The two lines intersected by the transversal are parallel. What is the value of x?

Sum of the interior angles of any triangle equal 180° .

So ;

A + B + ECB = 180°

A = B = μ

So : 2μ + ECB = 180°

→ ECB = 180° - 2μ

_________________________________

ECF + ECB = 180°

ECF + 180° - 2μ = 180°

ECF = 180° - 180° + 2μ

ECF = 2μ

_________________________________

∆ ADE :

A + D + E = 180°

μ + 90° + E = 180°

E = 180° - 90° - μ

E = 90° - μ

_________________________________

AED + AEF = 180°

90° - μ + AEF = 180°

AEF = 180° - 90° + μ

AEF = 90° + μ

_________________________________

AEF + FEC = 180°

90° + μ + FEC = 180°

FEC = 180° - 90° - μ

FEC = 90° - μ (( # ))

_________________________________

∆ BDF :

B + D + F = 180°

μ + 90° + F = 180°

F = 180° - 90° - μ

F = 90° - μ ((★))

_________________________________

((#)), ((★)) say :

FEC = 90° - μ

F = 90° - μ

So : F =~ FEC

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Answer:

C is the correct answer

Answer:

The mistake is that the denominators are not the same in these fractions so you cannot add them yet. So, you would have to change the denominators to be the same before adding. The denominators I chose is 15, 2/5 times 3 which is equal to 6/15 and 1/3 times 5 which is equal to 5/15. Now, we can add 6/15 and 5/15 which is equal to 11/15!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

67.91

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

Answer:B,D,F,G

Step-by-step explanation:

[tex]t(n) = 2 {n}^{2} + 2n [/tex]

_________________________________

[tex]t(1) = 2 ({1})^{2} + 2(1) [/tex]

[tex]t(1) = 2 \times 1 + 2 \times 1[/tex]

[tex]t(1) = 2 + 2 = 4[/tex]

##############################

[tex]t(2) = 2 ({2})^{2} + 2(2) [/tex]

[tex]t(2) = 2 \times 4 + 2 \times 2[/tex]

[tex]t(2) = 8 + 4 = 12[/tex]

##############################

[tex]t(3) = 2 ({3})^{2} + 2(3) [/tex]

[tex]t(3) = 2 \times 9 + 2 \times 3[/tex]

[tex]t(3) = 18 + 6 = 24[/tex]

##############################

[tex]t(4) = 2 ({4})^{2} + 2(4)[/tex]

[tex]t(4) = 2 \times 16 + 2 \times 4[/tex]

[tex]t(4) = 32 + 8 = 40[/tex]

##############################

[tex]t(5) = 2 ({5})^{2} + 2(5) [/tex]

[tex]t(5) = 2 \times 25 + 2 \times 5[/tex]

[tex]t(5) = 50 + 10[/tex]

[tex]t(5) = 60[/tex]

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

Answer:

The answer is 112ft

Step-by-step explanation:

All you would do is multiply 8x14

Answer:

1.2n=0.45n+1.5

Step-by-step explanation:

Answer:

[tex]2x {}^{2} + 3x - 1[/tex] option(c)

Step-by-step explanation:

[tex]its \: 2x {}^{2} + 3x - 1 \\ because \: the \: highest \: power \: of \: the \: unkown \: is \: 2[/tex]

Answer:

I think only 1 but not 100% sure

Step-by-step explanation:

Answer:

One solution

Step-by-step explanation:

Combine like terms and simplify.

20z - 5 - 12z = 10z + 8

⇒ z(20 - 12) - 5 = 10z + 8

⇒ z(8) - 5 = 10z + 8

⇒ 8z - 5 = 10z + 8

Subtract 8z both sides.

⇒ 8z - 8z - 5 = 10z + 8 - 8z

⇒ -5 = 2z + 8

Subtract 8 both sides.

⇒ -5 - 8 = 2z + 8 - 8

⇒ -13 = 2z

⇒ -13/2 = 2z/2

⇒ -6.5 = z

Thus, there is 1 solution.

Answer: The width would be 5 and the length would be 16

Step-by-step explanation:

If the length is 5… double that up, and you get 10. Six more than ten is 16… double that and you get 32. And then if you add 32+10 you get your total of 42 for the perimeter.

Answer:

Step-by-step explanation:

The minimum value of sinx is -1 when x = 3π/2, 7π/2, ...

In [2π, 4π), x = 7π/2

The function f(x)=sin(x) achieves its minimum value of -1 at x=3π.

The function f(x)=sin(x) is a periodic function with a period of 2π, meaning it repeats every 2π units. Within the interval [2π,4π), which is one period of the function, the minimum value of sin(x) occurs at x=3π.

This is because at x=3π, the sine function reaches its minimum value of -1. As you move further away from 3π, the sine function starts increasing again.

So, within the interval [2π,4π), the function f(x)=sin(x) achieves its minimum value of -1 at x=3π.

To know more about function:

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Answer:

42 inches²

Step-by-step explanation:

→ Work out area of full triangle

0.5 × 10 × 10 = 50

→ Work out area of smaller triangle

0.5 × 4 × 4 = 8

→ Minus the answers

50 - 8 = 42

Answer:

19

Step-by-step explanation:

First, You want to add all of the data below and you get 133 and with that data you divide 133 by 7 because you have 7 values. I hope i'm right and have a great day :)

The yard is obtuse!

[tex]\large\underline{\underline{\maltese{\red{\pmb{\sf{\: Explanation :-}}}}}}[/tex]

[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]

[tex] \sf \longrightarrow \: {120}^{2} > {85}^{2} + {84}^{2} [/tex]

[tex] \sf \longrightarrow \:14400> 7225 + 7056[/tex]

[tex] \sf \longrightarrow \:14400> 14281[/tex]

[tex] \qquad \mathbb{TRUE}[/tex]

Thus, The triangle is obtuse angled...~

We need angle

Apply law of cosines

[tex]\\ \rm\Rrightarrow c^2=a^2+b^2-2abcos\gamma[/tex]

[tex]\\ \rm\Rrightarrow 2abcos\gamma=a^2+b^2-c^2[/tex]

[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{a^2+b^2-c^2}{-2ab}[/tex]

[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{120^2+84^2-85^2}{-2(120)(84)}[/tex]

[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{14400+7056-7225}{-20160}[/tex]

[tex]\\ \rm\Rrightarrow cos\gamma=\dfrac{14231}{-20160}[/tex]

[tex]\\ \rm\Rrightarrow cos\gamma=-0.714[/tex]

[tex]\\ \rm\Rrightarrow \gamma=cos^{-1}(-0.714)[/tex]

[tex]\\ \rm\Rrightarrow \gamma=135.56°[/tex]

The yard is obtuse

Answer:

The slope of the perpendicular line is [tex]-\frac{5}{3}[/tex]

Step-by-step explanation:

Let us solve the question

∵ The equation of a line is y = [tex]\frac{3}{5}[/tex] x - 8

→ The form of the equation is y = m x + b, where m is the slope

∴ The slope of the line is  [tex]\frac{3}{5}[/tex]

→ To find the slope of the line perpendicular to it reciprocal it and

   reverse its sign

∵ The reciprocal of  [tex]\frac{3}{5}[/tex]  is  [tex]\frac{5}{3}[/tex]

→ Change its sign from positive to negative

∴ The slope of the perpendicular line is [tex]-\frac{5}{3}[/tex]

Answer:

4 hours

Step-by-step explanation:

What I did was since he automatically makes 30 dollars when mowing lawns, you can take it away then you have 8 and divide it by 2 then get 4 hours

Answer:

Step-by-step explanation:

she uses 3/8's of one of them and 7/10 of the other one. first, you need to make the denomanators the same number. so the answer is 3/16 of the starting amount

Question :-

Answer :-

Explanation :-

As per the provided information in the given question, we have been given that the Length of a Rectangular Parking Area is Two times the Width . The Perimeter is given as 90 yards . And, we have been asked to calculate the Length and the Width .

Let the Values be like :-

Now, for calculating the Length & Width , we will use the Formula :-

[tex] \bigstar \: \: \boxed{ \sf{ \: Perimeter \: _{Rectangle} \: = \: 2 \times [ \: Length + Breadth \: ] \: }} [/tex]

Therefore , by Substituting the given values in the above Formula :-

[tex] \dag \: \: \: \sf{Perimeter \: _{Rectangle} \: = \: 2 \: \times \: [ \: Length \: + \: Breadth \: ]} [/tex]

[tex] \longmapsto \: \: \: \sf { 90 \: = \: 2 \: \times \: [ \: x \: + \: 2x \: ]} [/tex]

[tex] \longmapsto \: \: \: \sf {90 \: = \: 2 \: \times \: [ \: 3x \: ]} [/tex]

[tex] \longmapsto \: \: \: \sf {90 \: = \: 2 \: \times \: 3x } [/tex]

[tex] \longmapsto \: \: \: \sf {90 \: = \: 6x } [/tex]

[tex] \longmapsto \: \: \: \sf {x \: = \: \dfrac { \: 90 \: }{6}} [/tex]

[tex] \longmapsto \: \: \textbf {\textsf{ x \: = \: 15}} [/tex]

Therefore :-

[tex] \Longrightarrow \: [/tex] Length = x = 15 yards

[tex] \Longrightarrow \: [/tex] Breadth = 2x = 2 × 15 = 30 yards

[tex] \underline {\rule {210pt} {4pt}} [/tex]

Note :-

The Length of Parking Area is 15 yards  and the Width of Parking Area is 30 yards .

The area of the rectangle is the product of the length and width of a given rectangle.

The Perimeter is given as 90 yards. we have been asked to calculate the Length and the Width .

Let the Values be like :-

Length = x

Breadth = 2x

Now, we will use the Formula :-

Perimeter = 2(L + B)

By Substituting the given values in the above Formula :-

Perimeter = 2(L + B)

90= 2(x + 2x)

90= 2(3x)

45 = 3x

x = 15

Therefore :-

Length = x = 15 yards

Breadth = 2x = 2 × 15 = 30 yards

Learn more about the area;

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Part (a)

The locus is the set of points that satisfy the given conditions. Namely that the point P needs to be 1 unit from the line given.

Think of a median along a highway. Then imagine the two shoulders of the road. The locus describes the two parallel lines that are to this given median. In other words, the median is y = x+2 and the road shoulders are unknown for now.

Though we do know that parallel lines have equal slopes (but different y intercepts).

Therefore, the answers to the next section will be of the form y = x+k for some real number k.

=============================================================

Part (b)

Use your favorite graphing tool to plot y = x+2. I recommend GeoGebra since I use it all the time, and it's what I used to make the drawing below. Desmos is another tool you can use. Both are free.

Note that point A(0,2) is on the line y = x+2. The line perpendicular to y = x+2 and goes through (0,2) is y = -x+2. From here, plot a circle centered at (0,2) with radius 1. The equation of this circle is x^2 + (y-2)^2 = 1

The intersection points of the circle and y = -x+2 will provide starting points, so to speak, for the two shoulder lines I mentioned in part (a).

The approximate locations of those points are:

B = (0.71, 1.29)

C = (-0.71, 2.71)

From here, it shouldn't be too hard to find the y = mx+b forms of the locus lines. Let me know if you need help with that, or if you need me to check your answers.

Side note: Why is it called a locus? I'm not sure, but my gut feeling tells me it has to do with the insects of a similar sounding name (locus the math term and locust the insect). Imagine millions of them forming various shapes in the sky, similar to how many points are used in the 2D plane to create various curves.

Answer:

B. $6,250

Step-by-step explanation:

Given data

constant function f(t)=5000

linear function g(t)=250t

new function= h(t)=f(t)+g(t)

the new value will be

5000+250t

substituting t = 5 in the linear function we have

=5000+250(5)

=5000+1250

=6250

the answer is $6250

the answer is option B

The solution to both inequality is [tex]x>-1[/tex] and  [tex]x\leq 7[/tex].

We have equation [tex]-2>-4x-6[/tex] and [tex]-34\leq -4x-6[/tex]

Let us solve the inequality

[tex]-2>-4x-6\\-2+6>-4x\\4>-4x\\x>-1[/tex]

Now, let us solve the inequality

[tex]-34\leq -4x-6\\-34+6\leq -4x\\-28\leq -4x\\x\leq 7[/tex]

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Answer:

nothing

Step-by-step explanation:

i live in kregon

Answer:

1rst one

Step-by-step explanation:

Answer:

1st

Step-by-step explanation:

Ratio remains same

[tex]\\ \sf\longmapsto \dfrac{18}{27}=\dfrac{x}{45}[/tex]

[tex]\\ \sf\longmapsto 2/3=x/45[/tex]

[tex]\\ \sf\longmapsto 3x=90[/tex]

[tex]\\ \sf\longmapsto x=30[/tex]

Answer:

33.3333333333

Step-by-step explanation:

100 divided 1/3 = 33.3333333333

hope it helped

Answer:

d=3

Step-by-step explanation:

multiply 2 to d and 2 then you'll have 2D + 4 = 10 then you subtract 4 to 10 you'll have six you divide 6 by 2 and then you'll have three which, d equals 3