All categories

3 years ago

7

Mathematics

1 answer:

jeyben [28]3 years ago

8 0

Answer:

x = -2

Step-by-step explanation:

Given the point, (-2, 9) and the linear equation of a horizontal line, y = 6:

The linear equation of a horizontal line with a slope of zero (m = 0) is y = b, for which the y-intercept is (0, b). Perpendicular lines comprise of the intersection of two lines forming 90° angles.

Since we are given the equation of a horizontal line, then we can assume that the line that intersects a horizontal line must be a vertical line in order to form perpendicular lines.

The linear equation of a vertical line with an undefined slope is x = a, for which the x-intercept is (a, 0). Vertical lines have an undefined slope because these lines do not have any horizontal change. Thus, when you try to solve for its slope, the denominator will have a difference of 0, making the mathematical operation undefined.

We can use the x-coordinate of the given point, (-2, 9), to formulate an equation for a vertical line: x = -2.

Therefore, the equation of the line that goes through y = 6 is x = -2.

Attached is a screenshot of the graph of both equations, y = 6 and x = -2, showing that their intersection form 90° angles, making them perpendicular lines.

You might be interested in

12x0.08 help me plss!!!

mel-nik [20]

Answer:

0.96

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

One truck delivered 3 4/5 tons of potatoes to a warehouse while another truck delivered 1/2 ton less. How many tons of potatoes

Savatey [412]

3 4/5 + (3 4/5 - 1/2) =
19/5 + (19/5 - 1/2) =
19/5 + (38/10 - 5/10) =
19/5 + 33/10 =
38/10 + 33/10 =
71/10 which equals 7 1/10 tons <==

5 0

4 years ago

Read 2 more answers

A circle is centered at the point (5,-4) And passes through the point (-3,2). What is the equation of the circle?

Natalka [10]

The equation of a circle is:

(x-h)2 + (y-k)2 = r2

where (h,k) is the location of the center and r is the radius. So we need to find h, k, and r. The center is given as (5,-4) so h = 5 and k = -4:

(x-5)2 + (y-(-4))2 = r2
(x-5)2 + (y+4)2 = r2

So we need to find r. Use the distance formula to find the distance between (5,-4) and (-3,2):

r = [(5-(-3))2+((-4)-2)2]1/2
r = [82 + (-6)2]1/2
r = [64 + 36]1/2
r = 1001/2

r= 10

The final equation is:

(x-5)2 + (y+4)2 = 102

8 0

3 years ago

A bag contain 3 black balls and 2 white balls.

Troyanec [42]

Answer:

Step-by-step explanation:

Total number of balls = 3 + 2 = 5

$Probability \ of \ taking \ 2 \ black \ ball \ with \ replacement\\\\ = \frac{3C_1}{5C_1} \times \frac{3C_1}{5C_1} =\frac{3}{5} \times \frac{3}{5} = \frac{9}{25}\\\\$

$Probability \ of \ one \ black \ and \ one\ white \ with \ replacement \\\\= \frac{3C_1}{5C_1} \times \frac{2C_1}{5C_1} = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25}$

Probability of at least one black( means BB or BW or WB)

$=\frac{3}{5} \times \frac{3}{5} + \frac{3}{5} \times \frac{2}{5} + \frac{2}{5} \times \frac{3}{5} \\\\= \frac{9}{25} + \frac{6}{25} + \frac{6}{25}\\\\= \frac{21}{25}$

Probability of at most one black ( means WW or WB or BW)

$=\frac{2}{5} \times \frac{2}{5} + \frac{3}{5} \times \frac{2}{5} \times \frac{2}{5} + \frac{3}{5}\\\\= \frac{4}{25} + \frac{6}{25} + \frac{6}{25}\\\\=\frac{16}{25}$

a) Probability both black without replacement

$=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}$

b) Probability of one black and one white

$=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}$

c) Probability of at least one black ( BB or BW or WB)

$=\frac{3}{5} \times \frac{2}{4} + \frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{6}{20} + \frac{6}{20} \\\\=\frac{18}{20} \\\\=\frac{9}{10}$

d) Probability of at most one black ( BW or WW or WB)

$=\frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{1}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{2}{20} + \frac{6}{20} \\\\=\frac{14}{20}\\\\=\frac{7}{10}$

6 0

3 years ago

Which of the following is a function equivalent to f(x) = 4(1.8)2x?

kvv77 [185]

If you would like to know which is a function equivalent to f(x) = 4 * (1.8)^(2x), you can calculate this using the following steps:

f(x) = 4 * (1.8)^(2x)
f(x) = 4 * 3.24^x
f(x) = 4 * (3.24)^x

The correct result would be f(x) = 4(3.24)x.

3 0

3 years ago

Read 2 more answers