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umka21 [38]
3 years ago
8

Line m passes through (4, 7) and (8, 2). Line n is parallel to line m. What is the slope

Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
4 0
X= 4 and Y=-5
or
X=-4 and Y=5
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Help?! No clue about functions...
olga_2 [115]
Method 1: Using Calculus

The first method in going about this is to use Calculus, a branch of mathematics interested in the rate of change of a certain graph. In order to use Calculus, we need to understand what we are required to do when finding minimum values.

We first need to take the derivative of the function, because this becomes our tangent or slope at any arbitrary point on the graph.

f'(x) = 2x - 8

We now need the derivative to be equal to zero, as this is will give us a horizontal tangent, which means we are able to find the turning point of a graph.

f'(x) = 0; 2x - 8 = 0
2x = 8; x = 4

So, at x = 4, there will be a minimum, since the second derivative is clearly greater than zero. By substituting this point back to f(x), we can find a value for y, and this is our minimum point of the curve.

f(4) = 4^{2} - 8(4) + 21
f(4) = 16 - 32 + 21 = 5

Thus, we know the minimum point of this curve, f(x), is at: (4, 5)

Method 2: Vertex form

For any given quadratic, or a polynomial with degree 2, 4, 6, etc., we can easily find the minimum point, as that simply is our vertex. By converting this into vertex form, we can find the coordinates that will satisfy the vertex of this function, which becomes our minimum point.

Start by completing the square:
f(x) = y= x^{2} - 8x + 16 - 16 + 21
y = x^{2} - 8x + 16 + 5
x^{2} - 8x + 16 = y - 5
(x - 4)^{2} = (y - 5)

Thus, the vertex becomes: (4, 5) which is our lowest point (ie our minimum point)
4 0
3 years ago
Read 2 more answers
Solve by using elimtation
Wewaii [24]

Answer:

1. x = 5, y = 13/2

2. x = 15 , y = 24

Step-by-step explanation:

Solve the following system:

{8 y + 6 x = 82 | (equation 1)

{6 y + 9 x = 84 | (equation 2)

Swap equation 1 with equation 2:

{9 x + 6 y = 84 | (equation 1)

{6 x + 8 y = 82 | (equation 2)

Subtract 2/3 × (equation 1) from equation 2:

{9 x + 6 y = 84 | (equation 1)

{0 x + 4 y = 26 | (equation 2)

Divide equation 1 by 3:

{3 x + 2 y = 28 | (equation 1)

{0 x + 4 y = 26 | (equation 2)

Divide equation 2 by 2:

{3 x + 2 y = 28 | (equation 1)

{0 x + 2 y = 13 | (equation 2)

Divide equation 2 by 2:

{3 x + 2 y = 28 | (equation 1)

{0 x + y = 13/2 | (equation 2)

Subtract 2 × (equation 2) from equation 1:

{3 x + 0 y = 15 | (equation 1)

{0 x + y = 13/2 | (equation 2)

Divide equation 1 by 3:

{x + 0 y = 5 | (equation 1)

{0 x + y = 13/2 | (equation 2)

Collect results:

Answer: {x = 5, y = 13/2

_____________________________________

Solve the following system:

{8 y + 3 x = 237 | (equation 1)

{3 y + 5 x = 147 | (equation 2)

Swap equation 1 with equation 2:

{5 x + 3 y = 147 | (equation 1)

{3 x + 8 y = 237 | (equation 2)

Subtract 3/5 × (equation 1) from equation 2:

{5 x + 3 y = 147 | (equation 1)

{0 x + (31 y)/5 = 744/5 | (equation 2)

Multiply equation 2 by 5/31:

{5 x + 3 y = 147 | (equation 1)

{0 x + y = 24 | (equation 2)

Subtract 3 × (equation 2) from equation 1:

{5 x + 0 y = 75 | (equation 1)

{0 x + y = 24 | (equation 2)

Divide equation 1 by 5:

{x + 0 y = 15 | (equation 1)

{0 x + y = 24 | (equation 2)

Collect results:

Answer: {x = 15 , y = 24

3 0
2 years ago
Evaluate the summation below.<br> ) (-1 + 6d)<br> d=2
weqwewe [10]

Answer:

− 1 + 6 d , d = 2

Step-by-step explanation:

4 0
3 years ago
Someone please help me will give BRAILIEST!!!!!
marishachu [46]
B. x > 70
 is the correct answer
3 0
3 years ago
Read 2 more answers
Hayley has $155 in savings, and her brother Hank has $230. Hayley is saving $10 each week, and her brother is spending $15 each
Sindrei [870]

Answer:

After 3 weeks they both will have the same amount in their savings account.

Step-by-step explanation:

Given:

Amount saved by Haley = $155

Amount saved by Hank = $230

Amount saving each week by Haley = $10

Amount spending each week by Hank = $15

We need to find Number of weeks when both both will have same amount in savings account.

Solution:

Let Number of week be 'x'.

Total Amount of Haley can be calculated by Amount saved by Haley plus Amount saving each week by Haley multiplied by number of weeks.

framing in equation form we get;

Total Amount of Haley = 155+10x

Also;

Total Amount of Hank can be calculated by Amount saved by Hank minus Amount spending each week by Hank multiplied by number of weeks.

framing in equation form we get;

Total Amount of Hank = 230-15x

Now we need to find the number of weeks when both will have same amount.

To find the same we will have to make both the equation equal.

So we can say.

155+10x=230-15x

On Solving above equation we get;

We will combine the like terms together;

10x+15x =230-155\\\\25x = 75

Now Dividing both side by 25 using Division property of equality we get;

\frac{25x}{25} = \frac{75}{25}\\\\x=3 \ weeks

Hence, After 3 weeks they both will have the same amount in their savings account.

4 0
3 years ago
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