Simplify the given expression below: (4 + 2i) − (1 − 7i)

Answer:

Step-by-step explanation:

we have to find the dot product here.

From the formula of dot product of vectors,

we know-

if  X=<a,b,c>   and    Y=<d,e,f>

Then dot product of  X and Y is-

X.Y=ad+be+cf

Here, we get

v=<2 , -8 , -8>

and   w=<-2 , 6 , -5>

So, the dot product is-

v . w=2(-2)+(-8)(6)+(-8)(-5)

    =-4-48+40

    =-52+40

   =-12

So,  

v . w= -12

Answer:

-12

Step-by-step explanation:

we have to find the dot product here.

From the formula of dot product of vectors,

we know-

if  X=<a,b,c>   and    Y=<d,e,f>

Then dot product of  X and Y is-

X.Y=ad+be+cf

Here, we get

v=<2 , -8 , -8>

and   w=<-2 , 6 , -5>

So, the dot product is-

v . w=2(-2)+(-8)(6)+(-8)(-5)

   =-4-48+40

   =-52+40

  =-12

So,  

v . w= -12

x * 6 = 3

x = 3 : 6

x = 3/6

x = 1/2 or 0.5

The answer is: [tex](5x^{6}+6y^{7}) (5x^{6} - 6y^{7})[/tex]

To get answer: Factor [tex]25x^{12} -36y^{14}[/tex]

[tex]-36y^{14} +25x^{12}[/tex]

[tex]= (6y^{7} +5x^{6})(-6y^{7}+5x^{6})[/tex]

(5x⁶+6y⁷)×(5x⁶−6y⁷)

This is your answer hope this helps! Have a good day/night whatever time it is near you!

Answer,

56

Hope this helps :-)

Hello there!

This question is super easy to me.

You had to find the prime factorization of 14.

7*2=14

Next, you had to find the prime factorization of 8.

2*2*2=8

7*2*2*2=56

Answer⇒⇒⇒56

The least common multiple of 14 and 8 is 56.

Hope this helps!

Thank you for posting your question at here on Brainly.

-Charlie

Distributive property

-8*4=-32          -8*9x=-72x

-32-72x=7(-2-11x)

7(-2)=-14      7(-11x)=-77x

-32-72x=-14-77x

Combine Like Terms

-32+14=-18       -77x+72x=-5x

-18=-5x

Divide both sides by -5 and theres your answer

Answer:

[tex]y=\dfrac{3}{4}x+7\dfrac{1}{4}[/tex]

Step-by-step explanation:

[tex]k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\ \iff\ m_1m_2=-1[/tex]

Let [tex]k:4x+3y=6\to 3y=-4x+6\ \ \ \ |:3\\\\y=-\dfrac{4}{3}x+2\\\\m_1=-\dfrac{4}{3}[/tex]

[tex]l:y=m_2x+b\\\\l\ \perp\ k\ \iff\ -\dfrac{4}{3}m_2=-1\qquad|\cdot\left(-\dfrac{3}{4}\right)\\\\m_2=\dfrac{3}{4}\\\\l:y=\dfrac{3}{4}x+b[/tex]

The line l passes through the point (-3, 5).

Substitute the coordinates of the point to the equation of the function l:

[tex]5=\dfrac{3}{4}(-3)+b\\\\5=-\dfrac{9}{4}+b\\\\5=-2\dfrac{1}{4}+b\qquad|+2\dfrac{1}{4}\\\\b=7\dfrac{1}{4}[/tex]

Finally [tex]l:y=\dfrac{3}{4}x+7\dfrac{1}{4}[/tex]

ANSWER

[tex]x=\frac{14.5\degree}{3}+120\degree n\:or\:x=\frac{165.5\degree}{3} +120\degree n[/tex], for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.

EXPLANATION

We want to solve the trigonometric equation;

[tex]Sin(3x)=\frac{1}{4}[/tex]

Since sine ratio is positive, it means the argument,[tex](3x)[/tex] is either the first quadrant or second quadrant.

This implies that;

[tex](3x)=arcsin(\frac{1}{4})[/tex]

[tex](3x)=14.5\degree[/tex] in the first quadrant.

Or

[tex](3x)=180\degree-14.5\degree=165.5\degree[/tex] in the second quadrant.

Since the sine function has a period of [tex]360\degree[/tex], The general solution is given by

[tex](3x)=14.5\degree+360\degree n\:or\:(3x)=165.5\degree +360\degree n[/tex],for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.

Dividing through by 3, we obtain the final solution to be;

[tex]x=\frac{14.5\degree}{3}+120\degree n\:or\:x=\frac{165.5\degree}{3} +120\degree n[/tex], for [tex]n\ge 0[/tex], where [tex]n[/tex] is an integer.

Wrong answer = x

Correct answer = y

Total questions: x+y = 30

Rewrite for x: x = 30-y

Total points:

-8x + 7y = 0

replace x with 30-y

-8(30-y) + 7y = 0

Simplify:

-240 + 8y + 7y = 0

Combine like terms:

-240 + 15y = 0

Add 240 to each side:

15y = 240

Divide both sides by 15:

y = 240 / 15

y = 16

There were 16 correct answers

30-16 = 14 wrong answers.

Answer: 12.817

Step-by-step explanation: hope it helps! PLEASE SELECT ME BRAINLIEST!♡

Answer:  There are 138 short sleeves t-shirts.

Step-by-step explanation:

Given : In August Emily's clothing store sold 460 shirts with the ratio of short sleeve to long sleeve being 3:7.

Let the number of short sleeves shirts be 3x and the number of long sleeves shirts be 7x.

Then, according to the given question,  we have

[tex]7x+3x=460\\\\\Rightarrow\ 10x=460\\\\\Rightarrow\ x=46[/tex]

Now, the number of short sleeves shirt = 3(46)=138

Hence , there are 138 short sleeves shirts.

Rule of trigonometric functions:-

sin a = cos(90 - a)

Here a = 90°.

sin 90 = cos (90 - 90)

1 = cos 0.

cos 0 = 1.

So the cos 0 = 1.

Answer:

Step-by-step explanation:

If sin 90 = 1

then cos 0 will be

as we know that

cosx = sin(90-x)

If we plug x = 0 ,

cos0  = sin 90 = 1

Answer:

940 people

Step-by-step explanation:

since we know that 423 is 45% of the vote, we would do

45/100 =423/x, when you simplify the proportion, you find out that 940 people

After 5 months, they would both have the same cost. If you were to cancel after 9 months, you would cancel $320 for the first option and $360 for the second option.

To solve this, you need to create an equation. You get $50+30x and let x=number of months. This would tell you how much you need to pay for option 1. In option 2, you would have $40x. This is because there is no setup fee and so there would only be the monthly cost.We then set thos equations both equal to each other because the first question asks for the options to be the same price. For the second question, you would need to substitute 9 for the x in those equations. That would have you find out which is more expensive.

R= c-s/t. For c

Switch the equation to have c on left side

C-s/t= r

Now multiply t both sides

C-s= r(t)

C-s= rt

Now add s both sides to get your answer

C= s+rt

Answer:

[tex]t=5x[/tex]

Step-by-step explanation:

So the number of questions in an exam varies with the number of minutes to take the exam.

For each question there are 5 minutes allotted.

Lets say that there are 'x' number of questions in the exam and 't' is the total time taken to finish the exam, in minutes. So the time taken to complete the exam would be

[tex]5 \times x=5x[/tex]

Therefore, the equation relating the time taken to complete the exam and the number of questions is given by:

[tex]t=5x[/tex]

So there are two variables in the equation, 't', and 'x':

t - time taken to complete the exam

x - number of questions on the exam

B is your answer.

(1000x0.0325)/100= 32.50.

Hope this helps & good luck. :)

We know that if m and n are parallel, then we know that they have the same slope. We can call it x in this case.

Since we know that p is a perpendicular transversal, then we know it is the opposite and reciprocal of m. Therefore, we can label it as -1/x.

Since p = -1/x and n = x, we can tell they are perpendicular.

Parallel lines m and n, with transversal p, imply that if p is perpendicular to m (forming a 90-degree angle), it must also be perpendicular to n because parallel lines have the same inclination. Thus, the angle between n and p also has to be 90 degrees.

In the scenario presented, we're dealing with parallel lines m and n, and a transversal, p. The fact that p is perpendicular to m implies that the angle between m and p is 90 degrees. Now, since m and n are parallel, this means they have the same angle of inclination. So, the angle between n and p is also 90 degrees. This essentially means p is perpendicular to n as well.

Parallel lines have the property that they never intersect and are always equidistant. In geometry, when a line crosses two or more other lines, it is called a transversal. And when a line is perpendicular to another, it forms a 90-degree or right angle with the other line.

https://brainly.com/question/2188951

#SPJ11

Answer:

From the comments below we see the missing part of the question is "in how many days will the ant farm consume 3 apples?"

The answer is 18.

Step-by-step explanation:

We will use a proportion to solve this.  It takes 3 days to consume 1/2 of an apple; this gives us the ratio

3/0.5

We want to know how many days, x, it will take to consume 3 apples; this gives us the ratio

x/3

Together this gives us the proportion

3/0.5 = x/3

Cross multiply:

3(3) = 0.5(x)

9 = 0.5x

Divide both sides by 0.5:

9/0.5 = 0.5x/0.5

18 = x

The ant farm will take 18 days to consume 3 apples.

Given that,

According to above information, calculation of data are as follows,

[tex]X = (3 \div 0.5) \times 3\\\\X = 6 \times 3[/tex]

X = 18

So, Total number of days required is 18 days.

Learn more: https://brainly.com/question/13609873

By using LCM, the result is-

Number between 10 and 20 divisible by 2, 3 and 9 = 18

What is LCM of two numbers?

LCM means Lowest Common multiple. LCM of two numbers a and b is the lowest numbers which is divisible by both a and b

LCM can be calculated by division method and prime factorization method.

Also there is an important formula relating HCF and LCM

HCF [tex]\times[/tex] LCM = Product of two numbers

Here,

The number which is divisible by 2, 3 and 9 = LCM of 2, 3 and 9.

2 = 2

3 = 3

9 = 3 [tex]\times[/tex] 3

LCM = [tex]2 \times 3 \times 3[/tex] = 18

Next number divisible by 2, 3 and 9 = 18  + 18 = 36

But 36 does not lie between 10 and 20

So number between 10 and 20 divisible by 2, 3 and 9 = 18

To learn more about LCM, refer to the link-

brainly.com/question/21504246

#SPJ2

33 hope this helps thanks

Answer:

44

Step-by-step explanation:

The answer is 44 because 66-22=44, 44+22=66 44 is twice of 22

15 i think sorry if its wrong

This kind of problems are solved using Bernoulli's distribution. Everytime you have a win/lose scenario, and you know the probability [tex] p[/tex] of winning, and you want [tex]k[/tex] successes over [tex]n[/tex] trials, you have the following probability:

[tex]\displaystyle P(k\text{ successes over }n\text{ trials}) = \binom{n}{k}p^k(1-p)^{n-k} [/tex]

You want the probability of having at least three successes, i.e. you are interested in the cases k=3 and k=4. The corresponding probabilities are

[tex]\displaystyle P(3 \text{ successes}) = \binom{4}{3}0.6^3 \cdot 0.4 = 4\cdot 0.216 \cdot 0.4 = 0.3456[/tex]

[tex]\displaystyle P(4 \text{ successes}) = \binom{4}{4}0.6^4 = 0.1296 [/tex]

So, the total probability is [tex] 0.3456+0.1296 = 0.4752[/tex]

Answer: x = 3, -5

Step-by-step explanation:

2 |x + 1| + 3 = 11

              -3   -3

2 |x + 1|       = 8

÷2               ÷2

  | x + 1 |    = 4

x + 1 = 4       or        x + 1 = -4

    -1   -1                       -1   -1

x       = 3       or        x      = -5

ANSWER

The correct answer is A.

EXPLANATION

The volume of a cube is given by

[tex]V=l^3[/tex]

First we find the volume of the cube with side length [tex]\frac{3}{4}cm[/tex]

[tex]V_{Cube}=(\frac{3}{4})^3[/tex]

[tex]V_{Cube}=\frac{27}{64} cm^3[/tex]

Next, we find the volume of the cubic block with side length [tex]\frac{3}{8}cm[/tex]

[tex]V_{Block}=(\frac{3}{8})^3[/tex]

[tex]V_{Block}=\frac{27}{512} cm^3[/tex]

We divide the volume of the cube by the volume of the block to get the number of cubic blocks

[tex]Number\: of \: blocks=\frac{\frac{27}{64}} {\frac{27}{512}}[/tex]

[tex]Number\: of \: blocks=\frac{27}{64} \times \frac{512}{27}[/tex]

[tex]Number\: of \: blocks=\frac{1}{1} \times \frac{8}{1}=8[/tex]

Answer:

The correct answer is option A.

8 blocks are needed to fill the box.

Step-by-step explanation:

Given data:

Side length of a block = 3/8 cm

Side length of main block = 3/4 cm

How many blocks are needed to fit in main blocks = ?

Solution:

Volume  = length³

Volume of one simple block = (3/8)³ = 27/512 cm³

Volume of one Main block = (3/4)³ = 27/64 cm³

Blocks are needed to fit in main blocks = (27/64) ÷ (27/512) = 8

                                                            Answer = 8 blocks

Hence 8 simple small blocks of one side length 3/8 cm will needed to fit in the main block of side length 3/4 cm.

From my research i found the answer to be that he rented 9 movies.

Final answer:

To find out how many movies Andrew rented, subtract the membership fee from the total bill, then divide by the cost per movie. This reveals Andrew rented 9 movies.

Explanation:

To solve how many movies Andrew rented this month, we first need to subtract the monthly membership fee from the total bill. Knowing the monthly membership fee is $5.00 and the total bill was $16.25, we can calculate the cost of movies rented alone.

First, subtract the membership fee from the total bill: $16.25 - $5.00 = $11.25. This is the amount spent on renting movies.

Next, divide the result by the cost per movie, which is $1.25 per movie. This gives us: $11.25 / $1.25 = 9.

Therefore, Andrew rented 9 movies this month.

Coterminal angles are angles in standard position (angles with the initial side on the positive x -axis) that have a common terminal side.

Coterminal angles are angles that have the same terminal sides in standard position.

Anytime we complete a full cycle( a complete revolution) we come back to the same terminal side.

Therefore to find all angles which are coterminal with [tex]-271\degree[/tex] we keep adding or subtracting [tex]360\degree[/tex].

For the given interval, that is, [tex]0\degree[/tex] to [tex]360\degree[/tex],

We add [tex]360\degree[/tex] so that we can obtain an angle coterminal with [tex]-271\degree[/tex] within this interval.

This means that

[tex]-271\degree[/tex] is coterminal with [tex]360\degree + \: -271\degree=89\degree[/tex]

Hence the correct and answer is D

The husband earns $42,000 per year.

Let's denote the husband's earnings as H.

According to the problem, the wife earns 16,000 less than twice what her husband earns. So, the wife's earnings can be represented as (2H - 16,000).

We know that together they earn 110,000 per year. This can be written as:

H + (2H - 16,000) = 110,000

Combining like terms, this equation simplifies to:

3H - 16,000 = 110,000

Add 16,000 to both sides to solve for H:

3H = 126,000

Divide both sides by 3:

H = 42,000

Therefore, the husband earns $42,000 per year.