The length of the pencil is 8x + 2 and length of pen is 4x + 1. Find the difference between their lengths.

49 - 2/3 x = 32 - 1/6 x

Move the constant terms to one side and the terms containing x to the other:

49 - 32 = 2/3 x - 1/6 x

Simplify the left side, and pull out the common factor of x on the right side:

17 = (2/3 - 1/6) x

Write the fractions in terms of a common denominator. In this case, you would take

2/3 = 4/6

so that

(2/3 - 1/6) x = (4/6 - 1/6) x = 3/6 x = 1/2 x

Then the equation is

17 = 1/2 x

Multiply both sides by 2:

2 × 17 = 2 × 1/2 x

34 = x

Solution:-1

Number be 27

[tex]\\ \sf\longmapsto 27^2[/tex]

[tex]\\ \sf\longmapsto (30-3)^2[/tex]

[tex]\\ \sf\longmapsto 30^2-2(30)(3)+3^2[/tex]

[tex]\\ \sf\longmapsto 900-180+9[/tex]

[tex]\\ \sf\longmapsto 909-180[/tex]

[tex]\\ \sf\longmapsto 729[/tex]

[tex]\\ \sf\longmapsto 27^2[/tex]

Hence verified

Solution:-2

[tex]\\ \sf\longmapsto 10^3+9^3[/tex]

[tex]\\ \sf\longmapsto (10+9)(10^2-10\times 9+9^2)[/tex]

[tex]\\ \sf\longmapsto 19(100-90+81)[/tex]

[tex]\\ \sf\longmapsto 19\times 91[/tex]

[tex]\\ \sf\longmapsto 1729[/tex]

Answer:

y=113*(1+0.82)^x

x=7

y=113*(1.82)^7=7474.43

Question 10

Draw a 30-60-90 triangle template. Refer to the diagram below.

We have 1 as the short leg, 2 as the hypotenuse and sqrt(3) as the long leg.

Place the angle theta as the reference angle such that it's opposite the sqrt(3) side.

That allows tan(theta) = sqrt(3)/1 = opposite/adjacent

In other words, tan(60) = sqrt(3)/1

So theta = 60 is one solution. We add on 180 to get the other solution. So the other solution is 60+180 = 240

So tan(60) = tan(240) = sqrt(3)

======================================================

Question 11a

sin(theta) = -0.8

theta = arcsin(-0.8) or theta = 180-arcsin(-0.8)

theta = -53.1301  or theta = 180 - (-53.1301)

theta = -53.1301  or theta = 233.1301

Add 360 to the first angle to find a coterminal angle counterpart.

-53.1301 + 360 = 306.8699

So the two approximate solutions are

theta = 306.8699  or theta = 233.1301

and those round to 306.9 and 233.1 respectively.

======================================================

Question 11b

cot(theta) = 1.8

tan(theta) = 1/(1.8)

theta = arctan( 1/(1.8) )  or theta = 180+arctan( 1/(1.8) )

theta =  29.0546 or theta = 180+29.0546

theta = 29.0546 or theta = 209.0546

theta = 29.1 or theta = 209.1

Does the answer help you?

Answer:

try D

Step-by-step explanation:

Answer:

The percentage is 81.35% (2.d.p)

Step-by-step explanation:

[tex]\frac{169.2}{208}[/tex] x 100 = 81.34615285

Answer:

Rectangular pyramid volume: 8×9×9/3 = 216 cm³

Rectangular prism volume: 8×9×7 = 504 cm³

Total volume of composite figure: 216+504 = 720 cm³

Answer:

720 cm³

Step-by-step explanation:

Rectangular pyramid:

Volume = [tex]\frac{1}{3}BH[/tex]

H = 9 cm

B-> base area =  area of rectangle

B = length * width = 8*9 = 72  square cm

[tex]Volume = \frac{1}{3}*72*9 = 216 \ cm^{3}[/tex]

Rectangular prism:

length = l = 8 cm

Width = w = 9 cm

Height = h = 7 cm

Volume of rectangular prism = l * w * h = 8 * 9 * 7 = 504 cm³

Volume of composite figure = volume of pyramid + volume of r. prism

      = 216 + 504

      = 720 cm³

Hey there! I'm happy to help!

When dealing with picking things and finding the number of possibilities, we can be dealing with two different types of things: permutations or combinations. We use permutations when order is important to the groups and we use combinations if order is not important.

It appears here that order is not important here as the subcommittee doesn't have to be in a specific order, so we will be using combinations.

So, we have ten seventh graders to choose from. Then we will have 9, and then 8. So, we multiply these numbers of choices.

10×9×8=720

Now, we need to divide by 6. This is to show that order doesn't matter. Why? Because there are  6 possible ways to organize 3 seats on the committee (3×2×1), and we want to divide out all of the different orders so it is just the specific group of people and not their different organizations that are counted.

720/6=120

Now, we need to find this with the eighth graders.

8×7×6=336

And we divide by the number of seats factorial (3 seats for the eighth graders, so 3×2×1=6 again)

336/6=56

Now, we multiply our numbers for seventh and eighth graders to find all off the possibilities.

120×56=6720

So, there are 6720 subcommittees possible.

Have a wonderful day and keep on learning! :D

Answer:

53640

Step-by-step explanation:

Answer:

[tex]\displaystyle m = \frac{22}{9}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

Point (1, 3)

Point (10, 25)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

c

Step-by-step explanation:

The method is Dr. Perry most likely to use is Participatory action research.

Participatory action research is a type of research characterized by :

Additionally, in this type of research, the community involved is treated as researchers and their contributions are taken into account in the result of the same.

According to the above, the type of research suitable for Dr Perry's study is participatory action research, since it includes all the factors that Dr Perry takes into account for her research such as quantitavie/qualitative method and active participation from the community involved.

On the other hand, case study, naturalistic observation, and focus group are not the correct options because they use other methods in which the studied community does not actively participate.

Learn more in: https://brainly.com/question/15930435

Note:

This question is incomplete because the options are missing. Here are the options.

A. Case study

B. Naturalistic observation

C. Participatory action research

D. Focus group

Step-by-step explanation:

Algebra is a topic that covers linear equations, system of equations, sequences, exponential functions, polynomials, quadratic, exponents, radicals, functions, and more. I'm going to give use algebraic formulas and not all the topics.

Like Terms Rule: If two terms that share the same variable are separated by a binary operation, we can combine them.

For example, look at

[tex]6 + 7x + 9x[/tex]

We can combine 7x and 9x.

[tex]7x + ( + 9x) = 16x[/tex]

Add the coeffceint and keep the variable.

16x+6

Solving Algebraic Equations:

Alot questions in Algebra asks you to isolate a variable. For example,

[tex] \frac{x}{2} + 6 = 9[/tex]

First step, is to get the x variable by itself. To do this subtract 6 by both sides. Why? Because Subtraction is a inverse operation off addition. Remeber the Golden Rule of Algebra,

WHAT WE DO TO ONE SIDE. WE DO TO THE OTHER.

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

Now, we multiply both sides by 2 because multiplying is the inverse operation of division and vice versa.

[tex]x = 6[/tex]

If we plug this in, it is indeed true.

[tex] \frac{6}{2} + 6 =[/tex]

[tex]3 + 6 = 9[/tex]

Some other rules are

If we multiply a term by a one term, we only affect the term that is being multiplied, for example

[tex]2x \times 3[/tex]

2 and 3 are both real numbers so we just multiply 2 and 3. and put x behind the answer.

[tex]2 \times 3 = 6(x)[/tex]

[tex]2x \times 3 = 6x[/tex]

When we multiply 2 variables, we put the variable near each other. For example,

[tex]x \times y = xy[/tex]

When we add term, we add the coeffcient parts

[tex]y + y = 1y + 1y = 2y[/tex]

Know that

[tex]y = 1y[/tex]

When we multiply same term variables, we get

[tex]x \times x = {x}^{2} [/tex]

There is more formulas for Algebra. But these are the basicis.

Answer:

Mathematics includes the study of such topics as quantity, structure, space, and change; It has no generally accepted definition.

Step-by-step explanation:

Answer:

Mathematics is like the study of numbers and relationships I guess.

Step-by-step explanation:

All branches of math seems to use relationships or numbers, whether it be ratios for Algebra, geometry stuff like SinCosSine and Tangent.

Basic Arthimetics seems to use ratios when counting, or patterns, ect.

100÷50000 can be written as 100/50000, then cancel out 2 of the zeroes, and you will get 1/500 or 0.002 as your final answer.

You want to try and get rid of one of the variables ( x or y) so you would multiply the second equation by 2 which would make the x variable -2x which then when added to the first equation would eliminate the x variable.

Answer: c. Multiply the second equation by 2.

Answer:

see below

Step-by-step explanation:

           x+5

y = ----------------------

        x^2 - 2x+1

Since the degree of numerator < degree of denominator ( 1 < 2) there is a horizontal  asymptote: y = 0

Answer:

Confidence Interval - "P" values  

(0.4433 , 0.5444 )

~~~~~~~~~~~~~~~~~~~~~~~

[tex]\mathrm{Expand\:}\left(x+4y\right)^3:\quad x^3+12x^2y+48xy^2+64y^3[/tex]

in you image it is the last on "D"

Step-by-step explanation:

Confidence Level - "P" values  

99% 2.58

Confidence Interval - "P" values  

(0.4433 , 0.5444 )  

Answer:

a1 =5

Step-by-step explanation:

an = 5,10,15,20,25......

a1 is the first term

a1 =5

Answer:

C x=8

Step-by-step explanation:

Chúc bạn ngày mới tốt lành

the answer Is found in the question

The least number of buses required for the trip will be 5 buses.

It is a method where we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.

Step 1: Let’s find the cost of 1 ice cream. In order to do that, divide the total cost of ice-creams by the total number of ice-creams. The cost of 1 ice-cream = Total cost of ice-creams/Total number of ice-creams = 125/5 = 25. Therefore, the cost of 1 ice cream is $25.

Step 2: To find the cost of 3 ice creams, multiply the cost of 1 ice cream by the number of ice-creams. The cost of 3 ice-creams is cost of 1 ice-cream × number of ice-creams = 25 × 3 = $75. Finally, we have the cost of 3 ice-creams i.e. $75.

Total number of classes = 9

Number of students in each class = 25

Number of teachers = 4

Number of chaperones = Double of teacher

Bus hold = 45 people

A total number of students.

= 9 × 25

= 225

A number of chaperones.

= 4 × 2

= 8

Total people = 225 + 8 + 4 = 237

Least number of buses required for trip = Total people / Bus hold

= 237 / 45

= 5.266

Learn more about the unitary method here:

brainly.com/question/22056199

#SPJ2

Answer:

let x be the complementary angle

then x + 2 is the angle

x+2 +x =90

2x = 88

x = 44°

x + 2° = 46°

Answer:

yes because the graph passes the vertical line test

Answer:

4) A

5) E

Step-by-step explanation:

#4

[tex]\frac{x}{y}=\frac{1}{10} * \frac{z}{y}[/tex]

[tex]\frac{x}{y} =\frac{1z}{10y}[/tex]

Cross multiply the equation and you get:

[tex]10xy=zy[/tex]

Since [tex]\frac{a}{b}=\frac{c}{d}[/tex]  is the same thing as [tex]ad=bc[/tex], you can change the equation into [tex]\frac{x}{z} =\frac{y}{10y}[/tex]

Cancel out the y on the top and bottom and you get 1/10

#5

[tex]\frac{2}{3} *\frac{x}{2} =5[/tex], simplify and you get [tex]\frac{x}{3} =5[/tex] so x=15

[tex]\frac{1}{5} * 3(x)[/tex] is equal to [tex]\frac{1}{5} *3(15)[/tex] after you plug in x, and that is equal to 9

Answer:

filtration system is not working

filtration

Answer:

biomass energy (such as ethanol), hydropower, geothermal power, wind energy, and solar energy.

Answer:

B

-10-10=20

10+10=20

20/20=0

Answer:

The equation would be y=m-2+6

Step-by-step explanation:

Have a great day :)

Answer:

Step-by-step explanation:

The numbers from 1 to 9999 can be shown in the form of:

Each of x, y, z represent the digits from 0 to 9, so 10 ways each.

For each of the forms we have:

Total of:

By the way this is applicable to any digit.

Max number of digits=4

Their can be 4ways to represent

Each form can repeat 3

Total repeating