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3 years ago

Find the x-intercept and y-intercept of the line. 3x + 5y = −15

Mathematics

1 answer:

insens350 [35]3 years ago

5 0

Answer:

The x intercept is (-5,0)

The y intercept is (0,-3)

Step-by-step explanation:

To find the x intercept we set y=0 and solve for x

3x+5y = -15

3x+0 = -15

3x = -15

Divide by 3

3x/3 = -15/3

x = -5

The x intercept is (-5,0)

To find the x intercept we set x=0 and solve for y

3x+5y = -15

0+5y = -15

5y = -15

Divide by 5

5y/5 = -15/5

y = -3

The y intercept is (0,-3)

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Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?

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Answer:

$Vertex = (\frac{1}{2},\frac{7}{4})$

Step-by-step explanation:

Given

$f(x) = x^2 - x +2$

Required

The vertex

We have:

$f(x) = x^2 - x +2$

First, we express the equation as:

$f(x) = a(x - h)^2 +k$

Where

$Vertex = (h,k)$

So, we have:

$f(x) = x^2 - x +2$

--------------------------------------------

Take the coefficient of x: -1

Divide by 2: (-1/2)

Square: (-1/2)^2

Add and subtract this to the equation

--------------------------------------------

$f(x) = x^2 - x +2$

$f(x) = x^2 - x + (-\frac{1}{2})^2+2 -(-\frac{1}{2})^2$

$f(x) = x^2 - x + \frac{1}{4}+2 -\frac{1}{4}$

Expand

$f(x) = x^2 - \frac{1}{2}x- \frac{1}{2}x + \frac{1}{4}+2 -\frac{1}{4}$

Factorize

$f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2 -\frac{1}{4}$

Factor out x - 1/2

$f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2 -\frac{1}{4}$

$f(x) = (x - \frac{1}{2})^2+2 -\frac{1}{4}$

$f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}$

$f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}$

Compare to: $f(x) = a(x - h)^2 +k$

$h = \frac{1}{2}$

$k = \frac{7}{4}$

Hence:

$Vertex = (\frac{1}{2},\frac{7}{4})$

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Find the coordinates of the point 7/10 of the way from A to B.

Mkey [24]

Answer:

The coordinates are (6.5, 1.7).

Step-by-step explanation:

The difference between A and B's x-coordinate is 15. 7/10 of this is 10.5, which added to -4 gives us an x-coordinate of 6.5.

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A farmer has a soybean field with an area of 55 square meters and a cornfield with an area of 58 square meters. he also has a wh

dexar [7]

A farmer has order the fields from least area to greatest area is,

Soybean field < Cornfield < Wheat field.

Based on the given conditions,

A farmer has a soybean field with an area = 55 square meters

A farmer has a corn field with an area = 58 square meters

He also has a wheat field that is 52 times the size of the soybean field.

So,

We can write,

52 times the size of the soybean field.

That means,

= 55 * 52

Calculate the product or quotient,

= 2860

Wheat field = 2860

Hence,

Soybean field = 55

Cornfield = 58

Wheat field = 2860

Soybean field < Cornfield < Wheat field

Therefore,

A farmer has order the fields from least area to greatest area is,

Soybean field < Cornfield < Wheat field.

To learn more about information visit Area problems :

brainly.com/question/16735292

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