Express $\frac{15 + 10i}{1 + 2i}$ in rectangular form.

Answer:

Step-by-step explanation:

If a shoemaker makes three new souls every four minutes, the number of soles he will make in an hour can expressed as shown;

3 souls = 4 minutes

x souls = 1hour (60 minutes)

Cross multiplying to get the number of souls;

4 * x = 3 * 60

4x = 180

x = 180/4

x = 45souls

Hence the number of souls made by this shoemaker in an hour is 45 souls.

Similarly, If another shoemaker makes two new souls every three minutes, the number of soles he will make in an hour can expressed as shown;

2 souls = 3 minutes

y souls = 1hour (60 minutes)

Cross multiplying to get the number of souls;

3 * y = 2 * 60

3y = 120

y = 120/4

y = 30souls

Therefore the number of souls made by this shoemaker in an hour is 30 souls.

The difference in the number souls they made in an hour will be x - y where x = 45 souls and y = 30 souls.

x - y = 45 - 30

The difference is equal to 15 souls

Answer:

2, 3

Step-by-step explanation:

5 lies between 2 perfect squares 4 and 9.

√4 < √5 < √9

√4 = 2

√9 = 3

2 < √5 < 3

Answer:

c. -1; no

Step-by-step explanation:

The inner product of 2 vector (a,b) and (c,d) is:

(a,b)(c,d) = a*c + b*d

If the inner product is equal to 0,  the vectors are perpendicular.

So, the inner product of (5,2) and (-3,7) is equal to:

 (5, 2)×(-3, 7) = 5(-3) + 2(7) = -1

The inner product is -1, it is different to 0, so the vectors are not perpendicular.

its A

Step-by-step explanation:

dividing or multiplying a negative number in this will completely change the sign to opp side

-3x + 15 < 12

-3x < -3

x > 1

Option d i.e x<-9 represents all possible solutions of -3(x+5)>12

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.

The given inequality is

-3(x+5)>12

-3x-15>12

-3x>12+15

-3x>27

Divide both sides by 3

-x>9

When we multiply negative sign on both sides the lesser than sign changes to greater.

x<-9.

Therefore option d represents all possible solutions of -3(x+5)>12.

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Answer:

5%, 33%, 1/2, 75%

Step-by-step explanation:

5% , 33%, 75%, 1/2

Change 1/2 to a percent.

1/2 = 0.5 = 0.5 * 100% = 50%

We are comparing

5%, 33%, 75%, 50%

From least to greatest:

5%, 33%, 50%, 75%

Now we convert 50% back to a fraction.

5%, 33%, 1/2, 75%

Answer:

[tex]Domain: \{0,1,2,3,4,5,6\}[/tex]

Step-by-step explanation:

Given

[tex]m = 45 - 7.5b[/tex]

[tex]Values: \{0,1,2,3,4,5,6,7,8,9,10\}[/tex]

Required

Select all values that belongs to the domain of the given function

Analyzing the question;

The question says that the function, m represent the amount left after buying b number of books

This means that, after purchasing b books, I'm expected to have a certain m amount of dollars left with me;

This implies that the value of m can never be negative;

So, the domain of m are values of b such that [tex]m \geq 0[/tex]

When b = 0

[tex]m = 45 - 7.5(0)[/tex]

[tex]m = 45 - 0[/tex]

[tex]m = 45[/tex]

When b = 1

[tex]m = 45 - 7.5(1)[/tex]

[tex]m = 45 - 7.5[/tex]

[tex]m = 37.5[/tex]

When b = 2

[tex]m = 45 - 7.5(2)[/tex]

[tex]m = 45 - 15[/tex]

[tex]m = 30[/tex]

When b = 3

[tex]m = 45 - 7.5(3)[/tex]

[tex]m = 45 - 22.5[/tex]

[tex]m = 22.5[/tex]

When b = 4

[tex]m = 45 - 7.5(4)[/tex]

[tex]m = 45 - 30[/tex]

[tex]m = 15[/tex]

When b = 5

[tex]m = 45 - 7.5(5)[/tex]

[tex]m = 45 - 37.5[/tex]

[tex]m = 7.5[/tex]

When b = 6

[tex]m = 45 - 7.5(6)[/tex]

[tex]m = 45 - 45[/tex]

[tex]m = 0[/tex]

When b = 7

[tex]m = 45 - 7.5(7)[/tex]

[tex]m = 45 - 52.5[/tex]

[tex]m = -7.5[/tex]

There's no need to check for other values, as they will result in negative values of m;

Hence, the domain of m are:

[tex]Domain: \{0,1,2,3,4,5,6\}[/tex]

The values that are in the domain of the function are 7, 8, 9 and 10

Given the linear function  m=45−7.5b

where:

For th domain to exist, then;

45 - 7.5b< 0

7.5 b > 45

b > 45/7.5

b > 6

Hence the values that are in the domain of the function are 7, 8, 9 and 10

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Answer:

260 cm^2

Step-by-step explanation:

The area of a parallelogram is given by this formula:

● A= b*h

b is the base and h is the heigth.

The heigth of this parallelogram is 13 cm and its base is 20cm.

●A= 13*20 = 260 cm^2

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

Explanation:

Writing [tex]P \to Q[/tex] is another way of saying "if P, then Q".

P and Q are placeholders. Instead of holding numbers, they hold statements. The statements can be anything you want (generally they should be something that can be verified).

The two statements are

P: x = 5

Q: 2x = 10

So the format "if P, then Q" turns into "if x = 5, then 2x = 10" after replacing P and Q with the proper definitions.

Side note: it might help to think of the "search and replace" feature in many word documents.

Answer:

Circle B:

[tex](x+4)^2+(y+3)^2=4[/tex]

Circle F:

[tex](x-4)^2+(y-1)^2=16[/tex]

Step-by-step explanation:

We can write the equation of a circle equation with center on (h,k) and radius r as:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Then, we analyze the circle will have for the circle B:

- It has a center in x=-4 and y=-3.

- It radius can be calculated from the distance from the center (x,y)=(-4,-3) to one of its points (x,y)=(-4, -1). Then, its radius is r=2.

Then, we can write the equation as:

[tex](x-h)^2+(y-k)^2=r^2\\\\h=-4\\k=-3\\r=2\\\\(x+4)^2+(y+3)^2=4[/tex]

we analyze the circle will have for the circle F:

- It has a center in x=4 and y=1.

- It radius can be calculated from the distance from the center (x,y)=(4, 1) to one of its points (x,y)=(0, 1). Then, its radius is r=4.

Then, we can write the equation as:

[tex](x-h)^2+(y-k)^2=r^2\\\\h=4\\k=1\\r=4\\\\(x-4)^2+(y-1)^2=16[/tex]

Answer:

work is shown and pictured

Answer:

30, 85, 95, 150

Step-by-step explanation:

The angles of a quadrilateral add to 360

Let x be the smallest angle

x+55

x+65

x+120 are the other three angles

Add the 4 angles together and they sum to 360

x+x+55 x+65+ x+120 = 360

Combine like terms

4x+240 = 360

Subtract 240 from each side

4x+240-240 = 360 -240

4x = 120

Divide by 4

4x/4 = 120/4

x = 30

x+55= 30+55 = 85

x+65 = 30+65 = 95

x+120 = 30+120 = 150

Answer:

Choice D - 8cm and 9cm.

Step-by-step explanation:

The other sides are not greater than 13.

A: 5 + 8 = 13

B: 6 + 7 = 13

C: 7 + 2 = 9

However, D is greater than 13 and is the correct answer.

D: 8 + 8 = 16.

Option d: 8 cm and 9 cm.

There is a theorem in mathematics stating:

" The sum of length of two sides of any triangle is greater than the rest third side"

According to that theorem, first three given options cant form the sides of the given triangle whose one side is 13 cm.

The 4th option has 8 cm and 9 cm for which we have:

8 + 9 > 13

Thus this option follows the theorem.

Hence fourth option is correct.

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Answer:

400milliliters

Step-by-step explanation:

Let x=ml of 30% solution B used in resulting mixture.

800+x=ml of resulting 30% solution

40%(800)+10%x=30%(800+x)

Then we can simplify the expression

0.4(800)+0.10x= 0.30(800+x)

320+0.10x=240+0.30x

80=0.20x

x= 400milliliters

Therefore, 400milliliters of 10% solution B used in resulting mixture.

Answer:

x=3

Step-by-step explanation:

7+4(5/4x-1)=18

7+5x-4=18

3+5x=18

5x=15

x=3

Answer:

x = 3

Step-by-step explanation:

18 = 7 + 4([tex]\frac{5}{4}[/tex]x - 1)

18 = 7 + 5x - 4

18 = 3 + 5x

15 = 5x

x = 3

Answer:

Hello!!...

I hope its helpful to you...

Answer:

true if I'm wrong I'm so sorry:/

Answer:

C

Step-by-step explanation:

1:draw a very simple Cartesian plane for the graph

2:label the quadrants 1-4 from top right round to bottom right as 4

3:then apply x>0 (1,2) is top right and y<0 is bottom right (-1,-2)

Using the standard calculation, the expected value is 46/11.

Answer:

a. 43,200 drips

b. 4 gallons (approximately, actual value is 3.8)

c. 61 cups(approximately, actual value is 60.8, using 3.8 gallons and not 4 gallons)

Step-by-step explanation:

Here, we have a faucet wasting water at a rate of 15 drips per 30 seconds, now we want to calculate the number of drips wasted in a day

To find this, what we need to do is fund the number of seconds in a day first

There are 24 hours with 60 minutes, with each minute having 60 seconds

So the number of seconds in a day = 24 * 60 * 60 = 86,400 seconds

Now 15 drips is wasted in 30 seconds

x will be wasted in 86,400 seconds

x = (15 * 86400)/30 = 43,200 drips are wasted in a day

b. Mathematically , there are about 3,000 drips in a liter of water

So;

3,000 drips = 1 liter

43,200 drips = x liter

x = 43200/3000 = 14.4 liters of water

Mathematically,

1 liter = 0.264 gallons

So 14.4 liters = 14.4 * 0.264 = 3.8 gallon

which is equal to 4 gallons of water approximately

c. Mathematically;

1 gallon = 16 cups of water

So 3.8 gallons of water will measure 3.8 * 16 = 60.8 which is approximately 61 gallons of water

Answer:

Barry has to pay back $1150

Step-by-step explanation:

We can set up an equation to help solve this problem

x is the amount he has to pay back

x=1000+3(1000/20)

1000/20 lets us know how many times he borrowed 20 dollars

x=1000+3(50)

x=1000+150

x=1150

Barry has to pay back $1150

If Barry also looks into the cost of repaying an easy access loan for $1000. The up-front cost of the loan is $3 for every $20 borrowed, plus the original $1000. Then Barry has to pay back $1150.

Two or more expressions with an equal sign is called as Equation.

We can set up an equation to help solve this problem

x is the amount he has to pay back.

x=1000+3(1000/20)

1000/20 lets us know how many times he borrowed 20 dollars

x=1000+3(50)

x=1000+150

x=1150

Hence, Barry has to pay back $1150.

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Answer:

500[tex]\pi[/tex] or around 1570

Step-by-step explanation:

The formula for a volume of a cylinder is [tex]r^{2}h\pi[/tex]

The cylindrical garbage pain has a volume of 15700 cm².

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

The given cylindrical garbage has a radius(r) = 10 cm and a height(h) of

50 cm.

∴ The volume of the cylindrical garbage is = π(10)²×50 cm².

= 5000π cm².

= 15700 cm².

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Answer:

y = 4x

Step-by-step explanation:

A direct variation is written in the form

y = kx where k is the constant of variation  ( or the slope)

y = 4x

Answer:

d. y = 4 x

Step-by-step explanation:

A direct variation

1. has no y-intercept

2. has a constant positive slope.

Out of

y = 4 x + 1   [has y-intercept of +1]

y = 1/4 x       [direct variation with a slope of 1/4, not 4]

y = -4 x        [has a negative slope]

y = 4 x         [direct variation with slope of 4]

Answer:

There's no results that appear below

Answer:

function 2

Step-by-step explanation:

To do this you would already know that the first function's slope is 1 since r represents the x in slope intercept form. 2 will just be 1/1.1 since if you do y2-y1/x2-x2 you get 1/1.1 as the slope so function 2 will have a greater slope

Answer:

70 degrees

Step-by-step explanation:

(360 - 90 - 130)/2=70

Answer:

y = - 4x - 10

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 4 , thus

y = - 4x + c ← is the partial equation

To find c substitute (- 4, 6) into the partial equation

6 = 16 + c ⇒ c = 6 - 16 = - 10

y = - 4x - 10 ← equation of line

Answer:

y = -4x+10

Step-by-step explanation:

Using the slope intercept form of a line

y = mx+b where m is the slope and b is the y intercept

y = -4x +b

Substituting the point in

6 = -4(-4) + b

6 = 16+b

Subtract 16 from each side

-10 =b

The equation is

y = -4x+10

Answer:

Proved

Step-by-step explanation:

2 sin square( 45°-A)

(therefore;

by trigonometry ratios

sin45°=1)

=2sin2(1-A)

=2sin(1-A)

=1+sin2A

hence proved

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Tysm

Work Shown:

sin(angle) = opposite/hypotenuse

sin(40) = 24/x

x*sin(40) = 24

x = 24/sin(40)

x = 37.33737184465

x = 37.3

When you use your calculator, make sure it is in degree mode. One way to check is to compute something like sin(30) and you should get 0.5

Answer:

                x = 37.3

Step-by-step explanation:

for the specified angle, the ratio of the length of the side that is opposite that angle to the length of the longest side (hypotenuse) of the triangle, it is sine.

[tex]\sin40^o=0.6428[/tex]

From triangle  [tex]\sin40^o=\dfrac{24}x[/tex]

so:

   [tex]0.6428=\dfrac{24}x\\\\0.6428\,x=24\\\\x=24\div0.6428=37.336652....\approx37.3[/tex]

Answer:

B) This student performed better than 78% of the other test-takers in the verbal part and better than 34% in the quantitative part.

Step-by-step explanation:

In Statistics, Percentile refers to how specific variables can be divided according to the distribution of values in a population of 100 equal groups.

The data value of a given percentile can be determined  as 100 times the cumulative relative frequency of that value.

From the given question.

Suppose a test-taker scored at the 78th percentile for their verbal sent to test-takers, the percentiles associated grade and at the 34th percentile for their quantitative grade.  

This implies that ;

The student score shows the relation between a particular score of :

78% and the scores of the rest of a group for the verbal test takers   &

34% and the scores of the rest of a group for the quantitative test takers.

Therefore; we can conclude that ;

This student performed better than 78% of the other test-takers in the verbal part and better than 34% in the quantitative part.

Answer:

Number of different cones made = 18

Step-by-step explanation:

Given:

Types of cone = 2

Number of flavors = 3

Number of toppings = 2

Find:

Number of different cones made

Computation:

Number of different toppings = 1(peanuts) + 1(sprinkles) + 1(both) = 3

Number of different cones made = Types of cone × Number of flavors × Number of different toppings

Number of different cones made = 2 × 3 × 3

Number of different cones made = 18