Solve for X (line a and b parallel)

Hello,

[tex]Let's\ say \\\\z=\sqrt{3+4*i} =a+b*i\\\\z^2=3+4*i=(a+b*i)^2=a^2-b^2+2i*a*b\\\\\\if \ a\neq 0\\\left\{\begin{array}{ccc}a^2+b^2&=&3\\2ab=4\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}b=\dfrac{2}{a}\\a^2-(\dfrac{2}{a})^2=2\\\end{array}\right.\\\\\\a^4-4=3*a^2\\a^4-3a^2-4=0\\\\\Delta=(-3)^2-4*1*(-4)=25=5^2\\\\a^2=4\ or \ a^2=-1 (impossible)\\\\So:\\(a=2\ and\ b=1)\ or\ (a=-2\ and\ b=-1)\\[/tex]

Roots are thus 2+i and -2-i

There is an other using a geometrical formula (formule de Moivre)

Answer:

4.8%

if we assume that the first card is REPLACED (otherwise the formula gets complex)

[tex](\frac{4}{52} )(\frac{32}{52} ) = \frac{8}{169} = .048[/tex]

Step-by-step explanation:

13/52 is the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9

It is a branch of mathematics that deals with the occurrence of a random event.

Given,

In a deck of 52 playing cards

We need to find the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9

n(S) =52

And the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9 is,

n(E) =13 a set of a diamond suit, because a diamond suit has {A, K ,Q ,J ,2,..,9}

Thus, the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9 is 13/52 or 1/4 .

Hence, 13/52 is the probability, as a fraction, of drawing a picture card (A, K, Q, and J) that is also a diamond then a card numbered 2-9

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Answer:

C; A singleton set

Step-by-step explanation:

Mathematically, when a number is non-negative; it is either positive or zero

Now, this is because 0 identifies as neither a positive or a negative number

hence, when we find the difference between the two sets, the only number that stands out unmatched is the value 0

What this mean is that we are having a set with a single number result

So we have our answer as {0}

Which is a singleton set

Answer:

(B)  [tex]\displaystyle \frac{W(3.1) - W(2.9)}{0.2}[/tex]

General Formulas and Concepts:

Calculus

Limits

Derivatives

Derivative Notation

Instantaneous Rates

Step-by-step explanation:

Since we are trying to find a rate at which W(t) changes, we must find the derivative at t = 3.

We are given 2 close answer choices that would have the same numerical answer but different meanings:

If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the rate at which the volume would be changing and it is not a derivative.

If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a derivative at t = 3, and a derivative tells us what rate something is changing.

∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when t = 3.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e

Answer:

b) y=sqrt(x) shifted 3 units left

Step-by-step explanation:

3rd line in the attached table:

f(x+3) = sqrt(x+3) horizontal translation left 3 units

Answer:

2.35 x 10^3

Step by Step:

2.35 x 10^3

Answer:

linear

Step-by-step explanation:

the graph in the above equation is linear function

Answer:

x > 4

Step-by-step explanation:

4x + 3 > 19

4x + 3 - 3 > 19 - 3

4x > 16

4x/4 > 16/4

x > 4

Hope this helps.

[tex]4x + 3 > 19 \\ = > 4x > 19 - 3 \\ = > 4x > 16 \\ = > x > \frac{16}{4} \\ = > x > 4[/tex]

Answer:

x > 4

Hope you could understand.

If you have any query, feel free to ask.

Orders of Magnitude are in terms of scientific notation.

23,000 written in scientific notation is 2.3 x 10^4, it's magnitude is 4 ( the number 10 is raised to)

56 in scientific notation would be 5.6 x 10^1, its magnitude is 1.

4 - 1 = 3

2300 is 3 order of magnitudes larger.

The answer is 3.

Answer:

Age of Pavel = y - 10

→ x - 7y = -60. Now, Calculating X. Hence, Present age of Abdul = 38.

Step-by-step explanation:

hope this is helpful.

Answer:

[tex]x=12,\\y=12\sqrt{3}[/tex]

Step-by-step explanation:

In any 30-60-90 triangle, the side lengths are in the ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse, or longest side, of the triangle and [tex]x[/tex] is the side opposite to the 30 degree angle.

In the given 30-60-90 triangle, the longest side (hypotenuse) is marked as 24. Since [tex]x[/tex] is opposite to the 30 degree angle,

Therefore, we have:

[tex]x=\frac{24}{2},\\x=\boxed{12}[/tex]

Based on our side length ratio [tex]x:x\sqrt{3}:2x[/tex], [tex]y[/tex] is then:

[tex]y=x\sqrt{3}\text{ for}\implies x=12,\\y=\boxed{12\sqrt{3}}[/tex]

Answer:

[tex]\huge\boxed{x=12;\ y=12\sqrt3\approx20.8}[/tex]

Step-by-step explanation:

Look at the picture.

We have:

[tex]2a=24\\a=x\\a\sqrt3=y[/tex]

Therefore:

[tex]x=24:2=12\\\\y=12\sqrt3\approx12\cdot1.73=20.76\approx20.8[/tex]

Answer:

please mark me brainlist

Step-by-step explanation:

Answer:

second one

Step-by-step explanation:

just read where the purple line finishes on the x axis, in this case it’s 5 so it’s greater than 5 or equal to it.

Answer:

f(3) = 28.26

Step-by-step explanation:

Substitute r = 3 into f(r) , that is

f(3) = 3.14 × 3² = 3.14 × 9 = 28.26

Answer:

1.5(B)

Step-by-step explanation:

This is a geometric sequence where each number is 1/2 times the last. So 3/2 is 1.5.

Answer:

{2,6,14}

Step-by-step explanation:

The range are the f(x) values

the domain are the x values

So we have it that;

f(-1) = 4(-1) + 6 = 2

f(0) = 4(0) + 6 = 6

f(2) = 4(2) + 6 = 14

so we have the range as;

{2,6,14}

Answer:

Reflected over y-axis

Answer:

The quotient is the answer to a division.

One of the properties of 0, is that 0 divided by any number is 0.

The exception is

0/0

which is undefined.

(the fact that 0 is being divided by a negative number makes no difference. There is no just thing as +0 or -0.)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Pls brain list if right :>

Answer:

If ABCD is congruent to RSTU

AB≅RS

BC≅ST

CD≅TU

AD≅RU

and ∠A≅CR

∠B≅∠S

∠C≅T

∠D≅CU

ANSWER: ∠A≅∠U

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

hope it helps...

have a great day!!

Answer:

x² + y² = 85

Step-by-step explanation:

Using the expansion

(x - y)² = x² + y² - 2xy , then

x² + y² - 2xy = (x - y)² ( add 2xy to both sides )

x² + y² = (x - y)² + 2xy ← substitute given values

          = 9² + 2(2)

          = 81 + 4

          = 85

The square root of 256 = X^2

X ^2 = X x X

A) 16 x 16 = 256

The answer is a) 16

Answer:

A. ) 16

Step-by-step explanation:

[tex] \small \sf \: \sqrt{256} [/tex]

Write 256 in the exponential form with the base of 16

[tex] \small \sf \: \sqrt{16 {}^{2} } [/tex]

Reduce the index of the radical and exponent with 2

16

[tex]1. \frac{20}{100} [/tex]

[tex]2. \frac{1}{5} [/tex]

Explanation:

There are a few ways to do this. One way is to notice that the jump from 5 to 100 is "times 20" (go from right to left across the bottom denominators).

So we must do the same "times 20" type of jump when going across the numerators. If x is the numerator for the right hand side, then we go from x to 20. That must mean x = 1

Put another way, we could have these steps

20/100 = x/5

20*5 = 100*x ... cross multiplication

100 = 100x

100x = 100

x = 100/100 .... dividing both sides by 100

x = 1

We see that the fraction 20/100 reduces fully to 1/5

To go from 1/5 to 20/100, we multiply both parts by 20 (divide both parts by 20 to go in reverse).

Answer: 60°

Step-by-step explanation:

If two angles are supplementary, that means they add up to 180°.

Therefore, if one angle is 120°, the other missing angle can be calculated by:

180° - 120° = 60°

Answer:

The answer is (A) 75

Step-by-step explanation:

Answer:

A 75

Step-by-step explanation:

10*5(number of ducks that lay an egg everyday)

5*5(number of ducks that lay an egg every second day)

10*5 + 5*5

Answer:

1/9

Step-by-step explanation:

You would multiply 1/3 by 1/3 since both of the spins are out of three for the probability of rolling on the same color two times.

Given:

Consider the given function is:

[tex]f(x)=5^x+1[/tex]

To find:

The average rate of change between x = 0 and x = 4.

Solution:

The average rate of change of a function f(x) over the interval [a,b] is:

[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]

We have,

[tex]f(x)=5^x+1[/tex]

At [tex]x=0[/tex],

[tex]f(0)=5^0+1[/tex]

[tex]f(0)=1+1[/tex]

[tex]f(0)=2[/tex]

At [tex]x=0[/tex],

[tex]f(4)=5^4+1[/tex]

[tex]f(4)=625+1[/tex]

[tex]f(4)=626[/tex]

Now, the average rate of change between x = 0 and x = 4 is:

[tex]m=\dfrac{f(4)-f(0)}{4-0}[/tex]

[tex]m=\dfrac{626-2}{4}[/tex]

[tex]m=\dfrac{624}{4}[/tex]

[tex]m=156[/tex]

Hence, the average rate of change between x = 0 and x = 4 is 156.

Step-by-step explanation:

this is the hardest I think

Answer:

[tex]\angle DFE = \angle DFG[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

What makes DEF and DGF congruent

We have:

[tex]EF = GF[/tex] --- this is indicated by the single line on both sides

Also:

[tex]DF = DF[/tex] --- both triangle share same side

For SAS to be true;

2 sides and 1 angle must be equal in either triangles

So far, we have:

[tex]EF = GF[/tex] ---- S

[tex]DF = DF[/tex] ---- S

The additional to complete the proof is:

[tex]\angle DFE = \angle DFG[/tex] ---- angle between the above sides

Reflection is a type of rigid transformation which requires the turning of an object, shape or figure about a reference point or line. Therefore, the needed additional information is ∠DFE ≅ ∠ DFG. Option B.

Reflection implies turning the given triangle DEF about its side DF, so as to produce an image with the same dimensions but different orientation.

The required proof by Side-Angle-Side (SAS) implies that the relations will be in respect of two of its sides and their included angle.

So that,

GF ≅ FE (given)

DF is the common side to triangles DEF and DFG.

DFG is the included side.

Thus;

∠DFE ≅ ∠ DFG (Side-Angle-Side postulate, SAS)

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