Please help!!! Having some trouble with this! 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:|

The total money the dance team would have to spend on the new uniforms is  $1099.25.

Percentage can be described as a fraction of an amount expressed as a number out of hundred.

Total amount = (25% of the amount raised at the sale) + amount raised during the car wash

$356+ ( $25% x $2,973) = $1099.25

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The word expression the cube of the sum of a number and 3 can be written as (x + 3)³ or x³ + 9x² + 27x + 27.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

Let x be the number:

The word expression is:

The cube of the sum of a number and 3.

The sum of a number x and 3 is:

x + 3

The cube of the number (x + 3)

= (x + 3)³

After expanding the cube of (a + b)

(a + b)³ = a³ + 3a²b + 3ab² + b³

Similarly,

(x + 3)³ = x³ + 3x²(3) + 3(x)(3)² + (3)³

(x + 3)³ = x³ + 9x² + 27x + 27

Thus, the word expression the cube of the sum of a number and 3 can be written as (x + 3)³ or x³ + 9x² + 27x + 27.

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Answer:

The amount after 6 years is $25,533.34.

Step-by-step explanation:

Use the formula f(t)=P(1+b)^t.

Plug in the information.

f(6)=18000(1+0.06)^6

Plug in 18000(1.06)^6 into calculator.

25,533.344020608.

Round to 2 decimal places.

25,533.34

The amount after 6 years is $25,533.34.

Hope this helps!

If not, I am sorry.

Answer: 120

Step-by-step explanation:

The interior angle of the 12-sided polygon is

[tex]\frac{180(12-2)}{12}=150^{\circ}[/tex]

So, if we consider the triangle with angle x, two of its angles are each [tex]30^{\circ}[/tex] since they are supplementary to the interior angle of the 12-sided polygon.

Therefore, as angles in a triangle add to 180 degrees, x=120.

The following logarithmic equation is equivalent to the given exponential equation,

[tex]log_{4}(256) = c[/tex]

Computing the Equivalent Logarithmic Equation

The given exponential equation is,

[tex](4)^{c} = 256[/tex]

As per the fundamental properties of exponentiation, the logarithmic equivalent equation of any exponential equation has the same base as that in the corresponding exponential equation. Exponentiation refers to the act of raising a number to the power of another number.

In the exponential equation, [tex](4)^{c} = 256[/tex], $ is the base. So, the base in its equivalent logarithmic equation will also be 4.

The result of the exponential expression becomes the operand for the log.

Terms in a Logarithmic Equation

For the logarithmic equation, [tex]log_{4}(256) = c[/tex],

4 is called the base of the log. The variable  'c' is the logarithm of 256 to base 'a'.

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The value of ? and X are 12 and 24 respectively

A triangles is 2D shape with three sides and angles.

From the given diagram, the ratio of similar sides is equal to a constant as shown;

15/20 = 9+15/20+x

Cross multiply

15/9+15 = 20/20+x

15/24 = 20/20+x

Comparing with the given ratio

? = 24

X = 20+x

Find x

15(20+x) = 480

300 + 15x = 480

15x = 180

x =12

Fro the given expression

x/32 = 9/?

12/32 = 9/?

12 ? = 32 * 9

? = 24

Hence the value of ?and x from the given diagram is 12 and 24 respectively

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Answer:

1750

Step-by-step explanation:

The equations are both the same with a slope of 2 and y-intercept of 3.

A line is the distance between two points. Given the equations below;

2y - 4x = 6

y = 2x + 3

___________

y - 2x = 3

y = 2x + 3

The equations are both the same with a slope of 2 and y-intercept of 3. The graph of the equation is plotted below.

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Answer:

Greg will walk 1 mile in 30 minutes, or 2 miles per hour.

Explanation:

Multiply the ratio of miles to minutes:

1/3 mi   :   10 min

1 mi      :    30 min

2 mi     :    1 hr

Answer:

y = 1/2 x -2

Step-by-step explanation:

rise/run from (-6, -5) to (-4, -4) = 1/2

(rise 1, run 2)

meaning that slope (m) = 1/2

we can now rewrite our points in y=mx + b formatting:

y = mx + b

-5 = (1/2)(-6) + b

-4 = (1/2)(-4)+b

now, let's solve for b

-5 = (1/2)(-6) + b

-5 = -3 + b

-2 = b

-4 = (1/2)(-4)+b

-4 = -2 + b

-2 = b

So, the equation for our line is y = [tex]\frac{1}{2}[/tex] x- 2

hope this helps!! have a lovely day :)

Answer: y = 1/2x - 2

Step-by-step explanation: it’s right on khan academy (picture for proof)

Answer:

B- Jenny must have driven more than 48 miles.

Step-by-step explanation:

If Jenny rode for 60 at 48 mph, it would be exactly 48 miles. Though there is only 60 minutes in an hour, and Jenny rode 5 minutes longer than that, her drive being 65 minutes. To find how much she rode, 5 extra minutes into an hour would divide equally into 60, resulting in 12. Divide 48 by 12, and Jenny would have driven 4 miles in the 5 minutes drive after 60 minutes.

(Jenny basically driven 52 miles in 65 minutes).

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Let's define some terms:

Let's find the domain:

   For log(x),

           ⇒ the only inputs that are accepted are nonnegative and nonzero

               ⇒ therefore: Domain is (0, ∞)

Now let's find out the range:

    The biggest constraint of the output is log(x)

         ⇒ however log(x) has a range of (-∞,∞)

             ⇒ therefore the entire equation's range is

                      (-∞,∞)

Answer:

Hope that helps!

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here is your answer

A geometric progression is a sequence that involves a rate, causing a change in the subsequent values of the sequence with respect to the given rate.

The answers to the given question are as follows:

a. It is a geometric progression.

b. Radius of the 6th circle ≅ 23. 73 ft.

c. The total length, l, can be determined by: l = ∑0.75[tex]R_{i}[/tex], i = 1 to n.

Geometric progression involves a change in the subsequent values of a given sequence due to a rate. So considering the given question, the circular iceberg melts at a certain rate per hour. Thus its radius decreases at the given rate per hour.

a. Therefore it can be deduced that the question is on geometric progression.

b. To determine the radius of the 6th circle, the:

radius of the 1st circle = 100 ft

radius of the 2nd circle = 0.75 x 100

                                        = 75 ft

radius of the t3rd circle = 0.75 x 75

                                        = 56.25 ft

radius of the 4th circle = 0.75 x 56.25

                                         = 42.1875 ft

radius of the 5th circle = 0.75 x 42.1875

                                        = 31.640625 ft

radius of the 6th circle = 0.75 x 31.640625

                                      = 23.73046875 ft

Thus the radius of the 6th circle is approximately 23. 73 ft.

c. Since the process is assumed to continue forever, let the number of hours required to be represented by n, and each radius of the iceberg be represented by R.

So then, we can say that the total length, l, of all the circles' radii is will be given by:

              l = ∑0.75[tex]R_{i}[/tex], i = 1 to n

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Answer:

Point-slope form of equation given as [tex]$y-2=-2(x+2)$[/tex].

Slope-intercept form of equation is given as [tex]$y=-2 x-2$[/tex].

Step-by-step explanation:

In the question, it is given that the slope of a line is -2 and it passes from (-2,2).

It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.

To do so, first find the values which are given in the question and put it in the formula of point-slope form. Simplify the equation to rewrite as slope-intercept form.

Step 1 of 2

Passing point of the line is (-2,2).

Hence, [tex]$x_{1}=-2$[/tex] and

[tex]$$y_{1}=2 \text {. }$$[/tex]

Also, the slope of the line is -2.

Hence, m=-2

Substitute the above values in point-slope form of equation given by [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]

[tex]$$\begin{aligned}&y-y_{1}=m\left(x-x_{1}\right) \\&y-2=-2(x-(-2) \\&y-2=-2(x+2)\end{aligned}$$[/tex]

Hence, point-slope form of equation given as y-2=-2(x+2).

Step 2 of 2

Solve y-2=-2(x+2) to write it as slope-intercept form given by y=mx+c.

[tex]$$\begin{aligned}&y-2=-2(x+2) \\&y-2=-2 x-4 \\&y=-2 x-4+2 \\&y=-2 x-2\end{aligned}$$[/tex]

Hence, slope-intercept form of equation is given as y=-2x-2.

Using the circle theorems, we have proven that m ∠RTW = 15°

From the question, we are to prove that m ∠RTW = 15°

In the given diagram,

measure of arc ST = 30°

∴ m ∠SRT = 30°

m ∠SRT = ∠T + ∠W ( Exterior angle of a triangle equals the sum of the two remote angles)

Also,

∠T = ∠W (Radii of the same circle)

∴ m ∠SRT = ∠T + ∠T

m ∠SRT = 2 × ∠T

30° = 2 × ∠T

∠T = 30° /2

∠T = 15°

∴ m ∠RTW = 15°  

Hence, we have proven that m ∠RTW = 15°

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The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

1st.) x = 5 /Sin(30°)

x = 10

!) sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°) = 3√3 / x

x = 3√3 / 3

W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3 = 4√3 / 3

S) Sin(60°) = x / (10/3)

x = 5√3 / 3

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Answer:

See below

Step-by-step explanation:

7 + 15 e^(1-3x) = 10        start by subtracting 7 from both sides

15  e^(1-3x) = 3               now divide both sides by 15

e ^(1-3x) = .2                   now take the ln  of both sides

1-3x = -1.6094379          subtract 1 from both sides

-3x = = 2.6094379         divide both sides by -3

x = .869813

Answer:

Could you please put a picture of the problem?

Step-by-step explanation:

We don't know what you are trying to solve.

Answer:

30

Step-by-step explanation:

[tex]5(3) - 3( - 5)[/tex]

[tex]15 + 15[/tex]

[tex]30[/tex]

hope it was helpful. any confusion u may ask

Step-by-step explanation:

The answer is 30 the value of X and y is given that put them in 5x-3y

Answer:

SHould be 11.6 degrees

The total packages the driver delivered is  805.

The total number of books in the local library is  14,260.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

Total packages delivered = total number of internet orders / percentage of internet orders

644 / 80%

644 / 0.8 = 805

Total number of books = total number of fiction books / percentage of fiction books

8556 / 60%

8556 / 0.6 = 14,260

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Answer: 81/100



Step-by-step explanation:

I don't guarantee you I am right but..

first, solve for the exponents after substituting the numbers in

3/5 x 3/5 is 9/25

since b's exponent is negative, you change the fraction into its reciprocal and then do it with the exponent but positive

2/3^-3 to 3/2^3 and 3/2 x 3/2 is 9/4

then you mutiply both numbers to get 9/4 x 9/25 is 81/100

[tex] \frac{p {}^{2} + 1 - 3p }{4 - 3} = -1[/tex]

[tex]p {}^{2} - 3p + 1 = -1[/tex]

[tex]p {}^{2} - 3p +2 = 0[/tex]

[tex](p-2)(p - 1) = 0[/tex]

[tex]p = 2 \: \: \: \: \: p = 1[/tex]

Step-by-step explanation:

7×5×6×x

7×5×6×392

210×392

82320

The option (B) is correct. Associative property was applied to create the given expression.

Given expression is 7x+(5+6x) rightarrow (7x+5)+6x.

Firstly, check the given expression by commutative property.

The commutative property of addition is a+b=b+a and the commutative property of multiplication is a×b=b×a.

The commutative property didn't satisfy the given expression.

Now, check the given expression by associative property.

The associative property of addition is (a+b)+c=a+(b+c) and the commutative property of multiplication is (a×b)×c=a×(b×c).

The associative property of addition satisfy the given expression.

Further, check the given expression by distributive property.

The distributive property is a×(b+c)=ab+bc.

The distributive property didn't satisfy the given expression.

Hence, the given expression 7x+(5+6x) rightarrow (7x+5)+5x s created by the associative property.

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Answer:

c.) y = -3x - 2

Explanation:

Given following:

Equation:

[tex]\sf y - y_1 = m(x - x_1)[/tex]

[tex]\sf y - 10 = -3(x - (-4))[/tex]

[tex]\sf y - 10 = -3(x + 4)[/tex]

[tex]\sf y = -3x -12 + 10[/tex]

[tex]\sf y = -3x -2[/tex]