Find the value of {2/3}^3 Explain or show how you got your answer.

Using order of operations , the expression ⇒4[2.5+3(20+7)] = 334

Order of mathematical operations are done in order with respect to PEDMAS rule.

PEDMAS: Parenthesis → Exponents→ Division→ Multiplication→ Addition→ Subtraction.

it states that we will start will solving brackets or Parenthesis then will solve powers or exponents , then division and so on in the same order as given in PEDMAS rule

For given expression 4[2.5+3(20+7)]

First solve brackets (20+7)

⇒4[2.5+3(20+7)] = 4[ 2.5 + 3(27)]

Then solve bracket 2(27) = 81

⇒4[2.5+3(20+7)] = 4[ 2.5 + 3(27)] =  4[ 2.5 + 81]

Solve the bracket [ 2.5 +81]

⇒4[2.5+3(20+7)] =  4[ 2.5 + 81] = 4[83.5] = 334

Also, Learn more about order of operation from the link below:

https://brainly.com/question/15840745

#SPJ1

Answer:

c

Step-by-step explanation:

The inequality equivalent to -m ≥ 15 is m ≤ -15, achieved by multiplying both sides of the inequality by -1, which reverses the inequality symbol. So the correct answer is C. m ≤ -15.

The question asks which inequality is equivalent to the inequality -m ">≥ 15. To find the equivalent inequality where m is positive, we need to multiply or divide both sides of the inequality by -1, remembering that doing so reverses the inequality symbol. Therefore, multiplying both sides by -1 gives m ≤ -15, which means that the inequality that is equivalent to -m ≥ 15 is m ≤ -15.

So the correct answer is C. m ≤ -15.

Answer:

1) C

2) A

3) D

Step-by-step explanation:

A) We substitute the values for a ,b , c and d in the given equation.[tex]\frac{6}{3} +4^2 (5) \\= 2+80\\=82[/tex]

Hence option c. 82 is the answer.

2) The product 6(-3)

Since positive x negative gives negative

we get -(6x3) = -18

Option A is the answer.

3) For this we have to find cube of a fraction with numerator 4 and denominator 7

We find cube of numerator first = 4x4x4 =64

Cube of denominator = 7x7x7 = 343

Hence cube of fraction = 64/343

Option D

Given slabs thicknesses 5in, 10in, and 15in.

Therefore, ratio of thicknesses in simplest form would be 1:2:3.

Metal 1 thicknesses =  150lbs, 300lbs, 600lbs

Dividing by 150, we get ratio of Metal 1 thicknesses = 1:2:4.

Metal 2 thicknesses = 130lbs, 260lbs, 390lbs.

Dividing by 130, we get ratio of Metal 2 thicknesses =  1:2:3.

Metal 3 thicknesses = 310lbs, 620lbs, 930lbs.

Dividing by 310, we get ratio of Metal 3 thicknesses = 1:2:3.

Metal 4 thicknesses = 140lbs, 280lbs, 420lbs.

Dividing by 140, we get ratio of Metal 4 thicknesses = 1:2:3.

We can see the ratios of thicknesses of Metal 1 are 1:2:4 but it should be 1:2:3.

Therefore, Metal 1 weight is not proportional to thickness.

Answer:

Weights of metal 1 is not proportional to thickness.

Step-by-step explanation:

We have been given 3 thicknesses of metal slabs and the weights of each thickness for each metal. We are asked to find out which of the metals weight is not proportional to thickness.

We can see that the thicknesses of slabs are first three multiples of 5 that is 5 inches, 10 inches and 15 inches.

Now let us see which of the metals have not their weights proportional to their thicknesses.

In our first option we can see that 300 is 2 times 150 and 600 is 4 times 150 which is not proportional to thickness. In order to metal 1's weight to be proportional with it's thickness it should be 450 lbs instead of 600.

Our second metal's weight is proportional to it's thickness as 130, 260 and 390 are 3 first consecutive multiples of 130.

Our third and fourth metal's weights are also proportional to their thicknesses.

Therefore, metal 1's weight is not proportional to thickness.

the slope of a perpendicular line = - [tex]\frac{3}{5}[/tex]

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 5x - 3y = 2 into this form

subtract 5x from both sides

- 3y = - 5x + 2 ( divide all terms by - 3 )

y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{2}{3}[/tex]

with slope m = [tex]\frac{5}{3}[/tex]

the slope of a line perpendicular = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{3}{5}[/tex]

According to question

[tex] 80\% of n = 72[/tex]

Change percentage to decimal by dividing it by 100

[tex] (80\div100)\mul n=72[/tex]

[tex]0.80\times n =72[/tex]

Now, crossmultiply we get,

[tex] n = \frac{72}{0.80}[/tex]

Now sloving we get

[tex] n = 90[/tex]

Answer:

The Average rate of the first plane is 560 mph

Step-by-step explanation:

x = first plane's average rate (in mph)

x−108 = second plane's average rate (in mph)

First planes total distance = 2.25x

Second planes total distance = 1.25(x−108)

2.25x + 1.25(x−108) = 1825

x = 560

3.8 miles per week

the miles ran last month is 2.8

let 2.8 be original , that is 100%

an increase of 36.2% is then

100 + 36.2 = 136.2% = [tex]\frac{136.2}{100}[/tex] = 1.362

multiply 2.8 by this quantity

= 2.8 × 1.362 = 3.8 miles per week ( to nearest tenth )

For this case we have the following expressions:

[tex]x = -4y + 4\\\\2x + 8y = 8\\[/tex]

Rewriting the second equation we have:

[tex]2x = -8y + 8\\[/tex]

It is observed that by multiplying the first equation by 2, the second equation is obtained.

Thus, the equations are linearly dependent and since the lines are equal then they are intercepted in infinite points. Therefore, the system has endless solutions.

Answer:

Option D

28.8

hope this helps :)

28 4/5 That is the answer for the question

Triangle ABC is equilateral, because AB=BC=AC=a. Then

m∠A=m∠B=m∠C=60°.

Let point D lie on the ray BC to the right from points B and C and let CD=x. Then BD=a+x, AB=a.

Consider triangle ACD. In this triangle, m∠ACD=180°-m∠ACB=180°-60°=120°.

By the cosine theorem,

[tex]AD^2=AC^2+CD^2-2\cdot AC\cdot CD\cdot \cos \angle ACD,\\\\AD^2=a^2+x^2-2\cdot a\cdot x\cdot \cos 120^{\circ},\\\\AD^2=a^2+x^2+ax,\\\\AD=\sqrt{a^2+x^2+ax}.[/tex]

Since [tex]a^2+x^2+ax=a^2+x^2+ax+ax-ax=(a+x)^2-ax,[/tex] then

[tex]AD^2=(a+x)^2-ax<(a+x)^2=BD^2\Rightarrow AD<BD[/tex]

and

[tex]AD^2=a^2+x^2+ax>a^2=AB^2\Rightarrow AD>AB.[/tex]

Therefore, you get double inequality

[tex]AB<AD<BD[/tex] or [tex]BD>AD>AB.[/tex]

Answer:

The proof is below

Step-by-step explanation:

Please look at the attachment below

Please let me know if this is wrong

Let me know if you have any questions

If right please give me brainiest

Thanks

subtracting term by term

(3.1x - 4.3x ) + (2.8z - (- 1.2z ) )

= - 1.2x + (2.8z + 1.2z ) = - 1.2x + 5z

Answer:

Question 7

Total area of the quadrilateral [tex]27[/tex].

Question 8

Angles on the side of a straight line adds up to 180°

Therefore we can write the sum of all the angles as;

[tex]x+4x+20=180[/tex]

Then you can solve the equation to find the [tex]x[/tex].

Step-by-step explanation:

(7)

First Plot the coordinates in the Cartesian plane. Then join all the points. Now you should get a graph as the graph shown in "red lines" in the attachment.

To make it easier we add another point in the graph as "E(2,3)". Now we have two shapes, one is a rectangle ABED and the other is a triangle BEC. Addition of these to makes the ABCD quadrilateral.

Before finding the areas we need to find the lengths of each side.

AB=3-(-1)=4

AD=BE=2-(-4)=6

EC=4-3=1

Area of ABED rectangle = AB*AD

                                        =[tex]4*6[/tex]

                                        =[tex]24[/tex]

Area of the BEC triangle= [tex]\frac{1}{2}[/tex]*BE*EC

                                        =[tex]\frac{1}{2} *6*1[/tex]

                                        =[tex]3[/tex]

Therefore, total area of the quadrilateral = [tex]24+3[/tex]

                                                                    =[tex]27[/tex]

(8)

Angles on the side of a straight line adds up to 180°

Therefore we can write the sum of all the angles as;

[tex]x+4x+20=180[/tex]

Then you can solve the equation to find the [tex]x[/tex] as follows.

[tex]5x+20=180[/tex]

[tex]5x=160[/tex]

[tex]x=32[/tex]

Then you can find 4x° also by multiplying x by 4.