help pls and thanks

We can show z = 1 ± i satisfies the equation [tex]z^2-2z+2=0[/tex] by putting the values of z in the given equation.

z = 1 ± i

Equation:

[tex]z^2-2z+2=0[/tex]

We have to show that z satisfies the given equation.

Complex numbers

A complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation [tex]i^2 = -1[/tex]; every complex number can be expressed in the form a + bi, where a and b are real numbers.

Putting z = 1 + i in the given equation, we get

[tex](1+i)^2-2(1+i)+2 = 1 + i^2+2i -2-2i+2[/tex]

= (1 - 1 -2 +2) + (2i - 2i)  

= 0 + 0 = 0

Putting z = 1 - i in the given equation, we get

[tex](1-i)^2-2(1-i)+2 = 1 + i^2-2i -2+2i+2[/tex]

= ( 1 - 1 - 2 + 2) + (-2i+2i)

= 0 + 0 = 0

As we can see that putting z = 1 ± i  in the given equation, we get 0, hence, we have shown that z satisfies the given equation.

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When working with unknowable numbers, we can simplify equations by using the distributive property. If the equation be 10x² - (9x + 4x²) + 7 + (5x - 8) then we get 6x² - 4x - 1.

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.

Let the equation be 10x² - (9x + 4x²) + 7 + (5x - 8)

Apply rule: a +(b + c) = a + b + c

7 + (5x - 8) = 7 + 5x - 8

= 10 x²- (9 x + 4 x²) + 7 + 5x - 8

simplifying the above equation, we get

= -(9x + 4x²) + 10x² + 5x + 7 - 8

Subtract the numbers: 7 - 8 = -1

= -(9x + 4x²) + 10x² + 5x - 1

Apply the distributive law: -(a + b) = -a - b = 0

-(9x + 4x²) = - 9x - 4x²

= -9x - 4x² + 10x² + 5x - 1

Add similar elements:

-4x² + 10x² = 6x² = -9x + 6x² + 5x - 1

simplifying the above equation, we get

= 6x² - 9x + 5x - 1

Add similar elements: -9x + 5x = -4x

= 6x² - 4x - 1

Therefore, by simplifying the equation, we get 6x² - 4x - 1.

The complete question is:

Simplify 10x² - (9x + 4x²) + 7 + (5x - 8)

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A woman has a total of $10,000 to invest and she invests part of the money in an account that pays 7 % per year, then she invested $4000 per year.

Simple interest can be said as a quick and simple formula for figuring out how much amount of interest will be charged on a loan. The daily interest rate, the principle, and the total number of days present between payments are multiplied to calculate the simple interest.

A = P (1 + rt)

FINAL AMOUNT = A

P is the starting primary balance.

Annual interest rate is r.

T = time (in years)

According to question,

7/100(x) + 12/100 (10000 -x) = 5900

7x + 120000 - 12x = 90000

30000 = 5x

x = $ 6000

P = 10000 - 600

= $ 4000

Simple interest is a kind of method for figuring out how much interest was paid on a sum of money during a specific time period at a specific rate. Simple interest has a constant principal amount. Simple interest is an absolutely clear-cut and simple method in order to compute financial interest.

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The gcf of 15 and 36 is 3 and   15 + 36 by distributive property is 51.

What is gcf?

The gcf(greatest common factor) is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number. 18 and 24 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 24.

What is distributive property?

According to the distributive property, multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.                         A (B + C) = AB + AC.

Given that, 15 and 36

Factor of 15 = 3 × 5

Factor of 36 = 2 × 2 × 3 × 3

gcf of 15 and 35 is 3 because 3 only one 3 is common in both the number.

Applying distributive property on 15 an 35 = 15 + 36

                                                                      = 3×5 + 3×12

                                                                      = 3(5 + 12)

                                                                      = 3(17) = 51

Therefore, the gcf of 15 and 36 is 3 and   15 + 36 by distributive property is 51.

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The algebraic expression for the difference of 13 and m is 13 - m

Algebraic expressions are simply defined as mathematical expressions made up of variables, terms, coefficient, constants, and factors

They are also composed of arithmetic or other known mathematical operations which includes;

Examples of an algebraic expressions;

2x - y + 4

Where;

Given the statement

The difference of 13 and m

Difference here signifies subtraction

m is the variables

It is represented as: 13 - m

Hence, the expression is 13 - m

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The complete question:

Write the algebraic expression for the difference of 13 and m

Answer:

(-∞, -3) and (-1, ∞)

Step-by-step explanation:

A function is increasing when the gradient is positive.

A function is decreasing when the gradient is negative.

A function is stationary when the gradient is zero.

From inspection of the given graph, the turning points of the function are (-3, 3) and (-1, -1).  Therefore, the gradient is zero at these points.

From inspection of the graph:

Therefore, the function is increasing on the intervals (-∞, -3) and (-1, ∞).

The probability that none of the solar panels are defective is 0.97.

So, the faulty solar panel percentage, p = 1/200 = 0.005.

Sample size, n = 6 likelihood that there are no damaged solar panels:

So, the probability: 0.97

Therefore, the probability that none of the solar panels are defective is 0.97.

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Answer:

the first choice

Step-by-step explanation:

C reflection of point D over x and y axis

If a car with an initial speed of 36 km/h accelerates at a uniform rate of 2.4 m/s^2 for 2.5 seconds. The final speed is 16m/s and displacement of the car during this time is 32.5m.

23.7 km/h = 10 m/s

Using this formula to find the speed  vf = vi + a(Dt) for the final speed

Where:

Initial speed = 10 m/s

Acceleration = 2.4 m/s2

Time = 2.5 s

Let plug in the formula

vf = (10 m/s) + (2.4 m/s2)(2.5 s)

vf = 16m/s  fast car

Now, let's find or determine  the displacement

Using this  formula  Dx = vi(Dt) + 1/2a(Dt)2

Let plug in the formula

Dx = (10 m/s)(2.5 s) + 1/2(2.4 m/s2)(2.5 s)²

Dx = 32.5 m

Therefore we can conclude that the speed is 16m/s and the displacement is  32.5 m.

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The money that she earns in total, after paying the vendor fees and repaying her brother's loan is $95.

From the information, Mia borrowed $800 from her brother to start a small business and she then applies to sell her products at a vendor fair.

Also, it should be noted that the vendor fair requires all businesses to pay a $50 entry fee, plus 10% of their sales.

The amount that she will earn after selling $1050. worth of product will be;

= $1050 - Amount borrowed - Entry fee - Percentage on sales

= $1050 - ($800) - $50 - (10% × $1050)

= $1050 - $800 - $50 - $105

= $95

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[tex] \frac{7}{10} x - 2 = \frac{2}{5} x + \frac{8}{3} \\ \frac{7}{10} x - \frac{4}{5} x = \frac{8}{3} + 2 \\ \frac{3}{10} x = \frac{14}{3} \\ x = \frac{14}{3} \div \frac{3}{10} \\ x = \frac{14}{3} \times \frac{10}{3} \\ x = \frac{140}{3} [/tex]

[tex]y = ( \frac{7}{10})( \frac{140}{3} ) - 2 \\ y = \frac{980}{30} - 2 \\ y = \frac{98}{3} - 2 \\ y = \frac{196}{3} - \frac{6}{3} \\ y = \frac{190}{3} \\ y = 63 \frac{1}{3} [/tex]

BE AWARE THERE WAS NO NEED FOR ME TO SOLVE THE EQUATION I JUST WANTED TO SHOW YOU HOW IT'S DONE THE ANSWER NOW TO YOUR QUESTION IS THERE IS 1 PAIR OF ANSWER BUT TWO ANSWERS FOR THE VARIABLES.

x = 6

Step 1: Simplify both sides of the equation.

5045x + 3000 = 5545x

Step 2: Subtract 5545x from both sides.

5045x + 3000 − 5545x = 5545x − 5545x

−500x + 3000 = 0

Step 3: Subtract 3000 from both sides.

−500x + 3000 − 3000 = 0 − 3000

−500x=−3000

Step 4: Divide both sides by -500.

−500x/−500 = −3000/−500

Answer: x=6

Answer:

a1=7

an=an-1+4

a2=a2-1+4

a2=a1+4

a2=7+4

a2=11

a3=a3-1+4

a3=a2=+4

a3=11+4

a3=15

a4=a4-1+4

a4=a3+4

a4=19

a5=23

a6=27

a15=62

The common difference is 4.

The sum is 517.

NSWER :

he answer is between 6 and 9

EXPLANATION :

room the problem, we have a graph with distance vs time.

Note that the steeper the line in the graph, the faster the speed or rate.

Looking at the graph, the steepest part is when the time is between 6 and 9

Check the picture below.

Answer: x=5.5

Step-by-step explanation:

All three medians of a triangle intersect at one point, which is called the centroid or center of gravity of the triangle, and are divided by this point into two parts in the ratio 2:1

Hence,

[tex]\displaystyle\\\frac{6x+12}{x+17}=\frac{2}{1} \\[/tex]

Multiply both part of the equation by (x+17):

[tex]6x+12=2(x+17)\\6x+12=2(x)+2(17)\\6x+12=2x+34\\6x+12-2x=2x+34-2x\\4x+12=34\\4x+12-12=34-12\\4x=22\\[/tex]

Divide both parts of the equation by 4:

[tex]x=5.5[/tex]

By evaluating the function f(x) = x² - 5 · x, the range of the function is {- 6, - 4, 14}.

In this problem we have a domain, that is, an input set, formed by three natural numbers and a quadratic equation that represents a function that allows us to find the corresponding elements of the range, that is, the output set. The elements of the range are found by evaluating the quadratic equation at each element from domain:

x = 2

f(2) = 2² - 5 · 2

f(2) = 4 - 10

f(2) = - 6

x = 4

f(4) = 4² - 5 · 4

f(4) = 16 - 20

f(4) = - 4

x = 7

f(7) = 7² - 5 · 7

f(7) = 49 - 35

f(7) = 14

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The simplest form of the given multiplication 7 1/2x2/3 = 5.

The given multiplication is;

7 1/2x2/3

Where, 7 1/2 is in the mixed fraction, convert it in simple fraction.

7 1/2 = (7×2 + 1)/2

7 1/2 = 15/2

Now, put the value in multiplication and find.

= 15/2 × 2/3

Multiply the numerators and denominators of each digit

= 30/6

Divide each digit by 6

= 5

Thus, the simplest form of the digit 7 1/2x2/3 after multiplication is found 15.

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IfIf a 4,800-pound wrecking ball is held in static equilibrium by two cables, one horizontal and one at an angle of 40° from vertical .the magnitudes of the tension vectors T  and H is: 6,266.32 lb,  3,085.44lb.

Let T h = H represent the horizontal

Let Tv  represent the vertical components of the vector T

Let W wball represent the weight of the wrecking ball

Hence,

T h =H

Tv = W wball

Where:

T h = T sin 40°

Tv =T cos 40°

Magnitude of the tension vector T:

Tv =4800lb

T=Tv/ cos 40°

T = 4800lb/ cos 40°

T = 4800lb/0.766

T= 6,266.318

T=6,266.32 lb (Approximately)

Magnitude of the tension vector H

W=T  h

T h =(4800lb) sin 40°

T h =(4800lb) 0.6428

H = 3,085.44lb

Therefore we can conclude that tension vector T magnitudes is 6,266.32lb and that of tension vector H magnitudes is 3,085.44lb.

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Answer:

(8,4) 8 is on the x axis and 4 is on the y axis

The quotient when 0.03 is divided by 0.148 after rounding it off is 0.2.

According to the question,

We have the following information:

0.03 is divided by 0.148

And it can be simply expressed as 0.03/0.148

Now, we have the quotient as:

0.2027

Now, when rounding off the numbers we know that the digits from where we are rounding off we look at the right next to that digit and when that digit is greater than 5 then the digit should be increased by 1 and when that digit is less than 5 then the digit should be the same.

So, we will round it off by taking the underlined digit to be next to first 2:

So, the digit is 0.

Butt if we are taking the underlined digit as 2 to be the next 2 then the digit next to it is 7 which is greater than 5.

Then, we have:

0.2

Hence, the quotient when 0.03 is divided by 0.148 after rounding it off is 0.2.

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Answer:

(0,5)(3,4)(4,5)(3,2)(4,3)(3,3)(2,3)

The equation of the line in the form y = mx + b are as follows:

The equation of a line can be found as follows:

Using the slope intercept form,

y = mx + b

where

Therefore, let's find the slope using the table.

(-4, 13)(-3, 11)

m = 11 - 13 / -3 + 4

m = - 2 / 1

m = -2

Let's find the y-intercept using (-4, 13)

13 = -2(-2) + b

13 - 4 = b

b = 9

Therefore, the equation of the line is y = -2x + 9

Using the second table,

(0, -3)(2, 1)

m = 1 + 3 / 2 - 0

m = 4 / 2

m = 2

y-intercept = b = -3

Therefore,

the equation of the line is y = 2x - 3

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a) As per the given percentage, the number of registered voters in the town who cast the votes are 155,952.

b) Reese claim is incorrect. The number he mentioned as registered voters is greater than the actual number of registered voters..

Percentage:

A percentage is a number or ratio which can be expressed as a fraction of 100.

For example, 57% can be written as 57/100.

Given,

The register voters and other in the town cast their vote on the election day.

a. In that particular town, 273,600 votes were cast in an election. And there are 57% of those who were registered voted.

Here we need to find how many registered voters are there in the town.

b. Reese claims that there are 60% of the registered voters cast 273,600 votes, there would be fewer registered voters than above.

Now we have also need to find whether his statement is correct or not with the reason.

Let x be the total number of registered voter who cast the vote.

From the given details, we know that, there are 273,600 voters are cast.

And 57% of them are registered voters.

So, it can be calculated as follows,

=> x  = 273600 of 57%

=> x = 273600 x 57%

=> x = 273600 x 57/100

=> x = 2736 x 57

=> x = 155, 952

Therefore, there are 155,952 registered voter in the town who cast the vote.

Based on these calculation we know that, Reese claims is incorrect because there the number of registered voters is 155, 952 which is not equal to the number he mentioned.

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