5.
Solve the equation.
(4x+10)^1/4 = (9+7x)^1/4

We have proved that the in radius of a right triangle with legs a and b and hypotenuse c is equal to a/(2+sqrt(a^2+b^2)).

Let ABC be a right triangle with legs a and b and hypotenuse c, and let r be the radius of the inscribed circle. Draw the perpendicular from the center of the inscribed circle to the hypotenuse c, and let the length of this segment be h. Then we have:

r = (a + b - c)/2 (since the inradius is half the perimeter minus the semiperimeter)

h = (a*b)/c (since the area of the triangle is (1/2)ab and also (1/2)ch)

Using the Pythagorean theorem, we have:

a^2 + b^2 = c^2

Multiplying both sides by r and substituting for r and h, we get:

r(a^2 + b^2) = rc^2

r(a + b - c)(a + b + c) = 2ab

r = 2a*b/(a + b + c)(a + b - c)

Substituting the expressions for a, b, and c in terms of sin and cos, we get:

r = 2sin(theta)cos(theta)/(2cos(theta) + 2sin(theta))(2cos(theta) - 2sin(theta))

r = sin(theta)*cos(theta)/(cos(theta) - sin(theta))^2

Simplifying using the identity (cos(theta) - sin(theta))^2 = cos^2(theta) - 2*cos(theta)sin(theta) + sin^2(theta) = 1 - sin(2theta), we get:

r = sin(theta)cos(theta)/(1 - sin(2theta))

r = (1/2)sin(2theta)/(1 - sin(2theta))

r = (1/2)(1 + sin(2theta))/(1 - sin^2(2theta))

r = (1/2)(1 + sin(2theta))/cos^2(2*theta)

Using the double angle identities, we get:

r = (1/2)(1 + 2sin(theta)cos(theta))/(2cos^2(theta) - 1)^2

r = (1/2)(1 + 2(ab/c^2))/(1 - (a^2 + b^2)/c^2)^2

r = (1/2)(c^2/(a^2 + b^2 - c^2))

r = (1/2)(c^2/b^2)

r = c/(2*b)

Substituting for c and b, we get:

r = (a/(2*sqrt(a^2 + b^2)))

Therefore, we have proved that the inradius of a right triangle with legs a and b and hypotenuse c is equal to a/(2+sqrt(a^2+b^2)).

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Answer:

d

Step-by-step explanation:

Answer:

$3.89

Step-by-step explanation:

Puppy 1 has  1.31 lbs more than puppy 12

From the question, the given parameters are

The additional weight of puppy 1 is calculated by subtracting the weight of puppy 2 from the weight of puppy 1

This is represented as

Additional weight = Weight of puppy 1 - Weight of puppy 2

Substitute the known values in the above equation

So, we have

Additional weight = 8.4 lbs - 7.09 lbs

Evaluate the difference

Additional weight = 1.31 lbs

Hence, the additional weight of puppy 1 is 1.31 lbs

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Answer:

$0

Step-by-step explanation:

      The chance of winning money is 2/6 -> 1/3, and sense 2/3 is larger than 1/3, we can conclude the expected value of a single roll is $0.

(I may be doing this problem wrong as I don't have context for what you're currently working on, but I hope this helps. Have a nice day!)

Answer:

1 dollar

Step-by-step explanation:

Because if u roll a six it gives you six dollars so how many rolls you roll you get that amount of money. :)

I hope im right :D

The number of people that can go to the amusement park is 10 people

There are three basic types of equation in mathematics. Namely:

259 = 6.50 + 25.25x

259 - 6.50 = 25.25x

252.50 = 25.25x

x = 252.50 / 25.25

x = 10 tickets

Therefore, the number of people that can go to the amusement park is 10 people

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cylinder:

V = πr²h

V = 3.14(2)² * 3

V = 3.14(4) * 3

V = 3.14(12)

V = 37.7m³

rectangular prism:

V = lwh

V = (2.4)(9)(5)

V = 108m³

the entirety of the sculpture:

V = volume of cylinder + volume of rectangular prism

V = 37.7 + 108

V = 145.7m³

Answer:

hrs 50   min 14

Step-by-step explanation:

hrs 45 min 67 = hrs 46 min 7

hrs 3. min 67​ = hrs 4 min 7

Total

  hrs 46 min 7

+   hrs 4 min 7

————————

 hrs 50   min 14

Answer:

a=30°; b=40°;c=40°; d=40°; e=110°: f=110°; g=30°; h=140°; i=70°; j=70°

The length of RS is 55 unit.

The addition axiom states that when two equal quantities are added to two more equal quantities, their sums are equal. Thus, if a = b and y = z, then a + y = b + z.

We have, ST = 15 and RT = 40

Then RS can be get by adding the value ST + RT.

Apply Axiom of addition

then, RS

= RT + ST

= 40 + 15

= 55 unit.

thus, the length of RS is 55 unit.

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The measure of angle t is 50°. therefore option are not related to answer.

An angle is defined as the intersection of two non-collinear rays with a common endpoint or the intersection of two

sides of a plane figure, sharing a common endpoint.

The given angle is coterminal with -710°. Coterminal angles have the same initial and terminal sides, i.e., the same initial

point and the same terminal point.

In order to find the measure of angle t, we must first find the equivalent angle between 0 and 360°.710° is equal to:

710° - 360° = 350°

Thus, the angle t's measure is equal to 350°.

Now, we must find the equivalent angle between 0 and 360°.350° is equal to:350° - 360° = -10° (not between 0 and 360)

Therefore, to find the equivalent angle between 0 and 360, we must add 360° to the angle that is negative.

Thus: -10° + 360° = 350°.So, the measure of angle t is 50°.Answer: 50°.

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Answer:

y = -3/2x + 3

Answer:

-5f + 6

Step-by-step explanation:

combining like terms

-4f - f = -5f

-9 + 15 = 6

Answer:

From the way the problem is worded:

CDE is a straight angle made up of three angles: CDF of measure 43, FDG of unknown measure and GDE of measure 8x + 1.

EDH is outside CDE and is of measure 6x + 15.

Since DE bisects GDH to form GDE and EDH, those latter two angles are equal and thus 8x + 1 = 6x + 15 and x = 7 and substituting 7 for x, both angles are equal to 57 degrees.

Since CDF is 43 and GDE is 57 and CDE is 180 in total, then FDG = 180 - 43 - 57 = 80 degrees.

Answer:

That would be :

4x – 10 = x2 – 5x + 10  ( y = 4x - 10 is substitute for y)

PROOF:        y + 5x = x² + 10

                    (4x - 10) + 5x = x² + 10

                     4x - 10  =  x² -5x + 10

   0 = x2 – 9x + 20  (liked terms are grouped and simplified)

PROOF:      4x - 10  =  x² -5x + 10

                  4x = x² -5x + 10 + 10

                   0  = x² -5x -4x + 20

                   0  = x² - 9x + 20

Solving:

            x² - 9x + 20 = 0

            x² - 5x - 4x + 20 = 0

            (x - 5) (x - 4)  = 0

         ⇒ x = 4  (as question says) OR x = 5

Step-by-step explanation:

hope this helps

Answer:

D,E

Step-by-step explanation:

Answer:1/6

Step-by-step explanation:

There are 6 sides of a dice. One side is a 5, so it would be 1/6

Answer:

1/6

Step-by-step explanation:

Answer:

-2.75h-1

Step-by-step explanation:

A) The linear cost function for manufacturing mountain bikes is given by Cost = $300,000 + ($300 × Number of Bicycles), where the fixed monthly cost is $300,000 and it costs $300 to produce each bicycle.

B) The average cost function represents the cost per bicycle produced and is calculated as Average Cost = ($300,000 + ($300 × Number of Bicycles)) / Number of Bicycles.

A) To find the linear cost function, we need to determine the relationship between the total cost and the number of bicycles produced. The fixed monthly cost of $300,000 remains constant regardless of the number of bicycles produced. Additionally, it costs $300 to produce each bicycle. Therefore, the linear cost function can be expressed as:

Cost = Fixed Cost + (Variable Cost per Bicycle × Number of Bicycles)

Cost = $300,000 + ($300 × Number of Bicycles)

B) The average cost function represents the cost per bicycle produced. To find the average cost function, we divide the total cost by the number of bicycles produced. The total cost is given by the linear cost function derived in part A.

Average Cost = Total Cost / Number of Bicycles

Average Cost = ($300,000 + ($300 × Number of Bicycles)) / Number of Bicycles

It's important to note that the average cost function may change depending on the specific context or assumptions made.

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The two equations  y=x²+6x+8 and y=(x+2)(x+4) are equal.

The given two equations are y=x²+6x+8 and y=(x+2)(x+4)

We have to check whether the two equations are equal or not

y=x²+6x+8 ----(1)

y=(x+2)(x+4) ---(2)

y=x² + 4x+2x+8

y=x² + 6x+8 ....(2)

From equation (1) and (2), y=x²+6x+8 and y=(x+2)(x+4) are equal.

Hence, the two equations  y=x²+6x+8 and y=(x+2)(x+4) are equal.

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Its speed of Rachel would be 30 meters per second.

Given that,

Stunt driver Rachel is trying to get out of a building that is going to blow up.

Here, the equation is,

\(d = - 38t + 220\)

Where, variable d models Rachel's distance from her exit (in meters) t seconds after the cameras began recording the stunt.

Now, Velocity is the rate at which a distance changes over time.

\(d = - 38t + 220\)

\(\dfrac{d(d)}{dt} = - 38\)

Hence, Speed is the magnitude of velocity.

\(|- 38| = 38\)

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The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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The number of years it will take for the guitar to be valued at $768 given the initial value and the rate of depreciation is  4 years.

When an asset deperciates, it means that with the passage of time, the value of the asset declines.

Number of years = (In FV / PV) / r

(In 768 / 1875) / 0.2 = 4 years

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The main answer to the question is the domain of the function h(x). The explanation is that the domain of h(x) is the set of all possible values of x for which the function is defined.

In this case, there are two restrictions on the domain: x cannot equal 6 or 0, since those values would result in a division by zero.

Therefore, the domain of h(x) is {x | x ≠ 6, x ≠ 0}.
would like to determine the domain of the function h(x) with the given information. However, the question seems to have some typos and formatting issues, making it difficult to provide an accurate answer. Please provide the correct function and any necessary information so I can help you determine the domain.

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The graph of the model is illustrated below and  the resistance when x = 85 is 1.12

The resistance of a conductor (such as a wire) is a measure of the opposition it presents to the flow of electric current. The resistance of a wire is dependent on various factors such as its length, cross-sectional area, and material. In this case, we are looking at the resistance of 1000 feet of solid copper wire, where the diameter of the wire is given in mils (0.001 inches).

The resistance of the wire can be approximated using the mathematical model:

=> y = 10,770/x² - 0.375,

where x is the diameter of the wire in mils and y is the resistance in ohms. The model is valid for values of x ranging from 5 to 100.

To complete the table, you need to plug in different values of x into the model and solve for y. For example, when x = 10,

=> y = 10,770/(10²) - 0.375 = 106.975 ohms.

The graph of the model can then be plotted by plotting the points (x,y) from the table and connecting them with a smooth curve. The graph can be used to estimate the resistance of the wire when x = 85.5 mils by finding the y-coordinate of the corresponding point on the graph.

Finally, you can use the model to algebraically confirm the estimate you found from the graph by plugging in the value x = 85.5 into the model and solving for y then we get the value as 1.12. This should give you the same answer as you found from the graph.

In conclusion, the resistance of a wire can be estimated using the mathematical model and can be used to make predictions about the resistance for different wire diameters.

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Answer:

The 66th term is 363.

Step-by-step explanation:

Here,

a = -92 b = -85

d = b - a = -85 -(-92) = 7

n = 66

t66 = ?

We know,

tn = a+(n - 1)d

t66 = -92+(66 - 1)7

= 363