What is the perimeter of a square whose area is 64 square kilometers?
.
A 16 km
B.32 km
c. 64 km
D.256 km

9514 1404 393

Answer:

  (x, y) = (5, 2)

Step-by-step explanation:

Given:

  LP = x

  MP = 2y+3

  NP = y+3

  KP = 3x -8

  KP = MP, LP = NP

Find:

  x, y

Solution:

The given relations between the segment lengths let us write two equations:

  KP = MP

  3x -8 = 2y +3   ⇒   3x -2y -11 = 0   [eq1]

  LP = NP

  x = y +3   ⇒   x -y -3 = 0   [eq2]

__

Subtracting 3 times [eq2] from [eq1] gives ...

  (3x -2y -11) -3(x -y -3) = 0

  y -2 = 0 . . . . . . . . simplify

  y = 2 . . . . . . . . . . add 2

Substituting this value into [eq2] gives ...

  x = 2 + 3 = 5

The values of x and y are ...

  x = 5, y = 2

Answer:

The age of Sydney's is 46 and the age of Devaughn is 61

Step-by-step explanation:

Here;

Devaughn: 15yrs older that S..= 15+7= 22yrs old

sum of their age= 107

Now;

Sydney age= 107 - 100

7yrs old,,

Answer:

-46

Step-by-step explanation:

4(-8x + 5) = -32x - 26

-32x + 20 = -32x - 26

-32x + 32x = -26 - 20

x = -46

Answer:

-32x+20=-32x-26

20=-26

so unequal or undefined

hope this helps

have a good day :)

Step-by-step explanation:

Given :

A man 1.30 m tall is on a top of a building. He observed a car on the road at an angle of 60 degrees if the building is 30 m high.

To Find :

How far is the car from the building.

Solution :

Let, distance between car and the building is x m.

So,

[tex]tan \ \theta = \dfrac{height\ of\ building + height\ of\ man}{distance \ between \ car \ and \ building}\\\\tan \ 60^o = \dfrac{30+1.3}{x}\\\\x = \dfrac{31.3}{1.73}\ m\\\\x = 18.09\ m[/tex]

Hence, this is the required solution.

Answer:

The equivalent angle on the first quadrant is 44º. On the second quadrant, it is the given angle of 146º.

The equivalent angle on the third quadrant is 214º.

The equivalent angle on the fourth quadrant is 316º.

Step-by-step explanation:

On the first quadrant:

The equivalent in the second quadrant of a angle on the first quadrant a is 180 subtracted by the angle, that is, 180 - a.

In this question, the reference angle is 146º, which is on the second quadrant.

So, on the first quadrant:

146 = 180 - a -> a = 180 - 146 = 44.

The equivalent angle on the first quadrant is 44º. On the second quadrant, it is the given angle of 146º.

Third quadrant:

The equivalent angle on the third quadrant is 2 multiplied by 180 and subtracted by the second quadrant angle. So

2*180 - 146 = 360 - 146 = 214º.

The equivalent angle on the third quadrant is 214º.

Fourth quadrant:

The equivalent angle on the fourth quadrant is 360 subtracted by the angle on the first quadrant. So

360 - 44 = 316º

The equivalent angle on the fourth quadrant is 316º.

Answer:

268 m²

Step-by-step explanation:

8x26=208

3x10x2=60

208+60=268

Answer:

x  =  28 m

y  =  14  m

A(max)  =  392 m²

Step-by-step explanation:

Rectangular garden    A (r ) =  x * y

Let´s call x the side of the rectangle to be constructed with a rock wall, then only one x side of the rectangle will be fencing with wire.

the perimeter of the rectangle is  p  =  2*x  +  2*y    ( but in this particular case only one side x will be fencing with wire

56   =   x    +  2*y      56   -  2*y  =  x

A(r)   =  ( 56  -  2*y ) * y

A(y ) =  56*y  -  2*y²

Tacking derivatives on both sides of the equation we get:

A´(y )  =  56  - 4 * y        A´(y) = 0     56  -  4*y  =  0    4*y  =  56

y =  14 m

and x  =  56  - 2*y    =  56 - 28  = 28 m

Then dimensions of the garden:

x  =  28 m

y  =  14  m

A(max)  =  392 m²

How do we know that the area we found is a local maximum??

We find the second derivative

A´´(y)  = - 4     A´´(y)  <  0   then the function A(y) has a local maximum at y = 14 m

Answer:

[tex]x=19.67[/tex]cm

Step-by-step explanation:

Por Pitágoras,

[tex]x^{2} = 26^{2} - 17^{2} \\\\x^{2} = 676 - 289\\\\x^{2} =387\\\\x=\sqrt{387} \\\\x=19.67[/tex]

Answer:

4 or....

Step-by-step explanation:

I think its 4. maybe not

Answer:

54°

Step-by-step explanation:

54°

Answer:

the missing angle is 54

Step-by-step explanation:

so first we need two triangle angles to get our measurement and we know straight lines add up to 180 so

180-123=57

57+69(other angle)=126

all triangle angles add up to 180 so subtract the two other angles to get your result

180-126=54

54 is your anwser

Answer:

a. Flipping a coin

b. heads ⇒ boy   tails ⇒ girl

c. Flip 4 coins (1 for each child) ten times

Step-by-step explanation:

9514 1404 393

Answer:

  ∛(2500π)√37 m² ≈ 120.911 m²

Step-by-step explanation:

If the height is 3 times the diameter, it is 6 times the radius. Then the volume is ...

  V = 1/3πr²h

  V = 1/3πr²(6r) = 2πr³

For a volume of 100 m³, the radius is ...

  100 m³ = 2πr³

  r = ∛(50/π) m

The lateral area of the cone is computed from the slant height. For this cone, the slant height is found using the Pythagorean theorem:

  s² = r² +(6r)² = 37r²

  s = r√37

Then the lateral area is ...

  LA = πrs

  LA = π(∛(50/π) m)(∛(50/π) m)√37

  LA = ∛(2500π)√37 m² ≈ 120.911 m²

The lateral area of the economical cone with a volume of 100 m³ is 120.911 m².

The lateral area of the cone is the curved area of the cone, therefore, the total area of the cone is without the base area.

As we know that the volume of the cone is given by the formula,

[tex]V = \dfrac{1}{3}\pi r^2h[/tex]

Now, for the right circular cone to be economical, the height must be 3 times the diameter or it should be 6 times the radius. Therefore, the economical volume can be written as,

 [tex]V = \dfrac{1}{3}\pi r^2h\\\\V = \dfrac{1}{3}\pi r^2(6r)[/tex]

Now, if cancel out the 3 in the remainder with the six in the numerator, the volume of the cone can be written as,

[tex]V = 2\pi r^3[/tex]

Further, we need to calculate the lateral area of the cone, whose volume is 100 m³. Now, in order to get the radius of the economic cone with the volume of 100 m³, substitute it with 2πr³,

[tex]V = 2\pi r^3\\\\100 = 2\pi r^3\\\\r = 2.5154\rm\ m[/tex]

We know that in order to calculate the lateral area of the cone we need to calculate the slant height. Thus, according to the Pythagorean theorem, the slant height can be written as

[tex]s^2 = r^2 +(6r)^2\\\\ s^2 = 37r^2\\\\ s = r\sqrt{37}[/tex]

Now, the lateral area of the economical cone with the volume of 100 m³ can be written as,

[tex]LA = \pi rs\\\\LA = \pi \times r \times r\sqrt{37}\\\\LA = \pi \times r^2 \times \sqrt{37}\\\\LA = \pi \times (2.5154)^2 \times \sqrt{37}\\\\LA = 120.911\rm\ m^2[/tex]

Hence, the lateral area of the economical cone with a volume of 100 m³ is 120.911 m².

Learn more about the Lateral Area of the Cone:

https://brainly.com/question/12267785

Answer:

(4.5, 0.3125)

Step-by-step explanation:

given that

The mean is 4.5 inches

the standard deviation is 1.25 inches

and, the sample of 16 rabbits is selected

we need to find out the approximate distribution

so,

= (4.5, 1.25 ÷√16)

= (4.5, 0.3125)

hence, the same is to be considered

Answer:

She Bought 40 Gallons of Milk

Step-by-step explanation:

Answer:

DE

Step-by-step explanation:

You can tell by the markings. Since there are two vertical markings it concludes that those sides are the same length.

Answer:

B) 204

Step-by-step explanation:

Rectangle 12 * 12 = 144

+

(2) Triangle A=h (b/2) = 12*(5/2) = 30 each

Answer:

B

Step-by-step explanation:

The line crossed the y axis at 4 and the slope is -2. you can do rise/ run to find the slope which is -2/1 or -2

Answer:

It would be 0.41 ft^3

Step-by-step explanation:

Alright, to start, lets get the volume of the entire cinder block and the holes within it.

1.31 * 0.66 * 0.66 ---> 0.5706...

Next with the holes, they are both 0.33 wide, 0.39 long, and just as tall at 0.66 feet.

0.33 * 0.39 * 0.66 ---> 0.0849...

Since there's two of them: 0.1698...

To finish it, subtract the hole volume from the total volume;

0.5806 - 0.1698 = 0.4108

Rounds to 0.41 ft^3

Answer:

you add an image

Step-by-step explanation:

Answer:

... if it had the same slope in the y=mx+b equation where m is the slope and x is just x and b is the y-intercept

Step-by-step explanation:

say Car A had the equation y=2x+3- Car B would also have to have be y=2x but the y intercept could be any value

Answer:

2. 2(7y-2)

3. -5-2x

4. 9+y

5. 5x-7

6. 3m+2

7. 8-9m

Step-by-step explanation:

collect like terms

Answer:

0.04997916927

Step-by-step explanation:

Answer:

30 degrees

Step-by-step explanation:

arcsin(0.5) deg

= 30

Answer:

x = -4,      y = 8

Step-by-step explanation:

y = 2x + 16 -----(1)

2x - 7y = - 64 -------(2)

Substitute (1) in (2)

2x - 7(2x + 16) = - 64

2x - 14x - 112 = - 64

-12x = -64 + 112

-12x = 48

x = -4

Substitute x = -4 in (1)

y = 2(-4) + 16

y = -8 + 16

y  =8

Answer:

It is -4,8.

Step-by-step explanation:

y=2x +16

{

-7y=-2x-64

-6y=-48

y=8 then using substitution you will get x=-4

Answer:

24 in total

Step-by-step explanation:

Answer:

Step-by-step explanation:

11.5 is greater than -12.5

Answer: -12.5 is greater

-

Step-by-step explanation:

Answer:

make x=0 then y=-3-7(0)= (0 -3)

Answer:

y=-3

Step-by-step explanation:

see steps below:)

Answer:

Surface Area = 2×(10×7 + 10×4 + 7×4) = 276 feet^2

Step-by-step explanation:

Hope this helps :)

Answer:

The margin of error is of 0.01.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.7}{2} = 0.15[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.15 = 0.85[/tex], so Z = 1.037.

The margin of error is of:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Standard deviation was 0.21.

This means that [tex]\sigma = 0.21[/tex]

Sample of 450:

This means that [tex]n = 450[/tex]

What is the margin of error, assuming a 70% confidence level, to the nearest hundredth?

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]M = 1.037\frac{0.21}{\sqrt{450}}[/tex]

[tex]M = 0.01[/tex]

The margin of error is of 0.01.

Answer: Rs 7600

Step-by-step explanation:

The interest will be calculated as:

= Principal × Rate × Time

= 40000 × 5% × 4

= 40000 × 0.05 × 4

= 8000

Since he has to pay 5% of the total interest as tax for the bank, the amount that he will he get after 4 years will be:

= 8000 - (5% × 8000)

= 8000 - (0.05 × 8000)

= 8000 - 400

= 7600

Therefore, he'll get Rs 7600

Answer:

60

Step-by-step explanation:

5 * 12 = 60