ointwise characterization of angle bisector. a point p lies on the bisector of ! †bac if and only if p is in the interior of †bac and the distance from p to ab !

Answer:

-10/9

Step-by-step explanation:

I made it so that 2/3 a -4/9 had the same denominator which turned 2/3 into 6/9

then I solved normally

Answer:

C = 49 degrees

a = 8.73 cm

c = 9.11 cm

Step-by-step explanation:

If angle A is 47 and angle B is 84, angle C = 180 - (A + B) = 180 - (47 + 84) = 49

length of b is 12 cm

so according to the formula

a/sin(A) = b/sin(B) = c/sin(C)

a/sin(47) = 12/sin(84) = c/sin(49)

a = sin(47) x 12/sin(84) = 0.731 x 12/0.995 = 8.73 cm

c = sin(49) x 12/sin(84) = 0.755 x 12/0.995 =  9.11 cm

The answer of the function found to be x = −4 and x = 2,  with M = 38.

We must consider the function,

f (x) = x³ + 6x² + 6

Over the interval  

-5 \(\leq\) x \(\leq\) 2

To obtain the extrema we start from the function's derivative.

f' (x) = 3x² + 12x

Equating it to 0,

f' (x) = 0 = 3x(x +4) = 0

We arrive at two solutions,

x1 = 0,     x2 = -4   both inside the interval.

Evaluating the function at the stationary points,

f (x1) = 6

f (x2) = (-4)³ + 6 . (-4)² + 6 = -64 + 96 + 6 = 38

These values must be compared to that of the function at the interval frontiers,

f (-5) = (-5)³ + 6 . (-5)² + 6 = -125 + 150 + 6 = 31

f (2) = 2³ + 6 . 2² + 6 = 38

Comparing the results we can conclude that the function attains its absolute minimum at,

x = 0,      m = 6

Meanwhile, the absolute maximum is attained at the points,

x = −4 and x = 2,  with M = 38.

Learm more about maxima and minima here; https://brainly.com/question/82347

#SPJ4

Answer:

Step-by-step explanation:

Pemdaa

Given that x and y are two non-negative numbers such that x+y=2. The expression is \(x²y²/30\), which represents the area of a rectangle with dimensions x/√30 and y/√30.

To calculate its maximum and minimum values, we must analyze the limits of the function as x and y vary within their possible ranges. To do so, we must first examine the boundary conditions.

Boundary conditionsThe domain of the function is the square defined by the points (0,2), (2,0), (0,0), and (2,2).

By applying the constraints \(x≥0 and y≥0\), we see that this region is reduced to the triangle bounded by points (0,2), (2,0), and (0,0).

In this triangular region, the maximum and minimum values of x and y are limited to the endpoints of the line x+y=2.

The graph of the function is a paraboloid of revolution with its apex located at the origin of the coordinate system.

As a result, the maximum and minimum values of the function correspond to its points of intersection with the boundary of the triangular region.

The minimum value of the function is 0, which is attained at the origin of the coordinate system.

The maximum value of the function is 4/15, which is attained at the two points (2,0) and (0,2).

\(The difference between the maximum and minimum of the quantity x²y²/30,\) where x and y are two non-negative numbers such that\(x+y=2 is 4/15 - 0 = 4/15\)

To know more about the word difference visits :

https://brainly.com/question/30241588

#SPJ11

Answer: f−1(y)=y−23.

Step-by-step Explanation: Let y=f(x)=3x+2. Solve for x ... Subtract 2 from both ends to get: y−2=3x. Divide both sides by 3 to get: x=y−23.

Answer:

The answer is 4cm.

Step-by-step explanation:

Given:

Height= 15cm

The volume of the Cylindrical bottle= 753.6

They have said to use π= 3.14

We are supposed to find r.

-------------------------------------------------------------

Volume of cylinder= πr²h

now substitute teh values given in the formula..we will get:

753.6 = 3.14× r²× 15

After u solve it , you will get

r²= 16

∴r = √16= 4cm

So,  the radius of the bottle is 4cm

Hope it helps!!

The exact length of the curve. y = 3 + 4x^3/2, 0 ≤ x ≤ 1 is L = ∫√(9+108x-144x^(5/2)) / √(9-16x^3) dx, from 0 to 1.

To find the length of the curve, we need to use the arc length formula:

L = ∫√(1+(dy/dx)^2) dx, where y = 3 + 4x^(3/2) and 0 ≤ x ≤ 1.

First, we need to find dy/dx:

dy/dx = (12x^(1/2))/2√(3 + 4x^(3/2))

dy/dx = 6x^(1/2)/√(3 + 4x^(3/2))

Now, we can substitute this into the arc length formula:

L = ∫√(1+(6x^(1/2)/√(3 + 4x^(3/2)))^2) dx, from 0 to 1.

Simplifying the inside of the square root, we get:

L = ∫√(1+(36x)/(3 + 4x^(3/2))) dx, from 0 to 1.

We can simplify this further by multiplying the numerator and denominator of the fraction by (3 - 4x^(3/2)):

L = ∫√(1+36x(3-4x^(3/2))/(9-16x^3)) dx, from 0 to 1.

Expanding the numerator, we get:

L = ∫√((9+108x-144x^(5/2))/(9-16x^3)) dx, from 0 to 1.

Simplifying the expression under the square root, we get:

L = ∫√(9+108x-144x^(5/2)) / √(9-16x^3) dx, from 0 to 1.

We can evaluate this integral using numerical methods, such as Simpson's rule or the trapezoidal rule, to get an approximation of the length of the curve. The exact length of the curve cannot be expressed in a finite number of terms, but it can be approximated to any desired degree of accuracy using numerical methods.

To learn more about trapezoidal rule click here

brainly.com/question/31426104

#SPJ11

The probability that a random sample of 12 students will have a mean reading rate of more than 95 wpm is 0.0418.

There are several sorts of mean in arithmetic, in particular in statistics. each implies serves to summarize a given institution of information, often to better recognize the general fee of a given record set.

They imply (aka the mathematics mean, extraordinary from the geometric imply) of a dataset is the sum of all values divided with the aid of the entire variety of values. it is the maximum commonly used a degree of crucial tendency and is regularly referred to as the “average.”

Common can truely be described as the sum of all of the numbers divided by means of the entire quantity of values. An average is described as the mathematical common of the set of or more statistics values. common is commonly described as implying or arithmetic mean. mean is really a method of describing the average of the sample.

Learn more about the mean here: https://brainly.com/question/12892403

#SPJ4

Answer:

A

Step-by-step explanation:

\(\frac{2x^2-10x-28}{6x} *\frac{6}{x-7}\\ = \frac{2(x^2-5x-14)}{6x} *\frac{6}{x-7}\\ = \frac{(x-7)(x+2)}{3x}*\frac{6}{x-7}\\ = \frac{(x+2)*6}{3x}\\ = \frac{2(x+2)}{x} \\ = (2x+4)/x\)

\(\large\underline{\sf{Solution-}}\)

\(\textsf{Given expression;}\\\)

\( \sf{( {6x}^{3} + {4x}^{2} + 2x) \div 2x} \\ \)

\( \sf \longmapsto \frac{ {6x}^{3} + 4 {x}^{2} + 2x}{2x} \\ \)

\( \sf \longmapsto \frac{ {6x}^{3} }{2x} + \frac{4 {x}^{2} }{2x} + \frac{2x}{2x} \\ \)

\( \sf \longmapsto \frac{ {6 \times x \times x \times x} }{2 \times x} + \frac{4 \times x \times x}{2 \times x} + \frac{2 \times x}{2 \times x} \\ \)

\( \sf \longmapsto (3 \times x \times x) + (2 \times x) + 1 \\ \)

\( \sf \longmapsto {3x}^{2} + 2x + 1 \: \: \: \red{ Ans.} \\ \)

\( \bf{Read \: more:} \\ \)

-32x^4 ÷ 8x^2 Solve urgent plz..

https://brainly.com/question/25452595

Answer:

5x^2 + 17xy - 12y^2

5x^2 + 5xy + 12xy - 12y^2

5x (x - y ) + 12 y ( x - y )

(5x + 12y ) (x-y).

Step-by-step explanation:

The monthly deposit Mona's parents need to start making when she is 7 is 109.42 / month.

How to calculate the monthly deposit to save $7500 by the time she reaches 13?

Savings Goal Calculator can be used to calculate this question.

Present Value of $7500 to be achieved at the age of 13 = $5,311.57.

Formula:Future Value = (Present Value) x (1 + i)^n

Where,i = rate of interest = 5% per annum

n = time period = 6 years (13 - 7)

Future Value = $7500 (as per question)

Present Value = ? = (Future Value) / (1 + i)^n= 7500 / (1 + 0.05)^6= 7500 / 1.3401

Present Value = $5,311.57

Let,Monthly Deposit = x

n = time period in months = 6 years (13 - 7) x 12 = 72

Formula:Monthly Deposit = (Future Value - Present Value) x i / [ (1 + i)^n - 1 ]

Monthly Deposit = (7500 - 5311.57) x 0.05 / [ (1 + 0.05)^72 - 1 ]

Monthly Deposit = 2188.43 x 0.05 / 7.759

Monthly Deposit = 109.42 / month

Therefore, the monthly deposit Mona's parents need to start making when she is 7 to have $7500 by the time she reaches the age of 13 is 109.42 / month.

Learn more about deposit at

https://brainly.com/question/30289330

#SPJ11

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

After calculations, it is determined that the required spacing of the closed stirrups is approximately 6 inches.

To determine the required spacing of closed stirrups for the given beam, we need to consider the factored shear and factored torsional moment. The formula for calculating the spacing of closed stirrups is given by:

s = (0.75√(f'c) / fy) * (Av / (bd - 2s))

where:

s = spacing of stirrups

f'c = specified compressive strength of concrete

fy = specified yield strength of steel reinforcement

Av = area of one closed stirrup

b = width of the beam

d = effective depth of the beam

Given information:

Width (b) = 15 in.

Effective depth (d) = 26.5 in.

Factored shear = 80 kips

Factored torsional moment = 50 ft-kips

Stirrup centroid from concrete face = 1.75 in.

No. 4 (no. 13) closed stirrup size = 0.2 square inches

First, we need to calculate the area of one closed stirrup:

Av = (No. of stirrups) * (Area of one stirrup)

Av = (2) * (0.2 square inches)

Av = 0.4 square inches

Next, we can substitute the values into the formula to calculate the spacing (s):

s = (0.75√(f'c) / fy) * (Av / (bd - 2s))

Assuming f'c = 4 ksi (common value for concrete strength) and fy = 60 ksi (common value for steel reinforcement strength), we can calculate:

s = (0.75√(4) / 60) * (0.4 / (15 * 26.5 - 2s))

Simplifying the equation, we get:

s = 0.0986 / (397.5 - 30s)

To solve for s, we can use an iterative approach or trial and error method. By substituting different values of s into the equation, we can find the spacing that satisfies the equation.

Know more about closed stirrups here:

https://brainly.com/question/541723

#SPJ11

Answer:

rhombuses are square.

rhombuses do have 4 congruent sides.

rhombuses have 4 congruent angles.

rhombuses are parallelograms.

Step-by-step explanation:

\(7x-28-3x+2=3x-2-x \\ \\ 4x-26=2x-2 \\ \\ 2x-26=-2 \\ \\ 2x=24 \\ \\ \boxed{x=12}\)

The height of the trapezoidal welcome mat that Polly Ester can create with 1114 ft2 of material, with bases of 5 ft and 4 ft, is approximately 247.56 ft.

To find the height of the trapezoidal welcome mat, we can use the formula for the area of a trapezoid, which is:

\($A = \frac{(b_1 + b_2)}{2} \cdot h$\)

where A is the area, \(b_1\) and \(b_2\) are the lengths of the parallel bases, and h is the height.

We know that the bases of the welcome mat are 5 ft and 4 ft, so we can substitute these values into the formula:

1114 = (5 + 4) / 2 * h

Simplifying this equation, we get:

1114 = 4.5h

Dividing both sides by 4.5, we get:

h = 1114 / 4.5

h ≈ 247.56 ft

To learn more about trapezoidal

https://brainly.com/question/22227061

#SPJ4

Answer:

I hope it will help you...

Answer:

=−23449/4

Step-by-step explanation:

=1190/40−5892

=119/4−5892

=−23449/4

The area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

To solve this problem, we can use the formula for the volume of a hexagonal prism:

V = (3√3/2) * a^2 * h

where V is the volume, a is the length of one side of the hexagonal base, and h is the height of the prism.

We are given that the height of the prism is 4 units and the volume is 98 units^3. Plugging these values into the formula, we can solve for the length of one side of the base:

98 = (3√3/2) * a^2 * 4
a^2 = 98 / (12√3)
a ≈ 2.95

Now that we know the length of one side of the base, we can find the area of the hexagon by using the formula:

A = (3√3/2) * a^2

where A is the area of one of the bases. Plugging in the value we found for a, we get:

A = (3√3/2) * (2.95)^2
A ≈ 7.39

Therefore, the area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

To know more about hexagonal prism visit:

https://brainly.com/question/10726499

#SPJ11

The equation of the transformed exponential function g(x) is g(x) = 2^-x - 1

From the question, we have the following parameters that can be used in our computation:

Parent function: y = 2^x

The graph of the transformed exponential function g(x) passes through the points  (-2,3), (-1,1), (0,0), (1,-0.5) and (2, -0.75)

So, we have the following transformation steps:

1st Transformation:

Reflect y = 2^x across the y-axis

So, we have

y = 2^-x

2nd Transformation:

Translate y = 2^-x down by 1 unit

So, we have

y = 2^-x - 1

This means that

g(x) = 2^-x - 1

Hence, the equation of the function g(x) is g(x) = 2^-x - 1

Read more about transformation at

brainly.com/question/1548871

#SPJ1

Answer:

352 lbs is correct

Step-by-step explanation:

They did estimate correctly. for how to do this look below:

So we have a elephant that gains 22 pounds every week and they estimated that at 16 week she would be at 352 lbs

22 which was current pounds at the time and she would keep gaining that every week for 16 weeks

So weight times weeks

22*16

22*16= 352

Hope this helps!

The question gives the relationship to be

We will interpolate to solve the question.

First Question: 147 mi

Cross multiplying,

At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).


To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.

Learn more about Compound interest here: brainly.com/question/13155407
#SPJ11

Answer:

800,653,284

Step-by-step explanation:

859*612 = 525,708

525,708*1523 =

800,653,284

Answer:

859 x 612 x 1523 =

Step-by-step explanation:

800653284  

hope this helps! :)