Find the length of the leg x

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Explanation:

For any cyclic quadrilateral (aka inscribed quadrilateral), the opposite angles are always supplementary.

One pair of such angles is A and C

A+C = 180

x+y = 180 is one equation to form

The other pair of supplementary angles is B and D

B+D = 180

y-45+2x+15 = 180

2x+y-30 = 180

2x+y = 180+30

2x+y = 210 is the other equation to form

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So the system of equations we have is

[tex]\begin{cases}x+y = 180\\2x+y = 210\end{cases}[/tex]

Both equations involve 'y', with the same coefficient, so we can subtract straight down to eliminate this variable.

We end up with -x = -30 which solves to x = 30

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Once we know x, we can determine y by plugging it into any equation involving x,y and solving for y

Let's say we picked on the first equation

x+y = 180

30+y = 180

y = 180-30

y = 150

Or we could pick on the second equation

2x+y = 210

2(30) + y = 210

60+y = 210

y = 210-60

y = 150

Only one equation is needed. However, doing both like this shows that we get the same y value, and it helps confirm the answers.

Answer:

?

Step-by-step explanation:

Answer:

2.45

Step-by-step explanation:

Given that :

α = 0.05

Larger sample variance= numerator, sample size = 9

Smaller sample variance = denominator, sample size = 21

Hence,

DFnumerator = n - 1 = 9 - 1 = 8

DFdenominator = n - 1 = 21 - 1 = 20

Critical value for upper tail test using the F distribution table at α = 0.05 ; DFnumerator on horizontal ; Df denominator as vertical ;

F critical = 2.447

F critical = 2.45

Answer:

18 divided by nine is two. so for every one table spoon of oil there's two table spoons of vinegar. Please give brainliest

Answer:

2

Step-by-step explanation:

Make a ratio:

Oil : Vinegar

9 : 18

1 : 2

For each tablespoon of oil, 2 tablespoons of vinegar is needed.

Hope this helped.

Answer:

Individual is represented by a single point

Step-by-step explanation:

Answer:

hey, how you're day going

Step-by-step explanation:

.................

Answer:

67

Step-by-step explanation:

DM=JM-JD=84-17=67

Answer:

Step-by-step explanation:

Answer:

290.44

Step-by-step explanation:

The whole figure area can be calculated by assuming that the whole floor is a complete square of 18.2 x 18.2 and subtracting the area of the rectangular cutout which is 10.2 x 4

Area of the the flooring=18.2 x 18.2 - (10.2*4)=290.44

Answer:

Step-by-step explanation:

there are function that "invert" each other..

subtraction inverts addition...

3+2 = 5 ... 5-2 = 3

division inverts multiplication

5*2 = 10 ... 10/2 = 5

Using that concept, "factoring" is basically the inverse of multiplication

3x^2 + 9x can be factored to 3x(x+3)

if you multiply that out it reverts back to the original equation

so  x^2 + 5x + 6 factors to (x+3)(x+2)

if you multiply that out (foil it)

you get x^2 + 5x + 6

1099.56m² is the surface area of a cylinder that has a radius of 7 m and a height of 18 m.

Mark as braianlist

15 multiple by 5 equal 75 -390 equal 315 -15equal 200

Answer:

Male-19&Female-13

Step-by-step explanation:

See the image for solution

Hope it helps

Have a great day

Answer:

$54

Step-by-step explanation:

10% of $60 is $6

$60-$6=$54

Answer:

2 is the factor of every even number hope this help you

Answer:

Hello,

polynomial is x²-x+1

Step-by-step explanation:

if a=b*c+r then a=c*b+r

Using a long division, see the picture.

Answer:

Step-by-step explanation:

Answer:

7yz

Step-by-step explanation:

You can take 7yz common from all the terms in the given expression

Answered by GAUTHMATH

Answer: 15

Step-by-step explanation:

Answer:

hello thereeeee

ans is 23.5

Step-by-step explanation:

so lets start

first of all remove decimal of divisor 1.1/25.85 multiplying by 10

11/258.5

now first multiply by 2

now we get 22 and subtract with 25 => 25-22 = 3

so left is

38

now 11*3 = 33

so now by 3

38-33= 5

bringing another 5 down

we get 55

now quotient is 23. something ( as we bought .5 down)

and now 11*5 = 55

so

23.5 is answer

Answer:

Hello,

in order to simplify, i have taken the inverses functions

Step-by-step explanation:

[tex]\int\limits^\frac{1}{2} _{-1} {(-2x^2-x+1)} \, dx \\\\=[\frac{-2x^3}{3} -\frac{x^2}{2} +x]^\frac{1}{2} _{-1}\\\\\\=\dfrac{-2-3+12}{24} -\dfrac{-5}{6} \\\\\boxed{=\dfrac{9}{8} =1.25}\\[/tex]

Answer:

3 times 10 ^ 9

Step-by-step explanation:

3 × 10 ^ 9 = 3000000000

Answer:

Step-by-step explanation:

Given,

[tex] {25x}^{2} - \frac{1}{49} [/tex]

[tex] = {(5x)}^{2} - {( \frac{1}{7}) }^{2} [/tex]

Since,

[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]

Then,

[tex] = (5x + \frac{1}{7} )(5x - \frac{1}{7} )(ans)[/tex]

Answer:

(a) No solution

(b)

[tex](x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)[/tex]

(c)  [tex](-6,1)[/tex]

Step-by-step explanation:

Given

See attachment for graph

Solving (a): Solution to p(x) and f(x)

Curve p(x) and line f(x) do not intersect.

So, there is no solution to the pair of p(x) and f(x)

Solving (b): Two solutions to f(x)

This means that we select any two point on straight line f(x)

From the line of f(x), we have:

[tex](x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)[/tex]

Solving (c): Solution to p(x) = g(x)

Here, we write out the point of intersection of p(x) and g(x)

From the graph, the point of intersection is: [tex](-6,1)[/tex]

Answer:

400 :D

Step-by-step explanation:

Answer:

7/3 is the answer

Step-by-step explanation:

Answer:

the answer to the question is a:-3

Answer: A: 22, 33, 45.5, 56, 59

Step-by-step explanation:

The minimum is the lowest number in the data, in this case, it was 22.

Q1 is the median of the lower quartile range, anything below the median of the overall data.

Median, the middle number in the overall data. You first need to put them from lowest to highest (numerical order). After that, I find it a lot easier to cross one from each side until I'm either left with one or two. If I'm left with one, then that is my median for the overall data set. If I'm left with two, then I simply need to add both the numbers together and divide it by 2. Typically if it is a whole number, and the numbers are 1 number value away from each other, it is usually just 0.5 more of the lower value of the two. (For example, the two numbers I come down to is 10 and 11. The median would be 10.5).

Q3 is the exact same principle as Q1 just on the upper quartile range. Just repeat what you did in Q1 but for the numbers above the overall median of the data set.

Maximum is the highest number in the data set, in this case, it was 69.

Hope this helps!

Graph is attached below ;

Answer:

Unit rate = 12 computers per day

Step-by-step explanation:

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

That is ; the gradient ;

Slope = change in y / change in x

Slope = (y2 - y1) / (x2 - x1)

y2 = 60 ; y1 = 36 ; x2 = 5 ; x1 = 3

Slope = (60 - 36) / (5 - 3) = 24 / 2 = 12

Slope = 12

Unit rate = 12 computers per day