16. In the adjoining figure, if ll|m, then find the value of angle x​

Answer:

Verified

Area = 13.12 square units.

Step-by-step explanation:

Let the given points / vertices of the parallelogram be represented as follows:

A(2,-1,1),

B(5, 1,4),

C(0,1,1),

D(3,3,4)

In vector notation, we can have;

A = 2i - j + k

B = 5i + j + 4k

C = 0i + j + k

D = 3i + 3j +4k

One of the ways to prove that a quadrilateral is a parallelogram is to show that both pairs of opposite sides are parallel.

(i) Now, let's find the various sides of the assumed parallelogram. These sides are:

AB = B - A = [5i + j + 4k] - [2i - j + k]            open the brackets

AB = 5i + j + 4k - 2i + j - k                            collect like terms and solve

AB = 5i - 2i + j  + j - k + 4k

AB = 3i + 2j+ 3k

BC = C - B = [0i + j + k] - [5i + j + 4k]            open the brackets

BC = 0i + j + k - 5i - j - 4k                             collect like terms and solve

BC = 0i - 5i + j  - j + k - 4k

BC = -5i + 0j - 3k

CD = D - C = [3i + 3j +4k] - [0i + j + k]            open the brackets

CD = 3i + 3j + 4k - 0i - j - k                             collect like terms and solve

CD = 3i - 0i + 3j  - j + 4k - k

CD = 3i + 2j + 3k

DA = A - D = [2i - j + k] - [3i + 3j +4k]            open the brackets

DA = 2i - j + k - 3i - 3j - 4k                             collect like terms and solve

DA = 2i - 3i  - j  - 3j + k - 4k

DA = - i - 4j - 3k

AC = C - A = [0i + j + k] - [2i - j + k]            open the brackets

AC = 0i + j + k - 2i + j - k                             collect like terms and solve

AC = 0i - 2i  + j  + j + k - k

AC = - 2i + 2j +0k

BD = D - B = [3i + 3j + 4k] - [5i + j + 4k]            open the brackets

BD = 3i + 3j + 4k - 5i - j - 4k                             collect like terms and solve

BD = 3i - 5i  + 3j  - j + 4k - 4k

BD = - 2i + 2j + 0k

(ii) From the results in (i) above, it has been shown that;

AB is equal to CD, and that implies that AB is parallel to CD. i.e

AB = CD => AB || CD

Also,

AC is equal to BD, and that implies that AC is parallel to BD. i.e

AC = BD => AC || BD

(iii) Therefore, ABDC is a parallelogram since its opposite sides are equal and parallel.

(B) Now let's calculate the area of the parallelogram.

To calculate the area, we find the magnitude of the cross product between any two adjacent sides.

In this case, we choose sides AC and AB.

Area = | AC x AB |

Where;

[tex]AC X AB = \left[\begin{array}{ccc}i&j&k\\-2&2&0\\3&2&3\end{array}\right][/tex]

AC X AB = i(6 - 0) - j(-6 - 0) + k(-4 -6)

AC X AB = 6i + 6j - 10k

|AC X AB| = [tex]\sqrt{6^2 + 6^2 + (-10)^2} \\[/tex]

|AC X AB| = [tex]\sqrt{36 + 36 + 100} \\[/tex]

|AC X AB| = [tex]\sqrt{172} \\[/tex]

|AC X AB| = 13.12

Therefore the area is 13.12 square units.

PS: The diagram showing this parallelogram has been attached to this response.

Complete Question

In a random sample of

five mobile​ devices, the mean repair cost was $75.00 and the standard deviation was ​$11.50

Assume the population is normally distributed and use a​t-distribution to find the margin of error and construct a 95​%

confidence interval for the population mean. Interpret the results.

Answer:

The margin of error is  [tex]E = 10.1[/tex]

The 95% confidence interval  is [tex]64.9 < \mu < 85.1[/tex]

Step-by-step explanation:

From the question we are told that

  The sample mean is  [tex]\= x = \$ 75.00[/tex]

   The  standard deviation is  [tex]\sigma = \$ 11.50[/tex]

   The sample size is  n = 5

Given the that the confidence level is  95% then the level  of significance is mathematically represented as

            [tex]\alpha = 100 -95[/tex]

            [tex]\alpha = 5\%[/tex]

            [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is  

         [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]

substituting values

         [tex]E = 1.96* \frac{11.50 }{ \sqrt{5} }[/tex]

        [tex]E = 10.1[/tex]

The 95% confidence interval  is mathematically represented as

        [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

        [tex]75 - 10.1< \mu < 75 + 10.1[/tex]

        [tex]64.9 < \mu < 85.1[/tex]

Step-by-step explanation:

(cos(3A) − sin(3A)) / (1 − 2 sin(2A))

Use double angle formula:

(cos(3A) − sin(3A)) / (1 − 4 sin A cos A)

Use triple angle formulas:

(4 cos³A − 3 cos A − 3 sin A + 4 sin³A) / (1 − 4 sin A cos A)

Group and factor:

(4 (cos³A + sin³A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)

Factor the sum of cubes:

(4 (cos A + sin A) (cos²A − cos A sin A + sin²A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)

Use Pythagorean identity:

(4 (cos A + sin A) (1 − cos A sin A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)

Factor out cos A + sin A:

(cos A + sin A) (4 (1 − cos A sin A) − 3) / (1 − 4 sin A cos A)

Simplify:

(cos A + sin A) (4 − 4 cos A sin A − 3) / (1 − 4 sin A cos A)

(cos A + sin A) (1 − 4 cos A sin A) / (1 − 4 sin A cos A)

cos A + sin A

Answer:

367.57 in³

Step-by-step explanation:

The formula for the volume of a cylinder is  [tex]V = h\pi r^2[/tex], where V is the volume, h is the height, and r is the radius. The picture shows you that r = 3 in and h = 13 in.

Plug these into the formula to find the answer:

[tex]V = (13)\pi 3^2=(13)(9)\pi =117\pi => 367.566[/tex]

Round that to the nearest hundredth to get 367.57. The units for the answer should be in cubic inches.

For the surface area, imagine laying the cylinder out. You'd see two circles, for the top and bottom, and then a rectangle, which is the side. The formula is A=2πrh+2πr². Try to do this yourself! You only need to plug in the values: r = 3 in and h = 13 in.

Answer:

The first table represents a function.

Explanation:

This is a function because "x" does not have more than one number corresponding "y".

The x is a placeholder for a number. Think of x like a box and inside the box will go a number. In this case, -4 will replace x

7 - 2x = 7 - 2(-4) = 7 + 8 = 15

Answer:

C and D

Step-by-step explanation:

We want to find the equations where b=11 is a solution. Let's test each answer. choice. Plug 11 in for b and solve.

A. 2b= 211

2(11)=211

Multiply 2 and 11.  

22≠211

22 does not equal 211, therefore this choice is not correct.

B. b+18=7

11+18=7

Add 11 and 18.

29 ≠ 7

29 does not equal 7, so this is not correct.

C. 77=7b

77=7(11)

Multiply 7 and 11.

77=77

77 does equal 77, so this is correct.

D. 9=b-2

9=11-2

Subtract 2 from 11.

9=9

9 equals 9, so this correct too.

E. 11=33/b

11=33/11

Divide 33 by 11.

11≠3

11 does not equal 3, so this is not the right choice.

b= 11 is a solution for C. 77-7b and D. 9=b-2

Answer:

2 b + a

Step-by-step explanation:

Simplify the following:

2 (a + 2 b) - a - 2 b

2 (a + 2 b) = 2 a + 4 b:

2 a + 4 b - a - 2 b

Grouping like terms, 2 a + 4 b - a - 2 b = (4 b - 2 b) + (2 a - a):

(4 b - 2 b) + (2 a - a)

4 b - 2 b = 2 b:

2 b + (2 a - a)

2 a - a = a:

Answer: 2 b + a

Answer: 7 units.

Step-by-step explanation:

Given: Point M is on line segment [tex]\overline{LN}[/tex].

So, point M must divide [tex]\overline{LN}[/tex] into [tex]\overline {LM}[/tex] and [tex]\overline{MN}[/tex].

Such that , [tex]\overline{LN}=\overline{LM}+\overline{MN}[/tex]   (i)

Since,  [tex]\overline{LM} = 5[/tex]  units and [tex]\overline{LN} =12[/tex] units  , then we will put values in (i), we will get

[tex]12=5+\overline{MN}\\\\\Rightarrow\overline{MN}=12-5=7[/tex]

Hence, the length of [tex]\overline{MN}[/tex] is 7 units.

Answer:

[tex] \boxed{\sf (x + y)(6x + 5y)} [/tex]

Step-by-step explanation:

Factor the following:

[tex] \sf \implies 6 {x}^{2} + 11xy + 5 {y}^{2} [/tex]

The coefficient of x² is 6 and the coefficient of y² is 5. The product of 6 and 5 is 30. The factors of 30 which sum to 11 are 5 and 6.

So,

[tex] \sf \implies 6 {x}^{2} + (6 + 5)xy + 5 {y}^{2} [/tex]

[tex] \sf \implies 6 {x}^{2} + 6xy + 5xy + 5 {y}^{2} [/tex]

[tex] \sf \implies 6x(x + y) + 5y(x + y)[/tex]

Factor (x + y) from 6x(x + y) + 5y(x + y):

[tex] \sf \implies (x + y)(6x + 5y)[/tex]

Answer:

Step-by-step explanation:

Given,

A ( 3 , 5 ) ⇒( x₁ , y₁ )

B ( 1 , 3 )⇒( x₂ , y₂ )

Let's find the midpoint of the line:

[tex] \sf{ (\frac{x1 + x2}{2} \: , \frac{y1 + y2}{2}) }[/tex]

plug the values

⇒[tex] \sf{( \frac{3 + 1}{2} \: , \frac{5 + 3}{2} )}[/tex]

Add the numbers

⇒[tex] \sf{( \frac{4}{2} \: , \frac{8}{2} )}[/tex]

Calculate

⇒[tex] \sf{(2 \:, 4 \: )}[/tex]

Hope I helped!

Best regards!

Answer:

x=5/3

Step-by-step explanation:

Answer:

from my calculation, the answer is B

The midpoint of the segment between the points (15,−9) and (−2,−18) will be (−13/2, −27/2). Then the correct option is C.

Let C be the mid-point of the line segment AB.

A = (x₁, y₁)

B = (x₂, y₂)

C = (x, y)

Then the midpoint will be

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

The midpoint of the segment between the points (15,−9) and (−2,−18) will be

x = (15 – 2) / 2

x = –13 / 2

y = (–9 – 18) / 2

y = –27/2

Then the correct option is C.

More about the midpoint of line segment AB link is given below.

https://brainly.com/question/17410964

#SPJ5

Answer:

A

Explanation

8/11 = 8 ÷ 11

BRAINLIEST PLEASE

Answer:

14 in base 10.

Step-by-step explanation:

working from right to left we have:

0 + 1*2 + 1*2^2 + 1*2^3

= 0 + 2 + 4 + 8

= 14.

Answer:

14

Step-by-step explanation:

trust me

Answer:

a. 45

b. -4

Step-by-step explanation:

f(x) = -6(-8) - 3

f(x) = 48 - 3 = 45

21 = -6x - 3

24 = -6x

-4 = x

Step-by-step explanation:

I think no. C is the answer. Please let me know by comment I am wrong or right

Answer:

C

Step-by-step explanation:

A set of coordinates is a function if and only if one input does not map onto two or more different outputs.

In other words, given (x,y), x should each have one distinct y. If an x has 2 or more y, then the y must be the same value.

Choice A:

We see that it has the pairs (1,1) and (1,4). 1 maps onto both 1 and 4, so this is not a function.

Choice B:

Again, we see that it has the pairs (2,2) and (2,5). 2 maps onto both 2 and 5, so this also isn't a function.

Choice C:

In this set, no x are repeated. Thus, this is a function.

Choice D:

In this set, we have the x repeated four times, with 1 mapping onto 2, 3, 5, and 6. Thus, this is not a function.

So, our answer is C.

Answer:

Step-by-step explanation:

if it is converting its 7253/10000

to percent 72.53

scientific notation is 7.253 *10-1 the -1 is on top of the 10

Answer:

27.50

Step-by-step explanation:

Answer:

can you type it out

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, first of all we can find a value for f(1)

[tex]xf(x)+f(x^2)=2 \\\\\text{So for x = 1, it gives}\\\\f(1)+f(1^2)=f(1)+f(1)=2f(1)=2\\\\<=> f(1) =1[/tex]

And we can get the derivative of the equation so.

[tex](uv)'=u'v+uv' \text{ and } \dfrac{df(x^2)}{dx}=2xf'(x^2) \text{ so we can write}\\\\f(x)+xf'(x)+2xf'(x^2)=0\\\\\text{And then, for x = 1}\\\\f(1)+f'(1)+2f'(1)=0\\\\<=> f(1)+3f'(1)=0\\\\<=> 3f'(1)=-f(1)=-1\\\\<=>\large \boxed{ f'(1)=-\dfrac{1}{3} }[/tex]

Thank you

All we need to do is substitute and solve.

A = P(1 + rt)

A = 5,100(1 + 0.035*60)

A = 5,100(3.1)

A = 15,810

Therefore, the answer is [ $15,810 ]

Best of Luck!

Answer:

1190

Step-by-step explanation:

Here, you need to add the squares of the measurements.

20² + 10² + 13² + 11² + 20² =

= 400 + 100 + 169 + 121 + 400

= 1190

Answer:

Step-by-step explanation:

liked- brought

Answer:

Hi, explanation and picture Is below :)

Step-by-step explanation:

K would equal: K = {0, 2, 4, 6, 8, 10}

^^^ (that is in order)^^

That would be the correct expression.

The numbers ‘2 and 0’ are both repeated twice...

So if you want to make it as “members of set” you have to represent each one only once, for it to be members of set...

REVEIW:

Question, Represent the following numbers as being members of set K: 2, 4, 2, 0,6, 0, 10, 8....

Answer,  {0, 2, 4, 6, 8, 10}....

By: ✨RobloxYt✨

(Picture attached)

Answer:

y=x+8

Step-by-step explanation:

First you use the points (-3,5) and (2,10) to find the slope and you use the equation y2-y1/x2-x1.

So that gives you 10-5/2-(-3) which equals 1 (that's the slope)

Next you take one set of the points say (2,10) and then plug those numbers into the y=mx+b equation so you have x (2) and y (10) and the slope is m (1).

That gives you 10=1(2)+b

multiply 1*2 and you get 2 and then subtract 2 from both sides to isolate b and then b=8 and that gives you the answer

y=1x+8 or y=x+8

Answer:

2:50 PM

Step-by-step explanation:

Step 1: State what is given

Roast takes 3 hours and 40 minutes or 220 minutes

Need the roast to be done by 6:30 PM

Step 2: Subtract 3 hours from 6:30

6:30 - 3:00

3:30 PM

Step 3: Subtract 40 minutes from 3:30

3:30 - 40

2:50 PM

Therefore the roast needs to be put into the oven at 2:50 PM

Answer:

variable x has value = -9

Step-by-step explanation:

x − 56 = −65

we have to isolate x by separating it from  56 by using property of equality.

to isolate x, we add 56 on both sides of equation.

x − 56 + 56 = −65 + 56

=> x = -9

Thus, variable x has value = -9

The correct answer is 21.5 days

Explanation:

We know Marissa has two paid days of vacation plus 1 day for every four months she works. In this context, the first step is to find how much paid days of vacation she will have for working 6.5 years and add this to the 2 paid days of vacation she was given when she began to work. The steps are shown below:

1. Find the number of months in 6.5 by considering each year has 12 months and half year (0.5) is equivalent to 6 months

6 (number of years)  x 12 months =  72 months

0.5 year = 6 months

72 months + 6 months = 78 months (Total of months in 6.5 years)

2. Divide the total of months into 4 considering every 4 months Marissa is given one paid day of vacation.

78 months ÷ 4 = 19.5 days (number of paid days of vacation for working 6.5 years)

Finally, add this result to the two paid days initially given 19.5 days + 2 days = 21.5 days

Answer:

(a) 57.8 cm²

(b) 158.7 in²

Step-by-step explanation:

(a)

The area of a circle is denoted by A = 2πr, where r is the radius.

Here the radius is r = 9.2, so plug this in:

A = 2πr

A = 2π * 9.2 ≈ 57.8 cm²

(b)

The diameter is twice the radius, so since the diameter is 50.5 inches, the radius will be 50.5/2 = 25.25 inches.

Plug this into the formula:

A = 2πr

A = 2π * 25.25 ≈ 158.7 in²

~ an aesthetics lover