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Anna [14]
3 years ago
9

Which expression represents the sum (3z−11)+(6−6z) ?

Mathematics
1 answer:
Fudgin [204]3 years ago
6 0

Answer: z = -5/-3

Step-by-step explanation:

(3z−11)+(6−6z)

3z - 11 + 6 - 6z

- 6z + 3z - 11 + 6

- 3z - 5

z = -5/-3

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01.05 what is the slope intercept form equation of the line that's passing through (1,3) and (3,7)
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Hello!

To find the slope-intercept form equation of the line that passes through the two points is found by first, calculating the slope using the slope formula and substitution, and secondly, finding the y-intercept of the equation through substitution.

Remember, slope-intercept form is written as: y = mx + b, where m is the slope and b is the y-intercept.

1. Find the slope

The slope formula is: \frac{y_{2}-y_{1}}{x_{2}-x_{1}}. To use this formula, you need two points and also, you need to assign these points to x_{1}, x_{2}, y_{1}, and y_{2}.

In this case, x_{1} and x_{1} is assigned to the ordered pair (1,3), while x_{2} and y_{2} is assigned to (3, 7). After assigning these points, you can substitute the pairs into the formula and simplify.

\frac{7-3}{3-1} =\frac{4}{2} = 2

The slope of these two points is 2.

2. Find the y-intercept

To find the y-intercept, you substitute an ordered pair into the slope-intercept equation with the slope that was just calculated. We can use either ordered pair because it will result in the same y-intercept.

y = 2x + b (substitute)

3 = 2(1) + b (simplify)

3 = 2 + b (subtract 2 from both sides)

1 = b

The y-intercept of the two points is (0, 1).

With the necessary values to complete the equation, we can write the final equation.

The slope-intercept form equation of the line that passes through the points (1, 3) and (3, 7) is y = 2x + 1.

7 0
3 years ago
Is the given point interior, exterior, or on the circle (x + 2)2 + (y - 3)2 = 81? P(8, 4)
Elodia [21]
From the equation we see that the center of the circle is at (-2,3) and the radius is 9.

So using the distance formula we can see if the distance from the center to the point (8,4) is 9 units from the center of the circle...

d^2=(8--2)^2+(4-3)^2  and d^2=r^2=81 so

81=10^2+1^2

81=101  which is not true...

So the point (8,4) is √101≈10.05 units away from the center, which is greater than the radius of the circle.  

Thus the point lies outside or on the exterior of the circle...
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2 years ago
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USPshnik [31]

Answer:

{x}^{3}  +  13 {x}^{2}   + 34x  - 56

Step-by-step explanation:

(x + 7)( {x}^{2}  + 6x - 8) \\  = x ( {x}^{2}  + 6x - 8)  +  7( {x}^{2}  + 6x - 8)  \\  =  {x}^{3}  + 6 {x}^{2}  - 8x + 7 {x}^{2}  + 42x - 56 \\  = {x}^{3}  +  6 {x}^{2}  + 7 {x}^{2} + 42x - 8x - 56 \\  = {x}^{3}  +  13 {x}^{2}   + 34x  - 56 \\

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Answer:

12

Step-by-step explanation:

Rotation doesn't alter the lengths.

6×2 = 12

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