which expressions are equivalent to 2(a+3b)

Answer:

...not lie on the same plane.

Step-by-step explanation:

Answer:

3 pyramids.

Step-by-step explanation:

The volume of one pyramid is 1/3 * b^2 * h

= 1/3 * 12^2 * 25

= 1200 cm^3.

The volume of one ball bearing = 4/3 * π * 0.7^3

= 1.43676 cm^3.

Therefore the volume of 2490 ball bearings = 2490 * 1 .43676

= 3577.53 cm^3.

So we need 3577.53 / 1200 = 2.98 = 3 pyramids.

Answer:

108

Step-by-step explanation:

they are supplemntary meaning the sum of the equals 180

180 - 72 = 108

Answer:

<7= 108

Step-by-step explanation:

Angle 6 and angle 7 form a straight line. A straight line always equals to 180, so you subtract 180 from 72. 180-72=108

Answer:

7

Step-by-step explanation:

We first start by simplifying the bracket.

(6 - 5) = 1,

Now we have

3(1) + 4

3 + 4 = 7

also, if you expand instead of simplifying, you get.

(3*6 - 3*5) + 4

(18 - 15) + 4

3 + 4 = 7

Irrespective, the answer is 7

Answer:

No  real solution

Step-by-step explanation:

First off I'm assuming that the 1 or -1 at the begging is just the problem number:

First you distribute on both sides

36 - 18x - 3 = 4 - 18x + 30

Then combine like terms

33 - 18x = 34 - 18x

Then rearrange the terms by adding 18x to both sides and subtracting both sides by 33. You should get:

0 = 1

When you add positive 18x it cancels the -18x out. And 34 - 33 is 1. Obviously, zero cannot equal 1 so there is no real solution

hey the square root is 20

Answer:

20.37

Step-by-step explanation: caculated!!

Answer: $90,000 at 12%

and $80,000 at 9%

Step-by-step explanation:

given data:

cost of property = $170,000.

short term = 12%.

long term = 9%.

total interest paid = $18,000.

Step 1

= 0.12x + 0.09 (170,000-x) = 18,000

collect like terms

= 0.12x +  15300 – 0.09x = 18,000

divide both Sides by 0.03

0.03x = 2700

x = $90,000 at 12%

and $80,000 at 9%

Answer:  see proof below

Step-by-step explanation:

Use the following Sum to Product Identities:

[tex]\sin x+\sin y=2\sin\bigg(\dfrac{x+y}{2}\bigg)\cos \bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x-\cos y=-2\sin\bigg(\dfrac{x+y}{2}\bigg)\sin \bigg(\dfrac{x-y}{2}\bigg)[/tex]

Proof LHS →  RHS

[tex]\text{LHS:}\qquad \qquad \qquad \qquad \dfrac{\sin \theta-\sin 3\theta+\sin 5\theta -\sin 7\theta}{\cos \theta -\cos 3\theta -\cos 5\theta +\cos 7\theta}[/tex]

[tex]\text{Regroup:}\qquad \qquad \qquad \dfrac{(\sin 5\theta+\sin \theta)-(\sin 7\theta +\sin 3\theta)}{-(\cos 5\theta -\cos \theta) +(\cos 7\theta -\cos 3\theta)}[/tex]

[tex]\text{Sum to Product:}\quad \dfrac{2\sin\bigg(\dfrac{5\theta +\theta}{2}\bigg)\cos \bigg(\dfrac{5\theta -\theta}{2}\bigg)-2\sin \bigg(\dfrac{7\theta + 3\theta}{2}\bigg)\cos \bigg(\dfrac{7\theta - 3\theta}{2}\bigg)}{2\sin\bigg(\dfrac{5\theta +\theta}{2}\bigg)\sin \bigg(\dfrac{5\theta -\theta}{2}\bigg)-2\sin \bigg(\dfrac{7\theta + 3\theta}{2}\bigg)\sin \bigg(\dfrac{7\theta - 3\theta}{2}\bigg)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{2\sin 3\theta \cos 2\theta-2\sin 5\theta \cos 2\theta}{2\sin 3\theta \sin 2\theta-2\sin 5\theta \cos 2\theta}[/tex]

[tex]\text{Factor:}\qquad \qquad \dfrac{\cos 2\theta(2\sin 3\theta -2\sin 5\theta \cos 2\theta)}{\sin 2\theta(2\sin 3\theta -2\sin 5\theta \cos 2\theta)}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{\cos 2\theta}{\sin 2\theta}\\\\.\qquad \qquad \qquad =\cot 2\theta[/tex]

LHS = RHS:  cot 2Ф = cot 2Ф   [tex]\checkmark[/tex]

Answer: (9,950 to 10,049)

Step-by-step explanation:

The nearest hundred is the third digit (counting from the right).

When we round up/down, we must look at the previous digit (the second in this case).

If the digit is larger than 5, we round up

if the digit is 5 or less, we round down.

Then if the rounded number is 10,000.

The rounded down version will be:

10,049

(49 < 50, then we should round down to 10,000)

The rounded up version will be:

9,950.

this number would be the smallest number that can be rounded up to 10,000.

Then the possible range is:

(9,950 to 10,049)

Answer:

750 minutes

Step-by-step explanation:

james read 2 pages in 3 minutes so to read 250 pages it will be 250 x 3=750

Answer:

Step-by-step explanation:

The point on the x-axis is 2

The point on the y - axis is -3

Answer:

[tex]\frac{s}{2t}[/tex]

Step-by-step explanation:

When you have exponents above a like term and they are being multiplied together, you add them.

For example:

[tex]a^{x} *a^{y} = a^{x + y}[/tex]

So let's group like terms in the numerator:

[tex]4r^{3} r^{-5} s^{-2} s^{-1}t[/tex]   We can add terms like in the example.

[tex]4 r^{-2} s^{-3} t[/tex]

Let's rearrange the denominator.

[tex]8r^{-2} s^{-4} t^{2}[/tex]

Now we have:

[tex]\frac{4r^{-2} s^{-3}t}{8 r^{-2} s^{-4} t^{2} }[/tex]  Cancel like terms

4/8 = 1/2    

[tex]r^{-2} /r^{-2}[/tex] = 1  So it cancels

[tex]s^{-3} / s^{-4} = s^{-1}[/tex] = s Since s is raised to the -1 it goes on top and becomes s.

[tex]t / t^{2} = 1/t[/tex]

Now we combine everything back together:

[tex]\frac{s}{2t}[/tex]

Answer:

Step-by-step explanation:

yes

Answer: 2,977,200 miles per hour

Step-by-step explanation: This is true because taking that that is miles per second there is 60 seconds in a minute so times that by 60 and there are 60 minutes in an hour so times that last answer by 60 again which gives you the answer

Answer:

4p - 7 = 13

Step-by-step explanation:

The first step of the solution should be to simplify the left side by combining like terms. In this case, 3p and p are the like terms and 3p + p = 4p so the answer is 4p - 7 = 13.

Answer:

4p - 7 = 13

Step-by-step explanation:

Answer:

The percentage difference between 3.4 and 3.42 is 0.58651% or 0.02.

Step-by-step explanation:

Find the absolute difference between two numbers: |20 - 30| = |-10| = 10

Find the average of those two numbers: (20 + 30) / 2 = 50 / 2 = 25

Divide the difference by the average: 10 / 25 = 0.4

Express it as percentages: 0.4 * 100 = 40%

in this case, it would be 3.4 and 3.42

Answer: 0.02

Step-by-step explanation: 3.42 is bigger than 3.4 and they are asking for the difference between the two measurements. So, you subtract the 3.4 from the 3.42

Answer:

Step-by-step explanation:

The question lacks the required diagram. Find the diagram attached below.

Since all the sides and angles of a rhombus are the same, hence, all the right angled triangle in each quadrant are also the same.

From the diagram, < XWZ = < XWV + < VWZ and < XWV = < VWZ

Therefore < XWZ = < VWZ + < VWZ

< XWZ = 2<VWZ

let us calculate the angle <VWZ first.

From ΔVWZ, <WVZ +<WZV + <VWZ  = 180°... 1

From the diagram <WVZ = 90°, <WZV = <VZY = 64°

On substituting into 1

90°+64°+ <VWZ  = 180°

154°+ <VWZ  = 180°

<VWZ  = 180°-154°

<VWZ  = 26°

Since < XWZ = 2<VWZ

< XWZ = 2(26°)

< XWZ = 52°

Hence the measure of < XWZ is 52°

Answer:  650 miles

Step-by-step explanation:

If it takes 5 hours to go from Paris to Geneva and a train is travelling at 130 miles per hour then multiply the total number of miles per hour by 5 to find how many miles you will have to travel from Paris to Geneva.

130 * 5 =  650

Answer:

The radius of each rug on the order is 6 ft

Step-by-step explanation:

The graph shows the relationship between the price of a rug and the radius of the rug

The number of rugs ordered by the customer = 3 rugs

The total cost of the rugs ordered by the customer = $1,350

Therefore, the cost of each rug = $1,350/3 = $450

The radius of the rugs as determined from the chart

At $450, the radius of the rug = 6 ft

Therefore;

Given that all the rugs are identical, the radius of each rug on the order = 6 ft.

Answer:

18

Step-by-step explanation:

I am assuming you meant 8r-rs, in this case:

Plug in r=6 and s=5:

8(6)-(6)(5)

8*6 = 48 and -6*5= -30

Thus,

48-30= 18

Answer  78

Step-by-step explanation:

there isn't enough information

you need to put the image or the amount of inches of rain to get an answer

Answer:

Step-by-step explanation

That's the answer

The position of the √6 on the number line is slightly right of the 2.4.

We need to determine the approximate location of √6 on the number line.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,

In the general conclusion,

√4< √6 < √9

2 < √6 < 3

So, the value of the √6 lies between 2 and 3.

√6 = 2.445

So the position of the √6 on the number line is slightly right of the 2.4.

Thus, the position of the √6 on the number line is slightly right of the 2.4.

Learn more about number line here:

brainly.com/question/17683084

#SPJ2

Answer:

a^ (5/2)

Step-by-step explanation:

a^5 ÷ a ^ (5/2)

We know that x^b ÷ x^c = x^ ( b-c)

a^ ( 5 - 5/2)

a^ ( 10/2 - 5/2)

a^ (5/2)

Answer:

[tex]a^{\frac{5}{2} }[/tex]

Step-by-step explanation:

Using exponent rules, if we have [tex]a^x \div a^y[/tex] then the result can simplify to [tex]a^{x-y}[/tex]

So [tex]a^5 \div a^{\frac{5}{2}}[/tex] is the same as [tex]a^{5 - \frac{5}{2}}[/tex].

[tex]\frac{5}{1} - \frac{5}{2} = \frac{10}{2} - \frac {5}{2} = \frac {5}{2}[/tex]

So [tex]a^{\frac{5}{2}}[/tex].

Hope this helped!

Answer:

Jose ends up with more money with $59 more than Peter.

Step-by-step explanation:

To determine the amount they will have, you have to use the formula to calculate the future value:

FV=PV(1+r)^n

FV= future value

PV= present value

r= rate of interest

n= number of periods of time

-Peter:

FV=1,000*(1+0.04)^10

FV=1,000*1.48

FV=1,480

-Jose:

FV=900*(1+0.05)^11

FV=900*1.71

FV=1,539

Difference: $1,539-$1,480=$59

According to this, the answer is that Jose ends up with more money with $59 more than Peter.

Answer:

L = 150 - 15t

Step-by-step explanation:

Money borrowed by Ariana = $150

Money she returns each week = $15

Amount of borrowed money will decrease by $15 each week.

In 1 week she will return $15

in 2 week she will return $15*2 = $30

in 3 week she will return $15*3 = $45

...........................

similarly after t week

money she will return = Money she returns in 1 week* no of weeks

money she will return in t weeks = 15*t = 15t

where 15t unit is dollar

So, Amount of borrowed money will decrease by $15t in  t week.

Amount of money she woes after t week = Money borrowed by Ariana - money returned in t weeks

Amount of money she woes after t week = 150 - 15t

Since L represents the amount Ariana owes  ,her friend after t weeks

L = 150 - 15t is the correct answer

Answer:

slope:  1 /8

y-intercept:  ( 0 , − 1 /4 )