Find the value of X and prove the following​

Find The Value Of X And Prove The Following

Answers

Answer 1

The value of the variable x can be determined using the circle theorem to

determine the angle formed by x.

The correct responses are;

(1) x = 30°(2) x = 100°(3) x = 60°

Reasons:

(1) From circle theorem, we have;

Equal chords subtends equal arcs and vice versaEqual chords subtend equal angles at the center of a circle

Therefore;

Angle subtended by [tex]\displaystyle \widehat {AB}[/tex] at center = Angle subtended by [tex]\widehat {BC}[/tex] at the center;

Angle at the center = 2 × Angle at the circumference

Therefore;

Angle subtended by [tex]\displaystyle \widehat {AB}[/tex] at the circumference = Angle subtended by [tex]\mathbf{\widehat {BC}}[/tex] at the circumference

Which gives;

x = 30°

(2) [tex]\displaystyle \widehat {AB} = \mathbf{\widehat {CD}}[/tex] given

Angle subtended by arc [tex]\widehat {CD}[/tex] at the center = x

Equal arcs subtend equal angles at the center of a circle.

Therefore;

Angle subtended by arc [tex]\mathbf{\widehat {AB}}[/tex] at the center = x

Angle at center = 2 × angle at circumference

Therefore;

x = 2 × 50° = 100°

x = 100°

(3) [tex]\displaystyle \widehat {AC} = \mathbf{ 3 \times \widehat {AB}}[/tex] given

By definition, we have;

Angle subtended by [tex]\widehat {AC}[/tex] at the center = 3 × Angle subtended by [tex]\widehat {AB}[/tex] at the center

According to circle theorem, we have;

Angle at the center = 2 × Angle at the circumference

Let y represent the angle subtended at the circumference by [tex]\widehat {AB}[/tex], we have;

y = 20°

[tex]\widehat {AB}[/tex] = 2·y

[tex]\widehat {AC}[/tex] = 3 × [tex]\widehat {AB}[/tex] = 3 × 2·y = 6·y

Therefore;

[tex]\widehat {AC}[/tex] = 6 × 20° = 120°

[tex]\widehat {AC}[/tex] = 120°

[tex]\widehat {AC}[/tex] = 2·x

Therefore;

2·x = 120°

[tex]\displaystyle x = \frac{120^{\circ}}{2} = \mathbf{ 60^{\circ}}[/tex]

x = 60°

Learn more circle theorems here:

https://brainly.com/question/16879446


Related Questions

Use substitution to solve each system of equations
2x -y = 6
-3y = -6x + 18

Answers

Hope this helps
Step are all below

I need help with this question

Answers

Answer:

Option D

Step-by-step explanation:

a^2 + b^2 = c^2

5^2+b^2=9^2

25+b^2=81

b^2=56

b=2√14

PLS HELP ASAP ILL GIVE BRAINLKEST THANKS

Answers

Answer:

C

Step-by-step explanation:

y = 10

x = 8

The y intercept is 0 and the line runs through (0,0)

m = y / x This formula can only be used when the y incept is 0.

m = 10/8

m = 5/4

Equation

y = 5/4 x

3

The table shows the linear relationship between the number of pages left to read in an
the number of hours a student has already spent reading the novel. Mark each stateme
or false. If false, rewrite the statement correctly.
HOURS
READ
RE
9. The student reads at a rate of 48 pages per hour.
1
4
10. The number of pages in the novel is 644.
8
12
11. The situation can be represented by the
equation y = -48x + 692.
14

Answers

The table is an illustration of a linear function

9. The student's rate

Take any two points from the table

[tex](x,y) =\{(1,644)\ (4,500)\}[/tex]

The rate is then calculated using:

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

This gives

[tex]Rate = \frac{644 -500}{1-4}[/tex]

[tex]Rate = \frac{144}{-3}[/tex]

[tex]Rate = -48[/tex]

The statement that the student reads at a rate of 48 pages per hour is true

10. The pages in the novel

From the table, there are 644 pages left, after the student read for 1 hour.

This means that there are more than 644 pages in the novel.

The statement that the number of pages in the novel is 644 is false

11. The linear equation

This is calculated as:

[tex]y = Rate(x -x_1) + y_1[/tex]

So, we have:

[tex]y = -48(x -1) + 644[/tex]

[tex]y = -48x +48 + 644[/tex]

[tex]y = -48x +692[/tex]

The statement that the situation can be represented by the  equation y = -48x + 692 is true

Read more about linear equations at:

https://brainly.com/question/15602982

Answer:

Step-by-step explanation:

4
en 2 = 21,426
6%-
*8 = 21 - 22 - 24
8
-8=24
16
44-8-8=24 -
2x
47.
4y

Answers

Answer:

Step-by-step explanation:

BOX #1 -- 2x

BOX #2 -- 4x

BOX #3 -- 8

BOX #4 -- 16

BOX #5 -- 4

12x+15y=-45 put into slope-intercept form, simplify all fractions.

Answers

Answer:

y = -4/5 x - 3

Step-by-step explanation:

15y = -45 - 12x

5y = -15 - 4x

y = -4/5 x - 3

A total of 11 trucks was used to carry 126 tonnes of iron. Some of the trucks carry
16 tonnes each, and the rest carry 6 tonnes each. Form an equation and solve it to
find the number of 16 tonne trucks.

Answers

Step-by-step explanation:

x = number of trucks with 16 tonnes capacity

y = number of trucks with 6 tonnes capacity

x + y = 11

16x + 6y = 126

the first equation gives us

x = -y + 11

and we use that in equation 2 :

16(-y + 11) + 6y = 126

-16y + 176 + 6y = 126

-10y = -50

10y = 50

y = 5

x = -y + 11 = -5 + 11 = 6

the number of 16 tonne trucks was 6.

Solve the system of linear equations y= 2x -3Y= x + 6

Answers

Answer:

x=9, y=15. (9, 15).

Step-by-step explanation:

y=2x-3

y=x+6

----------

2x-3=x+6

2x-x-3=6

x-3=6

x=6+3

x=9

y=9+6=15

Please help I’ll give brainliest ASAP

Answers

Answer:

1 I don't know if those are questions but try if they are try the first one a

Find the zeros of ƒ(x) = x3 + 6x2 + 8x.
A) x = 0, –2, –4
B) x = 0, 2, 4
C) x = 2, 4
D) x = –2, –4

Answers

Answer:

Option A: [tex]x=0[/tex], [tex]x=-2[/tex], and [tex]x=-4[/tex]

Step-by-step explanation:

[tex]f(x)=x^3+6x^2+8x[/tex]

[tex]0=x^3+6x^2+8x[/tex]

[tex]0=x(x^2+6x+8)[/tex]

[tex]0=x(x+2)(x+4)[/tex]

[tex]x=0[/tex], [tex]x=-2[/tex], and [tex]x=-4[/tex]

[tex]x^3+6x^2+8x = 0\\\\\implies x^3+2x^2 +4x^2+8x =0\\\\\implies x^2(x+2) +4x (x+2) =0\\\\\implies (x+2)(x^2 +4x) = 0\\\\\implies x (x+2) (x+4)=0\\\\\text{Hence,} \\\\x = 0 ,-2,-4[/tex]

During a cold winter day, the temperature change was - 2.3 f per hour for a period of 6.5 hours. What was the change in temperature during that time?

Answers

Answer:

-14.95 F

Step-by-step explanation:

Given:

Temperature change rate is - 2.3 F per hourTime is 6.5 hours

The change in temperature is:

temperature change rate * time -2.3 * 6.5 = -14.95 F

Which description best describes the three-dimensional object
that is formed when the shape is rotated about the axis as
shown?

Answers

Answer:

cylinder

Step-by-step explanation:

a cylinder would be formed, as the rotation forms a circular base and a rectangular body which can be seen in a cylindrical net.

Answer: A Hollow Cylinder

what color is my shirt?? PLEASE HELP I FORGOT

Answers

Answer:

um

Step-by-step explanation:

Answer:

Its white! atleast i think its white because your pfp has white clothes on

.guys can you solve anything please ​

Answers

Answer:

3.a)2[tex]\sqrt[3]{2}[/tex]

5.a) x=2

Step-by-step explanation:

Answer:

1. If 3^x = 1 then x =0

Step-by-step explanation:

3^0 = 1

3. 2, 9 3, 7, 5, the median is 5

4.3,5,3,4,3 the mode is 3

5. A cube whose volume is 8^3 =(512cm^3)

3. B

A company rents out 11 food booths and 20 game booths at the county fair. The fee for a food booth is $100 plus $9 per day. The fee for a game booth is $95 plus $6 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount in dollars, that the company is paid. The expression is?​

Answers

Answer:

  3000 +219d

Step-by-step explanation:

The food booth rental revenue is ...

  11(100 +9d) = 1100 +99d

The game booth rental revenue is ...

  20(95 +6d) = 1900 +120d

Then the total revenue is ...

  (1100 +99d) +(1900 +120d) = 3000 +219d

which equation is equivalent to -2 (x+3) - 4x = 10?

Answers

Answer:

-6x -6= 10

Step-by-step explanation:

-2(x +3) -4x= 10

Expand:

-2(x) -2(3) -4x= 10

-2x -6 -4x= 10

Simplify:

-6x -6= 10

Thus, the second option is correct.

Write TWO different equations that you could use to solve for x. You don't need to solve.

Answers

Answer:

see explanation

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos52° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{18}{x}[/tex] → (1)

The 3rd angle in the triangle is

180° - (90 + 52)° = 180° - 142° = 38°

Using the sine ratio in the right triangle

sin38° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{18}{x}[/tex] → (2)

Order these numbers from least to greatest

Answers

Answer:

5.125 < 5.14 < 5.15 < 5 2/9

Step-by-step explanation:

i changed 103/20 to a decimal to make it easier and just left 5 2/9 the same, hope this helps <3

Help me plzzzz

Graph y = -3x + 7.​

Answers

Answer:

This is the graph. Hope the pic loads.

anybody help please hehehe​

Answers

Answer:

It is the second one 20^247

Step-by-step explanation:

8x7= something x0.1


please help me

Answers

let something = x

[tex]8 \times 7=x \times 0.1 \\ x = \frac{8 \times 7}{0.1} \\ x = \frac{8 \times 7 \times 10}{1} \\ x = 560[/tex]

therefore, something = 560

correct answer:-8x7= 560 x0.1

Find the value of x and the perimeter of the following shapes:

Answers

Answer:

x=2, perimeter=14

Step-by-step explanation:

Finding x

(x+1)(x+2)

x^2+2x+x+2=12

x^2+3x-10

x^2-2x+5x-10

x(x-2)5(x-2)

(x+5)(x-2)

x=-5

x=2

Length or Width should be a positve number.

x=2

Perimeter:

3+3+4+4=14

IS IT VALID OR NOT (explaining would be helpful) you want to determine how many students consider math to be their favorite school subject. you randomly survey 75 students. thirty-three students consider math to be their favorite subject while forty-two does not. so, you conclude that 40% of students at your school consider math to be their favorite subject.

Answers

Answer:

I would say not valid

Step-by-step explanation:

well, it would actually be 44% since 33/75= 0.44 to represent the number of ppl hat consider math their favorite subject

which of the following equations could be parallel to the equation x = 5

A. y = 5x

B. x = -2

C. y = 5

D. y = x​

Answers

Answer:

B

Step-by-step explanation:

x = 5 is the equation of a vertical line parallel to the y- axis

The equation of a line parallel to it must have the same form, that is

x = - 2 ← vertical line parallel to x = 5

Put the following equation of a line into slope-intercept form, simplifying all
fractions.
x + 2y = -16

Answers

Answer:

y = -1/2x - 8

Step-by-step explanation:

You are looking for the equation in the form of y=mx + b, so you need y on the left hand side without x. Subtract x from both sides.

2y = -x - 16

Now you want 1y instead of 2y. So divide everything by 2.

y = -1/2x - 8

Pilar used five reusable shopping bags on a recent purchase she made at a grocery store. Each bag decreased the amount she spent by 5 cents. What was the change to the amount Pilar spent at the grocery store by using the reusable bags?
A.
-10 cents
B.
25 cents
C.
-25 cents
D.
10 cents

Answers

Answer:

B

Step-by-step explanation:

5x5 = 25

She used 5 bags and saved 5 cents on each one.

1 - 5, 2 - 10, 3 - 15, 4 - 20, 5 - 25.

Hope that helps

HELP SOLVE THIS QUICK
y = 6x + 20
y = -4x + 150

Answers

Answer:

13

Step-by-step explanation:

set equations equal to each other and solve for x

6x + 20 = -4x + 150

10x = 130

X = 13

7m 28cm ÷8= something cm

Answers

Answer:

4cm

Step-by-step explanation:

it this the answer you were looking for?

Answer:

91cm

Step-by-step explanation:

7m to cm =700m

28cm+700cm=728cm

728cm/8=91cm

4 An item is priced at $14.05. If the sales tax is 4%, what does the item cost including sales tay?​

Answers

Answer:

$14.61

Step-by-step explanation:

14.05 * 1.04 = 14.612

what is 21-3+18 divided by 6=6 equal
ehhehehehe u will never find out

Answers

Answer:

I really :3? i’m up for a challenge

Step-by-step explanation:

21 - 3 = 18

18 + 18= 36

36/6= 6

hope this helped!

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