Helppp pleaseeee I really need help

Answer:

[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]

[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1, \frac{\sqrt{3}}{2} - 1[/tex]

Step-by-step explanation:

we are given two coincident points

[tex] \displaystyle P( \sin(θ)+2, \tan(θ)-2) \: \text{and } \\ \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]

since they are coincident points

[tex] \rm \displaystyle P( \sin(θ)+2, \tan(θ)-2) = \displaystyle Q(4 \sin ^{2} (θ)+4 \sin(θ )\cos(θ)+2a \cos(θ), 3 \sin(θ)-2 \cos(θ)+a)[/tex]

By order pair we obtain:

[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2a \cos(θ) = \sin( \theta) + 2 \\ \\ \displaystyle 3 \sin( \theta) - 2 \cos( \theta) + a = \tan( \theta) - 2\end{cases}[/tex]

now we end up with a simultaneous equation as we have two variables

to figure out the simultaneous equation we can consider using substitution method

to do so, make a the subject of the equation.therefore from the second equation we acquire:

[tex] \begin{cases} \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sinθ \cos(θ)+2a \cos(θ )= \sin( \theta) + 2 \\ \\ \boxed{\displaystyle a = \tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) } \end{cases}[/tex]

now substitute:

[tex] \rm\displaystyle \displaystyle 4 \sin ^{2} (θ)+4 \sin(θ) \cos(θ)+2 \cos(θ) \{\tan( \theta) - 2 - 3 \sin( \theta) + 2 \cos( \theta) \}= \sin( \theta) + 2 [/tex]

distribute:

[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ)+4 \sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) - 6 \sin( \theta) \cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]

collect like terms:

[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + 4 \cos ^{2} ( \theta) = \sin( \theta) + 2 [/tex]

rearrange:

[tex]\rm\displaystyle \displaystyle 4 \sin ^{2}( θ) + 4 \cos ^{2} ( \theta) - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) + = \sin( \theta) + 2 [/tex]

by Pythagorean theorem we obtain:

[tex]\rm\displaystyle \displaystyle 4 - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) + 2 [/tex]

cancel 4 from both sides:

[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+2 \sin(θ ) - 4\cos( \theta) = \sin( \theta) - 2[/tex]

move right hand side expression to left hand side and change its sign:

[tex]\rm\displaystyle \displaystyle - 2\sin(θ) \cos(θ)+\sin(θ ) - 4\cos( \theta) + 2 = 0[/tex]

factor out sin:

[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) - 4\cos( \theta) + 2 = 0[/tex]

factor out 2:

[tex]\rm\displaystyle \displaystyle \sin (θ) (- 2 \cos(θ)+1) + 2(- 2\cos( \theta) + 1 ) = 0[/tex]

group:

[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(- 2 \cos(θ)+1) = 0[/tex]

factor out -1:

[tex]\rm\displaystyle \displaystyle - ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]

divide both sides by -1:

[tex]\rm\displaystyle \displaystyle ( \sin (θ) + 2)(2 \cos(θ) - 1) = 0[/tex]

by Zero product property we acquire:

[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) + 2 = 0 \\ \displaystyle2 \cos(θ) - 1= 0 \end{cases}[/tex]

cancel 2 from the first equation and add 1 to the second equation since -1≤sinθ≤1 the first equation is false for any value of theta

[tex] \begin{cases}\rm\displaystyle \displaystyle \sin (θ) \neq - 2 \\ \displaystyle2 \cos(θ) = 1\end{cases}[/tex]

divide both sides by 2:

[tex] \rm\displaystyle \displaystyle \displaystyle \cos(θ) = \frac{1}{2}[/tex]

by unit circle we get:

[tex] \rm\displaystyle \displaystyle \displaystyle θ= {60}^{ \circ} , {300}^{ \circ} [/tex]

so when θ is 60° a is:

[tex] \rm \displaystyle a = \tan( {60}^{ \circ} ) - 2 - 3 \sin( {60}^{ \circ} ) + 2 \cos( {60}^{ \circ} ) [/tex]

recall unit circle:

[tex] \rm \displaystyle a = \sqrt{3} - 2 - \frac{ 3\sqrt{3} }{2} + 2 \cdot \frac{1}{2} [/tex]

simplify which yields:

[tex] \rm \displaystyle a = - \frac{ \sqrt{3} }{2} - 1[/tex]

when θ is 300°

[tex] \rm \displaystyle a = \tan( {300}^{ \circ} ) - 2 - 3 \sin( {300}^{ \circ} ) + 2 \cos( {300}^{ \circ} ) [/tex]

remember unit circle:

[tex] \rm \displaystyle a = - \sqrt{3} - 2 + \frac{3\sqrt{ 3} }{2} + 2 \cdot \frac{1}{2} [/tex]

simplify which yields:

[tex] \rm \displaystyle a = \frac{ \sqrt{3} }{2} - 1[/tex]

and we are done!

disclaimer: also refer the attachment I did it first before answering the question

Answer:

∠ G ≈ 8.3°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan G = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{HI}{GI}[/tex] = [tex]\frac{1.1}{7.5}[/tex] , then

∠ G = [tex]tan^{-1}[/tex] ([tex]\frac{1.1}{7.5}[/tex] ) ≈ 8.3° ( to the nearest tenth )

The total mass of 5 x 10³ microorganisms is  1.2 x [tex]10^{-2}[/tex].

Option C is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Mass of an organism = 2.4 x [tex]10^{-6}[/tex] grams

The total mass of 5 x 10³ microorganism.

= 5 x 10³ x 2.4 x [tex]10^{-6}[/tex]

= 12.0 x [tex]10^{3 - 6}[/tex]

= 12 x [tex]10^{-3}[/tex]

= 1.2 x [tex]10^{-2}[/tex]

Thus,

The total mass is 1.2 x [tex]10^{-2}[/tex]

Learn more about expressions here:p

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Answer:

4.2

Step-by-step explanation:

By intersecting chords theorem:

[tex]x \times 10 = 6 \times 7 \\ \\ 10x = 42 \\ \\ x = \frac{42}{10} \\ \\ x = 4.2[/tex]

Answer:

12

Step-by-step explanation:

Answer:

71

Step-by-step explanation:

ndndnrbrjen3n3nn3b2n2b2b

Answer:

Step-by-step explanation:

so we know that a triangle degrees have to add up to 180 in the inside right? So we know c is 90 and so you need to find A and B. The left over degrees you have is 90 so the sum of B and A would have to be 90, thats all i can help you with sorry.

I guess so 35 ft or more than it

Answer:

There is a little over 1 gallon

Step-by-step explanation:

Answer:

x=0, y=-2

Step-by-step explanation:

6x0=0

2(-2)=-4

so, -4=-4 so it is determined true

Then 0-2(-2), -2(-2)=4

subtract 0 from 4 which is 4

so, 4=4, so it is determined true

Answer:

What?

Step-by-step explanation:

G8ve me more info and Ill answer again

Answer:

Its A let me know if im wrong!

Answer:

Fourth option is most suitable here.

Answer:

6 passengers got off at New Jersey

Step-by-step explanation:

let the number of passengers who got off be x and let the number of passengers who boarded the bus be y

y=2x

44 - x + y=50

y=50-44+x

y=6+x

subst y=2x

2x=6+x

2x-x=6

x=6

Answer:

hope this helps

Step-by-step explanation:

31 divided by 2 = 15.5 then do 15.5 x 15.5= 240.25 then you do 240.25 x 3.14 = 754.385

Answer:answer is 2.5v+5<5v A.k.a:A

Step-by-step explanation:

Answer:

[tex] \frac{108}{2 } = 54[/tex]

The value of y for the given circle will be 54°.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

The diameter is the longest line that can be drawn inside a circle.

In our daily life, we always see circle objects for example our bike wheel.

Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.

In the given question by the circle theorem that if a curve makes a 2x angle then the extreme point will make the angle on circle as x.

So angle y = half of angle 108°

∠Y = 108°/2 = 54°

Angle w will also same as 54° because it also satisfies the theorem of the circle.

To learn more about the circle,

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Answer:

The angle between the two blades is 120 degree.

Step-by-step explanation:

number of blades = 3

The blades are equally spaced.

The total angle around a circle is 360 degree.

So, the angle between the two blades is given by

[tex]\theta =\frac{360}{n}\\\theta =\frac{360}{3} = 120^{o}[/tex]

Answer:

8 1/3 or 8.33 yards per second

Step-by-step explanation:

100/12 = 8 1/3

Answer:

Hi, there the answer is Graph A because the y-intercept and I did rise over run

Step-by-step explanation:

Hope this helps :)

Answer:

Option 2

Step-by-step explanation:

10:28 plus 47 is 11:15

Answer:

Taking 45 degree as reference angle

Then using sine rule

sin 45=

p/h

replacing the value of sin 45 degree by 1/root 2.so

1/root 2=9/c

doing cross multiplication

9*root 2=1*c

9 root 2 =c

therefore the value of c is 9 root 2

Step-by-step explanation:

Answer:

-|7|, |4|, |2-9|, |6+4|

Step-by-step explanation:

I think this is correct

Answer:

i don't know that language sorry

Step-by-step explanation:

Answer:

Hello! answer: 62.8

Step-by-step explanation:

Cirmcumfrence is just diameter × pi so since we are using 3.14 for pi we can just do 3.14 × 20 so...

3.14 × 20 = 62.8 Therefore the circumference is 62.8 Hope that helps!

I'll do problem 1 to get you started

First sort the values from smallest to largest and you should end up with this set

{1, 6, 7, 11, 13, 16, 18, 21, 22, 23}

The smallest value is 1 and the largest value is 23, so the min and max are 1 and 23 in that order.

We have ten values in this set. The middle-most number is going to be between the 10/2 = 5th slot and the 6th slot. The numbers 13 and 16 are in the fifth and sixth slots respectively. Average those values to get (13+16)/2 = 29/2 = 14.5

The median is 14.5 which is another name for the second quartile (Q2).

Now split the data set into two halves

L = lower half of values smaller than the median

U = upper half of values larger than the median

In this case,

L = {1, 6, 7, 11, 13}

U = {16, 18, 21, 22, 23}

sets L and U have five items each

Find the median of set L and U to get 7 and 21 respectively. These medians of L and U represent the values of Q1 and Q3 in that order.

Q1 = first quartile = 7

Q3 = third quartile = 21

===================================================

Answer:

The five number summary for problem 1 is

Answer: False and x = sqrt(10^2 - 6^2) km

Step-by-step explanation:

1. False

2.Use Pythagoras theorem. The distance between the cars, 10km, is the hypotenuse of a right angled triangle, one leg of which is 6km and the other of which is, say, x km

x = sqrt(10^2 - 6^2) km.

Please mark me brainliest

Answer:

B 18.79

Step-by-step explanation:

Answer:

B

Step-by-step explanation: