in the pair of triangle, write the similarity statement and identify the postulate of theorem that justifies the similarity.​

Answer with Step-by-step explanation:

We are given that

[tex]a+ib=\sqrt{\frac{1+i}{1-i}}[/tex]

We have to prove that

[tex]a^2+b^2=1[/tex]

[tex]a+ib=\sqrt{\frac{(1+i)(1+i)}{(1-i)(1+i)}}[/tex]

Using rationalization property

[tex]a+ib=\sqrt{\frac{(1+i)^2}{(1^2-i^2)}}[/tex]

Using the property

[tex](a+b)(a-b)=a^2-b^2[/tex]

[tex]a+ib=\sqrt{\frac{(1+i)^2}{(1-(-1))}}[/tex]

Using

[tex]i^2=-1[/tex]

[tex]a+ib=\frac{1+i}{\sqrt{2}}[/tex]

[tex]a+ib=\frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}}[/tex]

By comparing we get

[tex]a=\frac{1}{\sqrt{2}}, b=\frac{1}{\sqrt{2}}[/tex]

[tex]a^2+b^2=(\frac{1}{\sqrt{2}})^2+(\frac{1}{\sqrt{2}})^2[/tex]

[tex]a^2+b^2=\frac{1}{2}+\frac{1}{2}[/tex]

[tex]a^2+b^2=\frac{1+1}{2}[/tex]

[tex]a^2+b^2=\frac{2}{2}[/tex]

[tex]a^2+b^2=1[/tex]

Hence, proved.

Answer:

Slope = [tex]\frac{4}{3}[/tex]

Equation of the line → [tex]y=\frac{4}{3}x[/tex]

Step-by-step explanation:

Let the equation of diagonal OA is,

y = mx + b

Here, m = Slope of the line OA

b = y-intercept

Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, slope of the line passing through O(0, 0) and A(3, 4) will be,

m = [tex]\frac{4-0}{3-0}[/tex]

m = [tex]\frac{4}{3}[/tex]

Since, line OA is passing through the origin, y-intercept will be 0.

Therefore, equation of OA will be,

[tex]y=\frac{4}{3}x[/tex]

Answer:

15:35

Step-by-step explanation:

50-35=Girls

50-35=15

SOLUTION:

10•10= 100

Answer:

Volume of composite figure = 44.9 feet³

Step-by-step explanation:

Given:

Height of cylinder = 3.5 feet

Diameter of cylinder = 3.5 feet

Diameter of hemisphere = 3.5 feet

Find:

Volume of composite figure

Computation:

Radius of cylinder and sphere = 3.5/2 = 1.75 feet

Volume of composite figure = Volume of cylinder + Volume of hemisphere

Volume of composite figure = πr²h + (2/3)πr³

Volume of composite figure = (3.14)(1.75)²(3.5) + (2/3)(3.14)(1.75)³

Volume of composite figure = (3.14)(3.0625)(3.5) + (2/3)(3.14)(5.359375)

Volume of composite figure = 33.656875 + 11.2189583

Volume of composite figure = 44.8758

Volume of composite figure = 44.9 feet³

Answer:

23/6

Step-by-step explanation:

Given fractions

4 3/5 to 1 1/5

Write 4 3/5 as improper fraction= 23/5

Write 1 1/5 as improper fraction= 6/5

Then find the ratio

23/5 : 6/5

Ratio is finding division of two terms

(23/5) / (6/5)

= 23/5 × 5/6

5 at the denominator cancel out 5 at numerator then we have

= 23/6

Hence, fraction in lowest terms here is

23/6

D. 2.3.5 is the correct answer

Answer:

A

Step-by-step explanation:

graph is 6 units to the right

if it had been (x+6)^2

it would have been 6 units to left

Answer:

The maximum error in calculating the surface area of the box is 72 square centimeters.

Step-by-step explanation:

From Geometry, the surface area of the closed rectangular box ([tex]A_{s}[/tex]), in square centimeters, is represented by the following formula:

[tex]A_{s} = w\cdot l + (w + l)\cdot h[/tex] (1)

Where:

[tex]w[/tex] - Width, in centimeters.

[tex]l[/tex] - Length, in centimeters.

[tex]h[/tex] - Height, in centimeters.

And the maximum error in calculating the surface area ([tex]\Delta A_{s}[/tex]), in square centimeters, is determined by the concept of total differentials, used in Multivariate Calculus:

[tex]\Delta A_{s} = \left(l+h\right)\cdot \Delta w + \left(w+h\right)\cdot \Delta l + (w+l)\cdot \Delta h[/tex] (2)

Where:

[tex]\Delta w[/tex] - Measurement error in width, in centimeters.

[tex]\Delta l[/tex] - Measurement error in length, in centimeters.

[tex]\Delta h[/tex] - Measurement error in height, in centimeters.

If we know that [tex]\Delta w = \Delta h = \Delta l = 0.2\,cm[/tex], [tex]w = 60\,cm[/tex], [tex]l = 50\,cm[/tex] and [tex]h = 70\,cm[/tex], then the maximum error in calculating the surface area is:

[tex]\Delta A_{s} = (120\,cm + 130\,cm + 110\,cm)\cdot (0.2\,cm)[/tex]

[tex]\Delta A_{s} = 72\,cm^{2}[/tex]

The maximum error in calculating the surface area of the box is 72 square centimeters.

Answer:

157.8

Step-by-step explanation:

Add them all up to get 789 and divide them by 5 as there are five numbers to get the answer:)

Step-by-step explanation:

Given: [tex]y = -\dfrac{2}{x}[/tex]

Derivative of a power function [tex]x^n[/tex]:

[tex]\dfrac{d}{dx}(x^n) = nx^{n-1}[/tex]

Therefore,

[tex]\dfrac{dy}{dx}=-2(-1)x^{-2} = \dfrac{2}{x^2}[/tex]

Answer:

B

Step-by-step explanation:

(6)^1/2 × (8)^1/2

6^1/2 × 2 (2)^1/2

4 (3)^1/2

Answer:

(a) Increase the differences between the sample means this will increase the Numerator.

(b) Increase the sample variances will increase the denominator.

Step-by-step explanation:  

F Ratio = Variance between treatments/ Variance within treatments.  

Here,  

(a) Increase the differences between the sample means:  

  - Will increase the Numerator and  

  - Size of the F-ratio would increase  

(b) Increase the sample variances:  

 - Will increase the denominator and  

 - Size of the F Ratio would decrease.

13,305 years

Step-by-step explanation:

[tex]A = A_02^{-\frac{t}{5730}}[/tex]

Since only 20% of the original C-14 is left, then [tex]A=0.2A_0[/tex]. We can then write

[tex]0.2A_0=A_02^{-\frac{t}{5730}}[/tex]

Taking the log of both sides,

[tex]\log 0.2 = \left(-\dfrac{t}{5730}\right)\log 2[/tex]

Solving for t,

[tex]t = \dfrac{-(5730\:\text{years})\log 0.2}{\log 2}[/tex]

[tex]\:\:\:\:\:\:\:= 13,305\:\text{years}[/tex]

Answer:

Huh? is it triangle? and right triangle? if it is its 62^2 = 12^2 + x^2

Step-by-step explanation:

Answer:

2sin.2(x) sd s

Step-by-step explanation:

Answer:

fgvilgiuhuikj

Step-by-step explanation:??????????????

Answer:

20 + 2x = 4x

Step-by-step explanation:

So you are setting the two expressions equal to each other.

buying a membership card  and paying each time looks like this: 20 + 2x where x is the number of times you go to the gym.  20 dollars base then 2 each time you go.

4 each time you go is just 4x

so just set the two equal to each other.

20 + 2x = 4x

If you solve it you will get x = something, which would be the number of times to make the two equal.  

Answer:

z (min)  =  2079

L = 26     D =  39.6    S  =  16.5

Step-by-step explanation:

L  numbers of hours assigned to Lisa

D numbers of hours assigned to David

S numbers of hours assigned to Sara

Objective Function to minimize:

z = 30*L  +  25*D  +  18*S

Constraints:

Total time available

L  +  D  +  S  ≤ 110

Lisa experience

L  ≥  0.4 *  ( L + D )  then    L ≥ 0.4*L  +  0.4*D

0.6*L - 0.4*D ≥ 0

To provide designing experience to Sara

S ≥ 0.15*110        then     S ≥ 16.5

Time for Sara

S  ≤ 0.25 * ( L + D )     S ≤ 0.25*L  +  0.25*D   or    -0.25*L - 0.25*D + S ≤0

Availability of Lisa

L ≤ 50

The Model is:

z = 30*L  +  25*D  +  18*S  to minimize

Subject to:

L  +  D  +  S  ≤ 110

0.6*L - 0.4*D ≥ 0

S ≥  16.5

-0.25*L - 0.25*D + S ≤0

L ≤ 50

L ≥   0  ;   D  ≥  0  , S  ≥  0

After  6  iterations  optimal ( minimum ) solution is:

z (min)  =  2079

L = 26     D =  39.6    S  =  16.5

The formula that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize the total cost is z = 30L + 25D + 18S and the minimum z is 2079.

Given :

The formula that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize the total cost is given by:

z = 30L + 25D + 18S

The constraints are given by:

1) L + D + S [tex]\leq[/tex] 110

2) L [tex]\geq[/tex] 0.4(L + D)  

   L [tex]\geq[/tex] 0.4L + 0.4D

   0.6L - 0.4D [tex]\geq[/tex] 0

3) S [tex]\geq[/tex] 0.15(110)

   S [tex]\geq[/tex] 16.5

Now, to minimize 'z' then use:

[tex]\rm -0.25L-0.25D+S\leq 0[/tex]

L [tex]\leq[/tex] 50

L [tex]\geq[/tex] 0, D [tex]\geq[/tex] 0, S [tex]\geq[/tex] 0

Now, the minimum z is given by:

z = 2079

L = 26,  D = 39.6,  S = 16.5

For more information, refer to the link given below:

https://brainly.com/question/23017717

Answer:

2.3 pounds

Step-by-step explanation:

First, the mean is equal to the sum divided by the number of numbers.

There are four packages, so there are four numbers. Let's say the fourth package has a weight of x. We can then write

mean = sum / number of numbers

2.5 = (1.8+3.2+2.7+x)/4

multiply both sides by 4 to remove the denominator

10 = 1.8+3.2+2.7+x

10 = 7.7 + x

subtract 7.7 from both sides to isolate the x

x = 2.3 pounds

The question isn't well stated ; If the question intends to ask the meaning of the inequality :

Answer:

Kindly check explanation

Step-by-step explanation:

Given the inequality : y ≥ 3

This inequality statement or expression means that :

y is true for all values beginning from 3 and beyond

That is values from 3 makes the expression a true statement.

Therefore values of y for which the inequality holds or is true are :

(3,....)

Answer:

32 = a*2 +b

64 = a*3 + b

Then 32 = a

32 = 32*2 +b

b = - 32

So

Y = 32a - 32

Is the equation

Answer:

3/2 + 7

Step-by-step explanation:

Answer:

for this case we have the following functions:

f (x) = x + 8

g (x) = -4x - 3

Subtracting the functions we have:

(f - g) (x) = f (x) - g (x)

(f - g) (x) = (x + 8) - (-4x - 3)

Rewriting:

(f - g) (x) = x + 8 + 4x + 3

(f - g) (x) = 5x + 11

Answer:

D. (f - g) (x) = 5x + 11

Answer:

2000*(1.08)^t where t is years after deposit

Step-by-step explanation:

Answer:

[tex]A = 200,000(1+.025) ^{t}[/tex]

[tex]A = 200,000(1+.025) ^{10}[/tex]

Step-by-step explanation:

9514 1404 393

Answer:

  372 m²

Step-by-step explanation:

A vertical line down the center of the figure will divide it into two congruent trapezoids, each with bases 13 and 18, and height 12.

The area of one of them is ...

  A = 1/2(b1 +b2)h

So, the area of the two of them together is ...

  A = (2)(1/2)(b1 +b2)h = (b1 +b2)h

  A = (13 m + 18 m)(12 m) = 372 m²

Answer:  [tex]y=\frac{1}{4}x-7[/tex]

Step-by-step explanation:

The perpendicular slope of the line(m) = [tex]-\frac{1}{m}[/tex]:

The function formula is y = mx + b, where the y-intercept(b) is found by substituting in the values of a point on the line ⇒ (4, -6):

[tex]y=\frac{1}{4}x+b\\-6=\frac{1}{4}(4)+b\\-6=1+b\\b=-6-1=-7[/tex]

So the perpendicular equation is [tex]y=\frac{1}{4}x-7[/tex].

Answer:

A. d

Step-by-step explanation:

If you find the 3rd square root or whatever its called, and multiply it by itself again 3 times, You end up with d again.

Answer:

100

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(-93 - 3)² + [-37 - (-9)]

√(-96)² + (-28)²

√9216 + 784

√10000

= 100