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natka813 [3]
3 years ago
9

Quadrilateral ABCD is inscribed in a circle. Angle B measures (x – 5)°, and angle D measures (3x + 5)°. Find x.

Mathematics
2 answers:
Mamont248 [21]3 years ago
8 0
Angle B is opposite to angle D.
Since quadrilateral ABCD is inscribed in a circle, it’s a cyclic quadrilateral.
The sum of the opposite angles of a cyclic quadrilateral is 180 degrees.
(x-5)+(3x+5)=180
4x=180
x=180/4
x=65 degrees
zepelin [54]3 years ago
7 0

Answer: x = 45

Step-by-step explanation:

Quadrilaterals inscribed in a circle have all four vertices on the circle.

A unique property of these types of quadrilaterals is their angle measures: Opposite angles of inscribed quadrilaterals will always add up to 180 (they are supplementary angles).

As such, the inscribed quadrilateral ABCD has opposite angles at AC and BD. Because the quadrilateral is inscribed, this means that the angles A + C and the angles B + D will equal 180 degrees. We can represent the angles measures for B and D in an equation where B + D = 180:

(x-5)+(3x+5)=180\\\\4x = 180\\\\x=45

When x = 45, the angle B is 40 degrees and the angle D is 140 degrees.

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Kittens weigh about 100 grams when born and gain 7 to 15 grams per day. If a kitten weighed 100 grams at birth and gained 8 gram
tangare [24]
25 days

First, start with an equation

100+8x= kittens weight

(X representing the days)

Since you’re trying to figure out the number of days it takes the kitten to triple it’s weigh you multiply it’s initial weight by 3 (100•3)

Then, you output 300 into the equation and solve

8 0
4 years ago
What is the best estimate of the sum of $14.30, $143.08, and $19.74
Feliz [49]

Answer:

Step-by-step explanation:

ok so you start off by adding

  14.30

143.08

  <u>19.74</u>

 177.12

177.12 is close to 180 if u estimate in tens, 177 if ones

6 0
4 years ago
Read 2 more answers
Factor each linear expression. If the expression cannot be factored, write cannot be factored. 36x – 9
ki77a [65]

Answer:

9(4x - 1)

Step-by-step explanation:

The given linear expression is:

36x - 9

Since, 36 can be written as 9 times 4, we can rewrite the above expression as:

9(4x) - 9

Taking 9 as common, the expression changes to:

9 (4x - 1)

This linear expression can no linger be factorized further.

So,

36x - 9 = 9(4x - 1)

3 0
3 years ago
Read 2 more answers
14. Find mMK please :)
MrRissso [65]

Answer:

Step-by-step explanation:

11) strategy:  since they tell us. indirectly,  that the length of  JK is the same as LM then we can set those two equal, solve for X  and then.. when we have X we can figure out the lenght of JK  and LM and then just divide that by 2 go get PK  ( :0 Player Killer ???  no , not that PK)    

solve JK and LM

3x + 23 =9x-19

42 = 6x

7 = x

now that we know x = 7 plug it into either equation to come up with the length of JK or LM .  I'll pick JK just b/c it was 1st

3(7) + 23 = JK

21+23 = JK

44 = JK

now take half of 1/2*JK= 22  that is PK    ( are you sure that 's not player killer?)

PK = 22

12) strategy: set the two arcs BG and GC equal and solve for X, then plug x into either equation and the multiply the answer by 2 to find arc AB

9x-20 = 5x + 28

4x = 48

X = 12

9(12) -20 = BG

88 = BG

2*88 + AB

176 = AB

13) done

14)  strategy: find the angle at L,  and that will also be the arc of MK

<em>copy and past the below</em> helpful trig functions into your computer

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

<em>copy and past the above</em> :

use which ever trig function you want , we have all the sides of the triangle, I'll use CAH

Cos(Ф) = 9/15

Ф = arcCos(9/15)

Ф = 53.13010°

arc MK = 53.13010°

15)   strategy:  arc JK is just 2 times MK

2*MK = 106.26020°

arc MK = 106.26020°

16) find arc JPK   strategy:  JPK is just the remaining part of a full circle of 360 - MK  = 253.7397°

arc JPK = 253.7397°

7 0
3 years ago
PLEASE HELP ILL GIVE BRAINLIEST!!
dlinn [17]

Answer:

Step-by-step explanation:

Radius r = 12.5/2 = 6.25 cm

Height h = 7 cm

volume = πr²h = 3.14⋅6.25²⋅7= 858.6 cubic cm

7 0
3 years ago
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