method d) 15 workers were employed to complete a piece of work in 36 days. How many more workers should be added to complete the work in 30 days?
Answer:
Step-by-step explanation:
total of 15(36) = 540 person•hours was used
540 / 30 = 18 people
18 - 15 = 3 people need to be added
Randy can run six-tenths of a mile every 4 minutes, but it takes Julie 5 minutes. By the time Julie has run for 20 minutes, how far has Randy run?
A
1.8 miles
B
2.4 miles
C
2.6 miles
D
3 miles
Answer:
D!!!
Step-by-step explanation:
you have to make a table to see that randy has run 3 miles.!!!
Answer: D is the correct answer!
Step-by-step explanation: Like the one above me!
From the graph, which statement is correct if x^2 – 13x + 22 ≤ 0?
A) 2 ≤ x ≤ 11
B) –11 ≤ x ≤ –2
C) x ≤ 2 or x ≥ 11
D) x ≥ 2 or x ≤ 11
please only reply if you know the answer!!
Answer:
a
Step-by-step explanation:
(x-2)(x-11) less than or equal to 0
which means x is between 2 and 11 when it is less than 0
18) Jacob is trying to decide whether to attend akeshore University or Bayside University. He
likes both schools equally, and both schools sent him letters of acceptance. Recently
Lakeshore University raised its tuition by 6%. Which statement is most reasonable in this
situation?
a) Jacob should attend Bayside University since it will be less expensive.
b) Jacob should gather more information about tuition before making a decision.
c) Jacob should not worry about a 6% tuition increase since this is a small percent.
Answer: B
Step-by-step explanation: Jacob doesn't know either colleges' actual price. Bayside could still be equal to or more expensive than Lakeshore.
a parking garage charges $4 for the first hour and $1.50 for each additional hour. sydney has 13$ in her purse
Answer:
7 hours
Step-by-step explanation:
Answer:
she could park there for 7 hours
Step-by-step explanation:
13-4=9 9/1.50=6
MATHS QUESTIONS PLEASE SOLVE
1. 121 Divided by 11 is
11
10
19
18
2. 60 Times of 8 Equals to
480
300
250
400
3. Find the Missing Term in Multiples of 6 : 6, 12, 18, 24, _, 36, 42, _ 54, 60.
32, 45
30, 48
24, 40
25, 49
4. What is the Next Prime Number after 7 ?
13
12
14
11
5. The Product of 131 × 0 × 300 × 4
11
0
46
45
6. Solve 3 + 6 × ( 5 + 4) ÷ 3 - 7
11
16
14
15
7. Solve 23 + 3 ÷ 3
24
25
26
27
8. What is 6% Equals to
0.06
0.6
0.006
0.0006
9. How Many Years are there in a Decade?
5 years
10 years
15 years
20 years
10. How Many Months Make a Century?
12
120
1200
12000
5x + 3y = 41
2x + 3y = 20
show me step by steps how to do this
The answers are:
x = 7y = 2Step-by-step explanation:5x + 3y = 41
2x + 3y = 20
=> 5x + 3y = 41-2x - 3y = -20
=> 3x = 21=> x = 7=> 5(7) + 3y = 41=> 35 + 3y = 41=> 3y = 41 - 35=> 3y = 6=> y = 2Conclusion:Therefore, the answers are:
x = 7y = 2Hoped this helped
[tex]-BrainiacUser1357-[/tex]
Answer:
Step-by-step explanation:
It looks like you need to solve this system of equations.
That means we need to find a value for x and a value for y that makes both equations true.
Since both equations have a 3y in them, this system is ready to use a method called "elimination method"
Since the x terms are lined up, and the y terms are lined up, the equal signs are lined up, and the constants are lined up...you can subtract the bottom equation from the top equation.
5x + 3y = 41
2x + 3y = 20
Subtract and you will get
3x + 0y =21
We don't need to write that 0y, because it is 0.
3x = 21, now divide by 3
x = 7, almost finished!
Use x = 7 in either of the original equations to find y.
5x + 3y = 41 and x = 7
5•7+ 3y = 41
35 + 3y = 41
-35 -35
3y =6
y = 2
So the solution is x=7 and y=2
That can also be written as an ordered pair (7, 2)
12. Graph each using graph paper:
X<5
Answer:
Step-by-step explanation.
If you connect the points where Muntinlupa City and Teresa, Rizal are located, what is the slope of the line formed from the two given places?
Using it's formula, it is found that the slope of the line formed from the two given places is of [tex]\mathbf{\frac{6}{7}}[/tex]
Given two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex], the slope is given by change in y divided by change in x, that is:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this problem:
Muntinlupa is at (-1,-4);Teresa, Rizal is at (6,2).Hence, applying the formula for the slope, considering [tex](x_1, y_1) = (-1, -4)[/tex] and [tex](x_2,y_2) = (6,2)[/tex]:
[tex]m = \frac{2 - (-4)}{6 - (-1)} = \frac{6}{7}[/tex]
The slope is of [tex]\mathbf{\frac{6}{7}}[/tex]
A similar problem is given at https://brainly.com/question/5427529
What is the gradient?
Answer:
The gradient is negative.
Step-by-step explanation:
The gradient represents the rise/run ratio. Always read the line's path left to right, and if it goes up, then it is positive, down means negative gradient, and if it doesnt move then it 0. It is undefined if the line is vertical.
A number is between 63 and 68 It has prime factors of 2 and 11 whats the number
Answer:
66
Step-by-step explanation:
66 is the only number between 63 and 68 that is divisible by both 2 and 11.
66/2=33 66/11=6
The sum of 21 and n is equal to 43.23
please help me!!!
I’ll give out 30 points!!!
Answer:
n=22.23
Step-by-step explanation:
21+n=43.23
-21 to both sides
0+n=22.23
n=22.23
2) through: (-4, 5) and (-5,0
what is the slope intercept form of the line
Answer:
hello
Step-by-step explanation:
say hell-o
Solve the equation for solutions over the interval [0°, 360°).
[tex]tan^{2}x + 7 tanx +8 =0[/tex]
Answer:
[tex]x=98.13^\circ,135^\circ,278.13^\circ,315^\circ[/tex]
Step-by-step explanation:
[tex]tan^2x+7tanx+8=0,[0^{\circ},360^\circ)[/tex]
[tex]tan^2x+7tanx+8=0[/tex]
[tex]u=tanx[/tex] <-- U-substitution
[tex]u^2+7u+8=0[/tex]
[tex](u+7)(u+1)=0[/tex]
[tex](tanx+7)(tanx+1)=0[/tex] <-- Replace u with tanx
[tex]tanx+7=0[/tex]
[tex]tanx=-7[/tex]
[tex]x=98.13^\circ,278.13^\circ[/tex]
[tex]tanx+1=0[/tex]
[tex]tanx=-1[/tex]
[tex]x=135^\circ,315^\circ[/tex]
Therefore, [tex]x=98.13^\circ,135^\circ,278.13^\circ,315^\circ[/tex]
Help pleasee :(
no links.
what is the point slope equation of the line that has a slope of 1/8 and goes through the point (2,-3)
Answer:
Step-by-step explanation:
(y + 3) = (1/8)(x - 2)
a recipe calls for 2 cups of flour for every 3 cups of sugar. If you are planning to use 5 cups of flour, how many cups of sugar should you use
Answer:
7½ cups of sugar
Step-by-step explanation:
2 cups of flour needs 3 cups of sugar
1 cups of flour needs 3/2=1.5 cups of sugar
1×5 cups of flour needs 1.5×5=7.5 cups of sugar=7½ cups of sugar ANS
help plssssssssssssssssss
Answer:
Diagonal and horizontal lines
Step-by-step explanation:
To answer this question it is first important to know what a function is. A function is a relationship that has a singular y value for each x-value. This means that x-values will never repeat.
Linear functions are functions that increase in a constant way. Meaning that the slope of the line is constant and there is a common difference between the points. Because the change is constant, there is no change in direction. Thus, the function will be one straight line.
This line can obviously be diagonal because a diagonal line has unique x and y values. However, the line can also be horizontal. Horizontal lines many have repeating y-values but because the x-values don't repeat it is still a function. This reason is also why vertical lines are the only straight line to not be a liner function. In vertical lines, the x-values repeat. So, it does not work as a function.
Help help help math math
Answer:
gradient M = 4
Step-by-step explanation:
pick any two pairs
M= change in Y / change in X
considering the last pairs
3--1/0--1=4✓
considering first pair
-1--5/-1--2 is also 4✓
I hope it helps
The owner of a small store buys coats for 55.00 each
He sells the coats for 66.00 each
he must buy 24 jackets to get atheist 260 dollars
It takes cadence 36 hours to read 12 books. Write a unit rate that models the situation.
Answer:
three hours every 1 book
Step-by-step explanation:
36-12
6-2
3-1
3x+4y+6z=15
Solve for x.
Answer:
[tex]x = 5 - \frac{4}{3} y - 2z [/tex]Step-by-step explanation:
Question:-To solve for xEquation:-3x + 4y + 6z = 15Solution:-=> 3x + 4y + 6z = 15
[On subtracting both sides with 4y]=> 3x + 4y + 6z - 4y = 15 - 4y
[On Simplification]=> 3x + 6z = 15 - 4y
[On subtracting both sides with 6z]=> 3x + 6z - 6z = 15 - 4y - 6z
[On Simplification]=> 3x = 15 - 4y - 6z
[On dividing both sides with 3][tex] = > \frac{3x}{3} = \frac{15 - 4y - 6z}{3} [/tex]
[On Simplification][tex] = > x = 5 - \frac{4}{3} y - 2z \: (ans)[/tex]
[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\huge\bold\orange{QUESTIONS:}[/tex]
3x+4y+6z=15 Solve for x.[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\huge\bold\orange{ANSWER:}[/tex]
[tex]x = 5 - \frac{4}{3} y - 2z[/tex]
[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
[tex]\huge\bold\orange{SOLUTION:}[/tex]
[tex]3 \orange{+ 4y + 6z = 15}[/tex]
Move the variables to the right-hand side and change their signs.
[tex]3x = 15 \orange{ - 4 - 6z}[/tex]
Divide both sides of the equation by 3
[tex]\orange{3x = 15 - 4 - 6z}[/tex]
[tex]↓[/tex]
[tex]\orange{x = 5 - \frac{4}{3} y - 2z}[/tex]
The x-intercepts of 3x+4y+6z=15 is
[tex]x = 5 - \frac{4}{3} y - 2z[/tex]
[tex]\orange{••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]
#CarryOnlearning
Explain this picture
Answer:
It's A bar graph but I got to see the question to be for sure but its a bar graph and it helps you measure rates of things from numbers , months , years etc .
Step-by-step explanation: