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3 years ago

A shade of orange paint is made with 5 parts red paint and 15 parts yellow paint.

1 answer:

3 0

A) 1/4 of the paint is made with read so that's 25 percent
B) yellow to red paint ratio is 3:1

please crown me if this helped you!<span> </span>

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Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)

vfiekz [6]

Answer:

Step-by-step explanation:

given a point $(x_0,y_0)$ the equation of a line with slope m that passes through the given point is

$y-y_0 = m(x-x_0)$ or equivalently

$y = mx+(y_0-mx_0)$ .

Recall that a line of the form $y=mx+b$ , the y intercept is b and the x intercept is $\frac{-b}{m}$ .

So, in our case, the y intercept is $(y_0-mx_0)$ and the x intercept is $\frac{mx_0-y_0}{m}$ .

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph $(x_0,\frac{1}{x_0})$ . Which means that $y_0=\frac{1}{x_0}$

The slope of the tangent line is given by the derivative of the function evaluated at $x_0$ . Using the properties of derivatives, we get

$y' = \frac{-1}{x^2}$ . So evaluated at $x_0$ we get $m = \frac{-1}{x_0^2}$

Replacing the values in our previous findings we get that the y intercept is

$(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}$

The x intercept is

$\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0$

The triangle in consideration has height $\frac{2}{x_0}$ and base $2x_0$ . So the area is

$\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2$

So regardless of the point we take on the graph, the area of the triangle is always 2.

6 0

3 years ago

A baby is born having a mass of 3,000 grams and gains 200 grams in the following week. How much does the baby weigh one week aft

nignag [31]

Answer:

7 pounds 0.8767 ounces

8 0

4 years ago

Read 2 more answers

Pls help! three arithmetic sequences are given below.

katrin [286]

The common difference is basically the number at which the pattern increases.

A's common difference: 2

B's common difference: 9

C's common difference: 5

answer: A, C, B

8 0

3 years ago

Solve the expression, 3-3x6+2.

sergey [27]

It would be 2 silly because 3-3=0 and 0 x 6=0 and 0 + 2 = 2 so that is the answer 2

3 0

3 years ago

Read 2 more answers

What type of triangle is triangle ABC give reasons for your answer help please I need 1 more mark But I don't know what I'm doin

ladessa [460]

Answer: isosceles

Step-by-step explanation:

By the alternate interior angles theorem, $\angle CAB=50^{\circ}$

Since angles in a triangle add to 180 degrees, $\angle ACB=180^{\circ}-80^{\circ}-50^{\circ}=50^{\circ}$

Since sides opposite equal angles in a triangle are equal, $AB=BC$ .

So, triangle ABC is <u>isosceles</u>

7 0

2 years ago