PLEASE HELP! I just need to find X!

Answer:

[tex]\displaystyle pm - qn = 0\text{ and } pn + qm \neq 0[/tex]

Or:

[tex]pm = qn \text{ and } pn + qm \neq 0[/tex]

Step-by-step explanation:

We are given two complex numbers:

[tex]\displaystyle m + ni \text{ and } p + qi[/tex]

Where m, n, p, and q are real numbers.

And we want to determine the relationship among m, n, p, and q such that the product of the two complex numbers will only have an imaginary part.

Find the product:

[tex]\displaystyle \begin{aligned} (m+ni)(p+qi) &= p(m+ni) + qi(m+ni) \\ &= (pm + pni) + (qmi + qni^2) \\ &= (pm + pni) + (qmi - qn) \\ &= (pm - qn) + i(pn + qm) \end{aligned}[/tex]

Therefore, for the product to have only an imaginary part, the real part must be zero and the imaginary part must not be zero. That is:

[tex]\displaystyle pm - qn = 0\text{ and } pn + qm \neq 0[/tex]

In conclusion, the relationship between m, n, p, and q is:

[tex]\displaystyle pm - qn = 0\text{ and } pn + qm \neq 0[/tex]

Or:

[tex]pm = qn \text{ and } pn + qm \neq 0[/tex]

(Note: I couldn't understand the provided answer choices, but the above answer is indeed correct (and the second equation can be ignored).)

Answer:

25 and 20 milies/gallons

Step-by-step explanation:

Let the fuell efficientcy of the first and the second car be f and s in gallons/miles.

Then the distance traveled by car 1 is 30 f and the car 2 is 25 s.

Since we also know that 1250 is the total distance traveled then

30 f + 25 s = 1250    (1)

Moreover we know that the efficiency is 45 miles/gallon. Hence

f + s  = 45

Multiply by 30 we have

30 f  + 30 s = 1350   (2)

Subtract the (1) equation from (2) we have

5s = 100

s = 20

f + 20 =45

f = 25

So the efficiency of the first car is 25 miles/gallons while the second one is 20 miles/gallons.

a.-40

b.--280

c.54

d.30

Answer:

[tex]x=7[/tex]

Step-by-step explanation:

Hi there!

[tex]-2^2(-5x+10)=100[/tex]

Solve -2^2:

[tex]-4(-5x+10)=100[/tex]

Divide both sides by -4:

[tex]\displaystyle \frac{ -4(-5x+10)}{-4}=\frac{100}{-4} \\\\-5x+10=-25[/tex]

Subtract 10 from both sides:

[tex]-5x+10-10=-25-10\\-5x=-35[/tex]

Divide both sides by -5:

[tex]\displaystyle \frac{-5x}{-5} = \frac{-35}{-5} \\\\x=7[/tex]

Therefore, x = 7.

I hope this helps!

Answer:

This word phrase into a equation is

4x -8 = 20

Step-by-step explanation:

a triangular number n is the sum of all natural numbers <= n.

t1 = 1

t2 = 1+2 = 3

t3 = 1+2+3 = 6

t4 = 1+2+3+4 = 10

...

so,

tn = tn-1 + n

47.

1×8 + 1 = 9 is a square number.

3×8 + 1 = 25 is a square number

6×8 + 1 = 49 is a square number

10×8 + 1 = 81 is a square number

48.

1/3 = 0 remainder 1

3/3 = 1 remainder 0

6/3 = 2 remainder 0

10/3 = 3 remainder 1

15/3 = 5 remainder 0

21/3 = 7 remainder 0

28/3 = 9 remainder 1

so, there seems to be a pattern 1 0 0 1 0 0 1 0 0 1 ...

49.

1/4 = 0 remainder 1

4/4 = 1 remainder 0

9/4 = 2 remainder 1

16/4 = 4 remainder 0

25/4 = 6 remainder 1

36/4 = 9 remainder 0

49/4 = 12 remainder 1

so, there seems to be a pattern 1 0 1 0 1 0 1 0 1 0 1 ...

50.

polygonal numbers is the real name for this.

the formula for dimensions = 5 is

(3n² − n)/2

for dimensions = 6 it is

2n² - n

so, dimensions=5 (and therefore dividing also by 5) we get the remainders

1/5 = 0 remainder 1

5/5 = 1 remainder 0

12/5 = 2 remainder 2

22/5 = 4 remainder 2

35/5 = 7 remainder 0

51/5 = 10 remainder 1

70/5 = 14 remainder 0

92/5 = 18 remainder 2

117/5 = 23 remainder 2

145/5 = 29 remainder 0

here the pattern is 1 0 2 2 0 1 0 2 2 0 1 0 2 2 0 ...

dimensions=6 (and therefore dividing also by 6) we get the remainders

1/6 = 0 remainder 1

6/6 = 1 remainder 0

15/6 = 2 remainder 3

28/6 = 4 remainder 4

45/6 = 7 remainder 3

66/6 = 11 remainder 0

91/6 = 15 remainder 1

120/6 = 20 remainder 0

153/6 = 25 remainder 3

190/6 = 31 remainder 4

231/6 = 38 remainder 3

276/6 = 46 remainder 0

325/6 = 54 remainder 1

here the pattern is 1 0 3 4 3 0 1 0 3 4 3 0 1 0 3 4 3 0 ...

Answer:

B is the answerrrrrrrrrr

Answer:

B

Step-by-step explanation:

The y-intercept is at -3 and the slope which is 2/4 simplified to 1/2x is going in a positive direction

Answer:

-3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

15+(-18)

15-18

NB: Negative plus positive is negative

-3

Therefore, the answer is -3.

The smallest of the three consecutive integers be x,(x+1),(x+2) = 12, 13,14  is 12

Let's consider the number will be in form of x

Consecutive Integers:

we number or count items in a sequence, we use consecutive integers. In other words, consecutive integers are integers that follow each other in a sequence with a difference that is fixed.

the three consecutive integers be x,(x+1),(x+2)

As per the problem,

Four times the smallest integer is equal to six more than three times the largest integer

4x=3(x+2) +6

∴4x=3x+6 +6

∴4x−3x=6+6

x= 12

Smallest number = x= 12

middle number   X+1 = 12+1 =13

Highest number = x+2 = 12+2 = 14

the three consecutive integers be x,(x+1),(x+2) = 12, 13,14

Learn more about the three consecutive integers: brainly.com/question/841485

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[tex]7^2=7\cdot7=49\\\\8^2=8\cdot8=64\\\\\sqrt{49}<\sqrt{52}<\sqrt{64}\\\\\text{Answer}:52[/tex]

Answer:

Its 52

Step-by-step explanation:

the square root of 52 is 7.2

Answer:

[tex]x_{1} =\frac{-17- \sqrt{129}}{2}, x_{2} =\frac{-17+ \sqrt{129}}{2} [/tex]

Step-by-step explanation:

[tex] \frac{x + 2}{x + 3} + \frac{x - 3}{x + 2} = \frac{5}{2} [/tex]

[tex] \frac{x + 2}{x + 3} + \frac{x - 3}{x + 2} = \frac{5}{2} [/tex]

[tex] \frac{x + 2}{x + 3} + \frac{x - 3}{x + 2} - \frac{5}{2} = 0[/tex]

[tex] \frac{2(x + 2 {)}^{2} + 2(x + 3) \times (x - 3) - 5(x + 3) \times (x + 2) }{2(x + 3) \times (x + 2)} = 0[/tex]

[tex] \frac{2(x + 2 {)}^{2} + 2( {x}^{2} - 9) + ( - 15x - 15) \times (x + 2) }{2(x + 3) \times (x + 2)} = 0 [/tex]

[tex] \frac{2( {x}^{2} + 4x + 4) - 3 {x}^{2} - 48 - 25x}{2(x + 3) \times (x + 2)} = 0[/tex]

[tex] \frac{2 {x}^{2} + 8x + 8 - 3 {x}^{2} - 48 - 25x }{2(x + 3) \times (x + 2)} = 0[/tex]

[tex] \frac{ - {x}^{2} - 17x - 40 }{2(x + 3) \times (x + 2)} = 0[/tex]

[tex] {x}^{2} + 17x + 40 = 0[/tex]

[tex]x = \frac{ - 17± \sqrt{ {17}^{2} - 4 \times 1 \times 40 } }{2 \times 1} [/tex]

[tex]x = \frac{ - 17± \sqrt{289 - 160} }{2} [/tex]

[tex]x = \frac{ - 17± \sqrt{129} }{2} [/tex]

[tex]x_{1} =\frac{-17- \sqrt{129}}{2}, x_{2} =\frac{-17+ \sqrt{129}}{2} [/tex]

Answer:

67 + 38(mod5)

= 67 + 38 =105÷5 (mod5)

= 21 reminder 0 ( mod 5)

Since while handling modes or finites the reminder is always considered therefore;

67 + 38 = 0 ( mod 5)

Answer:

b

Step-by-step explanation:

Answer:

The angle in the upper right quadrilateral corner = 68 degrees because vertical angles are equal.

Angle Y = 68 (opposite quadrilateral angles are equal).

All quadrilateral angles add to 360 so:

68 + 68 + x + z = 360 = 292

angle X + Z = 292

Therefore angle x = angle z = 146

Step-by-step explanation:

Answer:

Step-by-step explanation:

angle Z = 68 degree (being alternate angles)

angle X = 68 degree (opposite angle of a parallelogram is equal)

y + z = 180 degree (sum of adjecent angles of a parallelogram is 180 degree)

y + 68 = 180

y = 180 - 68

y = 112 degree

Answer:

<SDQ

Step-by-step explanation:

Eg if a = b, b = c, then a = c

Answer:

B, F

Chow,...!

[tex]3x=-39\\\\x=-39:3\\\\\huge\boxed{x=-13}[/tex]

Answer:

y = -9

x = -8

Step-by-step explanation:

x = 28 + 4y

7y - 6(28 + 4y) = -15

7y - 168 - 24y = - 15 ---> *distribute the -6, not positive 6*

-17y = 153

y = -9

x = 28 + 4(-9)

x = -8

Using area of a rectangle, it is found that the area of the iPad's screen is of 45.2 square inches.

---------------------

The area of a rectangle of length l and width w is given by:

[tex]A = lw[/tex]

---------------------

The diagonal of a rectangle is the hypotenuse of a right triangle, in which the sides are the length and the width.

---------------------

[tex]x^2 + (\frac{4x}{3})^2 = (9.7)^2[/tex]

[tex]x^2 + \frac{16x^2}{9} = 94.09[/tex]

Multiplying everything by 9:

[tex]9x^2 + 16x^2 = 846.81[/tex]

[tex]25x^2 = 846.81[/tex]

[tex]x^2 = \frac{846.81}{25}[/tex]

[tex]x = \sqrt{\frac{846.81}{25}}[/tex]

[tex]x = 5.82[/tex]

---------------------

[tex]A = lw = 7.76(5.82) = 45.2[/tex]

The area of the iPad's screen is of 45.2 square inches.

A similar problem is given at https://brainly.com/question/10489198

Answer:

180 feet

Step-by-step explanation:

|-60+120| is 180

Answer:

is it 180 feet apart if it is then here is the steps

Step-by-step explanation:

120+60 = 180

please mark as brainiest

Answer:

-59049/1048576

Step-by-step explanation:

using indices law you just follow the steps

42 feet.

Step-by-step explanation:

I think that it is 42 but don't know

Answer:

im sorry about that bro

Step-by-step explanation:

im not smart as well

Answer:

9[tex]\frac{75}{84}[/tex]

get a common denominator between 6,12,7,2 = 84

Step-by-step explanation:

[tex]$x$: $x = \frac{x}{6} + \frac{x}{12} + \frac{x}{7} + 5 + \frac{x}{2} + 4$[/tex]

The solution is x = 84

The value of the equation is A = 84

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

x = ( x/6 ) + ( x/12 ) + ( x/7 ) + 5 + ( x/2 ) + 4   be equation (1)

On simplifying the equation , we get

x = [ ( x/6 ) + ( x/12 ) + ( x/7 ) + ( x/2 ) ] + 9

Now , on further simplification , we get

x = [ ( x/7 ) + ( x/2 ) ] + [ ( 2x + x ) / 12 ] + 9

x = ( 3x/12 ) + [ ( 2x + 7x ) / 14 ] + 9

x = ( 3x/12 ) + ( 9x/14 ) + 9

On simplifying the equation , we get

x = ( x/4 ) + ( 9x/14 ) + 9

x = [ ( 14x + 36x ) / 56 ] + 9

x = ( 50x / 56 ) + 9

Subtracting ( 50x/56 ) on both sides of the equation , we get

9 = x - ( 50x/56 )

9 = ( 56x - 50x ) / 56

6x/56 = 9

Multiply by 56 on both sides of the equation , we get

6x = 504

Divide by 6 on both sides of the equation , we get

x = 504/6

x = 84

Therefore , the value of x is 84

Hence , the equation is A = 84

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https://brainly.com/question/19297665

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