Multiply x^2-8x+15/3x * 8x/x-3

The rate at which the angle between the sides of the triangle is changing is 4/9 radians per second.

In this problem, we are given that one side of the triangle is increasing at a rate of 9 cm/s and a second side is decreasing at a rate of 2 cm/s. We need to find the rate at which the angle between the sides is changing.

To solve this, we can use the formula:

angle_rate = (-side2_rate/side1)*(cos(angle))/(sin(angle))

Substituting the given values:

angle_rate = (-(-2)/9)*(cos(π/6))/(sin(π/6))

Simplifying, we get:

angle_rate = 4/9

Therefore, the rate at which the angle between the sides is changing is 4/9 radians per second.

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Subtract p² - 4p from p² + p - 6 to get 5p - 6. To obtain p - 9, subtract 15 from 5p - 6.

Let's break it down step by step:

1. Subtracting p² - 4p from p² + p - 6:

  Start by writing down the expression p² + p - 6.

  Now, subtract p² - 4p from it term by term.

  (p² + p - 6) - (p² - 4p)

2. Expand and Simplify:

  Distribute the subtraction across each term inside the parentheses:

  p² + p - 6 - p² + 4p

  This simplifies to: (p² - p²) + (p + 4p) - 6

  = 0 + 5p - 6

  = 5p - 6

3. Now, to get p - 9:

  We want to manipulate 5p - 6 to p - 9.

  Subtracting 15 from 5p - 6 gives:

  5p - 6 - 15

  = 5p - 21

Therefore, subtracting 5p - 21 from 5p - 6 results in p - 9.

Final answer:

Tran must calculate the surface area of the hemisphere, including the base, to determine the amount of paint needed, which is the sum of half the surface area of the sphere and the area of the base.

Explanation:

The question is asking what Tran would compute when using π to determine the amount of paint required for a hemisphere. First, Tran needs to calculate the surface area of the sphere to determine the paint needed. Given the circumference C = 18.84 cm, the radius r can be found using C = 2πr, which gives us a radius of r = C / (2π). Once we have the radius, we can find the surface area A of the sphere using A = 4πr², which is necessary to determine the paint needed for the outer surface.

However, when the sphere is cut into two hemispheres, the flat face of each hemisphere (base) also needs paint. The area of the base is a circle with an area of πr². Thus, the total surface area that Tran would need to paint for one hemisphere, including the base, is πr² + 2πr² (half of the sphere's surface area).

Final answer:

Option  D.) Tran found the minimum amount of paint needed to cover both hemispheres.

Explanation:

Tran found the minimum amount of paint needed to cover both hemispheres. To calculate the amount of paint needed to cover a hemisphere, we need to find the surface area of the hemisphere. The formula for the surface area of a sphere is 4πr², where r is the radius.

Given that the circumference of the sphere is 18.84 centimeters, we can use the formula C = 2πr to solve for the radius. Plugging in the value for C, we get 18.84 = 2πr.

Simplifying the equation, we find that the radius of the sphere is approximately 3 centimeters.

The surface area of a hemisphere is half the surface area of a sphere, so the surface area of one hemisphere is 2πr²/2 = πr².

Substituting the value of r, we find that the surface area of one hemisphere is approximately 9π square centimeters.

Since Tran cut the sphere in half and created two identical hemispheres, the minimum amount of paint needed to cover both hemispheres would be twice the surface area of one hemisphere, which is approximately 18π square centimeters.

The values of x that satisfy the absolute value equation |x – 3| = 40 are 43 and -37. These are derived from solving the two possible scenarios for absolute value equations, resulting in a positive and a negative solution.

To find which values of x will make the absolute value equation |x – 3| = 40 true, we need to consider both the positive and negative scenarios that can result from the absolute value. The absolute value of a number equals the number itself if it is positive or zero, and it equals the negative of the number if it is negative.

So, we set up two equations:

Solving the first equation for x, we add 3 to both sides:

x = 40 + 3

x = 43

Solving the second equation for x, we add 3 to both sides:

x = -40 + 3

x = -37

Therefore, the values of x that will satisfy the equation are 43 and -37. Option D is the correct answer.

Final answer:

The values of x that make the absolute value equation true are 43 and -37.

Explanation:

To solve the equation |x-3| = 40, we need to consider two cases:

1. x-3 = 40: In this case, we add 3 to both sides to isolate x and get x = 43.

2. -(x-3) = 40: In this case, we distribute the negative sign and add 3 to both sides to isolate x, which gives x = -37.

Therefore, the values of x that make the absolute value equation true are {43, -37}.

The result of 4,816.40625 cubic inches is rounded to 4,816 cubic inches to the nearest cubic inch.

To find the volume of Miguel's aquarium, which is in the shape of a rectangular prism, we use the formula for the volume of a rectangular prism:

Volume = length * width *  height

In this case, the length is 30.25 inches, the width is 12.5 inches, and the height is 12.75 inches.

So, the calculation for the volume would be:

Volume = 30.25 inches * 12.5 inches * 12.75 inches
= 4,816.40625 cubic inches.

Rounding to the nearest cubic inch, the volume of the aquarium is 4,816 cubic inches.

The number of  gallons of fuel Roselyn need for her journey is:

                      D.   5 gallons

It is given that:

Roselyn wants to drive her car at a speed of 60 miles per hour for 1.25 hours.

This means that the total distance she covers in 1.25 hours is:

[tex]60\times 1.25=75\ \text{miles}[/tex]

( Since, we know that speed is defined as the ratio of distance to time.

i.e.

[tex]Speed=\dfrac{Distance}{Time}\\\\i.e.\\\\Distance=Speed\times Time[/tex] )

Also, Her car has a fuel efficiency of 15 miles per gallon.

i.e.

She could cover 15 miles with 1 gallon of fuel.

Hence, in order to cover 75 miles.

i.e. to cover (15×5) miles she needs (1×5) gallons of fuel

i.e. she needs 5 gallons of fuel to cover 75 miles.

Answer:  7.1 inches

Step-by-step explanation:

Given: One leg of isosceles right triangle = 5 inches

Since in isosceles right triangle , two sides have same side length , therefore the length of the other leg should be 5 inches.

Let H be the hypotenuse of the isosceles right triangle

Now, by Pythagoras Theorem , we have

[tex]H^2=5^2+5^2=25+25=50\\\\\Rightarrow\ H=\sqrt{50}=5\sqrt{2}\\\\\Rightarrow\ H==5\times(1.41421356237)\\\\\Rightarrow\ H==7.07106781187\approx7.1\ inches[/tex]

Hence, the approximate length of the hypotenuse = 7.1 inches

Answer: C

Step-by-step explanation: 7.1 inches

Answer:

The measure of DE is 108°. What is the measure of ZDEF, the tangent-chord angle?

54

Step-by-step explanation:

Final answer:

To solve the problem, a system of equations is set up with the second number as 'x' and the first as 'x + 124.' The equations are simplified to find 'x = 106,' which makes the first number '230.' The two numbers are 106 and 230.

Explanation:

To find the two numbers that add to 336 and where the first number is 124 larger than the second, we need to set up a system of equations based on the information given:

Let the second number be x.

Then the first number will be x + 124 since it is 124 bigger than the second.

The sum of the two numbers is 336, so we can write the equation x + (x + 124) = 336.

Simplifying this equation, we get 2x + 124 = 336.

Subtract 124 from both sides to isolate the term with x, yielding 2x = 212.

Divide both sides by 2 to find x, which gives x = 106.

Since the first number is 124 larger, we add 124 to 106, resulting in the first number being 230.

Therefore, the two numbers are 106 and 230.

Using function concepts, it is found that the correct option is:

d. domain: x > 3; range: y > 0; Yes, it is a function.

A relation is a function if for each value of the input, there is only one respective value of the output. In a graph, it means that for each value of x, there is only one respective value of y.

The domain of a function is the set that contains all possible input values. In a graph, it is the values assumed by x, the horizontal axis.

The range of a function is the set that contains all possible output values. In a graph, it is the values assumed by y, the vertical axis.

A similar problem is given at https://brainly.com/question/10891721

Answer:

The value of x is 6  

Step-by-step explanation:

Given the figure in which

DE=3x-8 and BC=20

we have to find the value of x.

By mid-point theorem which states that the line segment which is drawn to the mid-points of two sides of triangle is parallel to the third side and also half of the length of third side.

[tex]DE=\frac{1}{2}BC[/tex]

[tex](3x-8)=\frac{1}{2}\times 20[/tex]

[tex]3x-8=10[/tex]

[tex]3x=18[/tex]

[tex]x=\frac{18}{3}=6[/tex]

The value of x is 6

Option 2 is correct.

For future reference, Scapazzi was correct.

The arc length will be given as the circumference of the circle is 150.56 inches long.

It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

In a circle with a radius of 27 + 2/5 inches.

That can be written as 27.4.

An arc is intercepted by a central angle of 7π/4 radians.

The arc length will be given as the circumference of the circle

[tex]\rm Arc \ length = \dfrac{\theta}{2\pi} 2 \pi*r\\\\Arc \ length = \theta * r\\\\Arc \ length = \dfrac{7 \pi }{4} * 27.4 \\\\Arc \ length = 150.56[/tex]

Thus, the arc length will be given as the circumference of the circle is 150.56 inches.

More about the circle link is given below.

https://brainly.com/question/11833983

Answer : The measurement of a central angle is, [tex]140^o[/tex]

Step-by-step explanation :

Formula used for angle subtended by an arc is:

[tex]s=\frac{\pi r\theta}{180}[/tex]

where,

s = arc length = [tex]\frac{7}{3}\pi m[/tex]

r = radius = [tex]\frac{diameter}{2}=\frac{6m}{2}=3m[/tex]

Now put all the given values in the above formula, we get:

[tex]s=\frac{\pi r\theta}{180}[/tex]

[tex]\frac{7}{3}\pi=\frac{\pi \times (3)\times \theta}{180}[/tex]

[tex]\theta =140^o[/tex]

Thus, the measurement of a central angle is, [tex]140^o[/tex]

Answer:

6% of a pound does not weigh more than 1 ounce.

Step-by-step explanation:

First, we will calculate 6% (0.06) of 1 pound.

0.06 × 1 lb = 0.06 lb

1 pound is equal to 16 ounces. 0.06 pounds, expressed in ounces is:

0.06 lb × (16 oz/ 1 lb) = 0.96 oz

6% of a pound = 0.96 oz

0.96 oz < 1 oz

Due to the transitive property, we can affirm that 6% of a pound does not weigh more than 1 ounce.