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2 years ago

What is the value of x in the equation 2 (4x+)-(3x+2)- 8(9-x) = x

Mathematics

1 answer:

Readme [11.4K]2 years ago

7 0

Answer:

open the bracket

(4X+)-3X-2-72+X=X

4X+(-3X)-74+X=X

X-74+X=X

2X-74=X

then collect the term

-74=X-2X

-74=-X

divide by negative every side then you get

X=74

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1) Find an equation of the line that passes through thr pair of points (-5,-9) and (2,-7).

Yuki888 [10]

1: Assuming this line is linear, the first thing to do is find the slope.
The slope formula is $m=\frac{ y_{2} - y_{1} }{ x_{2} - x_{1} }$ , so in this case, it is $m=\frac{ (-7) - (-9) }{ 2 - (-5) }$ , which comes to $\frac{2}{7}$ . Then, use your slope and one of the points given to write the point-slope formula of the linear equation, and then written in standard form:
y= $\frac{2}{7}$ x- $\frac{53}{7}$ .

2. Use the same process as in question 1 to find:
y=-7x+11

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3 years ago

The diagram shows a sketch of John's yard. He wants to plant grass, so he must calculate the area of the yard. The distance from

Arturiano [62]

The area of the yard is 50,600 square feet.

Option: C.

Step-by-step explanation:

The given information forms a trapezoid.

The AB is the upper base (a) and its length is 200 feet.

The CD is the lower base (b) and its length is 260 feet.

A straight line distance from AB and CD is the height (h) and its measures as 220 feet.

The area of trapezoid A= $\frac{a+b}{2} (h)$ .

A= $\frac{200+260}{2} (220)$ .

= $\frac{460}{2}(220)$ .

=230(220).

=50600 $ft^2.$

Thus the area of John's yard is 50,600 square feet.

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3 years ago

a carton length of 2 1/4 feet, width of 1 3/5 feet , and height of 2 1/3 feet. what is the volume of the carton?

babunello [35]

8.4 feet cubed or 8 2/5 feet cubed

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2 years ago

Find the directional derivative of the function at the given point in the direction of the vector v. G(r, s) = tan−1(rs), (1, 3)

alexandr1967 [171]

The directional derivative of $f$ at the given point in the direction indicated is $\frac{5}{2}$ .

<h3>How to calculate the directional derivative of a multivariate function</h3>

The directional derivative is represented by the following formula:

$\nabla_{\vec v} f = \nabla f (r_{o}, s_{o})\cdot \vec v$ (1)

Where:

$\nabla f (r_{o}, s_{o})$ - Gradient evaluated at the point $(r_{o}, s_{o})$ .
$\vec v$ - Directional vector.

The gradient of $f$ is calculated below:

$\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{\partial f}{\partial r}(r_{o},s_{o}) \\\frac{\partial f}{\partial s}(r_{o},s_{o}) \end{array}\right]$ (2)

Where $\frac{\partial f}{\partial r}$ and $\frac{\partial f}{\partial s}$ are the partial derivatives with respect to $r$ and $s$ , respectively.

If we know that $(r_{o}, s_{o}) = (1, 3)$ , then the gradient is:

$\nabla f(r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{s}{1+r^{2}\cdot s^{2}} \\\frac{r}{1+r^{2}\cdot s^{2}}\end{array}\right]$

$\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{1+1^{2}\cdot 3^{2}} \\\frac{1}{1+1^{2}\cdot 3^{2}} \end{array}\right]$

$\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right]$

If we know that $\vec v = 5\,\hat{i} + 10\,\hat{j}$ , then the directional derivative is:

$\nabla_{\vec v} f = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right] \cdot \left[\begin{array}{cc}5\\10\end{array}\right]$

$\nabla _{\vec v} f (r_{o}, s_{o}) = \frac{5}{2}$

The directional derivative of $f$ at the given point in the direction indicated is $\frac{5}{2}$ . $\blacksquare$

To learn more on directional derivative, we kindly invite to check this verified question: brainly.com/question/9964491

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2 years ago

Mr. McLaughlin was setting up for parent teacher meetings in the gym. The door was 42 inches wide and 84 inches tall. He needed

xz_007 [3.2K]

Yes he would be able to because the guy could just put it a a diagonal angle and it would fit but it you can't do that then no it wouldn't fit

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3 years ago