The temperature dropped 2°F every hour for six hours what was the total number of degrees the temperature change in the six hours?

Given

The line equation is        

[tex]y= \frac{4}{9}x-2[/tex]

passes through the line (4,3 )

Find out the equation of the perpendicular line.

To proof

given equation is

 [tex]y= \frac{4}{9}x-2[/tex]

the equation of line is in the form y = mx +c

where m = slope

           c is the intercept on the y axis.

compare this equation to the above equation

we get

[tex]m =\frac{4}{9}[/tex]

In perpendicular line case

The slope of a perpendicular line is the "negative reciprocal" of the slope of the original line.

thus slope of the perpendicular line

= [tex]\frac{-9}{4}[/tex]

Than equation perpendicular line becomes

[tex]y= \frac{-9}{4}x + c[/tex]

as the line passes through the point( 4,3)

put these value in the above equation

we get

[tex]3= \frac{-9}{4}\times 4 + c[/tex]

solving the above equation

3 +9 =c

12 =c

put this value in the above equation

we get

[tex]y= \frac{-9}{4}\times x + 12[/tex]

this is equation of the perpendicular line.

Hence proved

A^2

-3^2 = 9

 the answer is 9

Final answer:

Explanation of independent and dependent variables in a linear equation

Explanation:

Independent variable: The hours worked by Ethan (x).

Dependent variable: Total amount earned (y).

Y-intercept: $25, this represents the initial charge even if no hours are worked.

Slope: $20, this represents the additional amount earned per hour of work.

The question about Ally working in a shop for $18 per hour relates to wage determination and labor economics within the field of Business. Discussions surrounding hourly wages, annual salaries, and job requirements touch upon various economic principles.

The number composed of 12 ten thousands, 8 thousands, 14 tens, and 7 ones is written in standard form as 128,147.

To write the number consisting of 12 ten thousands, 8 thousands, 14, and 7 ones in standard form, each element must be placed according to its value in our base-ten number system. First, we note that 14 needs to be broken down into 'tens' and 'ones' as well.

12 ten thousands = 12 times 10,000

8 thousands = 8 times 1,000

14 tens = 14 times 10

7 ones = 7 times 1

Next, we translate these values into their numeral counterparts:

12 ten thousands = 120,000

8 thousands = 8,000

14 tens = 140

7 ones = 7

Now we simply add these numbers together:

120,000 + 8,000 + 140 + 7 = 128,147

The number 12 ten thousands, 8 thousands, 14 tens, and 7 ones written in standard form is 128,147.

The number 567,433 nearest hundred thousand is 600,000 after rounding off, the answer is 600,000.

Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.

It is given that:

The number is 567,433

600,000

Rounded to the nearest 100,000 or

the Hundred Thousands Place.

Thus, the number 567,433 nearest hundred thousand is 600,000 after rounding off, the answer is 600,000.

Learn more about the rounding off number here:

https://brainly.com/question/13391706

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Answer:

x= [tex]\frac{b}{3+9y}[/tex] .

Step-by-step explanation:

Given :  b = 3x + 9xy.

To find :  Solving the equation for x.

Solution : We have given

b = 3x + 9xy.

Taking common 3x from right hand side

b = 3x ( 1 + 3y).

On dividing both sides by 1 + 3y .

[tex]\frac{b}{1+3y}[/tex] = 3x

On dividing both sides by 3

[tex]\frac{b}{(3+9y)}[/tex] = x .

Therefore, x =[tex]\frac{b}{(3+9y)}[/tex] .

x = b/(3 + 9y)

[tex]\boxed{ \ b = 3x + 9xy \ }[/tex]

In the equation, there are three variables, namely b, x, and y. The coefficients of x and xy are 3 and 9, respectively.

We need solving for x from the equation.

Let us reposition it by swapping sides. The aim is to prepare x as the subject on the left-hand side.

[tex]\boxed{ \ 3x + 9xy = b \ }[/tex]

On the left-hand side, 3x is pulled out of the brackets because it is the GCF (The Greatest Common Factor) of 3x and 9xy.

[tex]\boxed{ \ 3x(1 + 3y) = b \ }[/tex]

Both sides divided by 3(1 + 3y).

[tex]\boxed{ \ x = \frac{b}{3(1 + 3y)} \ }[/tex]

Hence, the final result is

[tex]\boxed{\boxed{ \ x = \frac{b}{3 + 9y} \ }}[/tex]

That's all the steps to get x as a subject.

Keywords: what’s b = 3x + 9xy?, solving the equation for x, solve for x, both sides, divide, GCF, subject, steps, b/(3 + 9y)

Final answer:

To simplify the expression, follow the order of operations: first perform the multiplication inside the parentheses, then multiply that result, and finally subtract it from the sum of 2 and 3. The expression simplifies to -75.

Explanation:

To simplify the mathematical expression 2 + 3 - 4 (5 × 4) we must apply the rules of order of operations, commonly remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Multiplication inside the parentheses: 5 × 4 = 20

Multiply 4 by the result of the previous step: 4 × 20 = 80

Subtract this result from the sum of 2 and 3: (2 + 3) - 80 = 5 - 80 = -75

Therefore, the expression simplifies to -75.

Remember that in subtraction, you change the sign of the number being subtracted, and then follow the rules of addition: e.g., 5 - 3 becomes 5 + (-3) = 2. Similarly, when two numbers with opposite signs multiply, the result has a negative sign: e.g., (-3) × 2 = -6.