The perimeter of a rectangular park is 200 feet. The length of the park is 40 feet longer than the width.Find the length of the park.

What is the length of the park?
feet?​

Answer:

3.049

Step-by-step explanation:

Let S be the sum of the integers 25-210:

S = 25 + 26 + 27 + … + 208 + 209 + 210

Let S₃, S₄, and S₁₂ denote the sums of the integers in S that are multiples of 3, 4, or 12, respectively. We'll also count how many terms each sum involves; it'll be useful later.

S₃ = 27 + 30 + 33 + … + 204 + 207 + 210 … … … (62 terms)

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

S₄ = 28 + 32 + 36 + … + 200 + 204 + 208 … … … (46 terms)

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₁₂ = 36 + 48 + 60 + … + 180 + 192 + 204 … … … (15 terms)

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

Let's look at S₃ :

S₃ = 3 (9 + 10 + 11 + … + 68 + 69 + 70)

By reversing the order of the sum, we get

S₃* = 3 (70 + 69 + 68 + … + 11 + 10 + 9)

Of course S₃ = S₃*, I'm just calling it something else temporarily. Notice that every term in the same position of either sum adds up the same number.

9 + 70 = 79

10 + 69 = 79

11 + 68 = 79

and so on. Then

S₃ + S₃* = 3 (79 + 79 + 79 + … + 79 + 79 + 79)

or

2S₃ = 3 × 62 × 79   ==>   S₃ = 7,347

We can compute the other two sums in the same way.

S₄ = 4 (7 + 8 + 9 + … + 50 + 51 + 52)

S₄* = 4 (52 + 51 + 50 + … + 9 + 8 + 7)

==>   2S₄ = 4 × 46 × 59  ==>   S₄ = 5,428

S₁₂ = 12 (3 + 4 + 5 + … + 15 + 16 + 17)

S₁₂* = 12 (17 + 16 +15 + … + 5 + 4 + 3)

==>   2S₁₂ = 12 × 15 × 20   ==>   S₁₂ = 1,800

Then the sum you want is

S₃ + S₄ - S₁₂ = 10,975

We subtract S₁₂ because each of its terms is counted twice (once in S₃ and again in S₄).

Answer:

Height of school building = 100 feet

Step-by-step explanation:

Given;

Shadow of school building = 25 feet

Height of individual = 6 feet

Shadow of individual = 18 inches = 1.5 feet

Find:

Height of school building

Computation:

Height of individual / Shadow of individual = Height of school building / Shadow of school building

6 / 1.5 = Height of school building / 25

Height of school building = 25 x 4

Height of school building = 100 feet

Answer:

$1,463

Step-by-step explanation:

38.50x38=1,463

The greatest counting number that divides 17, 25 and 41 and leaves the same remainder in each case is 8

Answer:

#3

20tan(53) + 5 feet   OR    31.54 feet (rounded to nearest hundredth)

#4

6tan(32) feet    OR    3.75 km (rounded to nearest hundredth)

Step-by-step explanation:

#3

The horizontal line is at Chloe's eye level, which is 5 feet.

She looks up at an angle of 53 degrees, and is 20 feet away from the statue. This creates a right triangle that you can use basic trigonometry to solve.

Let's call the shorter leg (upper half of statue) as x and the longer leg (distance between Chloe and statue) is 20 feet. We are given the opposite and adjacent sides (from the given angle) so we can use tan.

tan = opp/adj, so tan(53)=x/20

If you plug 20 tan 53 into your calculator to find x, you get 26.54089643

But you have to add 5 feet to your answer because that is her eye level.

#4

The horizontal distance from airplane to raft is 6km, the angle of depression is 32 degrees from the airplane, and we are asked to find the altitude of the plane (x).

We are given an adjacent side and are tasked to find the opposite side, so we will use tan.

tan 32=x/6

Plug this  into your calculator and you get x=3.749216111 km.

Answer:

-w²+49x²-8wx

Step-by-step explanation:

if you want how I did this it's quite lengthy so let me know if you want the process

Answer:

-w^2 + 21xw - 64x ^2

Step-by-step explanation:

Answer:

12.92

Step-by-step explanation:

rounding the 1 hundredth up to 2 because of the 5 thousandth

Answer:

Step-by-step explanation:

See explanation in attached image

Answer:

[tex]17x-23=1/2\times81[/tex]

[tex]17x-23=40.5[/tex]

[tex]17x=40.5+23[/tex]

[tex]17x=63.5[/tex]

[tex]x=63.5/17[/tex]

[tex]x=3.73[/tex]

OAmalOHopeO

D [tex]\bold{16x^{6}y^{10}z²}[/tex]

Answer:

John needs to rewrite the expression [tex](4x^{3}y^{5}z)²[/tex]. Identify which of the following is the simplified form of the expression.

[tex](4x^{3}y^{5}z)²[/tex]

remenber that square is for all

and power is multiplied

[tex]4²x^{3*2}y^{5*2}*z²[/tex]

[tex]16x^{6}y^{10}z²[/tex]

Step-by-step explanation:

[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boldsymbol{Rule: (a^n)^m=a^{n\cdot m }} \\\\\\ (4x^3\cdot y^5\cdot z)^2=4^2\cdot x^{3\cdot 2}\cdot y^{5\cdot 2}\cdot z^2=16 \ x^6 \cdot y^{10} \cdot z^2 \\\\\\ Answer : \boxed{ D)16 \ x^6 \cdot y^{10} \cdot z^2 }[/tex]

Answer:

x ≤ -15

Step-by-step explanation:

-x/3 ≥ 5

or, -x ≥ 15

or, x≤ -15

Answered by GAUTHMATH

Answer:

x**9

Step-by-step explanation:

(x**3/2)**6 = x**18/2 = x**9

Answer:

DE=27

EF=13

DG=13

GF=27

Step-by-step explanation:

12x+3=5x+17

12x-5x=17-3

u'll get 14 then simply it by the numbe of X u'll get 2 then replace the X with the number

Answer:

829.6

Step-by-step explanation:

Volume = sh

= (5+12) x 6.1 / 2 x 16

= 12 x 6.1/2 x 16

= 17 x 6.1 x 8

= 829.6 mi^3

Answered by Gauthmath

The values of BMW after 2, 4 and 8 years  according to the EXPONENTIAL FUNCTION are $33,462, $20,358.28 and $7,535.63 respectively.

Using the parameters given, we define an decreasing exponential function :

[tex]A = A_{0} (1 - r)^{t}[/tex]

Where,

[tex]A_{0}[/tex] = initial amount ; r = Rate ; t = time ; A = final amount

Value after 2 years :

t = 2

A = 55000(1 - 0.22)²

A = 55000(0.78)²

A = $33,462

Value after 4 years :

t = 4

A = 55000(1 - 0.22)^4

A = 55000(0.78)^4

A = $20,358.28

Value after 8 years :

t = 4

A = 55000(1 - 0.22)^8

A = 55000(0.78)^8

A = $7,535.63

Therefore, the value of BMW after 2, 4 and 8 years are $33,462, $20,358.28 and $7,535.63 respectively.

Learn more about Exponential functions :

https://brainly.com/question/14355665

Answer: First option (your selected answer)

Step-by-step explanation:

(rotating an object 360° will bring it to its original position)

(rotating an object 180° will turn it upside-down)

(rotating an object 90° will make it sideways)

(to calculate the scale factor, pick a point on both triangles that are of the same corner)

ex: A: (-12,12) and A': (4,-4)

(ask yourself what you need to multiply the x and y coordinates of ΔABC by to get the resulting x and y coordinates of the ΔA'B'C')

[tex]-12*-\frac{1}{3}=4\\12*-\frac{1}{3}=-4[/tex]

(you multiply -1/3 to get the x and y value of the second triangle)

(though the provided options do not display the negative scale factor, the scale factor should be negative)

ΔABC - ΔA'B'C', because ΔA'B'C' is obtained by dilating ΔABC by a scale factor of 1/3 and then rotating it about the origin by 180°

Answer:

[tex] \sqrt[]{ \frac{0}{0} } [/tex]

Explainion are shown in pictures above

Answer:

20 batches

Step-by-step explanation:

Cups of sugar in a bag = 15

Cups of sugar per batch of cookie = 3/4 cup

Cups of sugar per batch of cookie : batch of cookies = 3/4 : 1

what's the greatest number of batches of cookies that can be made with the bag of sugar

Let

x = batches of cookies made with a bag of sugar

Cups of sugar per batch of cookie : batch of cookies = 15 : x

Equate the ratios

3/4 : 1 = 15 : x

3/4 ÷ 1 = 15/x

3/4 × 1/1 = 15/x

3/4 = 15/x

Cross product

3 * x = 4 * 15

3x = 60

x = 60/3

x = 20

x = batches of cookies made with a bag of sugar = 20 batches

Answer:

2[tex]\sqrt{10\\}[/tex]

Step-by-step explanation:

Because this is a right triangle, we have:

[tex]x^{2} + 3^{2} = 7^{2} (Pytago)\\x^{2} + 9= 49\\x^{2} =40\\x=\sqrt{40} \\x=2\sqrt{10}[/tex]

Answer:

The best option would be the second one.

Step-by-step explanation:

This is the only option that shows that x can only be greater than -8. The circled dot means x cannot be the number the dot is sitting on, in this case, -8.

Answer:

B. on edge 2021

Step-by-step explanation:

y 1 = StartFraction log x Over log 2 EndFraction + StartFraction log (x minus 2) Over log 2 EndFraction, y 2 = 4; x = 4

Answer:

It's B :))

Step-by-step explanation:

Answer:

228573

Step-by-step explanation:

a = 219 (first term)

an = 2018 (last term)

Sn->Sum of n terms

Sn=n/2(a + an)         [Where n is no. of terms] -> eq 1

To find number of terms,

an = a + (n-1)d     [d->Common Difference] -> eq 2

d= 226-219 = 7

=> d=7

Substituting in eq 2,

2018 = 219 + (n-1)(7)

1799 = (n-1)(7)

1799 = 7n-7

1799 = 7(n-1)

1799/7 = n-1

257 = n-1

n=258

Substituting values in eq 1,

Sn = 258/2(219+2018)

    = 129(2237)

    = 228573

Answer:

x = 4

139.2

Step-by-step explanation:

Given the Cost function :

C(x) = 1.7x² - 13.6x + 166.4

To achieve minimum cost ;

dc/dx = 0

dc/dx = 2(1.7)x - 13.6

3.4x - 13.6 = 0

3.4x = 13.6

x = 13.6 / 3.4

x = 4

To achieve minimum cost, speed = 4 ;

Minimum cost will be :

C(x) = 1.7x² - 13.6x + 166.4

Put x = 4

C(4) = 1.7(4)² - 13.6(4) + 166.4

C(4) = 27.2 - 54.4 + 166.4 = 139.2

Minimum cost = 139.2

Answer:

y = -5/4x^2

Step-by-step explanation:

I'm assuming the 2 are the exponents. Make sure to use ^ to type exponents.

Green = 1/3x^2

Blue = -5/4x^2

Answer:

q = 1/4

Step-by-step explanation:

-5/4 - (-1/4) = -1

-1/(q-1/2) = 4

-1 = 4(q-1/2)

-1 = 4q - 2

1 = 4q

q = 1/4

Answer: D) 20/21

Explanation:

Recall that sin(theta) = opposite/hypotenuse.

sin(theta) = 20/29 tells us that 20 is the vertical side while 29 is the hypotenuse. Note how the vertical side is opposite the reference angle theta.

Use these two sides to find that the missing side is 21. You'll need the pythagorean theorem a^2+b^2 = c^2.

Once you determine that the adjacent side is 21 units long, we can then say,

tan(theta) = opposite/adjacent = 20/21

Answer:

D. 20/21

Step-by-step explanation: