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4 years ago

9

3 times the sum of 6 and a number is 33

1 answer:

Citrus2011 [14]4 years ago

6 0

Answer:

Step-by-step explanation:

Let the number in question be 'n'. Then twice the sum of the number and 3 is written as:

2(n + 3)

Three times the difference of the number and 9 is written as:

3(n - 9)

The problem says these two are equal, so:

2(n + 3) = 3(n - 9)

2n + 6 = 3n - 27

Add 27 to both sides:

2n + 33 = 3n

Subtract 2n from both sides:

33 = n (the number is 33)

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Fill in each balance???

tatiyna

Answer:

Step-by-step explanation:

Take the beginning number and add or subtract each transaction to get a new balance. For example,

349.45

- 23.42 = 326.03

- 14.95 = 311.08

+ 276.50 = 587.58

- 219.93 = 367.65

- 76.84 = 290.81

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3 years ago

Write an equation of the line that passes through (18,2) and is parallel to the line 3y-x=-12 .

uysha [10]

Answer:

$y = \frac{1}{3}x-4$

Step-by-step explanation:

<u>Step 1: Solve for y in the first equation</u>

$3y - x = -12$

$3y - x + x = -12 + x$

$\frac{3y}{3} = \frac{x}{3} - \frac{12}{3}$

$y = \frac{1}{3}x - 4$

<u>Step 2: Determine the important aspects</u>

We know that our line is parallel to the other line that has a slope of 1/3 which means that our slope is also going to be 1/3. We also know that our line crosses the point (18, 2) which means that we can use the point slope form to determine our equation

Point Slope Form → $(y-y_1) = m(x - x_1)$

<u>Step 3: Plug in the information and solve</u>

$(y-2) = \frac{1}{3}(x - 18)$

$y - 2 = \frac{1}{3}x - 6$

$y - 2 + 2 = \frac{1}{3}x - 6 + 2$

$y = \frac{1}{3}x-4$

Answer: $y = \frac{1}{3}x-4$

7 0

2 years ago

Find the composite functions (f ∘ g) and (g ∘ f). what is the domain of each composite function? \[ \begin{array}{rcl} f(x) &amp

Burka [1]

Always remember two steps while finding the domain of composite function.

1) <em>First find the domain of inside/ input function( A common mistake is to skip this point).</em>

2) <em>Find the domain of new function after performing the composition.</em>

In our case, the given functions are

$f(x)=\frac{3}{x}$ , $g(x)= x^{2} -81$

Now,

1) (f ° g)(x)

= f[g(x)]

=f[x²-81]

$= \frac{3}{x^{2}-81}$ (this is (f ° g)(x) function)

Now, its domain

First find the domain of input function which is x²-81, its domain is the set of all real numbers.

domain of new function after performing composition which is $\frac{3}{x^{2}-81}$ .

x²-81=0 ⇒ (x-9)(x+9)=0

(x-9)=0 , (x+9)=0

x=9 , x=-9 (exclude these points from the domain because anything/0 does not exist in math)

So, the Domain of Composite function (f °g)(x) is the set of all real numbers except x=9, x=-9.

Domain= (-infinity, -9)U(-9, 9)U(9, infinity)

2) (g °f)(x)

= g[f(x)]

= g[3/x]

= (3/x)² -81

= 9/x² -81

$=\frac{9-81x^{2}}{x^{2}}$

First find the domain of input function 3/x which is set of all real numbers except x=0

$\frac{9-81x^{2}}{x^{2}}$

Domain of above function after performing composition is set of all real numbers except x=0

So, the domain of (g° f)(x) is the set of all real numbers except x=0.

Domain= (-infinity, 0)U(0, infinity)

6 0

3 years ago

Help fast I NEED IT RN

Ivahew [28]

Answer:

204 people

Step-by-step explanation:

The manager has interviewed 50 people, which is 1/6 of 300. Just times it by 6 to get an approximate amount of people :)

8 0

3 years ago

What is mass in Science

asambeis [7]

Mass in science is like weight. Everything is basically mass, you are mass!

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3 years ago

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