Tom, Jim, and Matt want to build a castle next to their swing set. The
castle is as wide as the swing set, and 6 feet long. The additional play
area is enlarged to yield the following layout !

Answer:

  (a) 7.1

  (b) (5/2, 3/2)

  (c) 2

  (d) y = -x +4

Step-by-step explanation:

The length of AC is found using the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((5 -(-2))² +(-1 -0)²) = √(49 +1) = 5√2 ≈ 7.1

The length of AC is about 7.1.

__

The midpoint has coordinates that are the average of the end point coordinates.

  midpoint BC = (B + C)/2 = ((0, 4) +(5, -1))/2 = (5, 3)/2

  midpoint BC = (5/2, 3/2)

__

The slope is found using the slope formula.

  m = (y2 -y1)/(x2 -x1)

For points A(-2, 0) and B(0, 4), the slope of the segment between them is ...

  m = (4 -0)/(0 -(-2)) = 4/2 = 2

The slope of AB is 2.

__

The slope of line BC is found in the same was as for AB.

  m = (-1 -4)/(5 -0) = -5/5 = -1

The y-intercept of the line is point B, at y=4. So, the equation of line BC is ...

  y = mx +b . . . . . where m is the slope, and b is the y-intercept

  y = -x +4

Answer:The answer is 60.90 I took te 2.03 math quiz and got 100 first A theater group is made up of 21 girls and 24 boys. Fifteen of the girls and 12 of the boys are also in a photography club.

What percent of the theater group is also in the photography club?

Enter your answer in the box. 60,  next questionA builder wants to increase the size of one of his square patios. The patio measures 16 feet on each side. The builder plans to increase each side of the patio to be 125% of its current measure.

How many square feet larger is the area of the new patio than the area of the current patio?

Responses

144   A manual with 325 pages has 3 pages without pictures.

What percent of the pages in the manual do not have pictures?

Enter your answer, as a decimal rounded to the nearest hundredth of a percent, in the box. 0.92

Step-by-step explanation: all answers

The cost of 2 pair of boots is given by A = $ 60.90

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the cost of 2 pair of boots be A

Now , the cost of pair of boots = 145 % the cost of pair of sneakers

Substituting the values in the equation , we get

The cost of pair of sneakers = $ 21

So , the cost of pair of boots = ( 1.45 ) x 21

The cost of pair of boots = $ 30.45

Now , the cost of 2 pair of boots A = 2 x cost of pair of boots

On simplifying , we get

The cost of 2 pair of boots A = $ 60.90

Hence , the cost of 2 pair of boots is $ 60.90

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Answer:

Step-by-step explanation:

5/1

Answer:500/100

Step-by-step explanation:

Answer:

x = 72

Step-by-step explanation:

A circle is 360 degrees

2x-61+ x-11 + 3x = 360

Combine like terms

6x-72=360

Add 72 to each side

6x-72+72 = 360+72

6x =432

Divide each side by 6

6x/6 = 432/6

x =72

Answer:

b

Step-by-step explanation:

Answer:

x is the center of i circle

Step-by-step explanation:

i am not sure if this is correct

- sorry if this does not help

Answer:

  (d)  y= (1 1/9)x

Step-by-step explanation:

A proportional relation is described by the equation ...

  y = kx

Dividing by x shows how to find the value of k:

  k = y/x

For the given values of y and x, the value of k is found to be ...

  k = (5/6)/(3/4) = (5/6)(4/3) = 20/18 = 10/9 = 1 1/9

The relationship is represented by the equation ...

  y = (1 1/9)x

Answer:

the answer is y=1 1/9x because i took thek12 quiz

Step-by-step explanation:

Answer:

the sum of the first 1000 positive integers is 500500

Step-by-step explanation:

Answer: 500500

Step-by-step explanation: 1000*(1000+1)/2 = 1000*1001/2 = 500500. Correct me if i'm wrong

Answer:

It must be a square because its sides are equal and have a 90° of angle. It is not a rectangle because its length and breadth are not equal. It is not a rhombus because it does not have a 90° of angle. Similarly, it is not a parallelogram because it does not have 90° of angle.

Step-by-step explanation:

Answer:

Its a square. with all sides equal and has four right angles.

Answer:

Exact Form:

16/15

Decimal Form:

1.06

Mixed Number Form:

1/1/15

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

Add 7 to 74, which gives you 81. Then divide by 9 for the value of w and you get 9.

Answer:

w = 9

Step-by-step explanation:

Isolate variable by adding 7 to both sides

9w = 81

Divide both sides by 9 to get w alone

w = 9

Check

9(9) - 7 =74

81-7 = 74

74 = 74

Answer:

200 meters = 7874.016 inches

Answer:

7874 inches

Step-by-step explanation:

200 times 39.37 and you get the answer 7874

Answer:

3X + 3Y +7

Step-by-step explanation:

Just combine like terms ( 2X and X)

The length of the square paving is the base unit to which the area of the

and patio and the border are evaluated.

Correct response:

Let s represent the size of the square paving, we have;

Area of the patio = s·x × s·y = s²·x·y

New area = (2·s + s·x) × (2·s + s·y) = 4·s² + 2·s²·y + 2·x·s² + s²·x·y

Area of the border = 4·s² + 2·s²·y + 2·x·s² = s²·x·y

2·s²·(2 + y + x) = s²·x·y

2·(2 + y + x) = x·y

4 + 2·y + 2·x = x·y

x·y - 2·x = 4 + 2·y

x·(y - 2) = 4 + 2·y

Which by using  gives;

[tex]x = \mathbf{ \dfrac{4 + 2 \cdot y }{y- 2}}[/tex]

By graphing the above equation on MS Excel, we have the following

possible values of x, and y combination; (10, 3) (6, 4), (4, 6), (3, 10).

Therefore;

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Answer:

285 degrees

Step-by-step explanation:

take 75 minus 360 and you get 285

Hope This Helps!

Answer:

X=2

Step-by-step explanation:

X(5-2)=4x-x

5x-2x=4x-x (then moving everything to one side)

5x-2x-4x+x=0 (5x-4x-x=5x-5x which is 0)

-2x=0

X=2

Answer:

  x ≈ 263.1

Step-by-step explanation:

The marked sides are the hypotenuse and the side adjacent to the given angle. The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

  cos(70°) = 90/x . . . . use given values

  x = 90/cos(70°) . . . . multiply by x/cos(70°)

  x ≈ 263.1

_____

Additional comment

The mnemonic SOH CAH TOA is intended to remind you of the primary trig relations:

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

  Tan = Opposite/Adjacent

Answer:

Yes

Step-by-step explanation:

To see if (2,0) works as a solution to the systems of equations, we plug in the values of x and y and simplify. If the results are equal, then (2,0) is a solution.

3x + y = 6:

3x - y = 6:

Therefore, the answer is yes, it does work as a solution.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$\stackrel{tripled}{(7550)3}\\ P=\textit{original amount deposited}\dotfill & \$7550\\ r=rate\to 7.25\%\to \frac{7.25}{100}\dotfill &0.0725\\ t=years \end{cases}[/tex]

[tex]3(7550)=7550e^{0.0725\cdot t}\implies \cfrac{3(7550)}{7550}=e^{0.0725t}\implies 3=e^{0.0725t} \\\\\\ \log_e(3)=\log_e\left( e^{0.0725t} \right)\implies \ln(3)=0.0725t \\\\\\ \cfrac{\ln(3)}{0.0725}=t\implies 15.15327\approx t\implies 15\approx t[/tex]

It will take approximately 9.55 years (rounded to the nearest year) for the money to triple.

Here, we have,

To determine how long it will take for the money to triple, we need to use the continuous compound interest formula:

A = P *[tex]e^{rt}[/tex],

where:

A = final amount (triple the initial amount)

P = principal amount (initial deposit)

e = Euler's number (approximately 2.71828)

r = interest rate

t = time (in years)

In this case, we have:

P = $7550

r = 7.25% = 0.0725 (converted to decimal)

A = 3P (triple the initial amount)

Substituting these values into the formula, we have:

3P = P *[tex]e^{rt}[/tex]

Dividing both sides of the equation by P, we get:

3 = [tex]e^{rt}[/tex]

To isolate the variable t, we take the natural logarithm (ln) of both sides:

ln(3) = ln[tex]e^{rt}[/tex]

Using the logarithmic property that ln(eˣ) = x, we have:

ln(3) = rt * ln(e)

Since ln(e) = 1, the equation simplifies to:

ln(3) = rt

Now, we can solve for t by dividing both sides by r:

t = ln(3) / r

Substituting the values:

t = ln(3) / 0.0725

Using a calculator or software, we find:

t ≈ 9.55 years (rounded to two decit will take approximately 9.55 years (rounded to the nearest year) for the money to triple. deimal places)

Therefore, it will take approximately 9.55 years (rounded to the nearest year) for the money to triple.

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Answer:

8.6

Step-by-step explanation:

radius = diameter/2 = 10/2 cm = 5 cm

V = (1/3)πr²h

225 cm³ = (1/3)π(5 cm)²h

h = 27/π cm

h = 8.6 cm

Answer:

Your answer is 22.5 or 22

Step-by-step explanation:

divide 10 by 225 to get your height.

Answer:

f^-1(x) = ( x + -1 )³

Step-by-step explanation:

f(x) = ∛x + 1

y  = ∛x + 1

we have to make x the subject to find the inverse

y  = ∛x + 1

y - 1 = ∛x

( y - 1 )³ = x

so Inverse: f^-1(x) = ( x + -1 )³

Answer:

Yes

Step-by-step explanation:

-0.2 is a negative number and is therefore always lesser than a positive, and 4/5 is a fraction-so any whole number is greater than it.

Answer:

Value in 2015 will be $ 143,000

Step-by-step explanation:

Data :

Value in 2010 = $ 110000

Increase rate = 6%

6% of  110000  =  (11000×6)÷100 =  6600

6600 × 5 = 33000

So add up    

   110000 + 33000 = 143,000

Mark brainliest if you understand

Step-by-step explanation:

refer the above attachment

Answer:1/5

Step-by-step explanation:

Hey there mate :)

Analysis :

[tex]401 = 515 - 114 = u - 6[/tex]

And

[tex]173 = 515 - 3.114 = u - 36[/tex]

[tex] = \frac{p(u - 36 < u < u + 36) - p(u - 6 < u < u + 6)}{2} [/tex]

[tex] = \frac{99.73percent - 68.21percent}{2} [/tex]

[tex] = \frac{31.46percent}{2} [/tex]

[tex] = {15.73percent}[/tex]

Then, calculating,

[tex]u - 26 = 515 - 2 \times 114 = 287[/tex]

And

[tex]u + 26 = 515 + 2 \times 114 = 743[/tex]

Then,

[tex]The \: Range = (287,743)[/tex]

Final Answers :-

15.73 %

(287,743)

~Benjemin360