Name the marked angle in 2 different ways.

Answer:

[tex]\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}[/tex]

Step-by-step explanation:

Given

[tex]\sin(105^o)[/tex]

Required

Solve

Using sine rule, we have:

[tex]\sin(A + B) = \sin(A)\cos(B) + \sin(B)\cos(A)[/tex]

This gives:

[tex]\sin(105^o) = \sin(60 + 45)[/tex]

So, we have:

[tex]\sin(60 + 45) = \sin(60)\cos(45) + \sin(45)\cos(60)[/tex]

In radical forms, we have:

[tex]\sin(60 + 45) = \frac{\sqrt 3}{2} * \frac{\sqrt 2}{2} + \frac{\sqrt 2}{2} * \frac{1}{2}[/tex]

[tex]\sin(60 + 45) = \frac{\sqrt 6}{4} + \frac{\sqrt 2}{4}[/tex]

Take LCM

[tex]\sin(60 + 45) = \frac{\sqrt 6 + \sqrt 2}{4}[/tex]

Rewrite as:

[tex]\sin(60 + 45) = \frac{\sqrt 2 + \sqrt 6}{4}[/tex]

Hence:

[tex]\sin(105) = \frac{\sqrt 2 + \sqrt 6}{4}[/tex]

Since your question doesn't specify what form you need your answer in, I’ll answer in slope intercept form.

Slope intercept form looks like this: y = mx + b.

m represents slope, b represents y intercept. we already have the slope, 2. To find the y intercept, we can plug in the given values for x and y and solve for x.

y = 2x + b

5 = 2(8) + b

5 = 16 + b

- 11 = b

so, the y intercept is - 11. we can plug this into your equation.

y = 2x - 11

There you go! this is your final answer.

Answer:

Given:

A figure in which a transversal line intersect the two parallel lines.

To find:

The missing value for the equation [tex]m\angle \_+m\angle BPD=180^\circ[/tex]

Solution:

In the given figure, the two parallel lines are line ED and line AB, and CD is the transversal line.

Angle BPC and angle BPD lie on a straight line CD. So,

[tex]m\angle BPC+m\angle BPD=180^\circ[/tex]          (Supplementary angles)

Angle APD and angle BPD lie on a straight line AB. So,

[tex]m\angle APD+m\angle BPD=180^\circ[/tex]          (Supplementary angles)

Therefore, the required complete equations are [tex]m\angle BPC+m\angle BPD=180^\circ[/tex] and [tex]m\angle APD+m\angle BPD=180^\circ[/tex].

Answer:

6.25

Step-by-step explanation:

3x+25=7x

3x-7x=-25

-4x=-25

x=6.25

Answer:

so easy q.

bc u r in 7th lol

it's 60

for both

Answer:

1. 4hrs and 10mnts

2. 13 builders

3. 25 walls

4. 52 toy soldiers

Step-by-step explanation:

1. then, one man can do it in 16hrs and 40mnts, so, 4 men would take 4hrs and 10mnts

2. one builder can build 4 houses in a year, so 13 builders are needed to build 52 houses

3. they can do it at a rate of 2 walls per person for 3 days, so 10 ppl can make 25 walls in 3.75 days

4. 4 toys per person for 2 weeks, so 7 makers can make 52 toys for 3 weeks

Answer:

Step-by-step explanation:

Compound ratio is the multiplication of the ratios:

Multiply to get:

Given ratios,

2/15 : 3/7 and 5/8 : 14/27

Then to find the compound ratio,

We have to multiply,

→ (2/15 × 5/8) : (3/7 × 14/27)

→ 10/120 : 42/189

Now simplify the ratio,

→ 1/12 : 2/9

Thus, required ratio is 1/12 : 2/9.

Answer:

The expression for the perimeter of the rectangle is:

P = 2*(12 cm) + 2*(7 cm)

And the perimeter is:

P = 38cm

Step-by-step explanation:

We know that for a rectangle of length L and width W, the perimeter is given by:

P = 2*L + 2*W

So, if we have a rectangle that is 12 cm long,  we have L = 12cm

and if the rectangle is 7cm wide, we have W = 7cm

Now we can replace these in the perimeter equation to get:

P = 2*(12 cm) + 2*(7 cm)

P = 24cm + 14cm

P = 38cm

[tex]804.2\:ft^{2}[/tex]

Step-by-step explanation:

[tex]A=4 \pi r^{2}[/tex]

We are given D = 16 ft, which means that r = (1/2)D = 8 ft. Therefore, the surface area of the sphere is

[tex]A=4 \pi (8 ft)^{2} = 804.2\:ft^{2}[/tex]

The surface area of the sphere is approximately 804.2 square feet.

It is a three-dimensional figure where the volume is given as:

The volume of a sphere = 4/3 πr³

We have,

The surface area of a sphere with diameter d is given by the formula:

SA = 4πr²

where r is the radius of the sphere, which is half the diameter. In this case, the diameter is 16 feet, so the radius is 8 feet.

Plugging in the value of r, we get:

SA = 4π(8²)

SA = 4π(64)

SA = 256π

Rounding to the nearest tenth gives:

SA ≈ 804.2 square feet

Therefore,

The surface area of the sphere is approximately 804.2 square feet.

Learn more about sphere here:

https://brainly.com/question/12390313

#SPJ7

Answer:

ok so this means 2/5 of the plant have germs and

5-2=3

so 3/5 plants are all good

5 times 20=100

3 times 20=60

so 60% of the plants have germs

Hope This Helps!!!

Answer:

87 minutes

Step-by-step explanation:

Let the total number of minutes = m

Our equation is given as:

$20.21 = $14.99 + 0.06m

20.21 = 14.99 + 0.06m

Collect like terms

0.06m= 20.21 - 14.99

0.06m = 5.22

m = 5.22/0.06

m = 87

Therefore, the total number rod minutes used is 87 minutes

Answer:

Draw the number line like in the picture.

Step-by-step explanation:

√5 is about 2.236, meaning it's kind of close to 2.25.

√7 is about 2.646, meaning it's very close to 2.625.

Answer:

question says D = f + fx,

then,

D = 2fx

so,

D/2f = x

Answer:

3/4 mile

Step-by-step explanation:

[tex]A = l *w\\\frac{1}{2} = \frac{2}{3} * w\\w = \frac{3}{2} * \frac{1}{2}\\w = 3/4 mile[/tex]

Answer:

option 4

Step-by-step explanation:

Given Equation :-

=> -4| x + 9 | = -8

To FinD :-

=> Solution of the equation .

Solving it :-

=> -4| x + 9 | = -8

=> | x + 9 | = -8/-4

=> |x + 9| = 2

=> ( | x + 9 | )² = 2²

=> x + 9 = ±2

=> x = -9 +2 , -9-2

=> x = - 7 , -11

Option 4 is correct.

Answer:

x = - 7 , - 11

Step-by-step explanation:

[tex]-4 | x +9| = - 8\\\\\frac{-4}{-4} |x+9| = \frac{-8}{-4}\\\\1 | x+9| = 2\\\\x+9 = - 2\ , x + 9 = 2\\\\x + 9 - 9 = - 2 - 9 , \ x + 9 - 9 = 2 - 9\\\\x + 0 = - 1 1 \ , \ x + 0 = - 7\\\\x = -11 \ , \ x = - 7[/tex]

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⊹˚ʚ ❑Answer︰3+(10n)

      ✎Daily reminder: make sure to eat food and stay hydrated, have a good day :D

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Answer:

½

Step-by-step explanation:

the scale factor of dilation = 6/12 = ½

Answer:

an irrational number

Step-by-step explanation:

Answer:

Irrational numbers

Step-by-step explanation:

First, to solve this question, we need to know what irrational numbers are. Irrational numbers are numbers that cannot be expressed as a simple fraction. A nonterminating decimal cannot be expressed as a simple fraction, therefore making it an irrational number.

Hope this helps!

Answer:

just click in the box it literally says

2.) z varies jointly as x and y. If z = 26 when x = 4 and y = 6, find the constant of variation and the equation of the relation.

[tex]\sf{z = kxy}[/tex]

[tex]\sf\rightarrow{16=k(4)(6)}[/tex]

[tex]\sf\rightarrow{K= \frac{16}{24} }[/tex]

[tex]\sf\rightarrow{K={\color{magenta}{ \frac{2}{3} }}}[/tex]

The equation of variation is,

[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \color{red}\sf{z = \frac{2}{3} \: xy.}[/tex]

[tex]{\large{——————————————————}}[/tex]

#CarryOnMath⸙

2.) z varies jointly as x and y. If z = 26 when x = 4 and y = 6, find the constant of variation and the equation of the relation.

[tex]\large \rightarrow \bf {The \: answer \:is \: {\green{z = \frac{3}{2} \: xy}}}[/tex]

Answer:

The length if the garden is 21 meters.

The width of the garden is 5.25 meters.

If the scale changes to 1 cm : 9 meters, the new length of the garden is 63 meters and the new width of the garden is 15.75 meters.

The new length of the garden is 3 times as long as the original length of the garden.

Answer:

D/4 - 21

C/3 - 5.25

D/4 - 63

C/3 - 15.75

B/2 - 3

Step-by-step explanation:

Answer:

brainllest if right

90

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

those alternate angles are equal to each other

5x+4=59

5x=55

x=11

Answer:

(5x + 4) = 59

5x = 59 - 4

5x = 55

x = 55/5

x = 11

Answer:

See Explanation

Step-by-step explanation:

According to the Question,

Thus, m∠T + m∠S = 90 ------ Equation 1

&  m∠S + m∠U = 90  ------- Equation 2

m∠T - m∠U = 0

Thus, m∠T = m∠U

The measure of angle T is equal to angle U.(∠U≅∠T).

Answer:

D

Step-by-step explanation:

90-55=35 degrees ;)

Answer:

D

Step-by-step explanation:

as we know that all the angles in a rectangle are 90° so the,

you will get 90° - 55° = 35°

option D is the right answer.

Answer: it should just be 6.57

Step-by-step explanation:

Answer:

y= 5x

Step-by-step explanation:

since each x number is 1/5 of the y, it's 5 times x = y

Answer:

x = 13°

Step-by-step explanation:

Since the lines are parallel , then

the lower left vertex of the triangle = 85° ( alternate angles )

the lower right vertex of the triangle = 180° - 98° = 82° ( adjacent angles )

Then

x = 180° - (82 + 85)° = 180° - 167° = 13° ( angle sum of triangle )

Answer:

The curve surface area(CSA) of a cylinder is 2πrh.

Since diameter=1.5 in.

          radius=diameter/2

                     =1.5/2 in.

                     =0.75 in.

And, the height of the bottle is 5 in.

Now,

CSA=2πrh

       =2π*0.75*5 in^2

       =15π/2 or 23.56 in^2

The size of the label needed to cover the entire bottle is 15π/2 or 23.56 in^2.

Answer:

5n - 2

Step-by-step explanation:

3 + x = 8

8 - 3 = 5

5 = x

3 (first term) - 5 = -2

5n - 2

Answer:

nth term = 5n - 2

Step-by-step explanation:

The given sequence is 3, 8, 13, 18.

To find the nth term, we have to find the algebraic expression.

So, d = 8 - 3

    d = 5

b = first term - common difference

b = 3 - 5

b = (-2)

Algebraic expression or the nth term =

5n + (-2)

5n - 2.

Thus, the nth term equals to 5n-2!