What is the product of ( 4 + 3 i ) and ( 12 − 2 i )

Answer:

Step-by-step explanation:

Find the slope of the line AB.

The slope:

Since the altitude is perpendicular to AB, it has a slope of -2.

The line with the slope of -2 and passes through point C(6, 16).

Use point-slope equation to find the line:

A = 2, B = 1, C = 28

Answer:

Solution given:

A(7,9)

B(11,11)

C(6,16)

Slope of AB=[tex]\frac{11-9}{11-7}=\frac{2}{4}=½[/tex]

since altitude is perpendicular to it .

so its slope becomes negative reciprocal to the slope of base

so

slope of altitude(m) =-2

now

equation of a line passing through C(6,16) perpendicular to its base is:

By using formula

[tex]y-y_{1}=m(x-x_{1})[/tex]

y-16=-2(x-6)

solve it

y-16=-2x+12

y+2x=12+16

in the form of Ax +By=C is:

2x+y=28

:.

B=1

C=28

Answer:

(1) 256 inches

(2) 5 feet

(3) 400 inches

(4) 10 feet

Step-by-step explanation:

(1) The function that gives the height in inches of the spray of water at a distance x from the sprinkler head is given as follows;

h(x) = 160·x - 16·x²

At x = 2 feet, we have;

h(2) = 160 × 2 - 16 × 2² = 256

Therefore, the height of the spray water at a horizontal distance of 2 feet from the sprinkler head h(2) = 256 inches

(2) The x-coordinate, [tex]x_{max}[/tex], of the maximum point of a parabola given in the form, y = a·x² + b·x + c is found using the following formula;

[tex]x_{max}[/tex] = -b/(2·a)

The x-coordinate, [tex]x_{max}[/tex], of the maximum point of the given equation of the parabola, h(x) = 160·x - 16·x², (a = -16, b = 160) is therefore;

[tex]x_{max}[/tex] = -160/(2 × (-16)) = 5

Therefore, the number of feet along the way, the function will reach maximum height, [tex]x_{max}[/tex] = 5 feet

(3) The function, h(x) = 160·x - 16·x², will reach maximum height, [tex]h_{max}[/tex], at x = 5, therefore;

[tex]h_{max}[/tex] =  h(5) = 160 × 5 - 16 × 5² = 400

The maximum height of the spray, [tex]h_{max}[/tex] = 400 inches

(4) The water is at ground level where h(x) = 0, therefore;

At ground level, h(x) = 0 = 160·x - 16·x²

160·x - 16·x² = 0

∴ 16·x × (10 - x) = 0

By zero product rule, we 16·x = 0, or (10 - x)  = 0, from which we have;

x = 0, or x = 10

The water is at ground level at x = 0 and x = 10 feet, therefore, the water will hit the ground again (the second time after leaving the sprinkler head at x = 0) at x = 10 feet.

Answer:

Size of the original rectangle is 30*20=600

Step-by-step explanation:

Let the length and width of rectangle be x+10 and x. After increasing the dimensions, the new length and width are x+20 and x+10

ATQ, (x+20)(x+10)=2(x+10)(x), x=20.

Answer:

It will take 5 yrs the sum of 5000 will take to reach Rs 8750 at the rate 15%

Step-by-step explanation:

T= ?

Amount = Rs 8750

R = 15%

P = Rs 5000

so

I = A-P

= 8750 - 5000

= Rs 3750

so

I = PTR/100

3750 = (5000*15*T)/100

or, 375000 = 75000*T

or, T = 375000/75000

so T = 5 yrs

Answer: x>12

so i think x is 16.

Answer:

Equation

ans = -1

Step-by-step explanation:

3x-2=-5

3x=-5+2

3x=-3

x=-3/3

x=-1

Answer:

6n+19

Step-by-step explanation:

6 times a number, n

6n

19 more

6n+19

Answer:

6n + 19

Step-by-step explanation:

Since the expression is 6 times n

We need to have 6 x n or simply just 6n

Since the expression is 19 more than 6n

We need to have 6n + 19

Answer: See explanation

Step-by-step explanation:

Since Smart Dot Company costs $12 per month plus $0.50 for each hour of Internet used, the equation to represent the cost of using the internet with them will be:

C = 12 + 0.5t

Since Communication Plus costs $2.50 for every hour of Internet used, the equation to represent the cost of using the internet with them will be:

C = 2.5t

x > 0.8

x > -2

hope it helps :)

The solution of the given inequalities will be x > 0.8 and x < -2.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Given inequalities are x-0.8>0, and -5x<10. the inequalities will be solved as:-

x-0.8>0

x > 0.8

-5x<10

Take -5 to the right side and divide 10 by -5 and solve further.

x < -10 / 5

x < -2

Therefore, the solution of the given inequalities will be x > 0.8 and x < -2.

To know more about inequality follow

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Answer:

D. rotation

uhhhh I need 20 characters so

Rotation is correct because the triangle ABC is rotated about the mid-point of B and B'. Then the correct option is D.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry. But flip the image.

Rotation does not change the size and shape of the geometry. But change the orientation of the image.

Translation does not change the size and shape of the geometry. But change the location of the shape.

Check all the options.

Translation is incorrect because orientation of the triangle is changed.

Reflection is incorrect because the line of the reflection is not possible for the triangles.

Rotation is correct because the triangle ABC is rotated about the mid-point of B and B'.

Then the correct option is D.

More about the transformation of geometry link is given below.

https://brainly.com/question/22532832

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Answer:

[tex]y = - \frac{3}{2} x + 1[/tex]

Step-by-step explanation:

Slope -intercept form: y= mx +c, where m is the slope and c is the y-intercept.

Parallel lines have the same slope. Let's find the slope of the given line.

Given points: (-2, 0) and (0, -3)

[tex]\boxed{slope = \frac{y1 - y2}{x1 - x2} }[/tex]

slope of given line

[tex] = \frac{0 - ( - 3)}{ - 2 - 0} [/tex]

[tex] = \frac{0 + 3}{ - 2} [/tex]

[tex] = - \frac{3}{2} [/tex]

[tex]y = - \frac{3}{2} x + c[/tex]

Given that the y- intercept is 1, c= 1.

[tex]y = - \frac{3}{2} x + 1[/tex]

Answer:

13

Step-by-step explanation:

the students took math and physics = 55

Answer:

p = -5

every element in the sequence is created by subtracting 3 from the pervious element.

Step-by-step explanation:

I am not sure you put every necessary information here.

but I'd the visible information is truly everything, then it's is trivial.

the difference between 4 and 1 is ... well, -3. meaning we subtract 3 from 4 to get 1.

we suspect this is the rule and keep trying.

1 -3 = -2

hey it works.

and -8 -3 = -11

hey, also correct.

and the difference between -2 and -8 is -6, and when we place another item in between (p), we cut that in half again to -3. so, it is all consistent.

therefore,

p = -2 -3 = -5

the rule is

an = an-1 - 3

Using the Central Limit Theorem, the mean height that is most likely closest to the average height of the population is:

B. 57.

It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

The interpretation of the equation for the standard error is that larger sample sizes will lead to estimates closer to the actual population parameters.

From the table, the largest sample size in this problem is of 40, and this sample had a mean of 57, hence the mean height that is most likely closest to the average height of the population is:

B. 57.

More can be learned about the Central Limit Theorem at https://brainly.com/question/16695444

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Two options are given to Tina. We find how much she pays for each option, and the one in which she pays less offers the better value.

Tina sends 12 text messages each day in June

June has 30 days, so in June, Tina sent 12*30 = 360 text messages.

Package A:

First 100 messages cost 3p, the next 100 cost $2 and after that each costs $1.

She sends 360 messages, with:

The first 100 costing 3p.

The next 100 costing 2p.

The final 360 - 200 = 160 costing 1p.

She pays:

[tex]100*3 + 100*2 + 160*1 = 660[/tex]

Package B:

2p for each message, 360 messages, so:

360*2p = 720p.

Which package is better?

Package A costs less, thus, it offers her the better value for money in 30 days.

Another example of a problem in which a person has to choose between two packages is given in https://brainly.com/question/10693932

Answer:

i think ..................

Step-by-step explanation:

society idsbwj ja

Answer:

where is the figure without figure how to find out

Answer:

1.0612

I tried using the alogarithm of ratios but am confused please help me

Answer:

-2 Answer

Step-by-step explanation:

SEE IMAGE for Solution

Answer:

a

Step-by-step explanation:

i took this and got a 100

Answer:

y = 9x

Step-by-step explanation:

other person is so wrong, hope this helps.

Answer: present statistical information in clear, meaningful terms.

Step-by-step explanation:

When using statistics, the information gathered should be presented in such a way that it is clear and meaningful as this would allow for the data to be tested using various statistical measures.

If data is unclear, the measures used for the test could be negatively impacted such that the results would not represent the most accurate of interpretations.

Use pythagoras theorem

d = √((x₁ - x₂)² + (y₁ - y₂)²)

d = √((-5 - 7)² + (3 - 3)²)

d = √((-12)² + 0)

d = √144

d = 12  

Answer:

Step-by-step explanation:

distance is √((x2-x1)^2+(y2-y1)^2)

so it will be √((12)^2+(0)^2)

or simply 12. since we are calculating distance, it is always going to be positive so technecally the formula is |√((x2-x1)^2+(y2-y1)^2)|

Answer:

(5-2z)(5+2z)

Step-by-step explanation:

25 -4z^2

Rewriting

5^2 - (2z)^2

This is the difference of squares  a^2 - b^2 = (a-b)(a+b)

(5-2z)(5+2z)

Answer:

25

Step-by-step explanation:

<ABD=<BDC

Check it out

Answer:

∠ BDC = 25°

Step-by-step explanation:

Since ABCD is a parallelogram , then

AB and DC are parallel , so

∠ BDC = ∠ ABD = 25° ( alternate angles )

Answer:

x = 20

Step-by-step explanation:

c^2 = a^2 + b^2

a = 12

b = 16

c = ?

c^2 = 12^2 + 16^2

c^2 = 144 + 256

c^2 = 400

sqrt(c^2) = sqrt(400)

c = 20

Answer:

90+ 135= 225

Step-by-step explanation:

a can be found with formula (n-2)×180/n, where n is number of sides

a= 135

b=90

Answer:

18.

Domain: X E \{-3,2}

Y-Intercept: 1/2

X-Intercept: 3

19.

Domain: (I think it's none)

Y-Intercept: -2

X-Intercept: 2

20.

Domain: X E R\ {-3,1}

y-INTERCEPT: 2/3

x-INTERCEPT: -1

Step-by-step explanation:

Answer:

We know that Sin,

 [tex]=\frac{perpendicular}{hypotenuse}[/tex]

[tex]SinA=\frac{BC}{AC}[/tex]

[tex]SinA=\frac{9}{41}[/tex]

OAmalOHopeO

Answer:

xy

Step-by-step explanation:

The HCF is known as the highest common factor. To find the HCF of two values, we have to take the greatest number that fits into all of their factors.

To start, we can list each value's factors.

For 4x²y, this can also be written as 4*x²*y = 4*x*x*y. In multiplication, we can take the factors of each value that is multiplied. Therefore, we can start with the factors of 4 and then go to the factors of x² and so on. Our factor list is thus 1,2,4,x,x²,y

Similarly, for xy² = x*y*y, our factors are x, y, and y²

The common factors for each of these are x and y. Assuming all values are positive and greater than 1, the x*y will be greater than either x or y. Therefore, the highest common factor would be x*y = xy