diane draws abtuse, isoscules triangle with one of the angle mesuring 35. what i sthe messer of teh obtuse triangle

Answers

Answer 1
Answer:

Answer:

All angle = (110°, 35°, 35°)

Step-by-step explanation:

Given:

Triangle is a Obtuse isosceles triangle

One angle = 35°

Find:

All angle

Computation:

In the Obtuse isosceles triangle, one angle is obtuse and the other two angles are acute so, two equal angles are 35°

So,

Sum of angle property

x + 35° + 35° = 180°

x = 110°

Obtuse angle = 110°

All angle = (110°, 35°, 35°)


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In the figure, side AB is given by the expression (5x + 5)/(x + 3), and side BC is (3x + 9)/(2x - 4).The simplified expression for the area of rectangle ABCD is _______, and the restriction on x is ____.

Answers

Answer:

The simplified expression for the area of rectangle ABCD is ( 15(x + 1))/(2(x - 2)), and the restriction on x is x≠2 .

Step-by-step explanation:

Side AB = Width of rectangle = (5x + 5)/(x + 3)

Side BC = Length of rectangle =  (3x + 9)/(2x - 4)

Area of Rectangle = Length * Width

Putting values:

Area\,\,of\,\,rectangle =( (3x + 9))/((2x - 4)) * ((5x + 5))/((x + 3))

Solving,

Area\,\,of\,\,rectangle =( 3(x + 3))/((2x - 4)) * (5x + 5)/((x + 3)) \nArea\,\,of\,\,rectangle =( 3)/(2(x - 2)) * 5x + 5\nArea\,\,of\,\,rectangle =( 3(5x + 5))/(2x - 4)\nArea\,\,of\,\,rectangle =( 15x + 15)/(2x - 4)\nArea\,\,of\,\,rectangle =( 15(x + 1))/(2(x - 2))

The restriction on x is that x ≠ 2, because if x =2 then denominator will be zero.

So, the answer is:

The simplified expression for the area of rectangle ABCD is ( 15(x + 1))/(2(x - 2)), and the restriction on x is x≠2 .

99% confidence interval for the population standard deviation

Answers

99% = 2.58

how to find ?

Divide your confidence level by 2: . 95/2 = 0.475. Step 2: Look up the value you calculated in Step 1 in the z-table and find the corresponding z-value. The z-value that has an area of .

Reuben attached a wire between two poles on a hill as shown which is the closest to x the distance between the two poles

Answers

Answer:

75 ft

Step-by-step explanation:

Here we are given a right angled triangle with a known angle of 20°, length of the hypotenuse to be 80 and we are to find the length of the base x.

For that, we can use the formula for cosine for which we need an angle and the lengths of base and hypotenuse.

cos \alpha =(base)/(hypotenuse)

So putting in the given values to get:

cos 20=(x)/(80) \n\nx= cos 20*80\n\nx=75.17

Therefore, the value of x is the closest to 75 ft.

Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your answers to three decimal places.) f(x) = x9 − 9, x1 = 1.6

Answers

Answer:

Iteration 1: x_(2)=1.446

Iteration 2: x_(3)=1.337

Step-by-step explanation:

Formula for Newton's method is,

x_(n+1)=x_n-(f\left(x_n\right))/(f'\left(x_n\right))

Given the initial guess as x_(1)=1.6, therefore value of n = 1.

Also, f\left(x\right)=x^(9)-9.

Differentiating with respect to x,

(d)/(dx)\left(f\left(x\right)\right)=(d)/(dx)\left(x^9-9\right)

Applying difference rule of derivative,

(d)/(dx)\left(f\left(x\right)\right)=(d)/(dx)\left(x^9\right)-(d)/(dx)\left(9\right)

Applying power rule and constant rule of derivative,

(d)/(dx)\left(f\left(x\right)\right)=\left(9x^(9-1)\right)-0

(d)/(dx)\left(f\left(x\right)\right)=9x^(8)

Substituting the value,

x_(1+1)=x_1-(f\left(x_1\right))/(f'\left(x_1\right))

x_(2)=1.6-(f\left(1.6\right))/(f'\left(1.6\right))

Calculating the value of f\left(1.6\right) and f'\left(1.6\right)

Calculating f\left(1.6\right)

f\left(1.6\right)=\left(1.6\right)^(9)-9

f\left(1.6\right)=59.71947674

Calculating f'\left(1.6\right),

f'\left(1.6\right)=9\left(1.6\right)^(8)

f'\left(1.6\right)=386.5470566

Substituting the value,

x_(2)=1.6-(59.71947674)/(386.5470566)

x_(2)=1.446

Therefore value after second iteration is x_(2)=1.446

Now use x_(2)=1.446 as the next value to calculate second iteration. Here n = 2

Therefore,

x_(2+1)=x_2-(f\left(x_2\right))/(f'\left(x_2\right))

x_(3)=1.446-(f\left(1.446\right))/(f'\left(1.446\right))

Calculating the value of f\left(1.446\right) and f'\left(1.446\right)

Calculating f\left(1.446\right)

f\left(1.446\right)=\left(1.446\right)^(9)-9

f\left(1.446\right)=18.63851065

Calculating f'\left(1.446\right),

f\left(1.446\right)=9\left(1.446\right)^(8)

f\left(1.446\right)=172.0239252

Substituting the value,

x_(3)=1.446-(18.63851065)/(172.0239252)

x_(3)=1.337

Therefore value after second iteration is x_(3)=1.337

Final answer:

To calculate two iterations of Newton's Method, use the formula xn+1 = xn - f(xn)/f'(xn). Given an initial guess of x1 = 1.6 and the function f(x) = x9 - 9, calculate f(xn) and f'(xn) at x1 and then use the formula to find x2 and x3.

Explanation:

To calculate two iterations of Newton's Method, we need to use the formula:

xn+1 = xn - f(xn)/f'(xn)

Given an initial guess of x1 = 1.6 and the function f(x) = x9 - 9, we can proceed as follows:

  1. Calculate f(xn) at x1: f(1.6) = (1.6)9 - 9 = 38.5432
  2. Calculate f'(xn) at x1: f'(1.6) = 9(1.6)8 = 368.64
  3. Calculate x2: x2 = 1.6 - f(1.6)/f'(1.6) = 1.6 - 38.5432/368.64 = 1.494
  4. Repeat the process to find x3 using the updated x2 as the initial guess.

Learn more about Newton's Method here:

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Which of the following is equivalent to 2 2/5​

Answers

Answer:

0.4 - 0.40 - 4/10 -

Step-by-step explanation:

Which expression is equal to “7 times the sum of a number and 4"?

Answers

Answer: 7 (x+4)

Step-by-step explanation: Since the expression asks for 7 times the sum of a number and 4, you would put x + 4 in parentheses since multiplying 7 comes afterwards.