4x+6<-6 how to solve

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.

Then,

[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.

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:

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

1 km = 1000 m, so:

23,769 km = 23,769 · 1000 m = 23 769 m

Answer:

23769m

Step-by-step explanation:

Basicly, 3.769x 1000= 23769m

Please mark brainliest

For the cut glass pieces to be rectangular in shape, the glass cutter should ensure:

Thus, to ensure the cut glass pieces are rectangular in shape, he should ensure the following:

Learn more about properties of rectangle on:

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Answer: call 911

Step-by-step explanation: call 911

Answer:

Step-by-step explanation:

65%

Step-by-step explanation:

Given: Full capacity= 200000 litres

          Amount of fuel used during flight= 130000 litres

Now, finding percentage of fuel used on the flight.

∴ Percentage of fuel used=  

Solving it, we will get  

∴ 65% of fuel capacity been used in this flight.

Answer:

65%.

Step-by-step explanation:

(130,000/200.000) * 100

= 0.65 * 100

= 65%.

Answer:

Rational

Step-by-step explanation:

It isnt whole because its a decimal,

It isnt an Integer because its a decimal

It isnt natural because its a decimal

Meaning it can only be rational

Answer:

1/3

Step-by-step explanation:

-2-4 = -6

-7-11 = -18

Answer:

Step-by-step explanation:

This is an isosceles triangle. You can tell because 2 of the sides are equal and the third is not equal to either of the other two.

x + x + 56 = 180                  Combine the left

2x + 56 = 180                      Subtract 56 from both sides.

2x = 180 - 56

2x = 124                               Divide by 2

x = 124/2

x = 62

Answer:

D

Step-by-step explanation:

BH is perpendicular to AC since an orthocenter is a point at which the three altitudes of a triangle intersect. The altitude of a triangle is that line that passes through its vertex and is perpendicular to the opposite side. Since you know that BH is an altitude due to Point H being an orthocenter, you know that BH is perpedendicular to AC.

Answer:

15-14=1

Step-by-step explanation:

1 apple left

Answer:

1 apple

Step-by-step explanation:

15-14=1

Hope the helps!

Answer:

39.0625

Step-by-step explanation:

15.625 times 2.5= 39.0625

You're just multiplying each value by 2.5

1 times 2.5= 2.5

2.5 times 2.5= 6.25

6.25 times 2.5= 15.625

and then 15.625 times 2.5= 39.0625

Answer:

263,870

Step-by-step explanation:

Answer:

263,870

Step-by-step explanation:

You have 26,387 then you will multiply it by 10 and you'll get 263,870

Answer:

This is indeed a function!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Assuming the density is the same for both lollipops, we can calculate what volume is required to make the 2158.7kg the same density of the smaller lollipop.  

Small Lollipop

r = 2cm

V=4 /3πr^3

V = 33.51 cm^3

Mass is 50 g in 33.51 cm^3, so the density is:

50g/(33.51 cm^3) = 1.492 g/cm^3

We have 2158.7kg in the larger lollipop.  That is 2158700 grams.

Find the volume required to contain 2158700 grams with a density of 1.492 g/cm^3.  :

       (2158700 grams)/(1.492 g/cm^3) = 1446775 cm^3

V=4 /3πr^3

1446775 cm^3 = (4/3)*π*r^3

r = 70.12 cm

Answer:

12c

Step-by-step explanation:

Note that when simplifying through adding or subtracting, the terms must have the same amount of the same variables to combine them.

In this case, all given terms have the same variable, denoted by c. Combine the given coefficients:

5c + 7c = 12c

12c is your answer.

~

Answer:

First Option, log 3x is equivalent to the expression shown

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!

Step-by-step explanation:

I don't really know what demonstrating with rigid motion means, never heard that before. But a method for demonstrating it could be drawing circumferences of radius:

1) R1 = d(O,S)

2) R2 = d(O,J)

3) R3 = d(O,M)

With O being the origin of the reference system.

*Note: d(A,B) means distance between point A and point B

After you've done that you can show that the points S and P are on the same circumference, J and W are on the same circumference (different from the one of S and P), M and D are on the same circumference.

After you've done that you calculate the angle between the points on the same circumference and demonstrating that they are all the same.

Answer:

Step-by-step explanation:

Congruent

Shift right 1 unit and up 5 units

Rotate 90 degrees clockwise about (-1, 2)

Or

just rotate 90 degrees clockwise about (1, -1)

Answer:    114

Step-by-step explanation:

3/4 * 152 = 3*38 =114

Answer: 24

Step-by-step explanation

8-8-16-24-32-40

6-6-12-18-24-30-36

Answer:

14,001

Step-by-step explanation:

old machine: 1,100+.12x

new machine: 1,520+.09x

if you plug in 14,000 for x, you get

old machine: 2,780

new machine: 2,780

therefore, you need 1 over 14,000 for it to be worth it because

if you plug in 14,001 for x, you get

old machine: 2,780.12

new machine: 2,780.09

which makes the new machine $.03 cheaper at this point (and the more snaps attached, the more the new machine will be worth it)

hope this helps!

Answer: - 0.3

Step-by-step explanation:

Correct me if I am incorrect.

Answer:

d-7 divided by 2 or over 2

Answer:

42 ft

Step-by-step explanation:

2(L + W ) = P

2 (12 + 9) = P

2 (21) = P

42 = P

P = 42

Answer:

34.5 people

Step-by-step explanation:

The capital formation of the investment function over a given period is the

accumulated  capital for the period.

Reasons:

(a) The given investment function is presented as follows;

[tex]I(t) = 100 \cdot e^{0.1 \cdot t}[/tex]

(a) The capital formation is given as follows;

[tex]\displaystyle Capital = \int\limits {100 \cdot e^{0.1 \cdot t}} \, dt =1000 \cdot e^{0.1 \cdot t}} + C[/tex]

From the end of the second year to the end of the fifth year, we have;

The end of the second year can be taken as the beginning of the third year.

Therefore,  for the three years; Year 3, year 4, and year 5, we have;

[tex]\displaystyle Capital = \int\limits^5_3 {100 \cdot e^{0.1 \cdot t}} \, dt \approx 298.87[/tex]

The capital formation from the end of the second year to the end of the fifth year, C ≈ 298.87

(b) When the capital stock exceeds $100,000, we have;

[tex]\displaystyle \mathbf{\left[1000 \cdot e^{0.1 \cdot t}} + C \right]^t_0} = 100,000[/tex]

Which gives;

[tex]\displaystyle 1000 \cdot e^{0.1 \cdot t}} - 1000 = 100,000[/tex]

[tex]\displaystyle \mathbf{1000 \cdot e^{0.1 \cdot t}}} = 100,000 + 1000 = 101,000[/tex]

[tex]\displaystyle e^{0.1 \cdot t}} = 101[/tex]

[tex]\displaystyle t = \frac{ln(101)}{0.1} \approx 46.15[/tex]

The number of years before the capital stock exceeds $100,000 ≈ 46.15 years.

Learn more investment function here:

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