MATHEMATICS HIGH SCHOOL

Joe has a rectangular chicken coop. The length of the coop is 4 feet less than twice the width. The area of the chicken coop is 510 square feet. What is the length of the chicken coup? PLEASE HELP ME!!!

Answers

Answer 1

Answer:

Let w and l be the dimensions (width and length, respectively) of the coop.

We know that the length of the coop is 4 feet less than twice the width, which means that

$l=2w-4$

Also, the area is 510, but the area is the product of the dimensions, so we have

$lw=510$

Plug the expression for l in the formula for the area:

$lw=(2w-4)w=510 \iff 2w^2-4w-510=0$

We can divide the whole expression by 2 and solve it with the quadratic formula:

$w^2-2w-255=0 \iff w=(2\pm√(4+1020))/(2)=(2\pm 32)/(2)=1\pm 16$

So, the two solutions are

$w_1=1-16=-15,\quad w_2=1+16=17$

The negative solution makes no sense (we can't have negative lengths), so the width must be 17.

We conclude that the length is

$l=2w-4=2\cdot 17-4=34-4=30$

Answer 2

Answer:

Final answer:

The length of the chicken coup is found to be 30.689 feet by setting up and solving a quadratic equation for the area of the rectangle.

Explanation:

To find the length of the chicken coop, we need to use the given information. Let's first define the width of the coop as 'w'. According to the problem, the length of the coop is 4 feet less than twice the width. So, the length can be represented as 2w - 4. The area of a rectangle is given by length multiplied by width. Hence, we have the equation (2w - 4)w = 510. Solving this equation will give us the width and length of the chicken coop.

Expanding the equation, we have 2 $w^2$ - 4w = 510. Rearranging it to the standard quadratic form, we get 2 $w^2$ - 4w - 510 = 0. To solve this quadratic equation, we can either use factoring, completing the square, or the quadratic formula. Factoring doesn't seem to work in this case, so let's use the quadratic formula: w = (-b ± sqrt( $b^2$ - 4ac)) / (2a). Substituting the values a = 2, b = -4, and c = -510 into the formula, we can find the values of w. Taking into account the physical context, we can discard the negative value. Once we have the value of w, we can substitute it into the equation for the length, 2w - 4, to find the length of the chicken coop.

So, the width of the chicken coop is approximately 17.355 feet and the length is approximately 30.689 feet.

Learn more about finding the length of a rectangular chicken coop here:

brainly.com/question/23142693

#SPJ12

Related Questions

The pair of points( 6 ,y) and (10, -1) lie on a line with slope 1/4. What is the value of y?
F(x) = 3x - 3 g(x) = 4x + 5find (f+g) (3)
Solve: (they're fractions) 3/6x + 1/2=8/x+4/3 The answer is -9 but i dont know how to solve it. Work please or explanation why. Thanks.
Calculate the area of the triangle 7m 4m is it (a) 14 m² (b) 18 m² (c) 28 m² (d) 56 m²
The school band is selling sweatshirts and baseball caps to raise $9000 to attend a band competition Sweatshirts cost $25 each and baseball caps cost $10 each. The equation 25x + 10y = 9000 models this situation, where x is the number of sweatshirts sold and y is the number of baseball caps sold. The number of shirts sold is 258 X - intercept = y - intercept = How many caps were sold?x int:y int:how many caps were sold? :

When a projector is placed 10 meters from a screen as shown, it produces an image 3 meters high. If the tallest image that the projector can produce without distortion is 4.5 meters high, what is the maximum distance the projector can be placed from the screen?

Answers

To get the maximum distance, you first use the given numbers as basis.

10 meters/3 meters =x/4.5 meters

Where x = the maximum distance the projector can be placed that can produce an image 4.5 meters high

3x = 10 (4.5)

3x = 45

X= 45/3

X= 15 meters

So, the maximum distance that the projector can be placed from the screen which produces an image 4.5 meters high is 15 meters.

Answer:

So, the maximum distance that the projector can be placed from the screen which produces an image 4.5 meters high is 15 meters.

Step-by-step explanation:

Claire has $300 in her account she decided she is going to take out half of what is left in there at the end of each month

Answers

300 divided by two is 150 so your answer would be 150 dollars

100 points!!!! and brainliest!!!!You keep track of the daily hot chocolate sales and the outside temperature each day. The data you gathered is shown in the data table below.
Hot Chocolate Sales and Outside Temperatures
Sales ($)
$100
$213
$830
$679
$209
$189
$1,110
$456
$422
$235
$199
Temperature (°F)
92°
88°
54°
62°
85°
16°
52°
65°
68°
89°
91°

a) Make a scatterplot of the data above.
b) Do you notice clusters or outliers in the data? Explain your reasoning.
c) How would you describe the correlation in the data? Explain your reasoning.
d) What are the independent and dependent variables?
Step 2: Evaluating trends of data
Because you want to prepare and serve the healthiest food possible, you monitor the fat and calorie content of items on your menu. Some of the menu items are included in the graph below.
a) Your business partner describes this as a high positive correlation. Is your partner correct? Why or why not
b) Using the drawing tools, draw a trend line (line of best fit) on the graph above.
c) Judge the closeness of your trend line to the data points. Do you notice a relationship between the data points?
d) Is the trend line linear? If so, write a linear equation that represents the trend line. Show your work.
Step 3: Making predictions using data
You and your business partner track the number of customers served and the amount of tips collected per day. The data you gathered is displayed in the chart below.
Servers’ Collected Tips
Customers
54
46
34
67
52
22
49
64
55
80
38
42
Tips ($)
$92
$80
$76
$121
$109
$43
$87
$114
$99
$174
$88
$91

a) Create a scatterplot displaying the data in the table. Be sure to include a linear trend line.
b) Find the equation of the trend line (line of best fit). Show your work.
c) Predict the amount of tips that would be collected if 100 customers were served at the restaurant on a given day.
d) Explain how to use the regression calculator to make a reasonable prediction given a data table.

Answers

Answer:

step 1

b) Yes,I do 1,110 is a cluster because it’s a very large number for 52 degrees and 189 is because it’s a very large number for 16 degrees.

c) There is a negative correlation.

d) The dependent variable is sales and independent variable is the temperature.

step 2

a) yes my partner is correct because the line goes diagonally upwards.

b) The trend line lies on the points (0,100) and (15,900)D .

c) Yes I do see a relationship. This line move one direction up. notice how the dots move up like an escalator

d) Yes do see a relationship. This line move one direction up. notice how the dots move up like an escalator.

step 3

b) 1.875x+12.25

c) 50

d) Given data, first determine which is the independent variable, x, and which is the dependent variable, y. Enter the data pairs into the regression calculator. Substitute the value for one variable into the equation for the regression line produced by the calculator, and then predict the value of the other variable.

1)Enter data into the regression calculator.

2)Determine the regression equation.

3)Substitute the correct value for x or y into the equation.

4)Simplify to find the value of the other variable.

(1,2,3,4, goes with step 3 D)

Step-by-step explanation:

Final answer:

This question involves scatterplots, correlations, identifying independent and dependent variables, trend lines, and making predictions through data analysis and regression.

Explanation:

This question requires a detailed understanding of data analysis, including scatterplots, correlation, trend lines, and regression. First, to make a scatterplot of the hot chocolate sales and outside temperatures, you would plot each pair of data points with the temperature on the x-axis and the sales on the y-axis. Detecting clusters or outliers would require inspecting the graph and watching for data points that stray far from the others. The correlation could be negative, as lower temperatures seem to correspond with higher sales.

The independent variable is the outside temperature, and the dependent variable is the hot chocolate sales. In the next part, a high positive correlation indicates that as the fat content increases, so does the calorie content. The trend line in this graph likely goes upwards when drawn. If it fits closely to the data points, then there is a strong positive correlation.

In the third part, you'd want to plot the number of customers against the amount of tips received to identify the trend. Using this trend line, you could then predict potential earnings given a certain number of customers. A regression calculator could be used to define precise relationships in the data and make accurate predictions.

Learn more about Data Analysis here:

brainly.com/question/33332656

#SPJ3

What is 15%off of $3.00

Answers

if u r getting 15% off, then ur paying 85% of $3.00.100%-15%=85%

multiply $3.00*.85=$2.55 hope it helps u

85% of $3.00 is
$2.55

What is 16,700,000,000,000,000 estimated as the product of a single digit and a power of 10?

Answers

First, the number of zeros you have is the power of 10 and as a product, it would look like:
167*10^14.

But we need a number with a single digit which means we have to divide 167 by 100=10^2. In order to have the same equation, we need also to multiply by 10^2. Now it would look like:

1.67 * 10^14* 10^2 = 1.67* 10^16
Now 1.67 rounded up is 2. The final solution is:

2* 10^16

16,700,000,000,000,000 = 1.67 x 10^16

start at the last 0....count the number of spaces till u can get a decimal right after the first digit....thats 16 spaces. Now take ur numbers that are not 0...1.67....and multiply it by 10^16...because of the 16 spaces. I hope I am making some kind of sense...I am better at doing then explaining how to do...lol

If y varies inversely with x, and y = -16 when x = -64, what is the constant of variation?a. 16
b. 64
c. 100
d. 1,024