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rodikova [14]
3 years ago
6

A line passes through the points ( − 16 , 14 ) and ( 8 , 35 ) . Calculate the slope of the line - simplify answer if possible. (

If the slope is undefined, enter "DNE") Then, write the equation of the line.
Mathematics
1 answer:
REY [17]3 years ago
7 0

Given two points (x_1,y_1),\ (x_2,y_2), the slope of the line connecting them is defined as

m=\dfrac{\Delta y}{\Delta x}=\dfrac{y_2-y_1}{x_2-x_1}

In your case, the points are

(x_1,y_1)=(-16,14),\ (x_2,y_2)=(8,35)

Plugging these values in the slope formula gives

m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{35-14}{8-(-16)}=\dfrac{21}{24}=\dfrac{7}{8}

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If x is a positive integer, for how many different values of x is sqrt48/x a whole number?
slava [35]

Answer:

<u>The only possible values of x that fulfill with both conditions are 3, 12 and 48.</u>

Step-by-step explanation:

1. What are the positive integers? Also know as the whole numbers or the counting numbers. They start from 1, and continue to 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, etc.

2. What are the whole numbers? The definition of whole numbers is that they are the number with no fractions or decimals.

3. According to those definitions, x must be a positive integer and the result of √48/x, must be a whole number.

4. For fulfilling the first condition, x must be only a value from 1 to 48.

5. For fulfilling the second condition, the result of √48/x must be a whole number. It means it must be 1, 2, 3, 4, 5 or 6. From 7 is not possible to continue because those numbers are bigger than 48, for example √49, √64, √81, √100 and so on, and it would be impossible to fulfill with the first condition.

6. So, we have just 6 possible options (√48/x = 1, √48/x = 2, √48/x = 3, √48/x = 4, √48/x = 5 and √48/x =6). Let's review in detail one by one.

√48/x = 1, Is there any value of x for fulfilling both conditions? <u>Yes, it's. It's 48. </u>

√48/x = 1 and let's replace x by 48.

√48/48 = √1 = 1

√48/x = 2, Is there any value of x for fulfilling both conditions? <u>Yes, it's. It's 12. </u>

√48/x = 2 and let's replace x by 12.

√48/12 = √4 = 2

√48/x = 3, Is there any value of x for fulfilling both conditions? No, it isn't.  

There isn't any whole number that allow us to fulfill with this: √48/x = √9 = 3

√48/x = 4, Is there any value of x for fulfilling both conditions? <u>Yes, it's. It's 3. </u>

√48/x = 4 and let's replace x by 3.

√48/3 = √16 = 4

√48/x = 5 Is there any value of x for fulfilling both conditions? No, it isn't.  

There isn't any whole number that allow us to fulfill with this: √48/x = √25 = 5

√48/x =6  Is there any value of x for fulfilling both conditions? No, it isn't.  

There isn't any whole number that allow us to fulfill with this: √48/x = √36 = 6.

<u>The only possible values of x that fulfill with both conditions are 3, 12 and 48.</u>

6 0
3 years ago
Can someone please help?
Vladimir [108]

Answer:

1.

C. 6561 is the answer that the table represents

6 0
3 years ago
Read 2 more answers
Find the value <br> If a=4 b=7, and c=-5<br> 3c
Luda [366]

Answer:

=-15

Step-by-step explanation:

3c

3(-5)

3×-5

=-15

8 0
3 years ago
Read 2 more answers
Pls help me with this
saul85 [17]

Answer:

The coordinates of S is ( 4 , -20 )

Step-by-step explanation:

To solve this you figure out how ( 0 , 4 ) relates to ( 2 , -8 ).

You can see that the 0 was added by 2, and the 4 was subtracted by 12 to make ( 2 , -8 ).

Now that you see how they relate, you can find the next point by repeating this pattern.

2 + 2 = 4

-8 - 12 = -20

( 4 , -20 )

I hope this helped! :)

7 0
3 years ago
Solve. 3x+4y=36y=-1/2x+8​
quester [9]

Answer:

7.5

Step-by-step explanation:

3x+4y=36y=-1/2+8=

5 0
2 years ago
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