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Studentka2010 [4]

3 years ago

5

Rectangle MNPQ is similar to rectangle RSTU. Given the information marked on the diagram, what is the perimeter of RSTU?

2 answers:

Ilya [14]3 years ago

8 0

Answer:

a .

Step-by-step explanation:

xenn [34]3 years ago

5 0

The perimeter of RSTU can be calculated alone without the help of MNPQ. It would be just 2(4) + 2(3) = 14 units. However, it would be much sensible if you want to find the parameter of the bigger rectangle. Since they are similar, you could use ratio and proportion.

(length/width)∨MNPQ = (length/width)∨RSTU
(x/9) = (3/4)
x = 6.75 units

Thus the perimeter of MNPQ is 2(6.75) + 2(9) = 31.5 units

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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

Which property is illustrated by the following statement? 3+x=x+3

stiks02 [169]

Commutative Property of Addition <span />

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3 years ago

Suppose Cone A is similar to Cone B and the scale factor between the solids is 3:2, respectively. If the height of Cone A is 15

blondinia [14]

Answer:

$10\ inches$

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

Let

x----> the height of cone B

using proportion

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4 0

3 years ago

Write slope intercept form of th equation of each line

Katen [24]

Answer:

y = 8/5x + (-4) or y = 8/5x -4

Step-by-step explanation:

Slope-intercept form is written like this:

y = mx + b

The variable <em>m</em>, represents slope and <em>b</em>, represents the y-intercept.

To find slope, you have to find the rise/run or in other words, change of y over change of x.

From the look of the line, the slope has to be positive because the line is going up.

To go from the bottom point to the top, we have to go up 8 points and go to the right 5 points. Thus the slope is 8/5.

Now for the y-intercept. This part is easy. Just ask yourself this...

"Which of the two points is on the y-axis?"

In this case, it is the bottom point which is -4.

So your equation should look like this:

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or y = 8/5x - 4 because when you have a plus sign and a minus sign, the result is negative.

hope this helps :)

5 0

2 years ago

Rex mixed x liters of fruit syrup with y liters of water to make a fruit punch. Three times the number of liters of water he mix

Ilia_Sergeevich [38]

Answer:

the solution is (3,4) (the second one)

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers