Which of the following are solutions to the equation below?
Check all that apply.
9x^2- 6x + 1 = 7

Answer:

θ = 5π/6 rad and 11π/6 rad

Step-by-step explanation:

Given the expression cotθ+√3=0

Subtract √3 from both sides

cotθ+√3-√3=0-√3

cotθ = -√3

Since cotθ = 1/tanθ

1/tanθ = -√3

Reciprocate both sides:

tanθ = -1/√3

θ = tan^-1(-1/√3)

θ = -30°

Since the angle is negative, and tanθ is negative in the second and fourth quadrant.

In the second quadrant;

θ = 180-30

θ = 150°

Since 180° = πrad

150° = 150π/180

150° = 5π/6 rad

In the fourth quadrant;

θ = 360-30

θ = 330°

Since 180° = πrad

330° = 330π/180

330° = 11π/6 rad

Hence the solutions are 5π/6 rad and 11π/6 rad.

Multiplication

2, 56, 0, 56, 18, 0, 3, 0, 20, 12

12, 54, 7, 64, 18, 25, 24, 0, 0, 28

14, 8, 6, 24, 35, 9, 27, 48, 40, 1

0, 3, 18, 16, 8, 7, 0, 0, 36, 48

49, 28, 40, 42, 15, 6, 27, 16, 36, 8

0, 32, 81, 4, 30, 0, 0, 9, 32, 10

30, 2, 45, 16, 5, 0, 0, 14, 35, 18

0, 54, 0, 12, 36, 24, 4, 8, 10, 18

72, 6, 63, 12, 0, 21, 0, 24, 63, 0

21, 20, 9, 15, 45, 0, 6, 72, 5, 4

Answer:

Because the base of this expression is not same.

Answer:

x < 6

Step-by-step explanation:

Given

5x - 9 < 21 ( add 9 to both sides )

5x < 30 ( divide both sides by 5 )

x < 6

Answer:

x < 6

Step-by-step explanation:

5x-9<21

Add 9 to each side

5x-9+9<21+9

5x < 30

Divide by 5

5x/5 < 30/5

x < 6

Answer:

Square Root 34

Step-by-step explanation:

Answer:

[tex]\sqrt{34}[/tex]

Explanation:

sub in the values for x1, x2, y1 and y2

[tex]\sqrt{(-2-3)^2+(2-(-1))^2}[/tex]

subtract and evaluate

= [tex]\sqrt{(-5)^2+3^2}[/tex]

= [tex]\sqrt{25+9}[/tex]

= [tex]\sqrt{34}[/tex]

Answer:

  z = {1 +i, 1 -i, -1 +i, -1 -i}

Step-by-step explanation:

Using Euler's formula, you can write this as ...

  z^4 = 4e^(i(π+2kπ))

Then the 4th root is ...

  z = 4^(1/4)e^(i(π/4 +kπ/2)) = √2(cos(π/4+kπ/2) +i·sin(π/4+kπ/2))

for integers k in the range 0 to 3.

  z = √2(±1/√2 ±i·1/√2) . . . signs are independent

  z = ±1 ±i . . . . . . signs are independent; hence 4 solutions

  z = {1 +i, 1 -i, -1 +i, -1 -i}

_____

Comment on roots of complex numbers

In the complex domain, each number has a number of roots equal to the index of the root. That is, there are four 4th roots. They all have the same magnitude, but their angles are separated by 360°/(root index) = 90°. Here, the principal fourth root of 4∠180° is 4^(1/4)∠(180°/4) = √2∠45° = 1+i.

Adding 90° is equivalent to multiplying by i, so the other 3 roots are √2∠135° = -1+i, √2∠225° = -1 -i, and √2∠315° = 1 -i.

 z = {1 +i, 1 -i, -1 +i, -1 -i}

Answer:

[tex]4x^3-7x^2-23x-10[/tex]

Step-by-step explanation:

So we have the expression:

[tex](4x+5)(x^2-3x-2)[/tex]

Distribute. Multiply (4x+5) to each term:

[tex](x^2)(4x+5)+(-3x)(4x+5)+(-2)(4x+5)[/tex]

Distribute:

[tex]=(4x^3+5x^2)+(-12x^2-15x)+(-8x-10)[/tex]

Combine like terms:

[tex]=(4x^3)+(5x^2-12x^2)+(-15x-8x)+(-10)[/tex]

Add and simplify:

[tex]=4x^3-7x^2-23x-10[/tex]

And this is in descending order, so it's in standard form.

Answer:

In exponential form

3.2615 X 10¹

Answer:

the volume of the 2nd box is 1200 cubic inches

Step-by-step explanation:

Answer:

198

Step-by-step explanation:

Given :

A vector v = 10i - 24k.

To Find :

A vector of magnitude 3 in the direction of v = 10i - 24k.

Solution :

Unit vector in the direction  of vector v is :

[tex]\^{v}=\dfrac{v}{|v|}\\\\\^{v}=\dfrac{10i-24k}{\sqrt{10^2+24^2}}\\\\\^{v}=\dfrac{10i-24k}{26}[/tex]

Now , vector of magnitude 3 in direction v is :

[tex]r=3 \^{v}\\\\r=3\times \dfrac{ (10i-24k)}{26}\\\\r=\dfrac{3}{13} (5i-12k)[/tex]

Hence , this is the required solution .

The vector of magnitude 3 in the direction of given vector is, [tex]\frac{30i-72k}{26}[/tex]

First we have to calculate unit vector of given vector.

    Given vector,  [tex]v=10i-24k[/tex]

Unit vector of vector v is,

                     [tex]v=\frac{10i-24k}{\sqrt{(10)^{2}+(24)^{2} } }\\ \\v=\frac{10i-24k}{\sqrt{100+576} }=\frac{10i-24k}{26}[/tex]

For vector have magnitude 3 is,

        [tex]v=3(\frac{10i-24k}{26} )=\frac{30i-72k}{26}[/tex]

The vector of magnitude 3 in the direction of given vector is, [tex]\frac{30i-72k}{26}[/tex]

Learn more about the magnitude of vectors here :

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Answer:

10626 ways

Step-by-step explanation:

Given

Number of students = 23

Prizes = 3

Required

Number of different outcomes for the top 3

This question will be solved using permutation formula because it implies selection of 3 students from 23

[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]

Where n = 23 and r = 3

The formula becomes

[tex]^{23}P_3 = \frac{23!}{(23-3)!}[/tex]

[tex]^{23}P_3 = \frac{23!}{(20)!}[/tex]

[tex]^{23}P_3 = \frac{23!}{20!}[/tex]

[tex]^{23}P_3 = \frac{23 * 22 * 21 * 20!}{20!}[/tex]

[tex]^{23}P_3 = 23 * 22 * 21[/tex]

[tex]^{23}P_3 = 10626[/tex]

Hence, there are 10626 ways

Answer:

Step-by-step explanation:

If A ⊂ B, that is, A is a subset of B

Also, B ⊂ A, that is, B is a subset A

Therefore, A = B in all respect.

A set is a mathematical model for a collection of items. If two sets are subsets of each other, the other relationship they must have is that they both are equal.

A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.

If there exist two subsets such that A is a subset of B, also, B is the subset of A. Then the two sets are equal or the same.

Hence, If two sets are subsets of each other, the other relationship they must have is that they both are equal.

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Answer:

find a shorter water-route to Asia.

Step-by-step explanation:

Answer:

a.  Point E

b  Line AB

Step-by-step explanation:

The lines AB and CD will intersect at a point

The Point is Point E

Planes will intersect at a line

Planes X and Plane Y intersect at line AB

Answer:

a.  point E

b.  points A and B ( which is line AB )

Step-by-step explanation:

a.  the intersection of AB and CD = point E

b.  the intersection of plane X and Y = points A and B ( which is line AB )

Answer:

32 miles per gallon

Step-by-step explanation:

351 divided by 11 = 31.90909090909090909090909090 e.t.c

Answer: 16

Step-by-step explanation:

The Histogram is attached blow.

A histogram is a representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most popular type of histogram.

Given:

Data: 4,4,6, 11, 11, 12, 14, 14, 21, 21, 24, 26

So, Interval           Frequency

      0- 5                     4 , 4 (2)

       5-10                      6(1)

      10- 15                    11, 11, 12, 14, 14  

     15- 20                      _

     20- 25                  21, 21, 24

     25- 30                        26

Hence, the Histogram is attached blow.

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Answer:

5 in the 85327= five thousand units

5 in the 435= five units

Step-by-step explanation:

85,327= eighty five thousand, three hundred and twenty seven

Value of five or the position if five in the above number is the thousand position

5 in the above = five thousand unit

435= four hundred and thirty five

The position of five in the above number is the unit position

Five in the above= five unit

Answer:

answer choice D

Step-by-step explanation:

CORRECT ANSWER IS D

i believe

don't give up you got it always stay positive

Answer:

138

Step-by-step explanation:

f(x)= 18x + 12

Let x = 7

f(7) = 18*7 +12

     = 126+12

     = 138

Answer:

f(7) = 138

Step-by-step explanation:

[tex]f(x)= 18x + 12\\f(7) = ?\\\\f(7) = 18(7) +12\\f(7) = 126+12\\f(7)=138[/tex]

Answer:

Two other names for WQ are QW and line g.

Step-by-step explanation:

A line can have as many points as possible. The two other names for WQ are QW and line g

From the given plane, we can observe the following:

This means that, we can rename WQ as

Hence, the two other names for WQ are QW and line g

Read more about points and lines at:

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Step-by-step explanation:

[tex]\huge{\purple{\underline{\underline{\bf{\pink{Answer}}}}}}[/tex]

[tex]\huge{\purple{\underline{\underline{\bf{\pink{Given}}}}}}[/tex]

It is a parrelogram

[tex]\huge\star{\underline{\mathtt{\red{To}\pink{f}\green{i}\blue{n}\purple{d}\orange{-:}}}}⋆[/tex]

X and Y

Solution

angle a = c. (opposite angles of 11gm is equal)

put the values of and c

x+45 = 3x-13

now take the variables to the l.H.S and number to R.H.S

x-3x = -13-45

-2x. = 58

x. = 58÷2

x. = 29

angle d + c = 180° (cointerior angle)

y + 3(29) + 13 =180°

y + 100 = 180°

y. = 80

Hope it helps

Answer:

C) 1 5/16

Step-by-step explanation:

(3/4)/(4/7)=(3/4)(7/4)=21/16=1 5/16

Answer:

5 + 4i

Step-by-step explanation:

In general, the conjugate of a + bi is a - bi

Answer:

A

Step-by-step explanation:

So we know that the point-slope form of the line that passes through the points (-4,-3) and (12,1) is:

[tex]y-1=\frac{1}{4}(x-12)[/tex]

And we want to convert this to standard form.

The standard form of a linear equation is:

[tex]Ax+By=C[/tex]

Where A, B, and C are integers, and, traditionally, A is positive.

So, first, multiply everything by 4 to remove the negative:

[tex]4(y-1)=4(\frac{1}{4}(x-12))[/tex]

Distribute the left. The right cancels:

[tex]4y-4=x-12[/tex]

Add 4 to both sides. The left cancels:

[tex]4y=x-8[/tex]

Subtract x from both sides:

[tex]-x+4y=-8[/tex]

As I mentioned previously, the coefficient of A tends to be positive. So, divide everything by -1:

[tex](-x+4y)/-1=(-8)/-1[/tex]

Simplify:

[tex]x-4y=8[/tex]

So, our answer is A

And we're done!

Answer:6

Step-by-step explanation:

The answer can be seen on the attachment that I have given.

The two equations that represent the remaining angle relationships are (x = 60 - 2(y + z)) and (x = 2z + 20) and this can be determined by using the given data.

Given :

The linear equation that represents the situation "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles" is:

x = 60 - 2(y + z)  --- (1)

The linear equation that represents the situation "The largest angle is twice the smaller angle plus 20 degrees" is:

x = 2z + 20  --- (2)

Therefore, the correct option is A) and E).

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