Rewrite in simplest radical form 1 . show each step of your process.

A builder is finishing a new vet clinic and wants to install a drip edge along the roof. The edging he has decided to use comes

Nata [24]

69 rolls in total will be needed

3 0

2 years ago

1. Solve for x. Then find the angle measures of the<br>triangle?<br>(4x)<br>(6x+55)<br>(9x+30)

nalin [4]

Answer:

x = 5.

First angle = 20°, Second angle = 85°, Third angle = 75°

Step-by-step explanation:

The first angle of the triangle = (4 x)

The second angle of the triangle = (6x + 55)

The third angle of the triangle = (9x + 30)

By ANGLE SUM PROPERTY of a triangle:

First angle + Second angle + Third angle = 180°

⇒ (4 x) + (6x+55) + (9x+30) = 180°

or, (4x + 6x + 9x) + ( 55 + 30) = 180°

or, 19x = 180 - 85

or, 19 x = 95 ⇒ x = 95 /19 = 5

or, x = 5

Hence, first angle of the triangle = (4 x) = 4 x 5 = 20°

Second angle = ( 6x + 30) = 6(5) + 55 = 85°

Third angle = (9x + 30 = 9(5) + 30 = 75°

8 0

3 years ago

Find an antiderivative F(x) with F′(x) = f(x) = 6 + 24x^3 + 18x^5 and F(1)=0.

7nadin3 [17]

Answer:

The antiderivative is $F(X) = 6x + 6x^4 + 3x^6 - 15$ .

Step-by-step explanation:

Antiderivative F(x)

This is the integral of $F^{\prime}(x)$

So

F′(x) = f(x) = 6 + 24x^3 + 18x^5

Then:

$F(x) = \int (6 + 24x^3 + 18x^5) dx$

$F(x) = 6x + \frac{24x^4}{4} + \frac{18x^6}{6} + K$

$F(x) = 6x + 6x^4 + 3x^6 + K$

F(1)=0

$F(X) = 0$ when $x = 1$ . We use this to find K.

$F(x) = 6x + 6x^4 + 3x^6 + K$

$0 = 6 + 6 + 3 + K$

$K = -15$

Thus

The antiderivative is $F(X) = 6x + 6x^4 + 3x^6 - 15$ .

7 0

3 years ago

What is the equation of the following graph in vertex form? parabolic function going down from the left through the point negati

Anestetic [448]

A parabolic function's key characteristic is either having 2 x-intercepts or 2 y-intercepts. That is the reason why the standard form of parabolic functions are:

(x-h)^2 = +/- 4a(y-k) or (y-k)^2 = +/- 4a(x-h), where

(h,k) is the coordinates of the vertex
4a is the lactus rectum
a is the distance from the focus to the vertex

This is also called vertex form because the vertex (h,k) is grouped according to their variable.

Since we don't know any of those parameters, we'll just have to graph the data points given as shown in the picture. From this data alone, we can see that the parabola has two x-intercepts, x=-4 and x=-2. Since it has 2 roots, the parabola is a quadratic equation. Its equation should be

y = (x+4)(x+2)
Expanding the right side
y = x²+4x+2x+8
y = x²+6x+8
Rearrange the equation such that all x terms are on one side of the equation
x²+6x+___=y-8+___
The blank is designated for the missing terms to complete the square. Through completing the squares method, you can express the left side of the equation into (x-h)² form. This is done by taking the middle term, dividing it by two, and squaring it. So, (6/2)²=9. Therefore, you put 9 to the 2 blanks. The equation is unchanged because you add 9 to both sides of the equation.

The final equation is
x²+6x+9=y-8+9
(x+3)²=y+1