Find the length of x?

The difference between the outside perimeter of the walkway and the perimeter of the pool in algebraic expression is (2x + 14).

Pool:

Length = 2x - 1

Width = 12

The perimeter of the pool = 2(length + width)

= 2{(2x - 1) + 12}

= 2(2x - 1 + 12)

= 2(2x + 11)

= 4x + 22

Outside perimeter of the walkway:

Length = (2x - 1) + x

= 3x - 1

Width = 12 + 7

= 19

The perimeter of the walkway = 2(length + width)

= 2{(3x - 1) + 19}

= 2(3x - 1 + 19

= 2(3x + 18)

= 6x + 36

Difference between the outside perimeter of the walkway and the perimeter of the pool = The perimeter of the walkway - The perimeter of the pool

= (6x + 36) - (4x + 22)

= 6x + 36 - 4x - 22

= 2x + 14

Hence, (2x + 14) is the expression which represents the difference between the perimeter of the walkway and the perimeter of the pool.

Read more on perimeter:

https://brainly.com/question/24571594

#SPJ3

Solution: (1) The expression [tex](5\sqrt{3} )^x[/tex]  [tex]\text{ is written as }[/tex] [tex]5^x3^{\frac{x}{2}[/tex].

[tex](5\sqrt{3} )^x=5^x(\sqrt{3} )^x\\(5\sqrt{3} )^x=5^x(3^\frac{1}{2} )^x\\(5\sqrt{3} )^x=5^x3^\frac{x}{2}[/tex]

The value of u is [tex]\frac{x}{2}[/tex].

(2) The expression [tex](\frac{1}{2})^x-3[/tex] is written as [tex]2^{-x}-3[/tex].

[tex](\frac{1}{2})^x-3=(2^{-1})^x-3\\(\frac{1}{2})^x-3=2^{-x}-3[/tex]

The value of u is -x.

(3) The expression [tex]\frac{9}{3\sqrt{3} }[/tex] is written as [tex]\sqrt{3} (2^0)[/tex].

[tex]\frac{9}{3\sqrt{3} }=\frac{9}{3\sqrt{3} }(\frac{\sqrt{3}}{\sqrt{3}} )\\\frac{9}{3\sqrt{3} }=\frac{9(\sqrt{3}) }{3(3) }\\\frac{9}{3\sqrt{3} }=\sqrt{3} \\\frac{9}{3\sqrt{3} }=\sqrt{3}(2^0)[/tex]

THe value of u is 0.

(4)The expression [tex]\frac{16}{3(\sqrt{2^{x}} )}[/tex] is written as [tex]\frac{1}{3}(2^{4-\frac{x}{2}})[/tex].

[tex]\frac{16}{3(\sqrt{2^{x}} )}=\frac{2^4}{3(2^x)^{1/2}}\\\frac{16}{3(\sqrt{2^{x}} )}=\frac{1}{3}(2^{4-\frac{x}{2}})[/tex]

The value of u is [tex]4-\frac{x}{2}[/tex].

Final Answer:

1. [tex]\( (5\sqrt{3})^x \) in the form \( 3^u \): \( 3^{x\log_3(5\sqrt{3})} \)[/tex]

2. [tex]\( (1/2)^{x-3} \) in the form \( 2^u \): \( 2^{-(x-3)} \)[/tex]

3. [tex]\( \frac{9}{3\sqrt{3}} \) in the form \( 2^u \): \( 2^{2/3} \)[/tex]

4. [tex]\( \frac{16}{3\sqrt{2^x}} \) in the form \( 2^u \): \( 2^{(2x-4)/3} \)[/tex]

Explanation:

1. [tex]\( (5\sqrt{3})^x \) in the form \( 3^u \): \( 3^{x\log_3(5\sqrt{3})} \)[/tex]

To express [tex]\( (5\sqrt{3})^x \)[/tex] in the form [tex]\( 3^u \)[/tex], we use the logarithmic property [tex]\( a^{\frac{1}{n}} = n\sqrt[n]{a} \)[/tex]. Applying this, we get [tex]\( 5\sqrt{3} = 3^{\frac{\log_3(5\sqrt{3})}{\log_3(3)}} \)[/tex], and raising it to the power ( x ) yields the desired form.

2. [tex]\( (1/2)^{x-3} \) in the form \( 2^u \): \( 2^{-(x-3)} \)[/tex]

To rewrite [tex]\( (1/2)^{x-3} \)[/tex] in the form [tex]\( 2^u \)[/tex], we use the property [tex]\( a^{-b} = \frac{1}{a^b} \)[/tex]. Applying this, we transform the expression to [tex]\( 2^{-(x-3)} \)[/tex], achieving the desired form.

3. [tex]\( \frac{9}{3\sqrt{3}} \) in the form \( 2^u \): \( 2^{2/3} \)[/tex]

By canceling out the common factor of 3 in the numerator and denominator, we simplify [tex]\( \frac{9}{3\sqrt{3}} \)[/tex]to [tex]\( 2^{2/3} \), as \( \sqrt{3} = 3^{1/2} \)[/tex].

4. [tex]\( \frac{16}{3\sqrt{2^x}} \)[/tex] in the form [tex]\( 2^u \): \( 2^{(2x-4)/3} \)[/tex]

Applying the property[tex]\( a^{-b} = \frac{1}{a^b} \)[/tex] to the denominator, we simplify [tex]\( \frac{16}{3\sqrt{2^x}}[/tex] to [tex]\( 2^{(2x-4)/3} \)[/tex], achieving the desired form.

The original number of spokes on the wheel was 36.

The question seeks to determine the original number of spokes on a bicycle wheel, given that the current number is 32 after reducing by 4. To find the original number of spokes, we need to use a simple algebraic equation that adds the removed spokes back to the current number.

Let x represent the original number of spokes. The manufacturer has reduced the number of spokes by 4, so we subtract 4 from the original number to get the current number of spokes. The equation that represents this scenario is:

x - 4 = 32

To find the original number of spokes, we need to solve for x:

x = 32 + 4

x = 36

Therefore, the original number of spokes on the wheel was 36.

Answer:

The length of EF is [tex]4\sqrt{17}[/tex] units.

Step-by-step explanation:

The vertices of triangle ABC are A(2,3), B(–1,2), and C(3,1).

Using distance formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]BC=\sqrt{(3+1)^2+(1-2)^2}=\sqrt{17}[/tex]

It is given that ΔDEF ∼ ΔABC.

If two triangles are similar then the corresponding sides are proportional.

[tex]\frac{AB}{DE}=\frac{BC}{EF}[/tex]

[tex]\frac{AB}{4AB}=\frac{BC}{EF}[/tex]        (DE = 4AB)

[tex]\frac{1}{4}=\frac{BC}{EF}[/tex]

[tex]EF=4\times BC[/tex]

[tex]EF=4\times \sqrt{17}[/tex]

[tex]EF=4\sqrt{17}[/tex]

Therefore the length of EF is [tex]4\sqrt{17}[/tex] units.

The length of the base of the isosceles triangle is 18 inches.

Let the length of the base be 'b' inches. According to the given information, each of the congruent sides of the isosceles triangle is 8 inches less than twice the base. So, the length of each congruent side is (2b - 8) inches.

The perimeter of the triangle is the sum of all three sides, which is given as 74 inches. So, we can write the equation:

(2b - 8) + (2b - 8) + b = 74

Simplifying the equation, we get:

5b - 16 = 74

5b = 90

b = 18

Therefore, the length of the base is 18 inches.

https://brainly.com/question/9183298

#SPJ11

Answer:

The answer is a. the real answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's model the cost by the following exponential function: c (t) = (7.50) * (1.035) ^ t Where, c (t): cost of the movie after t years. 7.50: initial cost of the movie in $ 1,035: annual percentage increase due to inflation. t: time in years. for t = 0 We have: c (t) = (7.50) * (1.035) ^ 0 c (t) = (7.50) * (1) c (t) = 7.50 Answer: The graph that best models the function is: GRAPH 2 (from left to right).

Answer:

The above one is partly correct the answer (for odyssey ware) is                        (-(1)/(2)x+2y)(-2)

-(1)/(2) (-2 x + 8 y)

and 3( x - 2 y) + 2( y - x)

Hope this helps people in the future ☜(ﾟヮﾟ☜)

Step-by-step explanation:

Answer:

The model that is most appropriate for the set is:

                Quadratic.

Step-by-step explanation:

Clearly after looking at the graph of the function which is made from the given set of points ; we observe that the graph is similar to a graph of the quadratic function whose vertex is at (0,-2) and also the line x=0 is the axis of symmetry of the graph.

Since, the graph is symmetric to this line.

Hence, the model is:

Quadratic.

Answer:

Step-by-step explanation:

The answer is fifteen

Explanation:  6-3/0.4-0.2=3 over 0.2 which is equivalent to 15

Answer B: 15

Step-by-step explanation:

Answer:

2.5 :)

Step-by-step explanation: