The 2 pentagons above are similar. What is the area of the smaller pentagon?

Answer:

The correct answers are:

A) 60 miles; and B) 3.375 hours.

Explanation:

We will use the equation d = rt for this.

For the first leg of the trip, the bird travels 20 miles per hour for x hours.  This gives us the equation

d = 20x

For the return trip, the bird travels 4 miles per hour slower, so 20-4 = 16 miles per hour.  He also travels 6 miles less than the return distance, for x hours:

d-6 = 16x

To isolate d, we will add 6 to each side:

d-6+6 = 16x+6

d = 16x+6

We will set the two equations equal to one another, since they both equal d:

20x = 16x+6

Subtract 16x from each side:

20x-16x = 16x+6-16x

4x = 6

Divide both sides by 4:

4x/4 = 6/4

x = 1.5

He travels for 1.5 hours both times.

The first time, 1.5 hours at 20 miles per hour is:

d = 1.5(20) = 30 miles

The original trip is 30 miles.  This makes the entire trip 30(2) = 60 miles.

On the return trip, he travels 30-6 = 24 miles at 16 miles per hour:

24 = 16x

Divide both sides by 16:

24/16 = 16x/16

1.5 = x

If he goes 24 miles in 1.5 hours at 16 miles per hour, we can use a proportion to find the time it takes for the entire return trip:

24/1.5 = 30/x

Cross multiplying,

24*x = 1.5(30)

24x = 45

24x/24 = 45/24

x = 1.875

This gives him a total time of 1.5+1.875 = 3.375 hours

Step-by-step explanation:

Answer:

I believe its (B.)

The width of the piece of metal will be 24 inches while the length will be 29 inches.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

Let's say the width of metal w then the length will be w + 5

Now if we cut 1 inch square from the corner of the metal and then fold then the resultant cuboid will have;

Length = w+5 - 2 -= w + 3

Width = w - 2

Height = 1

So,

Volume = (w+3)(w-2)1

594 = w² + 2w + 3w - 6

w² + w - 600 = 0

By solving this

w = 24 so width will be 24 and length will be 24 + 5 = 29.

Hence "The width of the piece of metal will be 24 inches while the length will be 29 inches".

For more about rectangles,

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Answer:answer is x=15=20

Step-by-step explanation:i did it before in class and got an A

Answer:

[tex]81.25[/tex]

[tex]45.55 + 35.7[/tex]

Answer:

465

Step-by-step explanation:

The way I thought about it was I subtracted 30 from 15 and got 15. Then I subtracted 60 from 30 and got 20. My conclusion is you continue to add 5 more to what you added before. 15, 30, 60, 85, 115, 150, 190, 235, 285, 340, 400, 465.

Answer:

0

Step-by-step explanation:

Jordan hasn't got enough money to buy any books, as $11.40<$280.

Answer:

  x = 9/4

Step-by-step explanation:

Locate point G on segment DE so that DG = 1 and GE = 4. CG is parallel to AD, so ΔCGE ~ ΔABC. Corresponding sides are proportional.

  AB/BC = CG/GE

  x/1 = 9/4

  x = 9/4

_____

Additional comment

Using the given triangles, you can write the proportion statement as ...

  (9+x)/x = 5/1

We judge this to take more steps to solve, so we prefer the method shown above.

Answer:

42.59 km

Step-by-step explanation:

Total distance = 17.9 + 6.03 + 15.66 + 3 = 42.59

Answer:

42.59 km

Step-by-step explanation:

When a question tells you to find the total of something it is usually means you need to add to add decimals you align the decimals and if a number doesn't have a decimal you add .0 on the end then line it up. It also might help to add a 0 in empty spots . Then you move the decimal to the same place in the solution and add like normal.

 17.90

 06.03

  15.66

+03.00

 42.59

Answer:

80

Step-by-step explanation:

Answer:

800 = 80 tens

Step-by-step explanation:

4800 / 60 = 800

Answer:  y = -(3/7)x - (36/7)

Step-by-step explanation:

Let's convert -3x - 7y = 10 to standard slope intercept form:  y=mx + b, where m is the slope and b is the y-intercept (the value of y when x=0).

-3x - 7y = 10

-7y = 3x + 10

y = -(3/7)x - (10/7)

This line has a slope of -(3/7).  Any line that is parallel will have the same slope, so we can write y = -(3/7)x + b to start our new line.  

We want a value of b that forces the line to go trough point (-5,-3).  Use this point in the partial equation and solve for b:

y = -(3/7)x + b

-3 = -(3/7)(-5) + b

-3 = (15/7) + b

b = -3 - (15/7)

b = -(21/7) - (15/7)

b = -(36/7), or -5 1/7

y = -(3/7)x - (36/7)

Answer:

120,000

Step-by-step explanation:

Let's say Rio gets 5x, Kim gets 7x, and Leo gets 3x. In the ratio 5:7:3:1, x = 1

5x + 7x + 3x = total = 15x

3x = 24000

divide both sides by 3 to get x

x = 8000

15x = 8000*15 = 120000

Answer:

b=20

Step-by-step explanation:

-185-5=9b

-180=9b

=>b= -20

[tex]\huge{\underline{\underline{\boxed{\sf{\purple{ǫᴜᴇsᴛɪᴏɴ}}}}}}[/tex]

[tex]\huge{\underline{\underline{\boxed{\sf{\ref{Answer}}}}}}[/tex]

[tex]\large\huge\green{\sf{♥ Explanation♥}}[/tex]

∴Hence, at standard it is 13.00-4 =99.00 STD talk

off reached at Manila +8 Zone at 20.00

∴Hence at standard & 2000 -8

reached.⇒ 12.00 STD

(i) Time at Manila, whicle Plane de parts

12-3+8 ⇒9+8 → 17.00

(ii) duration = 3 hours.

(iii) in dubai 13.00 + 3 = 16,00

_____________________

Ans

i)17.0.0 (ii) 3 hours (iii) 16.00

________________________

♕ hence we done:) xD

Answer:

2x + 7y = 35

Step-by-step explanation:

Multiply the equation with 7

7 ( y = -2x/7 + 5 )

7y = -2x + 35

2x + 7y = 35

Answer:2/8, 0.3215, 9/16, 0.75

Step-by-step explanation:

2/8 = 0.25  0.3215 is higher then 9/16 =0.5625 next is 0.75

[tex]\\ \sf\longmapsto 2m^2=-200[/tex]

[tex]\\ \sf\longmapsto m^2=-100[/tex]

[tex]\\ \sf\longmapsto m=√-100[/tex]

[tex]\\ \sf\longmapsto m=√100i[/tex]

[tex]\\ \sf\longmapsto m=10i[/tex]

Answer:

i am not to sure but i think its 5/13 or 5/40

Answer:

The answer would be -12, I'm not to sure what simplify means

Answer:

36

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

Step-by-step explanation:

You have two pieces if information: the slope of a line and a point on the line. So you can use the "point-slope" formula in order to write the equation of this line. It is a fill-in-the-blank type of formula.

y - y1 = m(x - x1)

In this fill-in-the-blank formula the y1, the m, and the x1 will be filled in with the numbers you were given.

The problem gave the slope as -3/2 , this is your m. On these linear equation problems and formulas, m always stands for the slope.

So fill that in:

y - y1 = -3/2 (x - x1)

They also gave you a point, that is the (x1, y1) that you need to fill in the formula. The point was (-12, 16), so -12 will be your x1 and 16 will be your y1. Fill it in!

y - 16 = -3/2 (x - -12)

Simplify that ugly 'minus a negative' in the parenthesis.

y - 16 = -3/2 (x + 12)

If you were never told what form of equation to write, or they said "any form of the equation", then you're done!

This is in "point-slope" form.

y - 16 = -3/2(x+12) Ta-da!

If you need to change it to "slope-intercept' form then there are a few more steps.

y - 16 = (-3/2)x + (-3/2)12

y - 16 = (-3/2)x - 18

+16 +16

y = -3x/2 - 2 This is y=mx+b (called slope-intercept form)

[tex]\huge \bf༆ Answer ༄[/tex]

The Additional information needed to prove the Triangles congruent by HL criteria is ~ D

ST = SE or US = FS

===========================================

Explanation:

As you mentioned, HL stands for hypotenuse leg. The sides EF and UT marked with triple tickmarks are congruent, and they are the congruent hypotenuses. That takes care of the "H" part of "HL". So we can cross off choice C because it mentions TU = EF, which is already taken care of.

The "L" part can involve either leg of the triangles. So we could involve the legs ST and SE (they appear to be the shorter legs), or we could involve the longer legs US and FS. We only need to pick one of those options to handle the "L" portion. If we knew all three aspects, then we could easily refer to the SSS (side side side) congruence theorem.

The HL theorem only applies to right triangles.

The length of the trails can be determined be using a formula related to

Pythagorean theorem, which makes use of the rise and run of a trail.

Reasons:

The location of the park = (1, 9)

The stating point of Trail A = (-7, -6)

Starting point of Trail B = (6, -3)

The length of a trail is adapted from the formula for the distance between points which is a form of Pythagorean theorem as follows;

[tex]Length \ of \ a \ trail, \ L = \mathbf{\sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}}[/tex]

Therefore;

[tex]Length \ of \ trail, \ A = \sqrt{\left (1-(-7) \right )^{2}+\left (9-(-6) \right )^{2}} = \mathbf{17}[/tex]

[tex]Length \ of \ trail, \ B = \sqrt{\left (1-6 \right )^{2}+\left (9-(-3) \right )^{2}} = \mathbf{13}[/tex]

The difference between the lengths of the trails = 17 mi - 13 mi = 4 miles

Therefore;

Trail A is 4 miles longer than Trail B

Learn more about finding the distance between two points on a graph here:

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Answer:

Lillian will have $170.56 in one year

Step-by-step explanation:

First we have to figure out what is 6.6% of 160.

160 * 6.6% = 10.56

Now we just add 160 with the 6.6% to figure out the answer.

160 + 10.56 = 170.56

So, the answer is 170.56 dollars.

Hope this helps! :)

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Answer:

60 have 12 factors :1,2,3,4,5,6,10,12,15,20,30,60

Answer:

y + 5z

Step-by-step explanation:

Hope this helps!