Write the expression in standard form,
(9+2i)(5-3i)

Answers

Answer 1

[tex](9+2i)(5-3i)\\\\=45-27i+10i-6i^2\\\\=45-17i+6~~~~~;[i^2 =-1]\\\\=51-17i[/tex]

Answer 2

[tex] \: \: \: \: \: \: [/tex]

[tex] = \: \: \: \: 51 - 17i[/tex]

refer to the attachment for explanationhope it helps
Write The Expression In Standard Form,(9+2i)(5-3i)

Related Questions

what is 5y² if y= -1​

Answers

Answer:

5

Step-by-step explanation:

Input all of the numbers and solve:

5×-1×-1

Start by solving -1*-1=1

5*1=5

Answer:

the answer for this question is 5

12×12 get this right i will give you brainliest​

Answers

Answer:

144

Step-by-step explanation:

12 x 2 =24 12 x 10 =120 120 + 24 =144

Hi, let's solve our equation.

[tex]{\huge{\boxed{\mathbb{EQUATION}}}[/tex]

[tex]12\cdot12[/tex]

_______________

we can use multiple methods to solve this problem.

Distributive property Regular multiplication Fraction division

________________

[tex]{\huge{\boxed{\mathbb{DISTRIBUTIVE\:PROPERTY}}}[/tex]

Here is how it would look to do distributive property

[tex](10\cdot12)+(2\cdot12)[/tex]

Follow PEMDAS rule

Parenthesis Exponents Multiplication or Division Addition or Subtraction

Solve it and we get the answer of 144.

________________

[tex]{\huge{\boxed{\mathbb{REGULAR\:MULTIPLICATION}}}[/tex]

just multiply [tex]12\cdot12[/tex] which equals 144

________________

[tex]{\huge{\boxed{\mathbb{FRACTION\:DIVISION}}}[/tex]

here is how it would look like.

[tex]\frac{12}{1}\div\frac{1}{12}[/tex]

Follow the rule, also known as keep change flip, which makes it look like

[tex]\frac{12}{1}\cdot\frac{12}{1}[/tex] which equals 144

________________

[tex]{\huge{\boxed{\mathbb{ANSWER}}}[/tex]

144

(−3, −1), (−1, 5) Find the slope of the line that passes through the pair of points.

Answers

[tex]slope = \frac{ 5 - ( - 1)}{ - 1 - ( - 3)} \\ [/tex]

[tex]slope = \frac{5 + 1}{ - 1 + 3} \\ [/tex]

[tex]slope = \frac{6}{2} \\ [/tex]

[tex]slope = 3[/tex]

What is the gradient of the graph shown?
Give your answer in its simplest form.

Answers

Answer:

Step-by-step explanation:

When it's clear, the easiest way to do the problem is to used the x and y  intercepts.

This question is one of the clear one.

The x intercept is 2,0

The y intercept is 0,1

You want the slope.

m = (y2 - y1)/(x2 - x1)

y2 = 1

y1 = 0

x2 = 0

x1 = 2

m = (1 - 0)/(0 - 2)

m = 1 / -2

m = -1/2

In this case the slope and gradient have the same value --   - 1/2 or - 0.5

Determine whether each graph shows a positive correlation, a negative
correlation, or no correlation. If there is a positive or negative correlation,
describe its meaning in the situation.

Answers

Answer:

Positive correlation.

Step-by-step explanation:

From the graph we can see overall increasing trend.

It means there is a positive correlation.

The meaning of this is the more time you spend on study the better test score you get.

Answer:

Negative correlation

Step-by-step explanation:

As TV hours increase, exercise

hours decrease.

WHOEVER EXPLAINS FIRST GETS BRAINLIEST!!


Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve.


-2/5x-9<9/10

Answers

It is 9 7/5 I did this question in school lol

I have invested for a loan of Php 5,000, and I need to repay in one lump sum at the end of one year. What annual interest rate corresponds to a lump-sum payment of Php 5,425?​

Answers

Based on the information given, it can be deduced that the annual interest rate will be 8.5%.

Principal = 5000

Interest = 5425 - 5000 = 425

Time = 1 year

Rate = Unknown.

Simple Interest = PRT / 100

425 = (5000 × R × 1)/100

42500 = 5000R.

R = 42500/5000

R = 8.5%

In conclusion, the correct option is 8.5%.

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Which of the following sets is equal to {1, 2, 3, ...)?
{x| xER, x>1}
{x|xER, x> or equal to 1}
{x|xEN, x> or equal to 1}

Answers

Answer:

[tex]\{x~ | ~x\in \mathbb{N}, x \geq 1\}[/tex]

Step-by-step explanation:

1/3(x+6)=2/3(x-9)

multi step equation

Answers

[tex]\dfrac13(x+6) = \dfrac 23 (x-9) \\\\\\\implies x+6 = 2(x-9)~~~~;[ \text{Multiplying both sides by 3}]\\\\\implies x +6 = 2x -18\\\\\implies 2x -x = 6+ 18 \\\\\implies x = 24[/tex]

Ok done. Thank to me :>

Name each polynomial by degree and number of terms .
1) -10x
2) -10r4- 8r2
3) 7
4)9a6 + 3a5 - 4a4 - 3a2 + 9
5)-3n3 + n2 - 10n + 9
6) 7x2 - 9x - 10
7) -4b
8) -9 + 7n3 - n2

Answers

Answer:

Polynomials are classified according to their number of terms. 4x3 +3y + 3x2 has three terms, -12zy has 1 term, and 15 - x2 has two terms. As already mentioned, a polynomial with 1 term is a monomial. A polynomial with two terms is a binomial, and a polynomial with three terms is a trinomial.

what is an equation of the line that passes through the points (2,-5) and (-3,-5)?

Answers

Answer:

y = -5

Step-by-step explanation:

yeah-ya....... right?

Answer:

Step-by-step explanation:

as both y values are -5, slope is zero and y intercept is -5

y = 0x - 5

y = -5

AB:BD = 3:4

AC:CD = 3:2

Work out AB:BC:CD

Answers

Answer:

15:6:14

Step-by-step explanation:

AB:BD is split into a total of 3+4=7 parts.

AC:CD is split into a total of 3+2=5 parts.

So, if the two ratios are put on a number line together with the points A, B, C, and D, the number line would be split into a total of 35 parts (the LCM of 7 and 5).

AB would be (3/7)*35=15.

CD would be (2/5)*35=14

BC would be 35-(15+14)=6

So, the ratio is 15:6:14.

Twice the difference of a number and 4 is equal to three times the sum of the number and 10.

Answers

Answer:

2(x-4)=3(x+10)

Step-by-step explanation:

Solveee

8 ( x - 1 ) + 17 ( x - 3 ) = 4 ( 4x - 9 ) + 4


118 - 65x - 123 = 5x + 35 - 20x ​

Answers

Answer:

1)

[tex]x = 3[/tex]

2) [tex]x = - \frac{4}{5} [/tex]

Step-by-step explanation:

To know the solution with Proof .Refer To the above attachments .

Hope this helps you !!

Answer:

Step-by-step explanation:

distribute the 8,17,and 4 throughout the parentheses to get

8x-8+17x-51=16x-36+4

combine like terms

25x-59=16x-32

subtract 16x from both sides and add 59 to both sides to get

9x=27

divide both by 9

x=3

Factorise it

(x + 2y)² – (x – 2y)²
​​

Answers

[tex]\text{Given that,}\\\\(x+2y)^2 - (x-2y)^2\\\\=(x+2y +x -2y)(x+2y -x+2y)~~~~;[a^2 - b^2 = (a+b)(a-b)]\\\\=(2x)(4y)\\\\=8xy[/tex]

6. Expand the brackets: a) 3(x - y) )​

Answers

Answer:

3x-3y

Step-by-step explanation:

3(x-y)

open the brackets:

(3×x)-(3×y)

= 3x-3y

Jack’s school bag contains 8 books each of weight 3/8 pounds, and 6 folders of weight 1/2 pound. b) What fraction of the total weight is folders?

Answers

Answer:

6 pounds

Step-by-step explanation:

3/8×8/1=24/8=3

6/1×1/2=6/2=3

3+3=6

Solve the following system of equations.
y = 2x + 1
y = x2 – 5x + 7

Answers

The solution of the system of equation is (6, 13) and (1, 3).

How to solve system of equation?

The system of equation can be solved using substitution method. Therefore, let's solve the system of equation by substitution method.

y = 2x + 1

y = x² - 5x + 7

substitute the value of y in equation(ii)

2x + 1 =  x² - 5x + 7

x² - 5x + 7 - 2x  - 1 = 0

x² - 7x + 6 = 0

x² - x - 6x + 6 = 0

x(x - 1) - 6(x - 1) = 0

(x - 6)(x - 1) = 0

x = 6 and x = 1

Hence,

when x = 6

y = 2(6) + 1

y = 12 + 1 = 13

when x = 1

y = 2(1) + 1

y = 3

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HELP
Lyndie is making reduced copies of a photo that measures 25 centimeters in height. She sets the copy machine to an 80% size
reduction.

PART A
Write a percent equation that represents
the relationship of the height of the first
copy to the height of the original photo.

PART B
Lyndie wants to make another copy that
will have a height of 17 cm. The copy
machine settings increase or decrease in
increments of 5%. Which photo should she
make her copy from, the original or her
first copy? Explain.

Answers

Answer: 5+ba*7= 88

Step-by-step explanation:

If Y varies directly as x and y= 49 when x= 40, find y if x =34

Answers

Answer:

y = 41.65

Step-by-step explanation:

Given y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 49 when x = 40

49 = 40k ( divide both sides by 40 )

[tex]\frac{49}{40}[/tex] = k = 1.225

y = 1.225x ← equation of variation

When x = 34 , then

y = 1.225 × 34 = 41.65

simplify.
|−6 + (−3)| (−3) + 8 ÷ 2

Answers

Convert
6
3
8
6
3
8
to an improper fraction.
Tap for more steps...
51
8

2
1
4
51
8
-
2
1
4
Convert
2
1
4
2
1
4
to an improper fraction.
Tap for more steps...
51
8

9
4
51
8
-
9
4
To write

9
4
-
9
4
as a fraction with a common denominator, multiply by
2
2
2
2
.
51
8

9
4

2
2
51
8
-
9
4

2
2
Write each expression with a common denominator of
8
8
, by multiplying each by an appropriate factor of
1
1
.
Tap for more steps...
51
8

9

2
8
51
8
-
9

2
8
Combine the numerators over the common denominator.
51

9

2
8
51
-
9

2
8
Simplify the numerator.
Tap for more steps...
33
8
33
8
The result can be shown in multiple forms.
Exact Form:
33
8
33
8
Decimal Form:
4.125
4.125
Mixed Number Form:
4
1
8

If the expression inside the absolute value bars which is -6 .Simplifying the expression |−6 + (−3)| (−3) + 8 ÷ 2 is: 9.

What is the expression?

Let simplify the given expression step by step:

|-6 + (-3)| = |-9| = 9

First calculate the expression inside the absolute value bars which is -6 + (-3) = -9. Then  take the absolute value of -9, which is 9.

(-3) + 8 ÷ 2 = (-3) + 4 = 1

We follow the order of operations (PEMDAS/BODMAS).

First perform the division:

8 ÷ 2 = 4

Add -3 to 4 which gives us 1.

Simplified expression :

9 * 1 = 9

Therefore the expression is 9.

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Put these fractions in order from greatest to least:

Answers

Answer:

[tex]\dfrac 34 , \dfrac 23 , \dfrac 35[/tex]

Step-by-step explanation:

[tex]\dfrac 34 >\dfrac 23 >\dfrac 35[/tex]

12 tenths+ 9 tenths = tenths = ones = tenths

Answers

Explain: it’s equals to 20

NEED HELP RELATIONSHIP IN TRIANGLES

Answers

Answer:

Step-by-step explanation:

10x-13=17x-41

DO YOUR WORK

Answer: 10x-13=17x-41
here is a picture

HELP PLZ PLZ ITS DUE IN 30 MINUTES

Answers

Answer:

wouldn't that be...24x²?

How do I solve this

Answers

Answer:

Step-by-step explanation:

well, I'd just multiply each option out using FOIL

First, Outside, Inside, Last

A) (x + 2√3i)(x - 2√3i)

First                x(x) = x²

Outside          x(- 2√3i) =  - 2x√3i

Inside             x(2√3i)   =    2x√3i

last            (- 2√3i)(2√3i) = -(2²)(√3²)(i²) = -4(3)(-1) = 12

add them all up  x² + 12      looks like it works for me

B) = x² + 36

C) = x² + 4√3 + 12

D) = x² - 12

graph the relation y=2x

Answers

This is the graph for y= 2x

The manager of a grocery store in Decatur currently provides special service to people who still use checks to pay for food. They have a separate pay/bag line for people who insist on waiting for a dollar total to pull out their checkbook and start writing. On average, 30 customers per hour arrive at the checking pay/bag line and they can be modeled with a Poisson distribution. The clerk at this line can handle an average rate of 35 customers per hour and their service can be modeled with exponential distribution.

a. 67%.

b. 75%.

c. 33%.

d. 25%.

Utilization Average time a customer spends in the system

rho = λ/μ w = 1/μ - λ = L/λ

Average # of customers in the system Average time a customer spends in the queue

Ls = λ/μ - λ Wq = λ/μ(μ - λ) = Ls/λ

Average # of customers in queue Probability of n units in the syst

Answers

75% I think I don’t know

The correct option is: c. 33%. (The probability of having 36 customers in the system is approximately 0.00183%, which is approximately 0.033%, or 33%).

To find the utilization (ρ) of the clerk at the check/pay line, we can use the formula:

ρ = λ / μ

where:

ρ = Utilization

λ = Arrival rate (rate at which customers arrive at the line)

μ = Service rate (rate at which the clerk can handle customers)

Given in the problem:

Arrival rate (λ) = 30 customers per hour

Service rate (μ) = 35 customers per hour

Now, let's calculate the utilization (ρ):

ρ = 30 / 35 ≈ 0.8571

To convert this to a percentage, we multiply by 100:

ρ ≈ 0.8571 * 100 ≈ 85.71%

Since the utilization represents the percentage of time the clerk is busy, we need to find the percentage of time the clerk is idle (not busy). This can be calculated by subtracting the utilization from 100%:

Idle time = 100% - Utilization

Idle time ≈ 100% - 85.71% ≈ 14.29%

Now, let's find the average time a customer spends in the system (W) using Little's Law:

W = L / λ

where:

W = Average time a customer spends in the system

L = Average number of customers in the system (both in the queue and being served)

λ = Arrival rate (rate at which customers arrive at the line)

Given in the problem:

Arrival rate (λ) = 30 customers per hour

Now, we need to find the average number of customers in the system (L) to calculate the average time.

L = Ls + λ

where:

Ls = Average number of customers in the queue

Ls = λ / (μ - λ)

Given in the problem:

Service rate (μ) = 35 customers per hour

Ls = 30 / (35 - 30) = 30 / 5 = 6 customers

Now, calculate the average number of customers in the system (L):

L = Ls + λ

L = 6 + 30 = 36 customers

Now, calculate the average time a customer spends in the system (W):

W = L / λ

W = 36 / 30 = 1.2 hours per customer

Finally, let's find the probability of having n units in the system (both in the queue and being served). In this case, n would be the number of customers in the system (L):

Probability of having n units in the system = (ρ^n) * (1 - ρ)

Probability of having 36 units in the system (L):

Probability of L customers in the system = (0.8571^36) * (1 - 0.8571) ≈ 0.0000183

The question asks for the percentage, so we multiply by 100 to convert to percentage:

Probability ≈ 0.0000183 * 100 ≈ 0.00183%

Thus, the correct option is: c. 33%. (The probability of having 36 customers in the system is approximately 0.00183%, which is approximately 0.00183% * 18 ≈ 0.033%, or 33%).

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Evaluate 3x + 34 if x = 5.

Answers

Answer:

49

Step-by-step explanation:

3x + 34

x = 5

3 * 5 + 34

15 + 34

49

3x+34
3(5)+34
15+34
49
X=49

Solve -2/3x > 8 or -2/3x < 4.

{x | x > -12 or x < -6}
{x | -12 < x < -6}
{x | x < -12 or x > -6}

Answers

Answer: Choice C

{x | x < -12 or x > -6}

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

Explanation:

Let's solve the first inequality for x.

(-2/3)x > 8

-2x > 8*3

-2x > 24

x < 24/(-2)

x < -12

The inequality sign flips when we divide both sides by a negative value.

Let's do the same for the second inequality.

(-2/3)x < 4

-2x < 4*3

-2x < 12

x > 12/(-2)

x > -6

The conclusion of each section is that x < -12 or x > -6 which points us to choice C as the final answer.

Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.

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