The distance between the complex numbers z1 = 7 – 2i and z2 = 3 - 3i is ________

Kyle filled 6 10-oz cup(s), 11 14-oz cup(s), and 4 ​20-oz cup(s).

Let's define the variables:

x = number of 10-oz cups of coffee sold.

y = number of 14-oz cups of coffee sold.

z = number of 20-oz cups of coffee sold.

We know that:

Kyle served 21 cups of coffee, then:

x + y + z = 21

He used 294 ounces of coffee, then:

x*10 oz + y*14 oz + z*20 oz = 294 oz

He collected a total of $24.35, then:

x*($0.95) + y*($1.15) + z*($1.50) = $24.35

Then we have a system of 3 equations:

x + y + z = 21

x*10 oz + y*14 oz + z*20 oz = 294 oz

x*($0.95) + y*($1.15) + z*($1.50) = $24.35

To solve this, the first thing we need to do is isolate one of the variables in one of the equations, let's isolate x in the first one.

x = 21 - y - z

Now we can replace this in the other two equations to get:

(21 - y - z)*10 oz + y*14 oz + z*20 oz = 294 oz

(21 - y - z)*($0.95) + y*($1.15) + z*($1.50) = $24.35

Now we can simplify these two equations:

y*4 oz + z*10 oz = 294 oz - 210oz = 84 oz

y*($0.20) + z*($0.55) = $24.35 - $19.94 = $4.40

Now we need to do the same thing, we need to isolate one of the variables in one of the equations, we can isolate z in the first one:

z*10 oz = 84oz - y*4 oz

z = (84oz - y*4 oz)/10oz

z = 8.4 - y*0.4

Now we can replace this in the other equation:

y*($0.20) + ( 8.4 - y*0.4)*($0.55)  = $4.40

Now we can solve this for y.

y*($0.20) + $4.62 - y*$0.22 = $4.40

y*$0.02 = $4.40 - $4.62 = $0.22

y = $0.22/$0.02 = 11

Now that we know the value of y, we can use:

z = 8.4 - y*0.4

z = 8.4 - 11*0.4 = 4

Now that we know the value of z and y we can use:

x = 21 - y - z

x = 21 - 11 - 4 = 6

Then we found:

x = 6

y = 11

z = 4

this means that:

Kyle filled 6 10-oz cup(s), 11 14-oz cup(s), and 4 ​20-oz cup(s).

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Answer: B (0,0) r=4

Step-by-step explanation:

(x+2)(x-2) / (x-1)(x-5) this is the simplified form of the expression.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities. It is a way of expressing a number as a quotient of two integers, where the top number is called the numerator, and the bottom number is called the denominator.

x²-3x-10/x²-6x+5 • x-2/x-5

We can factor the numerator and denominator of the first fraction as follows: (x-5)(x+2) / (x-5)(x-1)

Notice that there's a common factor of x-5 in both the numerator and denominator. We can cancel them out, leaving: (x+2) / (x-1)

Now let's simplify the second fraction:

x-2 / x-5

We can't simplify this fraction any further, so we leave it as is.

Putting it all together, we get:

(x+2) / (x-1) * (x-2) / (x-5)

Multiplying the two fractions, we get:

(x+2)(x-2) / (x-1)(x-5)

This is the simplified form of the expression.

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Answer:

3.75cm 44.16cm²

20cm 314cm²

42cm 1384.74cm²

Step-by-step explanation:

Area of a circle = πr²

Where : = π = pi = 3.14

R = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

16. Radius = 7.5 / 2 = 3.75

Area = 3.14 x 3.75² = 44.16

17. Diameter = 10 x 2 = 20

Area = 10² x 3.14 = 314

18. Diameter = 21 x 2 = 42

Area = 21² x 3.14 = 1384.74

Answer:

x ≥ 12

Step-by-step explanation:

-3/4x +2 ≤ -7

Subtract 2 from each side

-3/4x +2-2 ≤ -7-2

-3/4x  ≤ -9

Multiply each side by -4/3, remembering to flip the inequality

-3/4x * -4/3 ≥ - 9 *(-4/3)

x ≥ 12

Answer:

x>=12

Step-by-step explanation:

-3/4x + 2<=-7

-3/4x <= -7 -2

-3/4x<=-9

cross multiply

-3x<=-36

dividing throughout by -3

x>=12

Step-by-step explanation:

Answer:

A = 286 episodes

B = 284 episodes

Step-by-step explanation:

Let n = the [tex]\text{number of episodes}[/tex] of show B

    n + 2 = the [tex]\text{number of episodes}[/tex] of show A

Therefore, according to the question,

The sum of the number of the episodes of each show are consecutive even integers  = 570

Therefore,

n + n + 2 = 570

2n + 2 = 570

2n = 568

n = 284

Therefore, the number of episodes for B = 284

The number of episodes for A = n + 2 = 284 + 2

                                                              = 286

Answer:

The last one!

Step-by-step explanation:

Answer:

last step is (2x + 5)(2x + 1)

Step-by-step explanation:

4x^2 + 12x + 5

4x^2 + (10 + 2)x + 5

4x^2 + 10x + 2x + 5

2x(2x + 5) +1(2x + 5)

(2x + 5)(2x + 1)

Answer:

y = -3x + 13

Step-by-step explanation:

First, find the slope:

[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{4-10}{3-1}\\\\m=\frac{-6}{2}\\\\m=-3[/tex]

Finally, find the equation:

[tex]y-y_1=m(x-x_1)\\\\y-4=-3(x-3)\\\\y-4=-3x+9\\\\y=-3x+13[/tex]

Hector is the one who discovered

Answer:

Correct answers= 18

Incorrect answers=30-18= 12 answers

Step-by-step explanation:

total questions=30

correct answers= x

incorrect answers= 30-x

given: 5 marks for each correct answer

therefore, marks for correct answers = 5*x = 5x

Given: 1 mark deducted for every incorrect answer

therefore, marks deducted = 1(30-x) = 30-x

Total marks scored= 78

★  The Difference of Marks scored for Correct Answers and Marks deducted for Incorrect Answers should be equal to 78

5x- (30-x) =78

5x-30+x=78

5x+x=78+30

6x= 108

x=108/6 = 18

Correct answers= 18

Incorrect answers=30-18= 12 answers

9514 1404 393

Answer:

  45

Step-by-step explanation:

Let x and y represent the tens and ones digits, respectively. The 5 times the sum of digits is 5(x+y). The value of the digit-reversed number is (10y+x), so the required relation is ...

  5(x +y) = (10y +x) -9

The other relationship between the digits is given as ...

  4y = 1/2(10x)

A graphing calculator shows the solution to these equations is (x, y) = (4, 5).

The two-digit number is 45.

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Additional comment

You can solve these equations in any of a variety of ways. Using a graphing calculator to find integer solutions is fast and easy, so is one of my favorites. Here, the coefficients on one equation are not easy multiples of those in the other, so substitution and/or elimination can get messy. In this situation, I like to use the "cross-multiplication" method, which starts with the equations in general form:

From the coefficients of these equations, differences of cross products are formed:

Then the solutions are the solutions to 1/d1 = x/d2 = y/d3:

(x, y) = (4, 5)   ⇒   the number is 45.

__

This method is one of several variations of Cramer's Rule, the general solution of systems of linear equations using matrix methods.

Answer:

No solution is possible from the informatin provided.

Step-by-step explanation:

You didn't include the table,

Answer:

y intercept is found from the pair that has a 0 for the x variable.

Step-by-step explanation:

if a choice was (0,2) this would be the point where the line intercepts the y axis.

x=0 is the position of the vertical line, and 2 is how high up the graph the line passes through the y-axis

Step-by-step explanation:

32/3+21/5÷7

14.87÷7

2.124

Answer:

[tex] { \tt{d = (r + c)t}}[/tex]

Divide ( r+c ) on both sides:

[tex]{ \tt{t = { \frac{d}{(r + c)} }}}[/tex]

Answer:

d / ( r + c) = t

Step-by-step explanation:

d = ( r + c ) t

Divide each side by ( r + c)

d / (r + c ) = ( r + c ) t / ( r + c)

d / ( r + c) = t

Answer:

Below.

Step-by-step explanation:

If the sum of any 2 sides are less than or equal to the third side then there's no triangle

1. N0 because 4 + 5 < 10

2. YES

3. NO because 2 + 3 = 5.

Answer:

Step-by-step explanation:

1 . 4,5,10 : this measurement does not form a triangle because the sum of two  sides is not greater than the third side (longest side)

4 + 5 > 10

9 > 10   (this is not satisfied)

2. 12,26,20 :this measurement forms  a triangle beacuse the sum of two sides is greater than the third side

12 + 26 > 20

38 > 20

3 .

2,3,4 : this measurement does not form a triangle because the sum of two sides is not greater than the third side.

2 + 3 > 5

5 > 5  (this is not satisfied)

Answer:

Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.

Step-by-step explanation:

Answer:

Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.

Answers:

===========================================================

Explanation:

We're given these three clues

Clue 3 is what we'll start with. Since Mrs. Gray is a doctor, this means that the doctor owns either a white horse or a brown horse. The doctor can't own a gray horse because the names can't match up (eg: the last name Gray with gray horse), due to clue 1.

If Mrs. Gray owned a brown horse, then she'd be a teacher (clue 2). But clue 3 says she's a doctor. We have a contradiction if Mrs. Gray owns the brown horse. Therefore, Mrs. Gray owns the white horse.

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

After we concluded the last section, we now know the following:

In short, we've just crossed "Mrs. Gray", "doctor", and "white horse" from the list.

Based on clue 1, we know that Mrs. Brown cannot possibly own the brown horse. Therefore, she must own the gray horse. So Mrs. White must own the brown horse.

Since Mrs. White owns the brown horse, she must be the teacher (clue 2). That leaves "lawyer" as the last profession, and that's assigned to Mrs. Brown.

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

Side note: I apologize for being a bit wordy, but I wanted to be very careful in the logical sense as to approach this problem. There's probably a much quicker efficient way to do this.

Answer:

The contrapositive of the statement is true.

Step-by-step explanation:

For a general statement:

p ⇒ q

The contrapositive statement is:

¬q ⇒ ¬p

where:

¬q is the negation of the proposition q.

Here we have the statement:

If two angles are not complements, then their measures do not add up to 180°

So we have:

p = two angles are not complements

q = their measures do not add up to 180°

Then the negations are:

¬p = two angles are complements

¬q = their measures do add up to 180°

The contrapositive statement is:

"if for two angles their measures do add up to 180°, then the two angles are complements"

This is true, if for two angles the sum of their measures is equal to 180°, then these angles are complementary.

Then: The contrapositive of the statement is true.

Answer:

Rs 440

Step-by-step explanation:

Price of bicycle = 3520

Price of mobile = 4690

Cost Price of both mobile and bicycle = 3520 + 4690

=> 8210

Selling price of both mobile and bicycle = 8650

Profit = selling price - cost price

= 8650 - 8210

= 440

Therefore he gained Rs 440

Answer:c

Step-by-step explanation:

The equivalent expression is 1 + In 2 - In x.

Given:

[tex]$\ln \left(\frac{2 e}{x}\right)$[/tex]

Apply log rule:

[tex]$$\log _{C}\left(\frac{a}{b}\right)=\log _{c}(a)-\log _{c}(b)$[/tex]

[tex]$&\ln \left(\frac{2 e}{x}\right)=\ln (2 e)-\ln (x) \\[/tex]

= ln (2e) - ln (x)

Apply log rule:

[tex]$\log _{c}(a b)=\log _{c}(a)+\log _{c}(b)$[/tex]

ln (2e) = ln (2) + ln (e)

= ln (2) + ln (e) - ln (x)

Apply log rule:

[tex]$\log _{a}(a)=1$[/tex]

= ln (2)+1-ln (x)

Therefore, the correct answer is option C. 1 + In 2 - In x.

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Answer:

i believe its 3 but i could be wrong

Step-by-step explanation:

sorry if i am..

Answer:

hope it helps you.......

It May Help You

Thank You:)

Answer:

8[tex]v^{-3}[/tex]z - [tex]\frac{5}{3}[/tex] vz

Step-by-step explanation:

11%

Hope this helps! :)

______________

Answer:

[tex] \frac{195.80}{220} \times 100 \% \\ = 0.89\%[/tex]