Rationalize the denominator.

10/√24x

write it in simplest form

Answer:

9.2

Step-by-step explanation:

We are given that a figure in which a tangent and a secant to the circle.

We have to find the value of x.

Length of tangent segment=x

Length of secant segment=12 +5=17 units

Length of external segment=5 units

We know that secant-tangent theorem

It states that product of length of secant segment and its external segment is equal to square of length of tangent segment.

[tex]x^2=17\times 5=85 [/tex]

[tex]x=\sqrt{85}=9.2 units[/tex]

Hence, the value of x=9.2

500= (19.50-8.00)x

500 = 11.50x

x=500/11.50=43.48

 so he needs to sell approximately 44 centerpieces to break even

Answer:

answer is D ;)

Step-by-step explanation:

The equation of the sphere with center (-3, 2, 9) and radius 6 is (x + 3)² + (y - 2)² + (z - 9)² = 6². The intersection of this sphere with the yz-plane is described by the equation (y - 2)² + (z - 9)² = 27.

The equation of a sphere with center (-3, 2, 9) and radius 6 is given by:

(x + 3)² + (y - 2)²+ (z - 9)² = 6²

To find the intersection of this sphere with the yz-plane, we need to set x = 0 in the equation:

(0 + 3)² + (y - 2)² + (z - 9)² = 6²

Simplifying this equation gives:

(y - 2)² + (z - 9)² = 27

So, the intersection of the sphere with the yz-plane is described by the equation (y - 2)² + (z - 9)² = 27.

I think it is C

BMK ><

Answer:

c)720

Step-by-step explanation:

The mean of a set of credit scores is u=690 and o=14.

mean = 690  and standard deviation SD = 14

We use z- score formula

[tex]z=\frac{x-mean}{SD}[/tex]

z= 3.3 given

Plug in the values and find out x

[tex]3.3=\frac{x-690}{14}[/tex]

Multiply 14 on both sides

46.2 = x- 690

Now add 690 on both sides

x= 736.2

Credit score is 720 that comes under 736.2

So answer is 720

Answer:

B. 0.813

Step-by-step explanation:

A sixteen-sided number cube has the numbers 1 through 16 on each face.

So, [tex]|\ S\ |=16[/tex]

Let us assume that, A be the event that the number will be an even number. So,

[tex]A=\left \{ 2,4,6,8,10,12,14,16 \right \}[/tex] and [tex]|\ A\ |=8[/tex]

Then,

[tex]P(A)=\dfrac{|\ A\ |}{|\ S\ |}=\dfrac{8}{16}[/tex]

Let us assume that, B be the event that the number will be an odd prime number.

[tex]B=\left \{3,5,7,11,13 \right \}[/tex] and [tex]|\ B\ |=5[/tex]

Then,

[tex]P(B)=\dfrac{|\ B\ |}{|\ S\ |}=\dfrac{5}{16}[/tex]

So the probability that you will roll an even number or an odd prime number will be,

[tex]P(A\cup B)=P(A)+P(B)-P(A\cup B)[/tex]

[tex]=\dfrac{8}{16}+\dfrac{5}{16}-0[/tex] ( as independent events)

[tex]=\dfrac{13}{16}[/tex]

[tex]=0.813[/tex]

The first step to solve for x in the given algebra using properties of equality is; Add 5 to both sides.

We want to simplify the algebraic expression;

3.7 = x + (-5)

When dealing with algebra like this, what we have to first do is to balance both sides of the equation.

To solve this particular algebra problem, we will use additional property of equality by adding 5 to both sides to get;

3.7 + 5 = x + (-5) + 5

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The first step to solving the expression 3.7 = x + (- 5) is,

''Add 5 to both sides''

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to give that,

An algebraic expression to simplify,

⇒ 3.7 = x + (- 5)

Now, Simplify the expression by combining like terms as,

⇒ 3.7 = x + (- 5)

⇒ 3.7 = x - 5

Use the additional property of equality by adding 5 to both sides to get;

3.7 + 5 = x + (-5) + 5

8.7 = x

x = 8.7

So, the first step is, ''Add 5 to both sides''.

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The answer is 5 units on e2020.

To find the rate of change of height with respect to time, we use the formula dh/dt = dV/dt / (πr²) and substitute the given values for the rate of volume change and the radius.

We have the rate of volume change as 23 cm³/sec and the cylinder has a radius of 12 cm. Note that the typo '2323 cm³/sec' and '1212 cm' should be read as '23 cm³/sec' and '12 cm,' respectively.

The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. To find the rate at which the height h changes over time, we can take the derivative of the volume with respect to time, which gives us dV/dt = πr² dh/dt. We can solve this equation for dh/dt (the rate of change of height with respect to time) by dividing both sides by πr² and substituting the given values. Therefore, dh/dt = dV/dt / (πr²).

Substituting the values, we get:

dh/dt = 23 cm³/sec / (π * (12 cm)²)

Upon simplifying, we will obtain the rate at which the height of the water is decreasing in cm/sec.

c:

 to find x multiply the side (24) by the tangent of the angle(13)

 so 24 * tan(13) = 5.5408

D:

 to find x

 divide the side (10) by the sin of the angle (20)

10/sin(20) = 29.238

 Round the answers as needed.

Using the trigonometric tangential function, the height of the tree casting a 26-meter shadow at an angle of elevation of 24° is approximately 11 meters.

The given problem can be solved by applying trigonometric principles, specifically the tangent function. In this case, we know the shadow length (26m) and the angle of elevation of the sun (24°). The height of the tree is the side opposite the angle, and the shadow is the adjacent side. Thus, we can use the tangent equation (Tan θ = Opposite/Adjacent). So, Tan 24° = Height of the tree / 26m. By cross multiplying and evaluating Tan 24°, we get the height of the tree to be approximately 11 meters.

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Answer:

B

Step-by-step explanation:

Step 2 he wrote distributive instead of associative

Rounded to the nearest meter, the height of the plane is approximately 405 meters.

So, the correct answer is B. 405 m.

To find the height of the plane, we can use trigonometry, specifically the tangent function.

Let's denote the height of the plane as h (in meters).

From the information given, we know that the angle of depression from the airplane to the atoll is 5 degrees, and the horizontal distance from the airplane to the atoll is 4629 meters.

Using the tangent function, we have:

tan(angle of depression) = height / horizontal distance

tan(5 degrees) = h / 4629

To find the value of h, we can rearrange the equation:

h = 4629 * tan(5 degrees)

Now, let's calculate the height of the plane:

h ≈ 4629 * 0.0874886635 ≈ 404.773 meters

Rounded to the nearest meter, the height of the plane is approximately 405 meters.

So, the correct answer is B. 405 m.

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To find the length of the new roofline, we can use the tangent function. The length is approximately 26.9 feet.

To find the length of the new roofline, we can use the trigonometric function tangent. Let's call the length of the new roofline 'x'. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the roofline, which is 32 feet, and the adjacent side is the horizontal distance, which is 'x' feet. So, we can set up the equation:

tan(50°) = 32/x

To solve for 'x', we can multiply both sides of the equation by 'x' and then divide both sides by tan(50°). This gives us:

x = 32/tan(50°)

Using a calculator, we can find that tan(50°) ≈ 1.1917. So, substituting this value into the equation, we get:

x ≈ 32/1.1917

By calculating this, we find that the length of the new roofline is approximately 26.9 feet.