Solve each equation. 0.2(x+3)-4(2 x-3)=0.9

Answer:

Step-by-step explanation:

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Answer:

a₂ = 101.5

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₁ = 104 and a₃ = 99 , then

104 + 2d = 99 ( subtract 104 from both sides )

2d = - 5 ( divide both sides by 2 )

d = - 2.5

then

a₂ = 104 - 2.5 = 101.5

pi or π is a Greek word and its value is approximately 3.14 and it is an irrational number.

It is given that the letter is pi or π.

We have to write the history of pi and its importance to the study of geometry.

What is pi or π ?

pi or π is the ratio of the circumference of any circle to the diameter of that circle.

We know that ;

pi or π is a Greek letter. In decimal form, the value of pi is approximately 3.14 and it is an irrational number.

According to Petr Beckmann's A History of Pi, William Jones first used this Greek letter for some purpose in 1706.  Around 30 years later, it became a standard symbol for mathematical notation.

Also ; it has been known for at least 4,000 years what Pi means. According to the history of Pi , who claims that by 2000 B.C , "the Babylonians and the Egyptians were aware about the existence and significance of this constant,"

Also ; every circle has the same ratio of circumference to diameter. Both the Babylonians and the Egyptians approximated the value of pi numerically, and later mathematicians in ancient Greece, especially Archimedes, improved these approximations.

Pi is a fundamental concept that appears in all branches of mathematics. It is a crucial concept that facilitates understanding of both universal truths and some mathematical concepts.

Thus , pi or π is a Greek word and its value is approximately 3.14 and it is an irrational number.

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Answer:

-4500

Step-by-step explanation:

-5300 - (-800)

Step-by-step explanation:

{36+7[10÷)+9(2)]}÷4. ....

The expression used to verify whether g(x) is the inverse of f(x) is 6( [tex]\frac{x+1}{6}[/tex])-1  and  [tex]\frac{(6x-1)+1}{6}[/tex]

Given that f(x) = 6x-1

and g(x) = [tex]\frac{x+1}{6}[/tex]

If inverse [tex]f^{-1}[/tex] exists for a function f(x), then [tex]f(f^{-1}(x)) = f^{-1}(f(x)) = x[/tex]

So to check if g(x) is the inverse of f(x) we find f(g(x)) and g(f(x))

f(g(x)) = f( [tex]\frac{x+1}{6}[/tex]) = 6( [tex]\frac{x+1}{6}[/tex])-1 = x

and g(f(x)) = g(6x-1) = [tex]\frac{(6x-1)+1}{6}[/tex] = x

So g(x) is the inverse of f(x) and the expressions used to verify this are:

6( [tex]\frac{x+1}{6}[/tex])-1  and  [tex]\frac{(6x-1)+1}{6}[/tex]

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The values of a9 and a10 are 52 and 58 respectively.

An ordered group of integers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

For the arithmetic sequence,

4,10,16,22, . . . .

a = 4

d = 6

an = a + (n - 1)d

a9 = 4 + (8)6

a9 = 4 + 48

a9 = 52

a10 = a + 9d

a10 = 4 + 9(6)

a10 = 4 + 54

a10 = 58

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Answer:

1 1/2 small cans of paint

Step-by-step explanation:

1/2 = 1/3 of the sprayer, so I had to multiply 1/2 x 3, which is 1 1/2.

44th term of the sequence is -82.

In an arithmetic sequence with a₁ =2 and d=-2  

-82 = 2 + (n-1)2

n-1 = -43

n = 44

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.

An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.

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Suppose we have to solve this equation ,

3x - 4 = 7x + 8

would be to first subtract 3x from both sides obtaining

-4 = 4x + 8,

then subtract 8 from both sides and get

-12 = 4x.

Now divide both sides by 4 obtaining

- 3 = x or x = - 3.

If we have to find the area of trapezoid,

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

There are three major forms of linear equations:

point-slope form, standard form, and slope-intercept form.

There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other.

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Answer:

11/12

Step-by-step explanation:

Point K is located at (-6, -3) on the coordinate plane. Point K' is produced by reflecting point K over the y-axis. The ordered pair of the described location is K'(6,-3).

Given that,

Point K is located at (-6,-3) on the coordinate plane.

The sign of the x-coordinate is altered by reflection across the y-axis:

When a point is reflected across the x-axis, the x-coordinate stays constant, but the y-coordinate is thought to be the additive inverse. The x-axis shows a reflection of the point (x, y) as (x, -y).

When a point is reflected across the y-axis, the y-coordinate remains constant, but the x-coordinate is believed to be the additive inverse. The y-axis shows a reflection of the point (x, y) as (-x, y).

That is,

(x,y)⇒(-x,y)

K(-6,-3)⇒[tex]K^{'}[/tex](6,-3)

Therefore, the Point K is reflected over the y-axis to create point K'(6,-3).

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Answer: How do you know if its rational or irrational?

What are rational and irrational numbers? Rational numbers are the numbers that can be expressed in the form of a ratio (i.e., P/Q and Q≠0) and irrational numbers cannot be expressed as a fraction. But both the numbers are real numbers and can be represented in a number line.

Step-by-step explanation: hope this helps!!!

Only 1 > 3 / π and 6 / √34 > 0.6 are true comparisons with irrational numbers.

Herein we find four cases of irrational numbers, whose quantities has to be compared with other numbers, by using algebra properties for inequalities:

Case 1

√75 > 9

√75 > √9²

√75 > √81      (FALSE)

Case 2

1 > 3 / π

π > 3              (TRUE)

Case 3

√8 > 10 /3

3√8 > 10

3√8 > √10²

√9 · √8 > √100

√72 > √100   (FALSE)

Case 4

6 / √34 > 6 / 10

10√34 > 36

√10² · √34 > √36²

√100 · √34 > √1296

√3400 > √1296    (TRUE)

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Answer:

-18 Degrees F

Step-by-step explanation:

Answer:

y=3x-7

Step-by-step explanation:

Equation of a Line: y=mx + b

Slope: 3/1 or 3

Y-int: -7

The equation of a line is a form of representing the set of points, which form a line in a coordinate system. 

The equation of a line that passes through the point (1, -4) and (2, -1) is

y = 3x - 7

The equation of a line is a form of representing the set of points, which form a line in a coordinate system. 

The general equation of a straight line is given as:

y = mx + c,

where m = slope of the line and c = y-intercept.

We have,

Two points:

(1, -4) = (a, b) and (2, -1) = (c, d)

The equation of a line can be written in the form:

y = mx + c

Slope:

m = (d - b) / (c - a) = -1 + 4 / 2 - 1 = 3 / 1 = 3

y-intercept:

Take a point (1, -4).

-4 = 3x1 + c

-4 - 3 = c

c = -7

Now,

The equation of a line is y = 3x - 7

Thus the equation of a line that passes through the point (1, -4) and (2, -1) is

y = 3x - 7

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The given series is a geometric series and its sum is -22

The summation or sigma notation is used to express long summation into a single formula.

The series, given in a summation notation, is:

     [tex]\sum\limits^6_{n=2} {(-2)^{n-1}}[/tex]

The formula inside the sum notation represent the nth term, a(n).

Let evaluate the terms for some n

a(2) = (-2)²⁻¹ = (-2)¹ = -2

a(3) =  (-2)³⁻¹ = (-2)² = 4

a(4) =  (-2)⁴⁻¹ = (-2)³ = -8

This form a new geometric series, with the first term, let say f(1) = -2 and common ratio = -2.

The number of terms in this new geometric series is 5.

Use the sum formula for a geometric series,

S(n) = a(1) . (rⁿ - 1)/(r - 1)

Substitute n = 5, a(1) = -2, and r = -2 into the formula:

S(5) = -2 . ((-2)⁵ - 1) / ((-2) - 1)

S(5) = -2 . (-33) / (-3) = -22

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The equation of the line in point-slope form, with slope equal to -3/5 and passing through the point located at (-4 , 0), is (y - 0) = -3/5(x + 4).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values to set up the equation.

(y - y1) = m(x - x1)

where m = -3/5 and (x1 , y1) = (-4 , 0)

(y - 0) = -3/5(x - -4)

(y - 0) = -3/5(x + 4)

In slope-intercept form, the equation of the line is:

(y - 0) = -3/5(x + 4)

y = -3/5 x - 12/5

In standard form, the equation of the line is:

y = -3/5 x - 12/5

3/5 x + y = -12/5

Multiplying both sides by 5,

3x + 5y = -12

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Answer:

total cars= 72 cars

cars that left=54 cars

percentage of cars left=

[tex] \frac{54}{72 } \times 100 =0.75 \times 100 = 75\%[/tex]

so the answer is 75%

The answer is 2 and 7/20 or the 3rd answer.

Source: Calculator soup.

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What is the question?

If there is a 'b' variable, switch it out with 3, so ex; 8b would then be 8(3), or 8*3. Same thing with h. If there is an 'a' variable, then you have to get everything gone but the variable. If you send over the question I can help

Step-by-step explanation:

1st=1 matchstick

2nd=4 matchsticks

3rd=7 matchsticks

1+4+7=12 matchsticks

Answer:

31 flowers in the bouquet

The value of the expression for x² + yz when x = 7, y = 5, and z = 3 is 64.

It should be noted that from the information, we are to evaluate x² + yz for x = 7, y = 5, and z = 3.

This will be illustrated as:

= x² + yz

= 7² + (5 × 3)

= 49 + 15

= 64

Therefore, the value of the expression for x² + yz when x = 7, y = 5, and z = 3 is 64.

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Equilateral ΔD E F with sides 4 b units long has been plotted below.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

An equilateral triangle is a triangle whose all sides are the same.

The all interior angle of an equilateral triangle is 60 degrees.

The length of each side of the given equilateral ΔDEF is 4b.

Hence "Equilateral ΔD E F with sides 4 b units long has been plotted below".

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Answer:

-3 1/24

Step-by-step explanation:

-7/8+(-2 1/6)

=-7/8-2 1/6

=-(7/8+2 1/6)

=-(21/24+2 4/24)

=-2 25/24

=-3 1/24

The first paycheck payment to the independent contractor is $4,615.38

Dr. salaries and wages expense $4,615.38

Cr. salaries and wages payable                     $4,615.38

What is the amount of first  bi-weekly pay to the contractors?

On the basis that there are 52 weeks in a year, hence, there would be 26 bi-weeks in a year, in order to determine the amount of first paycheck payment to the independent contractor, we simply divide the annual cost of contract by 26 bi-weeks in a year.

first paycheck payment =annual contract fees/26 bi-weeks

first paycheck payment =$120,000/26

first paycheck payment =$4,615.38

The paycheck refers to first 2 weeks which ends on on  12th January, whereas the actual payment would occur a week later on 19th of January, as a result, the amount is owed until 19th January, which means that salaries and wages expense would be debited and salaries and wages payable would be credited until actual payment is made on the 19th of January.

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