For $360, a rock-climbing gym offers a yearly membership where members can climb as many days as they want and pay $4 per day for equipment rental. Nonmembers pay $10 per day to use the gym and $6 per day for equipment rental. Find the total number of visits when the cost for a member and nonmember will be the same.

The value of X  are x = 3 and x = -3. using square root.

A square root can be regarded as a factor of a number in the sense that when that number is multiplied by itself, it gives the original number.

3x²– 27 = 0

⇒3x²= 27

⇒x²= 27/3

⇒x² = 9

⇒x = sqrt(9)

⇒ x =±3

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Answer:

896 cm^3

Step-by-step explanation:

formula for the triangle prism is

V= 1/3 Bh

V = 1/3 (8 x 3) (8)  The base is 8 seen the base of the rectangel prism is 8 to its consider as base to.

V= 1/3 (24 x 8)

V= 1/3 (192)

V = 64

Now we need to find the volume so the rectangle formula is

V= lwh

V= (13x 8) (8)

V= 832cm

Add your two answers and u get

832 + 64 = 896 cm^3

The solution is :  896 cm^3 is the volume of the composite figure.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

Here, we have,

Volume formula for the triangle prism is

V= 1/3 Bh

V = 1/3 (8 x 3) (8)  

The base is 8 seen the base of the rectangle prism is 8 to its consider as base to.

V= 1/3 (24 x 8)

V= 1/3 (192)

V = 64

Now we need to find the volume so the rectangle formula is

V= lwh

V= (13x 8) (8)

V= 832cm

Add your two answers and u get

832 + 64 = 896 cm^3

Hence, The solution is :  896 cm^3 is the volume of the composite figure.

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Answer: [tex]243.3\ mm^2[/tex]

Step-by-step explanation:

Given: The diameter of smaller circle = 13.2 mm

Then the radius of smaller circle r =[tex]\frac{13.2}{2}=6.6\ mm[/tex]

Also, the radius of larger circle R= [tex]6.6+4.4=11.0\ mm[/tex]

Now, the area of the washer is given by :-

[tex]\text{Area of washer=Area of larger circle-Area of smaller circle}\\\\\Rightarrow\\text{Area of washer}=\pi R^2-\p r^2\\\\\Rightarrow\\text{Area of washer}=\pi(R^2-r^2)\\\\\Rightarrow\\text{Area of washer}=(3.14159265359)((11.0)^2-(6.6)^2)\\\\\Rightarrow\\text{Area of washer}=243.284935094\approx243.3\ mm^2[/tex]

The area of the washer is 0 mm2.

To find the area of the washer, we first need to find the area of the larger circle and the area of the smaller circle. The formula for the area of a circle is A = πr^2.

The larger circle has a diameter of 13.2 mm, so the radius is half of that, which is 6.6 mm. Plugging this value into the formula, the area of the larger circle is approximately 136.78 mm2.

The smaller circle has a diameter of 13.2 mm, so the radius is again 6.6 mm. Using the same formula, the area of the smaller circle is also approximately 136.78 mm2.

To find the area of the washer, we subtract the area of the smaller circle from the area of the larger circle: 136.78 mm2 - 136.78 mm2 = 0 mm2. Rounded to the nearest tenth, the area of the washer is 0 mm2.

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Answer:

C

Step-by-step explanation:

The formula is S=a1/1-r

The series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a series shown in the picture.

The geometric sequence is shown in the options.

As we know, in the geometric sequence there is a first term and common difference

In the first sequence:

First term a = 2

Common difference = 2(0.1)/2

Common difference d = 0.1

The sum of the infinite series is:

S = a/(1 - r)

S = 2/(1 - 0.1)

S = 2.22

In the second sequence:

First term a = 15

Common difference = 15(0.3)/15

Common difference d = 0.3

The sum of the infinite series is:

S = a/(1 - r)

S = 15/(1 - 0.3)

S = 21.42

In the third sequence:

First term a = 4

Common difference = 4(0.2)/4

Common difference d = 0.2

The sum of the infinite series is:

S = a/(1 - r)

S = 4/(1 - 0.2)

S = 5

Thus, the series third has a sum of 5 option (C) is correct because the sequence represents the sum of the infinite terms.

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The solution of the  equation 3x-3= -18 is  -5.

The  algebraic expressions which are separated by an equal symbol  in between them and with the same value is called is an equation

Example = 5x + 5 = 12

here, x is a variable and 5 and 12 are constants.

Given equation;

3x-3= -18

To find the value of x add 3 to both side, we get

3x = -18 +3

we get

3x = -15

divide both side by 3 we get

[tex]x = \dfrac{-15}{3}[/tex]

Convert in into the lowest form we get,

x = -5

The solution of the  equation 3x-3= -18 is  -5

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The correct answer is D (x - 5)(x - 2)

You can tell this because in the picture, we are looking for all of the cross sections to multiply to their appropriate boxes. In the bottom right corner, we see the number 10. This means that the bottom number and the right number must multiply to 10. This only happens in A and D, whereas in B and C those equal -10.

To determine between A and D, you must find the ones that have negatives, since the two x values are both negatives. D is the only one with negative numbers out of the ones we are left working with. Therefore, D is the correct answer.

Answer:

its C i just did that question

Step-by-step explanation:

The population of a major U.S. city = 8,550,405

Area of the city = 1213.4 sq.km

Density = [tex] \frac{Population}{area} [/tex]

Density = [tex] \frac{8,550,405}{1213.4} [/tex]

Density = 7046.6499 [tex] \frac{People}{km^{2}} [/tex]

As the density here will not be in decimal so after rounding the density in whole number,

Density = 7047 [tex] \frac{People}{km^{2}} [/tex]

Option A is the answer

Final answer:

To complete the square for the equation x^2-14x+33=0, the constant 33 is moved to the other side, and the number needed to make the left side a perfect square trinomial, 49, is added to both sides, resulting in factoring and solving (x - 7)^2 = 16 to find x = 11 and x = 3.

Explanation:

To complete the square for the equation x^2-14x+33=0, you need to form a perfect square trinomial on the left side of the equation. First, you'll move the constant term to the right side:

x^2 - 14x = -33

Next, find the value that completes the square for the x-terms. This value is obtained by taking half of the coefficient of x (which is -14 in this case) and squaring it, giving us (-7)^2 = 49.

Add 49 to both sides of the equation:

x^2 - 14x + 49 = -33 + 49

x^2 - 14x + 49 = 16

Now, the left side of the equation is a perfect square trinomial, and can be factored into:

(x - 7)^2 = 16

To solve for x, take the square root of both sides:

x - 7 = [tex]\sqrt{16}[/tex]

x - 7 = +- 4

Finally, solve for x by adding 7 to both sides:

x = 7 +- 4

x = 11 or x = 3

Answer:

The length of BC is 11√2 ft.

Step-by-step explanation:

Given,

A right angled triangle ABC,

In which,

AC = 11 ft ( By diagram ),

∠A = 90°,

∠B = 45°,

By the law of sine,

[tex]\frac{sin B}{AC}=\frac{sin A}{BC}[/tex]

[tex]\implies BC\times sin B = AC\times sin A[/tex]   ( By cross multiplication )

[tex]\implies BC = \frac{AC\times sin A}{sin B}[/tex]

By substituting the values,

[tex]BC=\frac{11\times sin 90^{\circ}}{sin 45^{\circ}}[/tex]

[tex]=\frac{11}{\frac{1}{\sqrt{2}}}[/tex]

[tex]=11\sqrt{2}[/tex]

Hence, the length of BC is 11√2 ft.

Hello!

I believe the answer is A) p(x) = 13x -20.

I hope it helps!

Answer:

[tex]10\frac{1}{2}\text{ pounds}[/tex]

Step-by-step explanation:

Given,

For a recipe,

Cindy needs tomatoes = [tex]4\frac{3}{4}[/tex] pounds,

While, Giovanni needs tomatoes = [tex]5\frac{3}{4}[/tex] pounds,

If they make both recipes,

Then, total tomatoes they need = [tex]4\frac{3}{4}+5\frac{3}{4}[/tex]

[tex]=\frac{19}{4}+\frac{23}{4}[/tex]

[tex]=\frac{42}{4}[/tex]

[tex]=10\frac{2}{4}[/tex]

[tex]=10\frac{1}{2}\text{ pounds}[/tex]

Answer: A.

Step-by-step explanation:

The product of equation is 18x² - 45x.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given equation -9x(5 - 2x)

product  = -9x(5) - (-9x)(2x)

= -45x + 18x²

= 18x² - 45x

Hence the product is 18x² - 45x.

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Answer:

the answer is 64%

Step-by-step explanation:

Answer:

D) 2.37 seconds

Step-by-step explanation:

Took the test and got it wrong.