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3 years ago

Which of the following is the equation of a line perpendicular to the line 7= –3/2 x + 4

Mathematics

1 answer:

frosja888 [35]3 years ago

8 0

Answer:

Option c is correct !!

Step-by-step explanation:

[ Refer to the attachment ]

As y = mx + c is an equation to represent the straight line ; we equate the given line with this equation !!

Where m is slope of the line

and c is y intercept !!

We get , m = -3/2 and c = 4

Also, two perpendicular lines follows the equation :-

$(m1)(m2) = - 1$

Where m nth is slope of nth line !!

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which of the following expresses the coordinates of the foci of the conic section shown below? (x-2)^2/4+(y+5)^2/9

elena55 [62]

Step-by-step explanation:

$\frac{(x - 2) {}^{2} }{4} + \frac{(y + 5) {}^{2} }{9} = 1$

This is the equation of the ellipse. Since the denominator is greater for the y values, we have a vertical ellipse. Remember a>b, so a

The formula for the foci of the vertical ellipse is

(h,k+c) and (h,k-c).

where c is

Our center (h,k) is (2, -5)

${c}^{2} = {a}^{2} - {b}^{2}$

Here a^2 is 9, b^2 is 4.

${c}^{2} = 9 - 4$

${c}^{2} = 5$

$c = \sqrt{5}$

So our foci is

$(2, - 5 + \sqrt{5} )$

and

$(2, - 5 - \sqrt{5} )$

6 0

1 year ago

How do I write each number as a power of the given base? example: 49; base 7

VLD [36.1K]

$7^n=49$
we know that 7*7=49 so thus $7^2=49$
$7^n=7^2$
therefor n=2
it is written as $7^2$

7 0

3 years ago

What is the slope that passes through the points (-5,0) and (-3,1)

tangare [24]

Answer:

1/2

Step-by-step explanation:

When given two points, we can find the slope by

m = (y2-y1)/(x2-x1)

= (1-0)/(-3- -5)

= (1-0) / (-3+5)

= 1/2

7 0

2 years ago

Read 2 more answers

Select ALL the correct answers.

aksik [14]

Answer: I think it’s A the cylinder

Step-by-step explanation:

8 0

3 years ago

What is the equation written in vertex from of a parabola with a vertex of (4, –2) that passes through (2, –14)?

vichka [17]

Answer:

y = -3(x - 4)² - 2

Step-by-step explanation:

Given the vertex, (4, -2), and the point (2, -14):

We can use the vertex form of the quadratic equation:

y = a(x - h)² + k

Where:

(h, k) = vertex

a = determines whether the graph opens up or down, and it also makes the parent function wider or narrower.

positive value of a = opens upward
negative value of a = opens downward
a is between 0 and 1, (0 < a < 1) the graph is wider than the parent function.
a > 1, the graph is narrower than the parent function.

h = determines how far left or right the parent function is translated.

h = positive, the function is translated h units to the right.
h = negative, the function is translated |h| units to the left.

k determines how far up or down the parent function is translated.

k = positive: translate k units up.
k = negative, translate k units down.

Now that I've set up the definitions for each variable of the vertex form, we can determine the quadratic equation using the given vertex and the point:

vertex (h, k): (4, -2)

point (x, y): (2, -14)

Substitute these values into the vertex form to solve for a:

y = a(x - h)² + k

-14 = a(2 - 4)² -2

-14 = a (-2)² -2

-14 = a4 + -2

Add to to both sides:

-14 + 2 = a4 + -2 + 2

-12 = 4a

Divide both sides by 4 to solve for a:

-12/4 = 4a/4

-3 = a

Therefore, the quadratic equation inI vertex form is:

y = -3(x - 4)² - 2

The parabola is downward-facing, and is vertically compressed by a factor of -3. The graph is also horizontally translated 4 units to the right, and vertically translated 2 units down.

Attached is a screenshot of the graph where it shows the vertex and the given point, using the vertex form that I came up with.

Please mark my answers as the Brainliest, if you find this helpful :)

8 0

2 years ago