if 2(a-3)=3(a+2) then a =6

Answer: there are 48 students in the class

Step-by-step explanation:

let x = the total number of students in the class

1 - 1/3 = 2/3

1/4 * 2/3 = 2/12 = 1/6

1/3x + 1/6x + 24 = x

2/6x + 1/6x + 24 = x

3/6x + 24 = x

1/2x + 24 = x

24 = x - 1/2x

24 = 1/2x

24 * 2 = x

x = 48

there are 48 students in the class

Answer:

H0 : μ = 18000

H1 : μ < 18000 - - - > Claim

Test value = - 3.578

Critical value = ±2.58

There is significant evidence to accept the claim that mean debt at graduation is less than $18000

Step-by-step explanation:

H0 : μ = 18000

H1 : μ < 18000

From the data:

Sample size, n = 30

Sample mean, x = 16298.37

The test statistic :

(16298.37 - 18000) ÷ (2605/sqrt(30))

−1701.63 / 475.60575

= - 3.578

The critical value :

Using the standard normal table;

Critical value at α = 0.01

Critical value = ±2.58

Decison region :

|test statistic | > |Critical value | ; reject H0

|3.578| > |2.58| ; We reject H0 and conclude that Mean debt at graduation is less than $18000

Answer:

[tex]\sqrt{3}[/tex]  sqrt(3)

Step-by-step explanation:

Pythagroean theorem shows that x^2+sqrt(2)^2=sqrt(5)^2

In other words,

x^2+2=5

x^2=3

x=sqrt(3)

9514 1404 393

Explanation:

The rules of equality tell you that you can do anything you like to an equation, as long as you do the same thing to both sides of the equal sign. This is the essence of Algebra, so is worth remembering. My teacher summarized it as "keep the equal sign sacred."

__

"Simple linear equations" come in several varieties. They are sometimes called "one-step", or "two-step", or "three step" linear equations, depending on how many steps are required to solve them. In what follows, we're using "x" as the variable, and the letters a, b, c, d as constants.

One-step

In general, the "one step" will be either an addition or a multiplication.

  x + a = b . . . . an addition equation

  ax = b . . . . . . a multiplication equation

The key in any case is to look at what is done to the variable and use an inverse operation to "undo" it. The opposite of addition is addition of the additive inverse (add the opposite). This is also called subtraction. For the addition equation, this looks like ...

  x + a - a = b - a . . . . . . add (-a) to both sides (or subtract 'a')

  x = b - a . . . . . . . . . . . the solution

The opposite of multiplication is multiplication by the multiplicative inverse (the reciprocal) This is also called division. For the multiplication equation, this looks like ...

  ax(1/a) = b(1/a) . . . . . multiply by (1/a) on both sides (or divide by 'a')

  x = b/a . . . . . . . . . . . the solution

__

Two-step

As with one-step linear equations, two-step equations come in some different forms.

  ax +b = c

  ax +b = cx

  a(x +b) = c

In general, the two steps are an addition step and a multiplication step, not necessarily in that order. You will notice that the first step can transform the equation to a "one-step" equation. As before, inverse operations are involved, and whatever is done is done to both sides of the equal sign.

  ax +b = c   ⇒   ax = (c -b) . . . . subtract b to get a multiplication equation

In this next, we have the variable on both sides of the equal sign. we can put the variable on one side of the equal sign by adding the opposite of the term we don't want where it is. Leaving the constant alone, we can add (-ax) to both sides to get ...

  ax +b = cx   ⇒   b = cx -ax   ⇒   b = (c -a)x

When you have numbers, you can go directly to (c-a)x by "combining terms". This is now the one-step multiplication equation.

Finally, another 2-step form is ...

  a(x +b) = c   ⇒   x +b = c/a . . . . . divide by 'a' to get an addition equation

This last equation can also be solved by using the distributive property first.

  ax +ab = c . . . . . still a 2-step equation, now of the first type

__

Three-step

The most typical "3-step" linear equation is of the form ...

  ax +b = cx +d

where both variables and constants are on both sides of the equal sign. As you may have noticed above, we prefer to have variables on one side and constants on the other side. So, add the opposite of the term you don't want where it is (to both sides, of course).

If we want variables on the left and constants on the right, we can add -cx and -b. The "3 steps" assume you do these as separate operations.

  ax +b -cx = cx +d -cx   ⇒   (a-c)x +b = d . . . a two-step equation

  (a-c)x +b -b = d -b    ⇒   (a-c)x = d-b . . . . a one-step multiplication equation

_____

Additional comments

There are some choices you can make that will tend to reduce errors. One of them involves selection of the variable term you want to eliminate (add the opposite of). Generally, if you choose the term with the lowest (most negative, left-most on the number line) coefficient, adding its opposite will result in a positive coefficient for the remaining variable term. Then when you divide by that coefficient, you're dividing by a positive number. Most folks perform arithmetic with fewer errors when they're working with positive numbers.

The general approach to any "solve for" situation is to look at what is done to the variable you're solving for. The Order of Operations is a useful lens for looking at this. When you list the operations, your "undo" sequence will start with the last operation on the list, and work backward.

Further note: your total comfort with doing arithmetic with any kind of numbers (integers, fractions, mixed-numbers, decimals, scientific notation, positive or negative) will aid you immensely. Always be careful with minus signs. They tend to get lost, forgotten, ignored, Be sure they don't.

Answer:

[tex]y = \frac{1}{2} x - 3[/tex]

Step-by-step explanation:

The equation of a line can be written in the form of y=mx +c, where m is the gradient and c is the y-intercept.

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

Using the gradient formula above,

gradient of line

[tex] = \frac{ - 1 - ( - 7)}{4 - ( - 8)} [/tex]

[tex] = \frac{ - 1 + 7}{4 + 8} [/tex]

[tex] = \frac{6}{12} [/tex]

[tex] = \frac{1}{2} [/tex]

Substitute m= ½ into the equation:

y= ½x +c

To find the value of c, substitute a pair of coordinates.

When x= 4, y= -1,

[tex] - 1 = \frac{1}{2} (4) + c[/tex]

-1= 2 +c

c= -1 -2 (-2 on both sides)

c= -3

∴ The equation of the line is y= ½x -3.

Answer:

The answer is C.

Step-by-step explanation:

to find the area you need to multiply the width times length, to find the length you need to add the c and 15 and have that mulitplied by 1/5

.

1/5(c+15)

11. y = -3x + 6 and y = 1/3 x -8 (perpendicular)

12. y = 5/4 x + 1 and y = 5/4 x - 7 (parallel)

13. 3x + 2y = 6 and y = -3/2 x + 5 (parallel)

14. 3y = 4x + 15 and 9x + 12y = 12 (perpendicular)

15. 10x - 2y = 16 and x + 5y = -20 (perpendicular)

For two equations to be parallel, the slope has to be the same

For two equations to be perpendicular, the product of their slopes must be equal to -1

The equation of a line is the slope-intercept form is:

y  =   mx   +   c

where m is the slope and c is the intercept

11) y = -3x + 6 and y = 1/3 x -8

The equations are perpendicular because -3 x 1/3  = -1

12) y = 5/4 x + 1 and y = 5/4 x - 7

The two lines are parallel because they both have a slope of 5/4

13) 3x + 2y = 6 and y = -3/2 x + 5

The equation 3x + 2y = 6 can be re-written as y = -3/2 x + 3

Therefore, the two equations are parallel since they have the same slope of -3/2

14) 3y = 4x + 15 and 9x + 12y = 12

3y = 4x + 15 can be re-written as y = 4/3 x + 5

9x + 12y = 12 can be re-written as y = -3/4 x + 1

The two lines are perpendicular because -3/4 x 4/3  = -1

15) 10x - 2y = 16 and x + 5y = -20

10x - 2y = 16 can be re-written as y = 5x - 8

x + 5y = -20 can be re-written as y = -1/5 x  -  4

Both equations are perpendicular since -1/5 x 5  =  -1

Learn more here: https://brainly.com/question/11482954

Answer:

Step-by-step explanation:

Answer:

It's 2/15

Step-by-step explanation:

9514 1404 393

Answer:

  B. (1/2)(4)(11)

Step-by-step explanation:

The length of the base is the sum of the lengths that make it up:

  3 + 8 = 11 . . . . feet

The height is 4 ft, so the area is ...

  A = 1/2bh

  A = 1/2(11)(4) . . . . . equivalent to choice B

Answer:

Here is your answer hope it helps u have a great day ahead....

Answer:

-1/3

Step-by-step explanation:

Find two points on the line  (0,2) and (3,1)

Using the slope formula

m = (y2-y1)/(x2-x1)

   = (1-2)/(3-0)

   = -1/3

Answer:

A

Step-by-step explanation:

1) take two points of the line

A(0,2) ; B(3,1)

2) use this formula for find the slope

(y2-y1)/(x2-x1)

(1-2)/(3-0)

slope = -1/3

Answer:

14x-9

Step-by-step explanation:

Answer:

um what

Step-by-step explanation:

Answer:

Year 1: 164.87

Year 2: 169.88

Year 5: 185.86

Step-by-step explanation:

She is earning 3% interest per year that compounds once yearly.

Answer:

A value of [tex]x^3 - 4x^2 + x - 4[/tex] is equivalent to [tex]f \times g[/tex]

Step-by-step explanation:

We are given the following functions:

[tex]f(x) = x^2 + 1[/tex]

[tex]g(x) = x - 4[/tex]

Which value is equivalent to f x g?

We multiply these functions, applying the distributive property. So

[tex]f \times g = (x^2+1)(x-4) = x^3 - 4x^2 + x - 4[/tex]

A value of [tex]x^3 - 4x^2 + x - 4[/tex] is equivalent to [tex]f \times g[/tex]

Answer:

5 hours

Step-by-step explanation:

Step-by-step explanation:

velocity = distance/time taken

distance=velocity ×time taken

distance=80×4

distance=320kilometers

Answer:

Step-by-step explanation:

3. A single sticky note is a three-dimensional object. Meaning it has a length, width and height. Therefore, it is taking up space, and anything that takes up space has a volume. If the sticky not did not have a volume then it would not be a three-dimensional object.

4. Yes, if we knew the volume of a single sticky note, then we would simply have to multiply the volume of that individual note by the total number of sticky notes in the pile. This would give us the volume of the entire pile.

Answer:

It is:

B.Divide the area of the triangle by the base and multiply the result by 2.

Answer:

354294

Step-by-step explanation:

-2,6,-18,54,-162,486,-1458,4374,-13122,39366,-118098,354294

multiply each number by -3

Answer:

Step-by-step explanation:

if they are saying  approximately  then y = 3 for the y intercept, and

the slope,  m ,   is   3/4    ( rise / run)

then the equation for this line is

y =  [tex]\frac{3}{4}[/tex] * x + 3

y = 3x/4 + 3

Answer:

192 is the answer

Step-by-step explanation:

Answer:

SA = 272 sq in

Step-by-step explanation:

SA = 2(8 x 2) + 2(8 x 12) + 2(2 x 12)

= 2(16) + 2(96) + 2(24)

= 32 + 192 + 48

= 272 sq in

Answer:

12

Step-by-step explanation:

Answer:

The answer is 15 ounces

Step-by-step explanation:

33/4 ÷ 4 pounds.

(4 × 3 + 3)/4 ÷ 4 pounds.

15/4 ÷ 4 pounds.

15/4 × 1/4 pounds.

15/16 pounds.

Now we know that, 1 pound = 16 ounces.

So, 15/16 pounds = 15/16 × 16 ounces = 15 ounces.

Thus, The answer is 15 ounces

Answer: 6

Step-by-step explanation:

Since we are informed that two pipes with lengths of 42 inches and 54 inches respectively are to be cut in pieces of equal lengths and we want to know the number of pieces that they can be cut into.

This question simply means that we need to find the factors of both 42 and 54 and choose the highest.

42 = 1, 2, 3, 6, 7, 14, 21, and 42.

54 = 1, 2, 3, 6, 9, 18, 27, and 54.

Therefore, the highest common factor is 6. Therefore, the greatest possible length will be 6 inches

Answer:

Acute

Step-by-step explanation:

All triangles have to have a acute or it would be to big

Answer:

yes it is because its a triangle and its acute

Answer:

[tex](4x + 1)(x - 4) = 4x( x - 4) + 1(x-4)[/tex]

                       [tex]=4x^2 -16x +x -4\\=4x^2 -15x -4[/tex]

option C

Answer:

Evaporation changes liquid water and even soled water (ice) to water vapor, which is a gas. This all part of the water cycle

Step-by-step explanation:

thank you