Which of the following tables represents a proportional relationship?

You are planning to make an open rectangular box from a 25-in.-by-49-in. piece of cardboard by cutting congruent squares from

Darya [45]

Answer:

The dimensions of the box are 38.48 x 14.48 x 5.26 in.

Step-by-step explanation:

We will have a piece of cardboard with squares of side x cut from the corners to make a open box.

The volume of the box can be written as:

$V=A\cdot B\cdot x\\\\V=(49-2x)\cdot (25-2x)\cdot x\\\\V=x\cdot (4x^2-2x*(49+25)+49*25)\\\\V=4x^3-148x^2+1225x$

To calculate the maximum volume, we derive and equal to zero

$dV/dx=12x^2-296x+1225=0$

We apply the quadratic equation to know the roots of the equation

$x=\frac{-b\pm\sqrt{b^24ac}}{2a}\\\\x=\frac{296\pm\sqrt{296^2-4*12*1225}}{2*12} =\frac{296\pm\sqrt{87616-58800}}{24}= \frac{296\pm\sqrt{28816}}{24}\\\\x=\frac{296\pm169.75}{24}= 12.333\pm7.073\\\\\\x_1=12.333+7.073=19.406\\\\x_2=12.333-7.073=5.26$

The first solution is physically impossible, as the side that is cut would be bigger than 25.

So the real solution is for x=5.26 in.

Then, the dimensions of the box are:

$A=49-2x=49-2*5.26=49-10.52=38.48\\\\B=25-2x=25-10.52=14.48$

8 0

3 years ago

Emma recently purchased a new car she decided to keep track of how many gallons of gas they used on five other business trips th

spayn [35]

Emma recently purchased a new car. She k business trips. The results are shown in the table below. decided to keep track of how many gallons of gas she used on five of her 1. Number of Miles Driven Gallons Used 150 200 400 600 1000 10 19 29 51 Write the linear regression equation for these data where miles driven is the independent variable. (Round all values to the nearest hundredth.) 2. The table below shows the number of grams of earbohydrates, x, and the number of Calories, y, of six different foods. Carbohydrates () Calories () 120 138 147 9.5 10 6 108 62 Which equation best represents the line of best fit for this set of data? 1) У-15х У-0.17-04 y-14.1x+5.8 3) 4) 2) у" 0.07x ow shows the median diameter of grains of sand and the slope of the beach for 9 naturally occurring ocean beaches. Median Diameter of 0.17 0.19 0.22 0.235 0.235 0.3 0.3 0.35 0.42 0.85 Grains of Sand in Millimeters (3) Slope of Beach 0.63 in Degrees (y) 0.7 0.82088 1 1.15 1.54.4 7.3 11.3 Write the linear regression equation for this set of data, ro at a degree, on a Using this equation, predict the slope of a beach, to the nearest tenth of a degree median diameter of 0.65 mm. on a beach with grains of sand having a

6 0

2 years ago

1. m∠ABD=50°, m∠DBC=40° Given 2. m∠ABD+m∠DBC=m∠ABC Response area 3. Response area Substitution Property of Equality 4. Response

galina1969 [7]

Answer:

<abd+<dbc=<Abc

50+40=90

triangle abc is a right angled triangle being one angle 90 degree

6 0

3 years ago

1

kherson [118]

Answer:

6000cm

Step-by-step explanation:

multiply all figures given

7 0

2 years ago

The lunch special at Scott's Restaurant is a sandwich, a drink and a dessert. There are 3 sandwiches, 1 drink, and 2 desserts to

mash [69]

Answer:

24 for being able to not have one, 6 for having one of each

Step-by-step explanation:

multiplication

with the option of none

4*2*3=24

without the option of none

3*1*2=6

4 0

2 years ago