Which angles are adjacent to each other?

Angle 8 and Angle 5
Angle 4 and Angle 6
Angle 5 and Angle 3
Angle 11 and Angle 8​

Answer:

a. i) ∠TUV = 39°

ii) The measure of arc VTS (the minor arc) = 102°

b. The diameter OT of the circle = 12

c. The angle which we can calculate, given ∠MOP, is angle ∠OTM = 51°

i) Arc MVT = 98° and arc MO = 82°

Step-by-step explanation:

The given parameters are;

The radius of the circle = 6

∠SUT = 39°, ∠MOP = 49°

a. i) According to two tangent theory, two tangents that meet at a given point are congruent

Therefore, VU is congruent to SU

Given that PU is congruent to PU by reflexive property and PV = PS = The radius of the circle, we have;

ΔPVU is congruent to ΔPSU by Side Side Side (SSS) rule of congruency

∠SUT ≅ ∠TUV by Congruent Parts of Congruent Triangles are Congruent (CPCTC)

Therefore, ∠SUT = ∠TUV = 39° by transitive property of equality

ii) Arc VTS is the minor arc while arc VOS is the major arc by size

The arc measure that describes arc VTS is the minor arc

iii) From circle theorem, we have that the sum of the angle formed by two tangents and the minor arc equals 180°

Therefore, ∠SUT + ∠TUV + arc VTS = 180°

∴ Arc VTS = 180° - (39° + 39°) = 102°

b. The line segment length that can be calculated based on knowing the radius length includes the length of the diameter OT of the circle

The diameter OT = 2 × The length of the radius

∴ The diameter OT = 2 × 6 = 12

c. The angle ∠MOP, is an interior angle of the right triangle ΔTMO formed by the diameter of the circle, OT, therefore, given that ∠MOP = 39°, we have;

∠OTM = 90° - ∠MOP

∴ ∠OTM = 90° - 39° = 51°

∠OTM = 51°

Therefore, given ∠MOP, we can calculate angle ∠OTM

i) The arc that we can calculate, given ∠MOP are arc MVT and arc MO

Arc MVT = 2 × ∠MOP

∴ Arc MVT = 2 × 49° = 98°

Arc MO = 2 × ∠OTM

∴ Arc MO = 2 × (90° - 49°) = 82°

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Work Shown:

4x^3 - 4

4(x^3 - 1)

4(x - 1)(x^2 + x + 1)

In the last step, I used the difference of cubes factoring formula which is

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Answer:

yes

Step-by-step explanation:

in parallelogram ,<A=<C

<C=<D

then <D=115=<C=115

X+115+30=180....TRIANGLE THEROME

X=35

so that,<A=65

<C=65

Answer:

x = 126

Step-by-step explanation:

The angles are complementary which means they sum to 180

x+54 =180

x = 180-54

x = 126

Answer:

....ans

hope it helps you

hope this help you

have a great day

Answer:

3/1 times 1/4, 3/2 times 1/2, 9/8 times 2/3

Answer:

1/2 & 3/2

Step-by-step explanation:

1/2 X 3/2 = 3/4

To get this answer, you need to think of two numbers which we can multiply to get 3 and two numbers which we can multiply to get 4.

Answer from Gauthmath

Answer:

80k

Step-by-step explanation:

let the previous weight be x

88=x + 10%of x

88=x+(10/100)of x

8800=110x

8800/110=x

x=80k

Answer: Original weight = 80 kg

Step-by-step explanation:

Given:

Current weight = 88 Kg

Gain weight rate = 10%

Solve:

Original weight = Current weight / Gain rate

Original weight = (88) / (1 + 10%)

Original weight = 80 Kg

Hope this helps!! :)

Please let me know if you have any questions

Answer:

They got 3.00 back

Step-by-step explanation:

Since they both bought a book it means you have to double the price of one book.

3.50+3.50=7.00

Then since you are looking for the difference of 10.00 you would subtract it.

10.00-7.00=3.00

Answer:

363

Step-by-step explanation:

Formula for area of a circle

A = πr^2

Where r = radius

The circle has a given radius of 11

To find the area of the circle we simply substitute r in the formula with the value of the radius (11)

( Also note that the question says to use 3 for π )

A = πr^2

π = 3

r = 11

Substitute values in formula

A = (3)(11)^2

11^2 = 121

A = 121(3)

121(3) = 363

A = 363

Answer:

22= 2(pi)(r)(45/360)

28.01

C=176

Step-by-step explanation:

Step-by-step explanation:

here's the answer to your question

Answer:

y^(2/3)

Step-by-step explanation:

( y ^ ( 7/3) * y^ ( 1/3)  ) ^ 1/4

Combine the terms in side the parentheses

a^b* a^c = a^(b+c)

( y ^ ( 7/3+ 1/3)  ) ^ 1/4

( y^( 8/3) )^1/4

We know a^b^c = a^(b*c)

y ^(8/3*1/4)

y^(2/3)

the answer to this question is the slope is 43

Answer:

Therefore, the slope is 3/4

Step-by-step explanation:

An x -intercept is the value of x when y=0 , so an x-intercept of 4 can be written as a coordinate on the graph as (4,0)

Likewise, an

y -intercept is the value of y when x=0 , so an y -intercept of −3can be written as a coordinate on the graph as (0,-3)

Now we have two points(4,0) (0,-3)

To find the slope given two points, we use the formula

rise÷run , or y2−y1÷x2−x1 .

Plug in the given points into the formula

-3-0/0-4

-3/-4

3/4

Therefore, the slope is 3/4

Hope this helps!

If the perimeter is 16' the sum of the length and width must be 8'. Assuming that area is non 0 possible dimensions are:

1x7 2x6 3x5 4x4 5x3 6x2 7x1

Answer:

a- 15 b- 1292^cm this is the answer

Answer:

x = 6

Step-by-step explanation:

Since GH bisects LM at K , then

LK = [tex]\frac{1}{2}[/tex] LM , that is

5x + 2 = [tex]\frac{1}{2}[/tex] × 64 = 32 ( subtract 2 from both sides )

5x = 30 ( divide both sides by 5 )

x = 6

The value of x is 6.

Here,

GH bisects LM at K.

LK = 5x+2 and LM = 64

We have to find the value of x.

What is Bisection in line?

Bisecting a line is cutting a line exactly in half. It may also be referred to as constructing a perpendicular bisector as the line you are drawing will be at a right angle to the original line.

Now,

GH bisects LM at K.

LK + KM = LM

2 LK = LM

2 ( 5x + 2 ) = 64

5x + 2 = 32

5x = 30

x = 6

Hence, The value of x is 6.

Learn more about the Bisection of line visit:

https://brainly.in/question/10606306

#SPJ2

[tex] \frac{ \sin(20 \degree) }{ \cos(70\degree) } + \frac{ \cos(35\degree) }{ \sin( 65\degree)} [/tex]

[tex] \frac{ \sin(20 \degree) }{ \cos(70\degree) } + \frac{ \cos(35\degree) }{ \sin( 65\degree)} [/tex]

[tex] \sin( \theta) = \cos(90 - \theta) \\ \\ \cos( \theta) = \sin(90 - \theta) [/tex]

So putting down the value

[tex] \frac{ \cos(90 - 20 \degree) }{ \cos(70\degree) } + \frac{ \sin(90 - 35\degree) }{ \sin( 65\degree)} [/tex]

[tex] \frac{ \cos(70\degree) }{ \cos(70\degree) } + \frac{ \sin(65\degree) }{ \sin( 65\degree)} [/tex]

[tex]\frac{\cancel{\cos(70\degree)}}{ \cancel{\cos(70\degree)}} + \frac{\cancel{\sin(65\degree)}}{\cancel{\sin( 65\degree)}} [/tex]

[tex] \frac{1}{1} + \frac{1}{1} \\ 1 + 1 = 2 \: \: ans[/tex]

Answer:

∠ L ≈ 52°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cosL = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{LM}{LN}[/tex] = [tex]\frac{8}{13}[/tex] , then

∡ L = [tex]cos^{-1}[/tex] ([tex]\frac{8}{13}[/tex] ) ≈ 52° ( to the nearest degree )

Answer:

Step-by-step explanation:

In the equation y = mx + b, which is the form Ingrid's equation is in, the m stands for the rate of change. If the water level is decreasing, the rate at which it is decreasing is what goes in for m. The "b" of that equation indicates the starting height of the water, which is 170. The equation should be:

y = -4x + 170, negative because the water is decreasing.

Answer:

"t" is not a specific thing, this is just the sign of your variable.

t = 4 × 2.5

t = 10

Answer:

[tex]{ \sf{( \sec \theta - \csc \theta)(1 + \tan \theta + \cot \theta) }} \\ = { \sf{( \sec \theta + \tan \theta \sec \theta + \cot \theta \sec \theta) - ( \csc \theta - \csc \theta \tan \theta - \csc \theta \cot \theta)}} \\ = { \sf{( \sec \theta + \sec \theta \tan \theta + \csc \theta) - ( \csc \theta - \sec \theta - \csc \theta \cot \theta)}} \\ = { \sf{ \sec \theta \tan \theta + \csc \theta \cot \theta }} \\ { \bf{hence \: proved}}[/tex]

Answer:

a. 29

b. 3 is added each time

Step-by-step explanation:

In the given rule, n represents the term number. So, when k=2, n would be 1 because it is the first term. Therefore, to find the 10th term, plug 10 in for n, then solve. The equation would look like [tex]k=3(10)-1[/tex] which equals 29.

The pattern for this type of sequence is known as the common difference because it is the amount that is added each term. You know this because when reading the sequence you can see that it is increasing by 3. Additionally, in the rule, 3 is being multiplied by n, this shows that 3 is the common difference/pattern.

Answer:

29

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number is in the form of aabb.

We can put it as:

The number is a perfect square so it must be divisible by 11.

It is divisible by 11 if (a + b) is divisible by 11..

On the other hand, b = 0, 1, 4, 5, 6, 9 as the last digit of a perfect square.

Also, both a and b must be within (0,9) interval.

Considering the above conditions we have options:

The numbers are:

By testing we confirm only one of them is a perfect square:

Answer:

All of them: A, B, and C

Step-by-step explanation:

Answer:

A, B, and C

Step-by-step explanation:

Recall the exponent property [tex](a^b)^c=a^{(b\cdot c)[/tex].

Therefore,

[tex](v^{-1})^{1/9}=(v^{1/9})^-1=v^{-1/9}[/tex]

In addition, fraction exponents can be written as radicals such that:

[tex]a^{b/c}=\sqrt[c]{a^b}[/tex]

Thus, [tex](\sqrt[9]{v})^{-1}=(v^{1/9})^{-1}=(v^{-1})^{1/9}[/tex].

Therefore, answer choices A, B, and C are correct.

Step-by-step explanation:

GIVEN =

d= 49cm

[tex]\pi = \frac{22}{7} [/tex]

To find = Circumference of a circle

SOLUTION =

CIRCUMFERENCE OF THE CIRCLE = πd

[tex] \frac{22}{7} \times 49[/tex]

= 22 × 7

154cm

the circumference of the given circle is 154cm

Answer:

Step-by-step explanation:

5) diameter = d = 49 cm

Circumference = πd

                         [tex]= \frac{22}{7}*49\\\\= 22 *7\\\\= 154 \ cm[/tex]

6) d = 20 mm

Circumference = π* 20

                         = 20π mm

Answer:

an = 400*(1/2)^(n - 1) which is C is the most common answer.

Step-by-step explanation:

What did you have to do to get 400 as the first term?

There are two answers.

an = 400 * (1/2)^(n - 1)

an = 400 * (1/2)^n

Which one is the answer?

The answer is the one that leaves 400 as the first term.

a1 = 400*(1/2)^(n-1) should be the answer.

400*(1/2)^n  is unfortunately sometimes used. In which case, the first term is a^0

A1 = 400 (1/2)^(n - 1) is the usual for that describes the series.

Answer:

the inequality is 0<x<4

Step-by-step explanation:

(0,4)

Answer:

FH ≈ 15.20

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

(leg of large triangle)² = (part of hypotenuse below it ) × (whole hypotenuse )

FH² = 11 × (11 + 10) = 11 × 21 = 231 ( take the square root of both sides )

FH = [tex]\sqrt{231}[/tex] ≈ 15.20 ( to 2 dec. places )