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3 years ago

What is the slope of the line that passes through the points (4, 7) and (5,8)?

Mathematics

1 answer:

slava [35]3 years ago

8 0

Answer:

Step-by-step explanation:

Use the coordinates of the points to determine the slope

slope = Δy/Δx = (8-7)/(5-4) = 1

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7. Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

morpeh [17]

Hey there!

Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

Answer :

x = -4 or x = 2 ✅

Explanation :

Quadratic formula : ax² + bx + c = 0 where a ≠ 0

The number of real-number solutions (roots) is determined by the discriminant (b² - 4ac) :

If b² - 4ac > 0 , There are 2 real-number solutions

If b² - 4ac = 0 , There is 1 real-number solution.

If b² - 4ac < 0 , There is no real-number solution.

The roots of the equation are determined by the following calculation:

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a}$

Here, we have :

a = 1
b = 2
c = -8

1) Calculate the discriminant :

b² - 4ac ⇔ 2² - 4(1)(-8) ⇔ 4 - (-32) ⇔ 36

b² - 4ac = 36 > 0 ; The equation admits two real-number solutions

2) Calculate the roots of the equation:

▪️ (1)

$x_1 = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_1 = \frac{ - 2 - \sqrt{36} }{2(1) } \\ \\ x_1 = \frac{ - 2 - 6}{2} \\ \\ x_1 = \frac{ - 8}{2} \\ \\ \blue{\boxed{\red{x_1 = -4}}}$

▪️ (2)

$x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 2 + \sqrt{36} }{2(1)} \\ \\ x_2 = \frac{ - 2 + 6}{2} \\ \\ x_2 = \frac{4}{2} \\ \\ \red{\boxed{\blue{x_2 = 2}}}$

>> Therefore, your answers are x = -4 or x = 2.

Learn more about quadratic equations:

brainly.com/question/27638369

6 0

2 years ago

Read 2 more answers

Determine the x- and y-intercepts of the graph ofx−4y=8Then plot the intercepts to graph the equation.

Over [174]

The x-intercept is the point where the graph cuts the x-axis, and the y-intercept is the point where the graph cuts the y-axis.

The x-axis is the line y = 0 and the y-axis is the line x = 0. To find the intercept between each axis and our graph, we just need to evaluate our function at x = 0 and y = 0.

Calculating the x-intercept, we have

$\begin{gathered} x-4\cdot0=8 \\ x=8 \end{gathered}$

The x-intercept is (8, 0).

Calculating the y-intercept, we have

$\begin{gathered} 0-4y=8 \\ y=-\frac{8}{4} \\ y=-2 \end{gathered}$

The y-intercept is (0, -2).

8 0

1 year ago

Please help with this thank youu

Arte-miy333 [17]

Answer:

D = 106

e = 54

f = 20

Step-by-step explanation:

its ur answer

6 0

3 years ago

Read 2 more answers

Which numbers are 4 units from -2 on this number line?

Nady [450]

Answer:

-6 and 2

Step-by-step explanation:

See attached worksheet.

6 0

2 years ago

frutty [35]

Answer:

The answer is B

Step-by-step explanation:

3 0

3 years ago