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2 years ago

6

Find the values of the variables in the parallelogram. The diagram is not drawn to scale. Use fear rams involving parallel lines

and the sum of the angles of a triangle.

1 answer:

Anarel [89]2 years ago

3 0

X = 21; y = 56; z = 103

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A rancher wishes to build a fence to enclose a 2250 square yard rectangular field. Along one side the fence is to be made of hea

Bess [88]

Answer:

The least cost of fencing for the rancher is $1200

Step-by-step explanation:

Let <em>x</em> be the width and <em>y </em>the length of the rectangular field.

Let <em>C </em>the total cost of the rectangular field.

The side made of heavy duty material of length of <em>x </em>costs 16 dollars a yard. The three sides not made of heavy duty material cost $4 per yard, their side lengths are <em>x, y, y</em>. Thus

$C=4x+4y+4y+16x\\C=20x+8y$

We know that the total area of rectangular field should be 2250 square yards,

$x\cdot y=2250$

We can say that $y=\frac{2250}{x}$

Substituting into the total cost of the rectangular field, we get

$C=20x+8(\frac{2250}{x})\\\\C=20x+\frac{18000}{x}$

We have to figure out where the function is increasing and decreasing. Differentiating,

$\frac{d}{dx}C=\frac{d}{dx}\left(20x+\frac{18000}{x}\right)\\\\C'=20-\frac{18000}{x^2}$

Next, we find the critical points of the derivative

$20-\frac{18000}{x^2}=0\\\\20x^2-\frac{18000}{x^2}x^2=0\cdot \:x^2\\\\20x^2-18000=0\\\\20x^2-18000+18000=0+18000\\\\20x^2=18000\\\\\frac{20x^2}{20}=\frac{18000}{20}\\\\x^2=900\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{900},\:x=-\sqrt{900}\\\\x=30,\:x=-30$

Because the length is always positive the only point we take is $x=30$ . We thus test the intervals $(0, 30)$ and $(30, \infty)$

$C'(20)=20-\frac{18000}{20^2} = -25 < 0\\\\C'(40)= 20-\frac{18000}{20^2} = 8.75 >0$

we see that total cost function is decreasing on $(0, 30)$ and increasing on $(30, \infty)$ . Therefore, the minimum is attained at $x=30$ , so the minimal cost is

$C(30)=20(30)+\frac{18000}{30}\\C(30)=1200$

The least cost of fencing for the rancher is $1200

Here’s the diagram:

3 0

2 years ago

A pet store sold 145 bags of beef flavored dog food and 263 bags of cheese-flavored dog food. How many bags of dog food were sol

Bingel [31]

Answer:

408 bags of dog foods were sold

Step-by-step explanation:

145 bags of beef flavored dog food

+

263 bags of cheese flavored dog food

=

408 bags of dog foods were sold.

8 0

3 years ago

Write the point slope form of an equation of the line through the points

denis23 [38]

Answer:

the answer is D

how to try the values of the x and y

(x,y)

7 0

2 years ago

Read 2 more answers

High in the rocky mountains, a biology research team has drained a lake to get rid of all fish. After the lake was refilled, the

nadya68 [22]

Answer:

Step-by-step explanation:

High in the Rocky Mountains, a biology research team has drained a lake to get rid of all fish. After the lake was refilled, they stocked it with an endangered species of Greenback trout. Of the 2000 Greenback trout put into the lake 400 were tagged for later study. An electroshock method is used on individual fish to get a study sample. However, this method is hard on the fish. The research team wants to know the smallest number of fish that must be electroshocked to be at least 50% sure of getting a sample of two or more tagged trout.

we have to find out smallest number fish (n) that must be electroshoked to be atleast 50% &

species of Greenback trout of the 2000 greenback trout put into the lake 400

6 0

3 years ago

Use function notation to write the equation of the line.<br><br> please help

umka21 [38]

Therefore the equation of the line in function-form is f(x)=-2x-1

An equation of a line on the cartesian plane is given by y=mx+c. Here m denotes the slope of the line and c denotes the y-intercept.

Slope of a line is defined as the inclination of the line along the positive x- axis . Slope is calculated by the formula $m=\frac{y_2-y_1}{x_2-x_1}.$ where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

y-intercept is defined as the point where the line passes through the y-axis.

From the graph we can see that the line passes through (0,-1)and (-1,1)

therefore slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}\\or, m=\frac{1-(-1)}{-1-0}\\or, m=-2$

Now we know that the equation of a line passing through a point $(x_1,y_1)$ and with slope m is given by

$y-y_1=m(x-x_1)\\$

Substituting the values in the equation we get

y-(-1)=-2(x-0)

or, y=-1-2x

Therefore the equation of the line in function-form is f(x)=-2x-1 .Hence the second option is correct.

To learn more about the equation of the line visit:

brainly.com/question/21511618

#SPJ9

8 0

1 year ago