Mathematics Middle School

State the main principle of solving equations

Answers

Answer 1

Answer:

The main principle of solving equations is to find the unknown value

Step-by-step explanation:

For example:

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

[tex]-3=-3[/tex]

[tex]x=3[/tex]

I hope this helps

Answer 2

Answer:

The fundamental principle of equation solving is based on the fact that after applying the same operation on both sides of the equation the solutions of the original equation are also solutions of the new equation.

Step-by-step explanation:

Related Questions

Write 9,622,000 in scientific notation.

Answers

Answer:

9.622 x 10^6

Step-by-step explanation:

Answer:

9,622*10 to the power of 3

Step-by-step explanation:

when using scientific notations you use ''10 to the power of ''

So in this case you have 3 zeroes which makes it 10 to the power of 3

[tex]9622000=9622*10^{3}[/tex]

help me i’m in need

Answers

Answer:DStep-by-step explanation:In a function, an input (x) value should have only one output (y) value.

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Example: (View attached image below). Table A is a function because each x value has only 1 y value. But Table B is not a function because the x value of 4 has 2 y values.

Answer:

D No, because on x values corresponds to two different y values

Step-by-step explanation:

This is not a function because an input has two different outputs

x=5 has two different y values

.
The table below shows the fees David
charges for yard work.
David's Yard Work Fees
Hours
2
4
6
Fee ($)
70
140
210
How much money does David charge for
yard work that takes 4.5 hours?

Answers

Find out how much David chargers for one hour.
That is 70÷2 which gives you 35.
Then multiply 4.5 hours by 35
your answer will be $157.5

2. Janice is buying paint to paint her new apartment. The store sells paint in one-gallon cans. How accurate does her estimate
need to be for the amount of paint needed?

Answers

Answer:

its 60-10+x why, because she bought the dress with $60 and she received $10 dollars back. We don't know the variable.

write the sum using sigma notation 3^2+4^2+5^2+...+10^2

Answers

[tex]\sum\limits_{i=3}^{10}\big i^2[/tex]

or:

[tex]\sum\limits_{i=1}^{8}\left(2+i\right)^2[/tex]

or:

x₁=3, x₂=4, x₃=5, .... x₈=10

[tex]\sum\limits_{i=1}^{8}\big x_i^2[/tex]

The sigma notation of 3^2+4^2+5^2+...+10^2 is: [tex]\sum\limits^{10}_{n = 3} n^2[/tex]

How to express the sum as a sigma notation?

The sum is given as;

3^2+4^2+5^2+...+10^2

The above means that the sum of the squares of integers from 3 to 10

Using the above statement, the sigma notation is:

[tex]\sum\limits^{10}_{n = 3} n^2[/tex]

Where n represents the current integer

Answers

Answer:

1/6 x 1/6 = 1/36

Step-by-step explanation:

We have to multiply as the odds get smaller as in every experimental probability being from experimental one dice and then trying to achieve that number alongside and same timing another number on an inclusive 2nd dice.

subtract the difference of p and a from 3

Answers

Answer:

see below

Step-by-step explanation:

Translating this into math we get 3 - (p - a).

The figure shows a carpeted room. How many square feet of the room is carpeted?

Answers

Answer:

Step-by-step explanation:

So split it into two shapes. Two rectangles.

Rectangle 1 = 4 * 5 = 20

Rectangle 2 = 2 * 10 = 20

20 + 20 = 40

Answer:

40 square feet

Step-by-step explanation:

we can cut the carpeted space into 2 parts for easier calculation.

we can do 4 x 5 to find the first part, which equals to 20 square feet.

then, to find the side length of the left over rectangle, you can do 6 - 4, making it the length of the side length, which is 2. then all you must do is multiply 2 by 10, which also equals to 20 square feet.

Just add up both of the calculations(20 +20) then you'll get your answer!

the answer is 40 square feet.

Hope this helps and you understand now!

*WORTH 15 POINTS!!!*

please answer this (photo attached - question below)

( the “<“ have _ under them in the real questions sorry if that’s confusing)

PART A:
the domain of the function is _____ < x < ______

PART B:
the range of the function is _____ < f(x) < _____

PART C:
the function decreases from _____ < x < _____

Answers

Answer:

what is this I don't kno!

y+7=-2(x-3) write in slope form

Answers

Answer:

y=2x-3

Step-by-step explanation:

The slope intercept form is y=mx+b, where m is the slope and b is the y intercept.

y+7=-2(x-3) in slope formula would be y=2x-3, which also means the slope would be m=-2

I hope this helps :)

hi can anybody give me the answer i will mark them as a brainliest

Answers

48 cm squared. Multiply both sides (4 times 12) and the units have to be squared.

Answer:

[tex]48cm^2[/tex]

Step-by-step explanation:

Use the area of rectangle formula.

[tex]A=lw[/tex]

[tex]A=12 \times 4[/tex]

[tex]A=48[/tex]

Find the missing side. Be sure to show all of your work. Round to the nearest tenth
if necessary

Answers

Answer:

x=3.9 approximately

Step-by-step explanation:

Using Pythagorean theorem:

[tex]x^{2} + (5x)^{2} = 20^{2}[/tex]

[tex]x^{2} + 25x^{2} = 400[/tex]

26x^2 =400

x^2 = 15.3846

x=3.9

General Formulas and ConceptsAlgebra I

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityGeometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

a is a legb is another legc is the hypotenuse

ApplicationStep 1: Define

Let's define what the problem gives us:

We are given a right triangle, indicated by the square box inside the triangle, with side lengths 5x and x and a hypotenuse of 20.

We can set these measurements equal to our variables defined above in our Pythagorean Theorem equation:

a = 5xb = xc = 20

Step 2: Work

Now, we can substitute our variables and solve for x, which will help us find the side lengths as well:

[Pythagorean Theorem] Substitute in variables:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\\end{aligned}[/tex][Order of Operations] Simplify:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\\end{aligned}[/tex][Simplify] Combine like terms:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\\end{aligned}[/tex][Equality Properties] Divide both sides by 26:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\\end{aligned}[/tex][Equality Properties] Square root both sides:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\x & = \sqrt{\frac{200}{13}} \\\end{aligned}[/tex][Simplify] Evaluate:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\x & = \sqrt{\frac{200}{13}} \\& = \frac{10 \sqrt{26}}{13}\end{aligned}[/tex][Evaluate] Approximate:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\x & = \sqrt{\frac{200}{13}} \\& = \frac{10 \sqrt{26}}{13} \\& \approx \boxed{3.9} \\\end{aligned}[/tex]

∴ our x approximately equals 3.9.

Now we can use our value of x to solve for the missing triangle lengths:

Length of 5x:

Substitute in x:
[tex]\displaystyle\begin{aligned}\text{Side Length} & = 5x \\& = 5(3.9) \\\end{aligned}[/tex]Evaluate:
[tex]\displaystyle\begin{aligned}\text{Side Length} & = 5x \\& = 5(3.9) \\& = \boxed{19.5}\end{aligned}[/tex]

∴ this particular side length has a length of 19.5.

Length of x:

Substitute in x:
[tex]\displaystyle\begin{aligned}\text{Side Length} & = x \\& = \boxed{3.9}\end{aligned}[/tex]

∴ this particular side length has a length of 3.9.

Answer

∴ the side lengths of this particular triangle are 19.5 and 3.9, respective to their variables 5x and x.

___

Learn more about Triangles: https://brainly.com/question/20094559

Learn more about Geometry: https://brainly.com/question/16909531

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Topic: Geometry

Unit: Triangles

Which of the following equations is equivalent to the slope formula

Answers

Answer: D

Step-by-step explanation: Notice that if you multiply both sides of the equation of y2 = m (x2 - x1) + y1 by X2 - X1.

This gives you m(X2 - X1) = Y2 - Y1.

Then add Y1 to both sides to get m(X2 - X1) + Y1 = Y2.

This slope would be equivalent to the usual slope formula.

4. A driver set a goal to earn $2,000 in March. He receives a base salary of $1,000 per month as well as a 20% commission for all sales in that month. What does his total sales have to be this month to reach his goal?

Answers

Answer:

X=$5,000

Step-by-step explanation:

You can write an equation in slope-intercept to find an answer.

y=0.2x+1000, 20% commission is the slope and the base pay is the y-intercept.

Now, just plug in 2,000 for y.

2,000=0.2x+1,000, subtract 1,000.

1000=0.2x, Multiply by 5 to get x by itself.

x = 5,000

Hope this helped youuuuu

-7n2 + 5n + 2 = 0
Find the discriminant of each quadratic equation then state the number and type of solutions.

Answers

Answer:

Step-by-step explanation:

D=5^2-4*(-7)*2

D=25+56

D=81

two real rational solutions, since 81 is a perfect square

Solve the following system:

y = x + 3
4x + y = 18

Your answer:

(6, 3)

(3, 6)

(−3, 6)

(3, −6)

Answers

Answer:

B (3,6)

Step-by-step explanation:

y = x + 3

then we will use this y to substitute the other y

4x + y = 18

4x + (x +3) = 18

4x + x + 3 = 18

5x = 18 - 3

5x = 15

x = 15/5 = 3

then we can find the value of y

y = x + 3 = 3 + 3 = 6

so the (x,y) is (3,6)

Answer this, please!! Its urgent

Answers

Answer:

Hello dear,

5.102 ×10⁸km

300000000

2.4×10⁵

149600000000m

Hope it will help you

please thank

ANSWER:
1)5.102 x 10^8 km
2)300000000m/s
3)2.4 x10^5
4)149600000000
HOPE IT HELPS,,!
PLEASE MARK BRAINLIEST!!!!

Given the speeds of each runner below, determine who runs the fastest.
Ron runs 8 feet per second.
Liz runs 104 feet in 7 seconds.
Katie runs 1 mile in 526 seconds.
Emily runs 835 feet in 1 minute.

Answers

Answer:

Liz

Step-by-step explanation:

lets make all speeds ft/1sec

Ron 8ft/1sec

Liz 104ft/7sec : 104/7=

14.8571428571 ft/1 sec

Katie

1 mile = 5280ft

5280ft/526sec

5280/526=

10.0380228137ft/1 sec

Emily,

1 min= 60 sec

835ft/60 sec

835/60=

13.9166666667 ft/sec

now, lets order from least to greatest

R:8ft/1sec, K:10.0380228137ft/1 sec,

E:13.9166666667 ft/sec, L:14.8571428571 ft/1 sec

Liz's speed is fastest

A survey was taken of a random sampling of residents of New York City and Los Angeles to compare how many of them own a car. A 4-column table with 3 rows. The first column has no label with entries L A residents, N Y C residents, total. The second column is labeled own a car with entries 3,251; 1,478, 4,729. The third column is labeled do not own a car with entries 869; 6,182; 7,051. The fourth column is labeled total with entries 4,120; 7,660; 11,780. Which statement about the two-way frequency table is true? The survey represents quantitative data. There is a greater percentage of LA residents who own a car than NYC residents who do. The total number of people in the poll who own a car is 4,120. More people in the poll own a car than do not own a car.

Answers

Answer:

The correct option is;

There is a greater percentage of LA residents who own a car than NYC residents who do

Step-by-step explanation:

The values are presented as follows;

LA residents who own a car = 3251

NYC residents who own a car = 1478

Total residents who own a car = 4729

LA residents who do not own a car = 869

NYC residents who do not own a car = 6182

Total residents who do not own a car = 7051

Total LA residents sampled = 4120

Total NYC residents sampled = 7660

Total residents of both cities sampled = 11780

Percentage of LA residents who own a car = (3251/4120)×100 = 78.9%

Percentage of NYC residents who own a car = (1478/7660)×100 = 19.3%

The total number of people in the poll who own a car = 4729

Therefore, the correct option is that there is a greater percentage of LA residents who own a car than NYC residents who do.

Answer: B. There is a greater percentage of LA residents who own a car than NYC residents who do.

What is the explicit formula for the geometric sequence with this recursive formula?

Answers

Answer:

Step-by-step explanation:

The explicit formula for a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

The recursive formula gives a term in the sequence by multiplying the previous term by r

Given the recursive formula

a₁ = - 6

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] ([tex]\frac{1}{4}[/tex] )

with r = [tex]\frac{1}{4}[/tex]

Then explicit formula is

[tex]a_{n}[/tex] = - 6[tex](\frac{1}{4}) ^{n-1}[/tex] → A

calculate 16% of £50

Answers

Do 50 x 0.16 Which is 8. 50-8 =£42.00

10% of £50= £50 divided by 10 = £5
1% of £50= 10% divided by 10 (£5 divided by 10) = 0.5 which is 50p.
50p x 6 = £3
6%=£3 and 10%=£5
£5+£3=£8 so the answer is £8

A colour printer prints 38 pages in 11 minutes. How many pages does it print per minute? round to nearest hundredth.

Answers

Answer:

3.45

Step-by-step explanation:

If the printer can print 38 pages in 11 minutes and we want to find how many it prints per minute, we can divide the number of pages printed by the time it took.

So, divide 38 by 11.

38/11 = 3.454545

Round to nearest hundredth: 3.45

Answer:

3.45 pages per minute

Step-by-step explanation:

Take the number of pages and divide by the number of minutes

38 pages/11 minutes

3.45454545 pages/minute

To the nearest hundredth

3.45 pages per minute

What is the slope of the line that goes through the points (1,5) and (4,1)

Answers

Answer:

[tex] - \frac{4}{3} [/tex]

Step-by-step explanation:

gradient formula:

[tex] \frac{y1 - y2}{x1 - x2} [/tex]

Thus, slope of the line

[tex] = \frac{5 - 1}{1 - 4} \\ = - \frac{4}{3} [/tex]

Slope of the line that passes through the points (1,5) and (4,1) is equals to [tex]\frac{-4}{3}[/tex].

What is slope?

" Slope is defined as the ratio of difference of the increase in y- coordinates to the difference of increase in x- coordinates."

Formula used

Two coordinates on line

[tex]( x_{1} ,y_{1})\\\\(x_{2}, y_{2})[/tex]

Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

According to the question,

Given,

Point on the line

[tex]( x_{1} ,y_{1})= ( 1,5)\\\\(x_{2}, y_{2})= ( 4,1)[/tex]

Substitute the value to get the slope of the line,

Slope = [tex]\frac{1-5}{4-1 }[/tex]

= [tex]\frac{-4}{3}[/tex]

Hence, slope of the line that passes through the points (1,5) and (4,1) is equals to [tex]\frac{-4}{3}[/tex].

Learn more about slope here

https://brainly.com/question/3605446

#SPJ2

Pizza is often circular shape and size of the pizza is the length of diameter with included crust. A 16 inch pizza is one with a 16 inch diameter. What is the area of a 16 inch pizza?

Answers

Answer:

≈201 in²

Step-by-step explanation:

Area= π×r²= π×d²/4Area of 16 in pizza= π×16²/4= 3.14× 256/4 ≈201 in²

Answer:

201 in²

Step-by-step explanation:

Hope this helps! :)

Bob buys eggs and potatoes at a store.
• He pays a total of $25.92.
• He pays $2.57 for the eggs.
• He buys 5 bags of potatoes that each cost the same amount, Which equation can be used to determine the cost, x, of each bag of potatoes?

a. X = (25.92 - 2.57) = 5

b. x = 25.92 = 5 + 2.57

c. X = (25.92 +2.57) = 5

d. x = 25.92 - 5 -2.57

Answers

Answer:

a. X = (25.92 - 2.57) ÷ 5

Step-by-step explanation:

shld be a divide sign instead of a equal sign before 5

i need 29 part b and c please help!

Answers

Answer:

$1.50

Step-by-step explanation:

29 part c

3÷2= 1.50

3 is the cost

and 2 is the cups

for 3 drinks it would cost $1.50

Which of the following describe an angle with a vertex at E?
Check all that apply.

Answers

The vertex of angle is the middle letter.

E is the vertex so the answers are:

A and C

Answer:

FED and DEF

Step-by-step explanation:

vertex is the middle letter

write a^4*a^2 without exponents

Answers

Answer:

a x a x a x a x a x a

Step-by-step explanation:

a^4 x a^2

a x a x a x a times a x a

= a^6 or a x a x a x a x a x a

Axaxaxaxaxaxaxaxaxaxax

Expand the binomial using Pascal's triangle
(3x+5)

Answers

Answer:

Step-by-step explanation:

0. 1

1. 1 1

2. 1 2 1

3. 1 3 3 1

4. 1 4 6 4 1

5. 1 5 10 10 5 1

6. 1 6 15 20 15 6 1

7. 1 7 21 35 35 21 7 1

8. 1 8 28 56 70 56 28 8 1

One-fourth of a certain number is removed from two- fifth of that number. if the result is 3, find the number.

Please Help It due soon.

Answers

Answer:

the answer is 20

Step-by-step explanation:

let the number be "x"

1st part = 2/5of x

2nd part = 1/4 of x

=) 2/5 x - 1/4 x = 3

=) lcm of 4 ,5 is 20

=) ( 2x * 4 ) - ( 1x *5) by 20 =3

=) 8x - 5x / 20 =3

=) 3x / 20 =3

=) 3x = 3 *20

=) 3x = 60

=) x = 60 /3

=) x = 20

the number is 20

Answer: 20

Step-by-step explanation:

2/5x -1/4x = 60

Multiply by 20 on both sides,

8x - 5x = 60

3x = 60

x = 60/3 = 20

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