If y= x^2+3x+5, evaluate y given x= 2+i .

Answer:

1/2

Step-by-step explanation:

We have [tex]\cos(\arccsc(\frac{2\sqrt{3}}{3}))[/tex].

Let [tex]u=\arccsc(\frac{2\sqrt{3}}{3})[/tex].

This implies [tex]\csc(u)=\frac{2\sqrt{3}}{3}[/tex].

Use that sine and cosecant are reciprocals.

[tex]\sin(u)=\frac{3}{2\sqrt{3}}[/tex]

Now I'm going to rationalize the denominator there by multiply numerator and denominator by [tex]\sqrt{3}[/tex]:

[tex]\sin(u)=\frac{3\sqrt{3}}{2(3)}[/tex]

[tex]\sin(u)=\frac{3\sqrt{3}}{6}[/tex]

Reduce the fraction:

[tex]\sin(u)=\frac{\sqrt{3}}{2}[/tex]

Now I'm going to use a Pythagorean Identity: [tex]\cos^2(u)+\sin^2(u)=1[/tex].

This will give me the value of cos(u) which would give me the answer to my question if it exists.

Replace [tex]\sin(u)[/tex] with [tex]\frac{\sqrt{3}}{2}[/tex] in:

[tex]\cos^2(u)+\sin^2(u)=1[/tex]

[tex]\cos^2(u)+(\frac{\sqrt{3}}{2})^2=1[/tex]

[tex]\cos^2(u)+\frac{3}{4}=1[/tex]

Subtract 3/4 on both sides:

[tex]\cos^2(u)=\frac{1}{4}[/tex]

Square root both sides:

[tex]\cos(u)=\pm \frac{1}{2}[/tex] (since 1/2*1/2=1/4 or -1/2*-1/2=1/4)

Now we must decide between the positive or the negative.

It depends where u lies.  What quadrant? Hopefully it lays between 0 and [tex]\pi[/tex].  Otherwise, it doesn't exist (unless you have a different definition for arc function).

So u led to this equation earlier:

[tex]\sin(u)=\frac{\sqrt{3}}{2}[/tex]

arcsin( ) only has outputs between [tex]\frac{-\pi}{2}[/tex] and [tex]\frac{\pi}{2}[/tex].

This would have to be in the first quadrant because we have only positive sine values there.

So this means cos(u)=1/2 and not -1/2 because we are using that u is in the 1st quadrant.

Remember u was [tex]\arccsc(\frac{2\sqrt{3}}{3})[/tex].

So we have actually evaluated

[tex]\cos(\arccsc(\frac{2\sqrt{3}}{3}))[/tex] without a calculator.

The value is 1/2.

Answer:

About 405

Step-by-step explanation:

570 CDs were sold the first quarter.

The second quarter CDs had dropped 29% from the first quarter (570).

Dropped, you should think you are subtracting.

So we need to

simplify 570-.29(570):

570(1-.29)

570(.71)

404.7

404.7 --> 405 (when rounded)

In order to find the answer to your question, we would need to find how much of 570 is 29%, and subtract that number to 570.

The reason why we would do this is because in the question, it says that the sales dropped 29% for one quarter to the next. This means that the next quarter would drop 29%.

We know that they sold 570 units, so we would use 570 in our calculations.

We know that the sales decrease by 29%, so we would multiply 570 by 0.29 to find how much of 570 is 29%.

[tex]570*0.29=165.3[/tex]

29% of 570 is 165.3

What we would do now is subtract 570 by 165.3 in order to fin how much sales they made in the next quarter.

[tex]570-165.3=404.7[/tex]

Once you're done solving, you would get the answer of 404.7

This means that they sold 404.7 (405 when rounded) CDs in the next quarter.

Answer:

D) 160π/3 units²

Step-by-step explanation:

Step 1: Write the formula for area of sector

Area of sector = 1/2 x r² x angle in radians

Step 2: Substitute values in the formula

Area of sector = 1/2 x 8² x 5π/3

Step 3: Solve to find the value of area of sector

Area of sector = 160π/3 units²

Therefore, the correct option is D

!!

Answer:

Step-by-step explanation:

3*√12 * 5*√2

15 √24

15 √(2*2*2*3)

15*2 √6

30√6

Answer:

y = x² ⇒ answer C

Step-by-step explanation:

* Lets explain the problem

∵ The function is y = 1/2 x² + 3 , that means the parent function is

  transformed by some transformation

- If the parent function is y = x²

- y = x² is a quadratic function represented graphically by upward

 parabola with vertex (0 , 0)

∵ y = x² changed to y = 1/2 x² that means we multiply each

  y-coordinates of the points on the graph of the function by 1/2

∴ The graph of the function is  compressed vertically by scale

   factor 1/2

- That means the graph is squeezing toward the x-axis

∵ y = 1/2 x² changed to y = 1/2 x² + 3 that means we add each

  y-coordinates of the points on the graph of the function by 3

∴ The function translated 3 units up

- That means the vertex of the parabola changed to (0 , 3)

∴ The new function is y = 1/2 x² + 3

* The parent function of y = 1/2 x² + 3 is y = x²

# Look to the attached graph for more understand

- y = x² ⇒ the red graph (parent function)

- y = 1/2 x² + 3 ⇒ the blue graph

Given that area of circle is 64cm we can assume we will need to first find radius and then calculate circumference.

First we know that area of a circle is [tex]A=\pi r^2[/tex] hence [tex]r=\sqrt{\dfrac{A}{\pi}}[/tex]

We can now put in our area,

[tex]r=\sqrt{\dfrac{64}{\pi}}\approx20.37[/tex]

Then we use the formula for circumference,

[tex]C=2\pi r\Longrightarrow C=2\pi\cdot20.37\approx\boxed{128\mathbf{cm}}[/tex]

Hope this helps.

r3t40

Answer:

120

Step-by-step explanation:

a pex

Step-by-step explanation:

Area of a rectangular backyard is given as 55 m²

the length is 1 m greater than the twice the width

=>l=2w+1---(say A)

we know that

Area of a rectangle is always length * width=A=l*w

Divide both sides by w

A/w=l

put this value of l in (A)

A/w=2w+1

multiply both sides by w

A=w(2w+1)

55=2w²+w

subtract 55 from both sides

2w²+w-55=0

2w²-10w+11w-55=0

2w(w-5)+11(w-5)=0

(2w+11)(w-5)=0

(2w+11=0 , w-5=0

2w=-11. , w=5

w=-11/2 m

width can never be a negative integer so we omit -11/2

we will consider w=5m

put this in (A)

l= 2(5)+1

l=10+1

l=11m

checking ,

A=lw

A=(11m)(5m)

A=55m²

Answer:

5

Step-by-step explanation:

Area= 55

width=y(unknown)

length=1+2y(given)

formula for finding A.=l*b

(1+2y)(y)= y+2y^2

y+2y^2=55

2y^2= 55-y

y=5

verification

2*5^2=55-5

2*25=55-5

Answer:

9:36 p.m.

Step-by-step explanation:

10 am + 12 hours = 10:00 pm

2 minutes every hour

12 hours x 2 = 24 minutes

12*2=24

10:00+12:00-0:24=21:36

Answer:

B. -2√2 - 5

C. 2√2 - 5

Step-by-step explanation:

The left side of the equation is already a perfect square.

Let us factorize it first.

x²+10x+25=8

x(x+5)+x(x+5)=8

(x+5)²=8

Let us take the square roots of both sides.

x+5=±√8

But √8=±2√2

Therefore in surd form, the two solutions become:

x+5=2√2 or x+5=-2√2

Therefore x= 2√2-5 and -2√2+-5

Answer:

C. 3.131131113…

Step-by-step explanation:

Irrational numbers cannot be written as a ratio of two integers and irrational numbers can have decimal that goes on forever without repeating

C. 3.131131113…

It's a decimal which is not repeating, therefore it's an irrational number.

[tex]\text{Use pythagorean theorem}[/tex]

[tex]$a^2 + b^2 = c^2 \longrightarrow a^2 +6^2=9^2 \longrightarrow a^2 =45\longrightarrow a =6.7082\longrightarrow a = 6.71$[/tex]

[tex]\textbf{a = 6.71}[/tex]

This is a right triangle and to solve this you must use Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 6

b = x

c = 9

^^^Plug these numbers into the theorem

[tex]6^{2} +x^{2} =9^{2}[/tex]

simplify

36 + [tex]x^{2}[/tex] = 81

Now bring 36 to the right side by subtracting 36 to both sides (what you do on one side you must do to the other). Since 36 is being added on the left side, subtraction (the opposite of addition) will cancel it out (make it zero) from the left side and bring it over to the right side.

36 - 36 + [tex]x^{2}[/tex] = 81 - 36

0 + [tex]x^{2}[/tex] = 45

[tex]x^{2}[/tex] = 45

To remove the square from x take the square root of both sides to get you...

x = √45

x ≈ 6.71

(choice A)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The correct answer option is B. 126°.

Step-by-step explanation:

We are given a figure where triangle within a triangle is inscribed in a circle and we are to find the measure of angle b.

From the given figure, we can see that the angle b is at the center of the circle. So this must be an isosceles with two sides equal to each other.

If that is the case, then angle a must be equal to 27° so we can find the measure of angle b.

∠b = 180° - (27° + 27°)

∠b = 126°

Answer:

The quotient is x³+x²+x+1

Step-by-step explanation:

=(x^4-1) ÷ (x-1)

=(x^4-1)/ (x-1)

Solve the numerator by using perfect square formula:

⇒x^4-1 = (x²-1)(x²+1)

=(x²-1)(x²+1)/(x-1)

Further solve the numerator by using perfect square formula:

=(x+1)(x-1)(x²+1)/(x-1)

Cancel the like terms of numerator and denominator

We get;

=(x+1)(x²+1)

Multiply the terms:

=x³+x+x²+1

Re-arrange the terms:

=x³+x²+x+1

Hence the quotient is x³+x²+x+1....

Answer:

C

Step-by-step explanation:

let's recall that a circular clock has 360° and 60 seconds per minute.

the seconds hand does 60 seconds in one go-around, and if it has covered 15 seconds on the clock, that gives us an angle of 90°, 15 is one quarter of 60, so in 15 seconds it has covered one quarter of the full circle or 90°.

we also know it covered 2cm, namely the arc's length on the 15 seconds is 2cm.

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ \cline{1-1} \theta =90\\ s=2 \end{cases}\implies 2=\cfrac{(90)\pi r}{180}\implies 2=\cfrac{\pi r}{2} \\\\\\ 4=\pi r\implies \cfrac{4}{\pi }=r\implies 1.27\approx r[/tex]

Answer:

sin²x

Step-by-step explanation:

we have

(1 − cos x)(1 + cos x)=1-cos²x

Remember that

sin²x+cos²x=1 ------> i-cos²x=sin²x

therefore

(1 − cos x)(1 + cos x)=sin²x

Answer:

[tex]sin^2x[/tex]

Step-by-step explanation:

Given expression,

[tex](1 - cos x)(1 + cos x)[/tex]

By using [tex]a^2-b^2=(a+b)(a-b)[/tex]

[tex](1 - cos x)(1 + cos x)=1^2 - cos^2x = 1 - cos^2x[/tex]

[tex]\because sin^2x+cos^2x=1[/tex]

[tex]\implies (1 - cos x)(1 + cos x)=sin^2x+cos^2x - cos^2x=sin^2x[/tex]

Since, further simplification is not possible,

Hence, the simplified form of the given expression is [tex]sin^2x[/tex]

Answer:

2x^3 - 6x^2 - 4x + 12.

Step-by-step explanation:

(p*q) (x)  = (2x^2 - 4)(x - 3)

= 2x^3 - 6x^2 - 4x + 12.

For this case we have the following functions:

[tex]p (x) = 2x ^ 2-4\\q (x) = x-3[/tex]

We must find [tex](p * q) (x).[/tex] For definition, we have to:

[tex](p * q) (x) = p (x) * q (x)[/tex]

So:

[tex](p * q) (x) = (2x ^ 2-4) (x-3)[/tex]

We apply distributive property:

[tex](p * q) (x) = 2x ^ 3-6x ^ 2-4x + 12[/tex]

Answer:

[tex](p * q) (x) = 2x ^ 3-6x ^ 2-4x + 12[/tex]

Answer:

18

Step-by-step explanation:

We can use a proportion to find out the number of teachers that are needed.

3/70 = x/14,700

70x = 3 * 14,700

70x = 44,100

x = 630

630 teachers are needed altogether. Since there are already 612 teachers, the number of more teachers who are needed is the difference between 630 and 612.

630 - 612 = 18

Answer: 18

The slope is the change in Y over the change in x:

Using the two points shown on the graph:

(1,7) and (0,0)

Slope = (7-0) / (1-0)

Slope = 7/1

Slope = 7

The number if front of the x would be the slope

The answer would be D. y = 7x

Angle Q = 93° & angle R = 87°

The sum of any two adjacent angles of a parallelogram is equal to 180°, i.e. they are supplementary angles.

In parallelogram QRST,

∠Q= (9x-6)° & ∠R= (8x-1)°

Here, angle Q & angle R are adjacent angles of the parallelogram QRST.

∴ ∠Q+∠R = 180°

⇒ (9x-6)+(8x-1)= 180

⇒ 9x-6+8x-1 = 180

⇒ 17x-7= 180

⇒ 17x = 180+7

⇒ 17x = 187

⇒ x = 187/17

⇒ x = 11

So, ∠Q= (9x-6)° = {(9×11)-6}° = (99-6)° = 93°

& ∠R= (8x-1)° = {(8×11)-1}° = (88-1)°= 87°

Learn more about measuring angle here :

https://brainly.com/question/331095

#SPJ2

Answer:

Step-by-step explanation:

Permutation is the ways in which a fixed group or members that can be arranged or ordered and combinations are used when a smaller group has to be chosen from a larger group.

Examples:

Permutation: How many unique combinations of the word MAHNOOR can be formed when the letters will be scrambled

2. In what order or arrangements five people can be seated in the front row?

The number of people are fixed, we have to find the order.

Combination: Choosing two cards from a deck of 52 cards. We are choosing a small group from a larger group of all cards.

2. Choosing 4 students from a class to take part in the competition.

The selection can be made in multiple ways ..

Answer:

Permutation - requires to arrange order with quantities

Combination - order is not required

Step-by-step explanation:

If a question demands you to select as well as arrange the given quantities then it means that it is a problem of permutation.

While on the other hand, a problem of combination would only ask you to select the quantities and not their order.

So with practice, you get to know how exactly it works.

Answer:

5 12/24 -> -0.5 -> -5 6/20

Step-by-step explanation:

Negatives are lasts and positive goes first! Since the order is greatest to least.

-5 6/20 is less than -0.5 because *think of a number line -5 6/20 will be all the way to the left because it large in negative value

Rewrite the equation in slope-intercept form:

y+5=2(x+1)

Use the distributive property:

y+5 = 2x +2

Subtract 5 from each side:

y = 2x -3

The slope is the value with the X

The slope = 2

Answer:

2.5

Step-by-step explanation:

2(x+1)=y+5

2x+1=y+5

y+5=6

in addtion y can be add

so we have now...

2x+1=6

minus 1 from 6 and get 5

2x=5

5 divide by 2 = 2/5

Hope it helps

Answer:

D

Step-by-step explanation:

Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.

A sequence could either be arithmetic or geometric. The truth statement about the correct student is:

Both students could be correct. Because two numbers are given in the original sequence, it is possible to find a common difference and common ratio between the successive terms.

Given that:

[tex]-5.5, 11, .....[/tex]

If the sequence is arithmetic, then the common difference is

[tex]d = 11 --5.5[/tex]

[tex]d = 16.5[/tex]

So, the next two elements are:

[tex]T_3 = 11 + 16.5 =27.5[/tex]

[tex]T_4 = 27.5 + 16.5 =44[/tex]

If the sequence is geometric, then the common ratio is

[tex]r =\frac{11}{-5.5}[/tex]

[tex]r= -2[/tex]

So, the next two elements are:

[tex]T_3 = 11 \times -2 = -22[/tex]

[tex]T_4 = -22 \times -2 = 44[/tex]

Based on the above computations, both students are correct.

Read more about sequence at:

https://brainly.com/question/3927222

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x ----> the number of open acres

y ----> the number of developed acres

we know that

[tex]x+y \geq 4[/tex] -----> inequality A

The solution of the inequality A is the shaded area above the solid line [tex]x+y=4[/tex]

[tex]y-x\leq 1[/tex] -----> inequality B

The solution of the inequality B is the shaded area below the solid line [tex]y-x=1[/tex]

so

The graph in the attached figure

Answer:

Option B.

Step-by-step explanation:

Let x be the number of open acres and y be the number of developed acres.

It is given that a community must have at least 4 acres of developed and open space.

[tex]x+y\geq 4[/tex]

The difference between the number of developed acres, y, and the number of open acres, x, can be no more than 1.

[tex]y-x\leq 1[/tex]

The relative equations of both inequalities are

[tex]x+y=4[/tex]

[tex]y-x=1[/tex]

The table of values

For line 1                      For line 2

x      y                            x      y

0     4                            0      1

4     0                           -1      0

Plot these ordered pairs on a coordinate plane and draw both lines.

The related line of first inequality is a solid line and shaded area lies above the line because the sign of inequality is ≥.

The related line of second inequality is a solid line and shaded area lies below the line because the sign of inequality is ≤.

Therefore, the correct option is B.

Answer:

starts wuth 46, and sells half, so she has 23. then when she buys 17 more she then has 40.

if you are asked to show work its 46/2=23, then 23+17=40!

Answer:

40 stamps

Step-by-step explanation:

She started with 46 stamps.

She sold half of them

46*1/2 = 23

She sold 23 46-23 = 23

So she has 23 stamps

Then she bought 17

23+17 = 40

She now has 40 stamps

Answer:

Option A   ∠RWQ, ∠WPS and ∠PWU

Step-by-step explanation:

we know that

Two angles are supplementary if their sum is equal to 180 degrees

Part 1)

∠OPW+∠WPS=180° ------> by supplementary angles

we have

∠OPW=110°

substitute

110°+∠WPS=180°

∠WPS=180°-110°=70°

Part 2) we know that

∠RWQ+(50°+60°)=180° ------> form a linear pair

∠RWQ=180°-(50°+60°)=70°

so

∠OPW+∠RWQ=180° -----> by supplementary angles

Part 3) we know that

∠PWU=∠RWQ -------> by vertical angles

so

∠OPW+∠PWU=180° -----> by supplementary angles

therefore

The angles that are supplements to angle ∠OPW are

∠WPS, ∠RWQ and ∠PWU

Answer:

Option A. The measure of angle C is 140°

Step-by-step explanation:

see the attached figure with letters to better understand the problem

we know that

The triangle OAB is an isosceles triangle

Because

OA=OB=radius

m∠BAO=m∠ABO=20°

Find the measure of angle C

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

so

m∠BAO+m∠ABO+m∠C=180°

substitute the given values

20°+20°+m∠C=180°

m∠C=180°-40°=140°

Answer:

(6,∞)

x > 6

Step-by-step explanation:

Solve by adding 4 to both sides.

[tex]x-4>2\\x>6[/tex]

To put this in interval notation for your solution set, consider your sign.

You have a greater than sign, which means that 6 is not a solution. In interval notation, that means that you should use parentheses " ( " instead of brackets " [ ".

Your solution set goes on infinitely, and infinity also uses parentheses rather than brackets.

You can write your solution set in interval notation as follows:

(6, ∞)