Multiply the following complex numbers (9-2i)(7+6i)

Answer:

-7a-51b

Step-by-step explanation:

-21(a+2b)+14a-9b

-21a-42b+14a-9b

-21a+14a-42b-9b

-7a-42b-9b

-7a-51b

Answer: -7a - 51b

Step-by-step explanation:

see photo for work

Answer:

Circumcenter of triangle [tex](4,-1)[/tex]

Step-by-step explanation:

Given coordinates are [tex](1,1)(1,-3)(7,-3)[/tex]

We will draw these points on the graph.

Let [tex]A(1,1)[/tex], [tex]B(1,-3)[/tex] and [tex]C(7,-3)[/tex]

We can see it is a right-angle triangle.

Let [tex]O[/tex] be the midpoint of line [tex]AC[/tex]

So, the coordinate of the point [tex]O[/tex] will be

[tex]A(1,1)\ C(7,-3)\\\\Midpoint\ O\ will\ be\\\\O=(\frac{1+7}{2},\frac{1+(-3)}{2})\\ \\O=(\frac{8}{2},\frac{-2}{2})\\\\O=(4,-1)[/tex]

Also, we know the coordinates of circumcenter of a right angle triangle will be midpoint of its hypotenuse.

So, coordinates of circumcenter is [tex](4,-1)[/tex]

Answer:

x=1, y=-4. (1, -4).

Step-by-step explanation:

y=-7x+3

y=-x-3

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

-7x+3=-x-3

-7x-(-x)+3=-3

-7x+x=-3-3

-6x=-6

6x=6

x=6/6

x=1

y=-1-3=-4

First: work out the difference (decrease) between the two numbers you are comparing.

Decrease = Original Number - New Number

Then: divide the decrease by the original number and multiply the answer by 100.  

% Decrease = Decrease ÷ Original Number × 100

If your answer is a negative number then this is a percentage increase.

Thus, the answer is a 86.7% (rounded) increase.

Final answer:

The sale of KIDZ sneakers increased by $1.3 billion, representing an 86.7% increase when rounded to the nearest tenth of a percent.

Explanation:

To find the percent of increase for the sale of KIDZ sneakers, we subtract the original amount ($1.5 billion) from the new amount ($2.8 billion) and then divide by the original amount. The difference between the two values is $2.8 billion - $1.5 billion = $1.3 billion. To calculate the percentage increase, we divide $1.3 billion by $1.5 billion, which gives us approximately 0.8667. To get the percentage, we then multiply by 100, resulting in an 86.67% increase. Finally, rounding to the nearest tenth of a percent, we get an increase of 86.7%.

Option B is correct.

Step-by-step explanation:

We need to identify which of the following equations has exactly one solution.

We will solve each equation to find the answer

A. [tex]ax+b=ax+b[/tex]

Solving and finding value of x:

[tex]ax+b=ax+b\\ax-ax=b-b\\0=0[/tex]

This equation has infinite number of solutions because both sides are equal to 0

B. [tex]ax=bx+c[/tex]

Solving and finding value of x:

[tex]ax=bx+c\\ax-bx=c\\x(a-b)=c\\x=\frac{c}{a-b}[/tex]

This equation has exactly one solution

C. [tex]ax+b=ax+c[/tex]

[tex]ax+b=ax+c\\ax-ax=c-b\\0=c-b[/tex]

This equation has no solution because both sides are not equal.

So, Option B is correct.

Keywords: Solving Equations

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Long-term purchase on a credit card better than taking out a loan when interest rate is 0% or very lower than loan, or any other benefits

We can use a credit card for long term purchases if there is a 0% interest rate on purchase is allowing you to pay off your shopping with no additional cost for an introductory period. Or some of the credit cards may offer interest-free purchases for 3 to 6 months others can run for as long as 12 to 14 months. An interest-free period could be considered long-term if it lasts between 12 and 14 months or more.

We could benefit from one of these cards if you are making a large purchase and need more breathing room to pay it off without any interest. This is especially useful if you have a high spending period such as an overseas holiday coming up.

A long  term purchase with loan or with a credit card will depends upon the interest rates offered in both the schemes.

In order to understand that what is more beneficial for us a long term purchase or taking out a loan we have to see the interest rates of the both the schemes.

If the interest  rate of loan is higher than the interest rate offered by credit card then we must go for long term purchase on credit card and the amount can be paid later .

Also credit cards often offer other benefits too. These options can also be seen as a determining parameters of whether to take loan or a long term purchase on credit card is beneficial.

Also we can have a look at the period of interest free purchase offered by the credit card.

Depending upon the credit card and its usage they can vary from three months to one year with multiple other benefits which promote the use of credit card.

so we can conclude that

A long  term purchase with loan or with a credit card will depends upon the interest rates offered in both the schemes.

For more information please refer to the link below

https://brainly.com/question/3685635

Answer:

Step-by-step explanation:

The given numbers:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

Getting the number 28 (using 4 numbers):

If we add the following 4 numbers from 1 to 14, we would get 28.

10 + 9 + 7 + 2 = 28

Getting the number 14 (using 3 numbers):

If we add the following 3 numbers from 1 to 14, we would get 14.

8 + 5 + 1 = 14

Getting the number 30 (using 4 numbers):

If we add the following 4 numbers from 1 to 14, we would get 30.

11 + 12 + 4 + 3 = 30

Getting the number 33 (using 3 numbers):

If we add the following 3 numbers from 1 to 14, we would get 33.

14 + 13 + 6 = 33

Keywords: addition, number

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Answer:

t = 51°

Step-by-step explanation:

The total sum of a polygon's exterior angles is always 360°.

Add all of the given angles and equate it to 360°.

40° + 34° + 34° + 46° + (2t - 50°) + (2t - 50°) + 2t = 360°     Collect like terms

154° + 2t - 50° + 2t - 50° + 2t = 360°    Remove brackets and collect like terms

54° + 6t = 360°   Isolate t by doing reverse operations in reverse BEDMAS

6t = 360° - 54°    Subtract 54° from both sides

6t = 306° Divide both sides by 6

t = 51°    Answer

Answer:

Larry is about 9 years old

Step-by-step explanation:

Subtract

Answer:

The mural in David's drawing is 4 cm long.

Step-by-step explanation:

Given:

David made a scale drawing of a mural he is going to paint.

He used a scale of 1 cm=4ft.

If the actual mural will be 16 feet long.

Now, to find how long is the mural in David's drawing.

Let the length of mural in David's drawing be [tex]x\ cm[/tex].

So, as given 1 cm = 4 ft.

1 cm is equivalent to 4 ft.

Thus, [tex]x\ cm[/tex] is equivalent to 16 feet.

Now, to get the length of mural in David's drawing by using the cross multiplication method:

[tex]\frac{1}{4} =\frac{x}{16}[/tex]

By cross multiplication:

[tex]16=4x[/tex]

Dividing both sides by 4 we get:

[tex]4=x[/tex]

[tex]x=4\ cm.[/tex]

Therefore, the mural in David's drawing is 4 cm long.

Answer:

Multiply the entire expression by the radical denominator. This keeps the expression equal and makes the denominator 3, a whole number.

Step-by-step explanation:

The denominator is irrational because it is a radical number, √3.

To rationalize the denominator, multiply the entire expression by √3. The denominator will become a whole number. This works because you multiply top and bottom by the same value.

[tex]\frac{3 + \sqrt{2} }{\sqrt{3}}[/tex]

[tex]= \frac{(\sqrt{3})(3 + \sqrt{2}) }{(\sqrt{3})(\sqrt{3})}[/tex]

[tex]= \frac{(\sqrt{3})(3 + \sqrt{2}) }{3}[/tex]  

√3 X √3 = 3 because:

√3 X √3 = √3²

Squaring a number and also finding its square root are opposites, or reverse operations. They cancel out

You probably need to simplify the rest of the equation too.

[tex]\frac{(\sqrt{3})(3 + \sqrt{2}) }{3}[/tex]

[tex]= \frac{3(\sqrt{3}) + (\sqrt{2})(\sqrt{3})}{3}[/tex]  Distribute over brackets

[tex]= \frac{3(\sqrt{3}) + \sqrt{2*3}}{3}[/tex]   Simplify

[tex]= \frac{3(\sqrt{3}) + \sqrt{6}}{3}[/tex]

Some people use a more simplified version whether they simplify each term in the numerator:

[tex]\frac{3(\sqrt{3}) + \sqrt{6}}{3}[/tex]    (3√3)÷3 = √3

[tex]\sqrt{3} + \frac{\sqrt{6}}{3}[/tex]

376 people visited the nature center in September.

Step-by-step explanation:

Given,

Number of visitors in December = 94 people

This number is one quarter of the number of people in September.

One quarter = [tex]\frac{1}{4}[/tex]

Let,

x represent the number of visitors in September.

[tex]\frac{1}{4}x=94[/tex]

Multiplying both sides by 4

[tex]4*\frac{1}{4}x=94*4\\x=376\\[/tex]

376 people visited the nature center in September.

Keywords: fraction, multiplication

Learn more about fractions at:

#LearnwithBrainly

Answer:

Step-by-step explanation:

consecutive numbers are one right after the other...

ur 3 consecutive numbers are :

x and x + 1 and x + 2.....and they total 84

x + x + 1 + x + 2 = 84.....combine like terms

3x + 3 = 84

3x = 84 - 3

3x = 81

3x = 81/3

x = 27

x + 1 = 27 + 1 = 28

x + 2 = 27 + 2= 29

so your 3 numbers are 27,28,29 with the lowest being 27

Answer: 24

Step-by-step explanation: This problem states that the sum of 3 consecutive numbers is 84 and it asks us to find the smallest number.

3 consecutive numbers can be represented as follows.

X ⇒ first number

X + 1 ⇒ second number

X + 2 ⇒ third number

Since the sum of our 3 consecutive numbers is 84, our equation will read X + X + 1 + X + 2 = 84.

Simplifying on the left we get 3x + 3 = 84.

Subtracting 3 from both sides, we have 3x = 81.

Now we can divide both sides by 3 to get x = 27.

This means that 27 will be the smallest number.

True options:

1. The vertex of the function is at (1,–25).

5. The graph is negative on the entire interval –4 < x < 6.

Step-by-step explanation:

Part of the graph of the function f(x) = (x + 4)(x – 6) is shown in attached diagram.

This graph intesects the x-axis at points (-4,0) and (6,0). So, the x-coordinate of the vertex is \dfrac{-4+6}{2}=\dfrac{2}{2}=1

The y-coordinate of the vertex is

y=(1+4)(1-6)=5\cdot (-5)=-25

Hence, the vertex is ar the point (1,-25) - frist option is true, second option is false.

For all x<1 the graph is decreasing, for all x>1 the graph is increasing. So, third option is false.

The graph is positive (placed above the x-axis) for all x<-4 or x>6. This means fourth option is false.

The graph is negative (placed below the x-axis) for all -4<x<6. This means fifth option is true.

hope this helps homie

Answer:

21

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

x = 5

y = 3

6(5) - 3(3)

30 - 9

21

Answer:

Step-by-step explanation:

1) Two angles supplementary. So sum of two angles is 180

One angle  = x

Other angle = 2x

x + 2x = 180

3x = 180

x = 180/3 = 60

The angles are 60, 120

2)Two angles complementary. So sum of two angles is 90

one angle  = x

Other angle = x + 20

x +x +20 = 90

2x + 20 = 90

2x = 90- 20

2x = 70

x = 70/2 = 35

The angles are 35,55

3) one angle =x

Other angle = 3x - 20

x + 3x - 20 = 120

4x = 120 + 20

4x = 140

x = 140/4 = 35

The angles are 35,85

5) x + 4x -20 = 180

5x = 180 + 20

5x = 200

x = 200/5 = 40

x = 40

6) This sum is not clear only half is visible

Answer:

a) Hence the Baby Manatee is 4 feet long.

b) Hence the Length of blue whale is 108 feet.

Step-by-step explanation:

Given:

Length of Mother manatee = 12 feet.

Now given that:

A mother  manatee is three  times as long as her baby manatee.

Let the length of baby manatee be 'x'.

So equation can be framed as

[tex]3x=12[/tex]

hence the equation is [tex]3x=12[/tex].

Solving the equation we get;

Dividing both side by 3 using Division property of equality we get;

[tex]\frac{3x}{3}=\frac{12}{3}\\ \\x=4\ feet[/tex]

a) Hence the Baby Manatee is 4 feet long.

Solving for part b we get;

Given:

If a blue whale is 9 times as long as the  mother manatee

Hence equation can be framed as;

Length of blue whale is = [tex]9 \times \textrm{Length of Mother manatee}[/tex]

Length of blue whale is = [tex]9\times 12 =108\ feet[/tex]

b) Hence the Length of blue whale is 108 feet.

The right answer is Option C.

Step-by-step explanation:

Given,

Pizzas made by Paul on first day = 12

Pizzas made each day after that = 6

Let,

p represent the number of pizzas made after first day.

Total pizzas = 6p + 12

Number of days = 8 because first day 12 pizzas are made

Total pizzas = [tex]6(8)+12=60[/tex]

Pizzas made by Cindy on first day = 16

Pizzas made each day after that = 4

Total pizzas = 4p + 16

Total pizzas = [tex]4(8)+16=48[/tex]

Paul has made more pizzas after 9 days. He has made 60 pizzas.

The right answer is Option C.

Keywords: comparison, addition

Learn more about addition at:

#LearnwithBrainly

Answer:

C

Step-by-step explanation:

Answer:

It will measure 75 millimetres on the plan.

Step-by-step explanation:

Given:

Scale on the plan = 1:100

Length of the fence =  7,500 mm

To find:

how many millimetres will it measure on the plan

Solution:

As the ratio on the plan is 1: 100, the for 7500 the ratio will

x : 7500

Now by cross multiplication we get

[tex]7500 \times 1 = x \times 100[/tex]

[tex]7500 = 100x[/tex]

[tex]x =\frac{ 7500}{100}[/tex]

x = 75

Final answer:

The fence will measure 75 millimeters on the plan.

Explanation:

To find out how many millimetres a fence that is 7,500 mm long in reality would measure on a plan with a scale of 1:100, you would convert the actual size to the scale size. You do this by dividing the actual size by the scale factor.

Here is the calculation for this scale conversion:

The fence would measure 75 mm on the plan.

Janet has remaining $ 149.16 in her paycheck

Given that Janet's paycheck was $248.60

She put 1/4 of her paycheck into a checking account

Therefore amount put into checking account is given as:

[tex]\text {amount put into checking account }=\frac{1}{4} \times 248.60=62.15[/tex]

So she spent $ 62.15 into checking account

Now the remaining paycheck amount left is:

remaining paycheck amount left = 248.60 - 62.15 = 186.45

Therefore remaining paycheck amount left is $ 186.45

Now she spent 1/5 of what was left to buy dinner for her family

[tex]\text { Amount spend on dinner }= \frac{1}{5} \times 186.45 = 37.29[/tex]

So she spent $ 37.29 on dinner

Now the remaining paycheck amount left is:

remaining paycheck amount left = 186.45 - 37.29 = 149.16

Thus Janet has remaining $ 149.16 in her paycheck

Answer:

Step-by-step explanation:

(-6,8)...x = -6 and y = 8

lets start subbing

5x + 3y = -6

5(-6) + 3(8) = -6

-30 + 24 = -6

-6 = -6

so (-6,8) IS a solution to this equation

2x + y = -4

2(-6) + 8 = -4

-12 + 8 = -4

-4 = -4

so (-6,8) IS a solution to this equation

A. It is the only solution to the system

Answer:

5 1/2 hours past 7:00 would be 12:30

Step-by-step explanation:

Answer:

12:30 a.m.

Step-by-step explanation:

You can automatically add 5 to the 7, 5 + 7 = 12. Then add 30 to the minuets. 00 + 30 = 30.

So, your answer is 12:30.

Hope this helps!!

The force of gravity acting on the block(and weight) in the air is 2403.45 newton

Step-by-step explanation:

Density of an object is defined as the ratio of mass to volume

So we can write it as:

[tex]d = \frac{m}{V}[/tex]

And the force is given by:

[tex]F_g = mg[/tex]

We know that

d = 3500 kg/m^2

V = 0.07 m^3

g = 9.81 ms^-2

So we will calculate the mass first

[tex]d = \frac{m}{V}\\3500 = \frac{m}{0.07}\\m = 3500*0.07\\m = 245\ kg[/tex]

Now,

[tex]F_g = 245 * 9.81\\= 2403.45\ N[/tex]

The force of gravity acting on the block(and weight) in the air is 2403.45 newton

Keywords: Force, gravity

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Answer:

6

Step-by-step explanation:

3/5 = 6/10

6/10 / 1/10

6/10 times 10/1

60/10

6

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Answer:

Step-by-step explanation:

80 minutes.......8 minutes played commercials....that means (80 - 8) = 72 minutes played music

so the ratio of music to commercials is : 72/8 which reduces to 9/1...so the ratio is 9:1 <=== ur answer

** pay attention to the wording, because if it would have asked for the ratio of commercials to music, it would have been 8/72....ratio would be 1:9

210 / x = 15

--> 210/15 = x

--> x = 14

Answer:

Slope = - 3, y-intercept is 4 and the equation is y = - 3x + 4.

Step-by-step explanation:

Slope of a straight line passing through two given points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given by the formula

[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].

Now, the given graph of the straight line passes through the points (0,4) and (1,1) points.

Hence, the slope of the straight line will be = [tex]\frac{1 - 4}{1 - 0} = - 3[/tex]

Again, the straight line intersects the y-axis at point (0,4) point. hence, its y-intercept is 4.

Therefore, the straight line has equation  

y = - 3x + 4 (Answer)