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Norma-Jean [14]
3 years ago
9

The perimeter of the original rectangle on the left is 30 meters. The perimeter of the reduced rectangle on the right is 24 mete

rs.
A small rectangle has a length of 8 meters. A larger rectangle has a width of x.


What is x, the width of the original rectangle on the left? Round to the nearest hundredth if necessary.

5 meters

8 meters

10 meters

12 meters
Mathematics
2 answers:
OlgaM077 [116]3 years ago
6 0

Answer:

5 meters

Step-by-step explanation:

If the smallest rectangle has a length of 8 meters, and a perimeter of 24 meters then its width is given by:

24 = 2*8+2*W_1\\W_1= 4\ meters

We can conclude that the width is half of the length for both rectangles. Therefore, the width of the larger rectangle, with a perimeter of 30 meters, is:

30 = 2*W_2+2*L_2\\30 = 2*W_2+4*W_2\\W_2=5\ meters

The width of the original rectangle is 5 meters.

deff fn [24]3 years ago
5 0

Answer:

5

Step-by-step explanation:

Find the scale factor

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z -----> the scale factor

P1 -----> the perimeter of the reduced rectangle on the right

P2 ----> the perimeter of the original rectangle on the left

substitute

step 2

Find the width of the reduced rectangle on the right

substitute the given values.

Find the width of the original rectangle on the left.

To find the width of the original rectangle on the left, divide the width of the reduced rectangle on the right by the scale factor.

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On a map 1/4 inch = 50 miles. If two cities appear 3 inches apart, how many
Mumz [18]

Answer:

Step-by-step explanation:

3⅛ inches × (50 miles)/(¼ inch) = 625 miles

4 0
3 years ago
I am having trouble with this relative minimum of this equation.<br>​
Norma-Jean [14]

Answer:

So the approximate relative minimum is (0.4,-58.5).

Step-by-step explanation:

Ok this is a calculus approach.  You have to let me know if you want this done another way.

Here are some rules I'm going to use:

(f+g)'=f'+g'       (Sum rule)

(cf)'=c(f)'          (Constant multiple rule)

(x^n)'=nx^{n-1} (Power rule)

(c)'=0               (Constant rule)

(x)'=1                (Slope of y=x is 1)

y=4x^3+13x^2-12x-56

y'=(4x^3+13x^2-12x-56)'

y'=(4x^3)'+(13x^2)'-(12x)'-(56)'

y'=4(x^3)'+13(x^2)'-12(x)'-0

y'=4(3x^2)+13(2x^1)-12(1)

y'=12x^2+26x-12

Now we set y' equal to 0 and solve for the critical numbers.

12x^2+26x-12=0

Divide both sides by 2:

6x^2+13x-6=0

Compaer 6x^2+13x-6=0 to ax^2+bx+c=0 to determine the values for a=6,b=13,c=-6.

a=6

b=13

c=-6

We are going to use the quadratic formula to solve for our critical numbers, x.

x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}

x=\frac{-13 \pm \sqrt{169+144}}{12}

x=\frac{-13 \pm \sqrt{313}}{12}

Let's separate the choices:

x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}

Let's approximate both of these:

x=0.3909838 \text{ or } -2.5576505.

This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.

The relative maximum is at approximately -2.5576505.

So the relative minimum is at approximate 0.3909838.

We could also verify this with more calculus of course.

Let's find the second derivative.

f(x)=4x^3+13x^2-12x-56

f'(x)=12x^2+26x-12

f''(x)=24x+26

So if f''(a) is positive then we have a minimum at x=a.

If f''(a) is negative then we have a maximum at x=a.

Rounding to nearest tenths here:  x=-2.6 and x=.4

Let's see what f'' gives us at both of these x's.

24(-2.6)+25

-37.5  

So we have a maximum at x=-2.6.

24(.4)+25

9.6+25

34.6

So we have a minimum at x=.4.

Now let's find the corresponding y-value for our relative minimum point since that would complete your question.

We are going to use the equation that relates x and y.

I'm going to use 0.3909838 instead of .4 just so we can be closer to the correct y value.

y=4(0.3909838)^3+13(0.3909838)^2-12(0.3909838)-56

I'm shoving this into a calculator:

y=-58.4654411

So the approximate relative minimum is (0.4,-58.5).

If you graph y=4x^3+13x^2-12x-56 you should see the graph taking a dip at this point.

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3 years ago
PLEASE HELP FAST!! Wally collects 15 baseball cards each week. He gave 10 cards to his friend James. Wright an expression to sho
mr Goodwill [35]
15x - 10 where x is equal to the number of weeks would respresent the situation above. This is because he gains 15 cards every week and gave ten cards to James once.

If it has only been one week, the expression will be 15 - 10 because 15 × 1 = 15.

I hope this helps!
3 0
3 years ago
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