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3 years ago

Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.

Mathematics

2 answers:

goldfiish [28.3K]3 years ago

8 0

Answer:

y = 6x direct variation

Step-by-step explanation:

Remember that direct variation is y = kx and inverse variation is y = k/x where k is a constant

x= 1 2 5 10

y= 6 12 30 60

First look at direct y = kx solving for k y/x =k

y/x from the table is 6/1 =6 12/2 = 6 30/5 =6 60/10 =6 so k=6

This is a direct variation with k=6

y = 6x

GarryVolchara [31]3 years ago

6 0

c. y=6x direct variation

Answer:

the table represent a <u>direct variation</u>

Step-by-step explanation:

as when x=1

y=2

and

x=10

y=60

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(5,12)and (2,6) rate of change?<br> Initial value?<br> HURRY i NEED this done.

Otrada [13]

Answer:

Part 1) The rate of change is $2$

Part 2) The initial value is $2$

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or rate of change

b is the y-intercept or initial value

step 1

Find the slope or rate of change

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the points

(5,12)and (2,6)

substitute the values in the formula

$m=\frac{6-12}{2-5}$

$m=\frac{-6}{-3}$

$m=2$

therefore

The rate of change is $2$

step 2

Find the initial value

we have

$m=2$

$point\ (2,6)$

substitute in the equation $y=mx+b$

$6=2(2)+b$

solve for b

$6=4+b$

$b=2$ ---> initial value

The linear equation is equal to

$y=2x+2$

The y-intercept or initial value is 2

8 0

3 years ago

8^x times 2^(4-x) = 1<br> Find x.<br> With detailed steps.

Dafna1 [17]

Answer: x= -1

Step-by-step explanation:

In mathematics when you have bases that are the same while multiplying you add the powers. In this case we do not have the same bases so we are going to make it look like 8 is 2. So we sort of simplify it. So we get 8 and put into like 2^4. We do not eliminate the power x that was already there though. So we will have 2^4x × 2^4-x. So like I said earlier we add the powers. Soo we will have

4x +4-x
4x-x=1
3x+4-4 =1-4
3x/3 = -3/3
x= -1

<h2>Hope that helped!</h2>

7 0

2 years ago

Solve. Write the solution in interval notation. -2x>-8 and -5x<20.

Novosadov [1.4K]

Answer:

The interval notation of the solution is (-4 , 4)

Step-by-step explanation:

* Let us explain a very important point in solving inequality

- When you multiply or divide an inequality by negative number we

must reverse the symbol of the inequality

- Ex:

∵ 2 < 3

- If we multiply the both sides of the inequality by -1, then the

inequality will be -2 < -3 and this is completely wrong, so we must

reverse the symbol of the inequality

∴ -2 > -3

* Now let us solve the problem

∵ -2x > -8

- Divide both sides by -2 and remember to reverse the symbol of the

inequality

∴ x < 4

∵ -5x < 20

- Divide both sides by -5 and remember to reverse the symbol of the

inequality

∴ x > -4

- From both solutions

∴ -4 < x < 4

∴ The solution is {x : -4 < x < 4}

- Interval notation is a way of writing the solutions of inequalities

( , ) if x does not equal the end numbers

[ , ] if x equals the end numbers

[ , ) , ( , ] if x equals one of the two end numbers

* The interval notation of the solution is (-4 , 4)

4 0

3 years ago

Find two consecutive whole numbers that 41 lies between.

Diano4ka-milaya [45]

I don't get this question. Because if it is this simple, the two whole numbers are 40 and 42

4 0

3 years ago

Read 2 more answers

Two-thirds a number plus 4 is 7

ICE Princess25 [194]

The equation (form) is: $\frac{2}{3}x + 4 = 7$

The solution of the equation is: $x = \frac{9}{2}$

Explanation:

First, let's call the number we are going to solve for "x".

Then two thirds of this number can be written as:

$\frac{2}{3}x$

Then "plus 4" means add 4 we get:

$\frac{2}{3}x + 4$

"is 7" means that the above expression is equal to 7 (as follows):

$\frac{2}{3}x + 4 = 7$

The solution of the above equation is:

$\frac{2}{3}x + 4 = 7 \\ \frac{2}{3}x = 3 \\ x = \frac{9}{2}$

6 0

3 years ago