simplify the following expression into the form a+bi where a and b are rational numbers
(3+7i) (-2-2i) -4i(5-9i)

To determine the time needed to layout a full magazine issue, multiply the time taken to layout 1/16 of an issue (3 days) by 16, resulting in 48 days total.

If a magazine can layout 1/16 of an issue in 3 days, then to calculate how many days it takes to layout one entire issue, we simply multiply the number of days it takes to layout 1/16 of the issue by 16.

This is because if 1/16 takes 3 days, then 1/8 (which is twice the amount of 1/16) would take twice as long

(3 days * 2 = 6 days),

and similarly, we can scale up to the full issue (1/1) by multiplying 3 days by 16.

The calculation would be:

Identify the portion of the issue completed: 1/16.

Identify the time taken for this portion: 3 days.

Calculate the time for the whole issue: 3 days * 16 = 48 days.

So, it would take 48 days to layout one full issue.

-92.34 is the answer

Final answer:

After Nicole's check for her electric bill was processed, her account was overdrawn. She then made a deposit equal to the overdraft amount, bringing her end-of-day balance to $0.00.

Explanation:

To determine the bank balance that Nicole had at the end of the day, we need to consider the transactions that affected her account. She started with $63.44. After her electric bill check of $186.56 was processed, her account would have been overdrawn by $186.56 - $63.44 = $123.12. To cover this overdraft, Nicole made a deposit equal to the amount her account was overdrawn. Therefore, she deposited $123.12, which brought her balance back to $0.

At the end of the day, Nicole's bank balance was $0.00.

The correct solution is shown in the graph (D)

Given that the budget is $24 and the minimum is 7 tubs, the fourth graph shows the area in which both constraints are satisfied: triangular area between the points

7 small tubs

8 small tubs

3 large and 4 small tubs

Lets x = # of small tub of popcorn and y = # of large tub of popcorn

She needs to buy at least 7 tubs of popcorn: x + y >= 7

Each small tub of popcorn costs $3 and each large tub of popcorn costs $4 but she only has $24 in her wallet.

3x + 4y <= 24

So now you have the system of inequalities

x + y >= 7

3x + 4y <= 24

Find x and y intercepts of blue line

x + y = 7

x = 0 then y = 7

y = 0 then x = 7

The inequality sign is >= so it's above.

The blue line,  B and D are matching the results

Find x and y intercepts of red line

3x + 4y = 24

x = 0 then 4y = 24; y = 6

y = 0 then 3x = 24;   x = 8

The inequality sign is <= so it's below.

The red line,  Only B is matching

Answer

D is the solution of the system of inequalities.

Answer:

easy 5 ,0 c the x axis is run 5 then you rise on the positive y axis 0 and theres your awnser

Step-by-step explanation:

The set of coordinates satisfies the equations 3x − 2y = 15 and 4x − y = 20 is (5, 0).

Option C is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

3x - 2y = 15 _____(1)

4x - y = 20 _____(2)

The point of intersection of (1) and (2).

3x - 2y = 15

3x = 15 + 2y

x = (15 + 2y) / 3 _____(3)

4x - y = 20

4x = 20 + y

x = (20 + y) / 4 ______(4)

From (3) and (4) we get,

(15 + 2y) / 3 = (20 + y) / 4

4(15 + 2y) = 3(20 + y)

60 + 8y = 60 + 3y

8y - 3y = 0

5y = 0

y = 0

Now,

y = 0 in (1) or (2) we get,

3x = 15

x = 5

(5, 0)

4x = 20

x = 5

(5, 0)

Thus,

The coordinates (5, 0) satisfy the equations.

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c > -13/10

The > should have _ under it.

Answer:

5x + (-6) = -2

Step-by-step explanation:

Times is used in multiplication

Sum is used in addition

Step-by-step explanation:

The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival

0.75 per ticket. So cost of 18 tickets= 0.75 * 18 = $13.5

Kendall spent $13.50 for tickets . Total spent = $33.50

Total spent = ticket cost + admission cost

33.50 = 13.50 + admission

Admission cost = 33.50 - 13.50 = $20

(a)  y to represent the total cost , x to represent the number of ride tickets.

'b' represents the admission cost

(b)  General form of linear equation is y=mx+b

m = 0.75 and b = admission cost = 20

So equation becomes y = 0.75x + 20

(c) Initially, she has to pay the admission price $20. then 0.75 per ticket.

The value of x changes depends on the number of tickets she wants to buy.

y is the total cost she has to pay for x tickets with admission price

To solve this problem yo must apply the proccedure shown below:

1. You must use the formula applied to calculate the area of the garden.

[tex]A=bh[/tex]

2. You know the value of the area ([tex]127^{\frac{1}{2}}ft^{2}=127.5ft^{2}[/tex] and the value of the heigth ([tex]8^{\frac{1}{2}}ft=8.5ft[/tex] , therefore, you only need to solve for the base:

[tex]b=\frac{A}{h}\\b=\frac{127.5ft}{8.5ft}\\b=15ft[/tex]

The answer is: 15 feet.

3 x 6 is the simplest way of saying it

Answer: 3x6 because there are 6 3's so it's 3x6

First of all this is a very poor question, and you should question it a bit. What are these figures? Are they regular? (first 2). Is the last one a parallelogram. I'm going to assume that the yellow one is a rectangle and the middle one is a pentagon and the last one is a parallelogram.

Yellow

A has 4 right angles (That's the property of a rectangle).

Green

B has 5 angles that are equal to 108 degrees. If you draw a 2 lines from any vertex you get 3 triangles. The size of the interior angles totals 3 triangles * 180 degrees = 540 degrees.

540/3 = 108.

Each angle in the interior is 108 degrees.

B has 5 angles all equal 108 degrees. All 5 are obtuse.

Red

Just by sight and assumption C has 2 obtuse angles, and 2 acute angles.

The equation that represents Jimmy's age is J = S + T - 1.

To represent Jimmy's age, we can use the equation:

J = S + T - 1

where J is Jimmy's age, S is Serena's age, and T is Tyler's age. By subtracting 1 from the sum of Serena and Tyler's ages, we account for Jimmy's age being one year less than theirs. This equation accurately represents Jimmy's age.

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M= change in y /change in x

(−10, 4), (2, −5)

M= -5-4/2-(-10)

M= -9/12

M- 3/4

Slope is - 3/4

answer:  [tex]m = -\frac{3}{4}[/tex]

work:

slope formula ==> [tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

plug the points in according to the formula

[tex]m = \frac{-5-4 }{2-(-10)}[/tex]

[tex]m = -\frac{9}{12}[/tex]

[tex]m = -\frac{3}{4}[/tex]  <== simplified, and final answer :)

hope this helps! ❤ from peachimin

Respuesta: x/2,5=y/5=4/5=0,8

x/2,5=y/5

Multiplicando ambos lados de la ecuación por 5:

5(x/2,5)=5(y/5)→2x=y→y=2x

Sustituyendo y por 2x en la ecuación x+y=6:

x+2x=6

Resolviendo para x: Sumando términos semejantes:

3x=6

Dividiendo ambos lados de la ecuación entre 3:

3x/3=6/3

x=2

Sustituyendo x por 2 en la formula y=2x

y=2(2)→y=4

Determinando la proporción:

x/2,5. Sustituyendo x por 2:

2/2,5

Multiplicando numerador y denominador por 2:

2*2/(2,5*2)=4/5

La proporción es 4/5=0,8

Si lo hacemos con y:

y/5

Reemplazando y por 4:

4/5=0,8 (la misma proporción)

Answer:

7/4 < x < 11/2

Step-by-step explanation:

PLATO

Inequality which ensure triangle exists is 22 > 4x > 7.

" Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."

Theorem used

In ΔABC,

AB + BC >AC

AC+ BC >AB

AC + AB > BC

According to the question,

In triangle ABC.

AC = 18units

BC = 6x units,

AB = 2x + 4 units

Substitute the value in the inequality to ensure triangle exists we get,

  [tex]AB + BC > AC[/tex]

⇒[tex]2x + 4 + 6x > 18[/tex]

⇒[tex]8x > 18 - 4[/tex]

⇒ [tex]8x > 14[/tex]

⇒ [tex]4x > 7[/tex]                                    ___(1)

[tex]AC + AB > BC[/tex]

⇒ [tex]18 + 2x + 4 > 6x[/tex]

⇒ [tex]22 > 6x-2x[/tex]

⇒[tex]22 > 4x[/tex]                                   ____(2)

From (1) and (2) inequality of triangle we get,

[tex]22 > 4x > 7[/tex]

Hence, Inequality which ensure triangle exists is 22 > 4x > 7.

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Answer:

The slope is 3 (answer choice A).

Step-by-step explanation:

Take a look at the two given points, (2, -5) and (4, 1).  As we move from the first point to the second, x increases by 2 and y increases by 6, so that the slope is m = 6/2, or 3.

Least common denominator is 24

Answer:

y< -1/2x +4

Step-by-step explanation:

The line crosses the y-axis at +4 and has a slope of -1/2. The shaded area below means that all answers below that line are correct (this is not part of the test answer but it is good information to know)

Hope this helped :)

Answer:

Her speed driving in nice weather is 50 mph and in thunderstorm is 32 mph.

Step-by-step explanation:

Barbara drives 50 miles in clear weather and then encounters a thunderstorm for the last 16 miles.

Suppose, her speed in nice weather is  [tex]x[/tex] mph.

As she drives 18 mph slower through the thunderstorm than she does in clear weather, so her speed in thunderstorm will be: [tex](x-18) mph[/tex]

We know that,  [tex]Time = \frac{Distance}{Speed}[/tex]

So, the time of driving in clear weather [tex]=\frac{50}{x}[/tex] hours

and the time of driving in thunderstorm [tex]=\frac{16}{x-18}[/tex] hours.

Given that, the total time for the trip is 1.5 hours. So, the equation will be......

[tex]\frac{50}{x}+ \frac{16}{x-18}=1.5 \\ \\ \frac{50x-900+16x}{x(x-18)}=1.5\\ \\ \frac{66x-900}{x(x-18)}=1.5 \\ \\ 1.5x(x-18)=66x-900\\ \\ 1.5x^2-27x=66x-900\\ \\ 1.5x^2-93x+900=0\\ \\ 1.5(x^2 -62x+600)=0\\ \\ x^2 -62x+600=0\\ \\ (x-50)(x-12)=0[/tex]

Using zero-product property.........

[tex]x-50=0\\ x=50\\ \\ and\\ \\ x-12=0\\ x=12[/tex]

We need to ignore [tex]x=12[/tex] here, otherwise the speed in thunderstorm will become negative.

So, her speed driving in nice weather is 50 mph and her speed driving in thunderstorm is (50-18) = 32 mph

Answer:

Drive Faster!

Step-by-step explanation:

The numbers 8/5 , 5 and -6 will have an expansion and numbers 0.9 and 3/8 will have contraction.

The scale factors are given which are 5, 0.9, -6, 8/5, 3/8

We have to find which one has a contraction or expansion.

What do you mean by contraction and expansion on a scale ?

If the scale factor is larger than 1 then it would be an expansion whereas the scale factor between 0 and 1 would be a contraction.

As per the question ;

The scale factors given are ;

5, 0.9, -6, 8/5, 3/8

We can also write it as ;

5 , 0.9 , -6 , 1.6 , 0.375

We know that ;

If the scale factor is larger than 1 , it would be an expansion.  

So ;

The factors we have listed that are larger than 1 are 8/5 and 5.

Also ;

If the scale factor is between 0 and 1 , it would be a contraction.  

So ;

The factors we have listed that are between 0 and 1 are 0.9 and 3/8.

Also ;

A negative scale factor will result in a larger, inverted value.  

So ;

The scale factor of -6 will also be an expansion.

Thus , the numbers 8/5 , 5 and -6 will have an expansion and numbers 0.9 and 3/8 will have contraction.

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Answer:

Option 3 is right

z37 is between 2 and 3 standard deviations of the mean.

Step-by-step explanation:

Let X be a random variable which represents the mean number of miles that the employees in a department live from work

X is normal (N(29,3.6)

WE have to find Z score for X

Z =[tex]\frac{x-29}{3.6}[/tex]

=2.22

i.e. 37 is 2.22 std deviations from the mean.

In other words, z37 is between 2 and 3 standard deviations of the mean.

The z-score for z37 is approximately 2.22. This indicates that it lies between 2 and 3 standard deviations of the mean. Hence, the correct statement is: z37 is between 2 and 3 standard deviations of the mean.

To determine which statement is true regarding the z-score for the value z37, we need to calculate the z-score using the given mean and standard deviation.

This means that z37 is approximately 2.22 standard deviations away from the mean. Therefore, the correct statement is:

z37 is between 2 and 3 standard deviations of the mean.

In a normal distribution, about 95 percent of the x values lie within two standard deviations, and about 99.7 percent lie within three standard deviations of the mean.

A translation moves the image up, down and/or right, left.  It does not change its size or shape.

Try this: Move your pencil up and to the right.  Did its size or shape change? no

Answer: D

5.1=s. Use the distributive property and add like terms

y=10x+5 because x=3 so 10*3=30 and 30+5=35 which would mean that $35 is the lowest amount you can spend.

To stay within a $50 daily budget for activities, equations are created to determine the number of tubes (t) and canoes (c) that can be rented. With tube rentals at $5 and canoe rentals at $10, the group of ten can only rent tubes (t = 10), as renting canoes would exceed the budget (c = 0).

The question involves creating and solving a budget constraint problem similar to the examples provided for Janet Bain and Mr. Higgins. To accommodate the group of 10 people with a budget of $50 per day for activities, we need to write equations to determine how many tubes (t) and canoes (c) can be rented. We know that tube rentals cost $5 and canoe rentals cost $10. Each canoe holds up to three people.

First, we write an equation that represents the number of tubes and canoes needed:

Everyone needs a tube: t = 10

Canoes can hold three people: 3c ≥ 10 (since not everyone needs to be in a canoe at the same time)

Next, we write an equation for the total cost to remain within the budget: 5t + 10c ≤ 50 (cost of tubes plus canoes must be less than or equal to $50)

Using t = 10, we can substitute t in the cost equation: 5(10) + 10c ≤ 50

50 + 10c ≤ 50

10c ≤ 0

From the final inequality, c = 0; meaning you cannot rent any canoes if you're buying a tube for each person and staying within a $50 budget. Therefore, the group can only rent tubes, with 0 canoes.

Givens

The numbers are n and n + 1

Average = Av = 105

Equation

Av = (n)(n + 1)/2

Solution

Av = 105

n(n +1)/2 = 105    Multiply both sides by 2

n(n + 1) = 105 * 2

n(n + 1) = 210      Remove the brackets.

n^2 + n = 210     Subtract 210 from both sides

n^2 + n - 210 = 0

factor

(n+15)(n - 14)

n + 15 = 0

n = - 15

n = - 15 which is the smallest of the two answers.

n + 1 = - 14

Check

(-15)*(-14)/2 =

210/2

105        It does check.

Answer:

The numbers are n and n + 1

Average = Av = 105

Step-by-step explanation: