Which values of x and y would make the following expression represent a real number? (4+5i)(x+ yi)
Ox=4,y= 5
Ox=-4, y = 0
Ox=4, y=-5
Ox=0, y= 5​

Which Values Of X And Y Would Make The Following Expression Represent A Real Number? (4+5i)(x+ Yi) Ox=4,y=

Answers

Answer 1

Answer:

C

Step-by-step explanation:

We have the expression [tex](4+5i)(x+yi)[/tex] and we want to find the values of [tex]x[/tex] and [tex]y[/tex] such that the expression will evaluate to a real number.

So, let's first expand the expression. Distribute:

[tex]=4(x+yi)+5i(x+yi)[/tex]

Distribute:

[tex]=4x+4yi+5xi+5yi^2[/tex]

Simplify:

[tex]=(4x-5y)+(4yi+5xi)[/tex]

So, we want to make the second part within the real numbers.

Notice that we only have two ways of doing this: 1) Either both [tex]x[/tex] and [tex]y[/tex] are imaginary numbers themselves canceling out the [tex]i[/tex], or 2), the entire expression equals 0.

Since our answer choices consists of only real numbers, this means that the imaginary part must be equal to 0. So:

[tex]4yi+5xi=0[/tex]

We can divide everything by [tex]i[/tex]:

[tex]4y+5x=0[/tex]

Now, we can use our answer choices.

Running down the list, we can see that the choice that works is C. If we substitute the values of C into the equation, we get:

[tex]4(-5)+5(4)=0\\\Rightarrow -20+20=0\stackrel{\checkmark}{=}0[/tex]

Therefore, our answer is C.

Answer 2

Answer:

c

Step-by-step explanation:


Related Questions

pls answer for points

Answers

Answer:

Step-by-step explanation:

5/6 - (2/5 + 1/3)

25/30 - (12/30 + 10/30)

25/30 - 22/30 = 3/30 = 1/10

answer is b

Which statement about the number 49 is true

Answers

Answer:

F.

Step-by-step explanation:

Prime means that it is only divisible by 1 and itself, and we know that it is also divisible by 7, therefore it is a composite number because it has 1, 7, and 49 as factors.

Please help me with this problem and explain

Answers

Answer: 29

It is very simple, just substitute.

x = 9, y = 10

Replace the x and y in the expression to that.

You get: 9 + 10 + 10. Just add and you will get 29.

Answer:

9+10+10=29

Step-by-step explanation:

We know that x=9, so where ever we see x we know it is 9. We also know that y=10, so where ever we see y we know it is 10. So then we just replace the variables with our numbers then just add them.  That is I got 9+10+10=29

Hope this helps!

Mr. Ortiz has 5/8 pound of oatmeal. He uses 4/5 of the oatmeal to bake muffins. How much oatmeal does Mr. Ortiz have left? Enter your answer in simplest form.​

Answers

He has 1/8 of a pound of oatmeal left
He has 1/8 pound left

Please, Please help me

One number is 7 times a first number. A third number is 100 more than the first number If the sum of the three numbers is 865, find the numbers.

Answers

I believe the answer is 85

I need help fast I’m timed!

Answers

Answer:

-5

Step-by-step explanation:

If your good at math and can do some one of my problems lmk but if not dont say yes or no just dont comment at all

Answers

Answer:

gbklkijgggddfhokjvhjk

Expressions equivalent to (7^3 x^4)^0

Answers

Answer:

Step-by-step explanation:

Any number or variable to the power of 0 is 1

(7^3 x^4)^0 = 1

Four students are to solve 5(x-3)=2x+6 which solution and explanation is right?

Answers

Answer:

pft

Step-by-step explanation:

not sure, im confused

Help ASAP please please plsssssssssssss

Answers

Answer: 11 1/3 (eleven and one third)

Step-by-step explanation:

I’ll give 10 points and brainliest

Answers

Answer:

Step-by-step explanation:

-(-2)^2 - (8(-2)-2(-3)) + 4(-3)

-4 -(-16 + 6) - 12

-4 - (-10) - 12

-4 + 10 - 12

6 - 12 = -6

they only said simplify and i guessed the answer as undefined

Answers

I think it is B but I’m not sure

What is the value of x?
(5х)

110°
110°
70
14

Answers

Answer:

The answer to your question is :The value of 5× = 110°

Name the slope of a line parallel to y = -3x -2

Answers

y=-3x for two slopes to be parallel they have to have the same slope but different y intercepts

19. A package of 12 confetti eggs costs $2.88.
At this rate, what is the cost of 1 confetti egg?

Answers

Answer:

0.24$

Step-by-step explanation:

Each egg costs 1/12 of 2.88.

So either you multiply 2.88 by 1/12

or you divde 2.88 by 12

Answer:

0.24

Step-by-step explanation:

you would divide 2.88 by 12 hope this helps.

If 4 batches of muffins and 5 loaves of bread are baked, how much flour will be left? Give your answer in kilograms. b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour? Explain your answer.

Answers

This question is Incomplete

Complete Question

The bakery bought 4 bags of flour containing 3.5 kg each. 0.475 kg of flour is needed to make a batch of muffins, and 0.65 kg is needed to make a loaf of bread.

a. If 4 batches of muffins and 5 loaves of bread are baked, how much flour will be left? Give your answer in kilograms.

b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour? Explain your answer.

Answer:

a. 8.85kg of flour is left.

b. 2.95 bins

Step-by-step explanation:

The bakery bought 4 bags of flour containing 3.5 kg each.

Total kg of flour the Bakery bought : 4 × 3.5kg

= 14 kg of flour

0.475 kg of flour is needed to make a batch of muffins

1 batch of muffin = 0.475kg of flour

4 batches of muffins = ???

Cross Multiply

4 batches × 0.475kg/ 1 batch

= 1.9kg of flour was used.

0.65 kg is needed to make a loaf of bread.

1 loaf of bread = 0.65kg of flour

5 loaves of bread = ???

Cross Multiply

5 loaves × 0.65/1 loaf

= 3.25 kg of flour.

Total kg of flour used = 1.9kg + 3.25kg

= 5.15kg of flour.

The amount of flour left = 14kg - 5.15kg

= 8.85kg of flour is left.

b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour?

3 kg of flour is stored = 1 bin

8.85 kg of flour is stored = x

Cross Multiply

3kg × x = 8.85kg × 1 bin

x = 8.85 kg × 1 bin/3kg

x = 2.95 bins

What is the solution to 4x3 - 3x2 - 7x<0?

Answers

Answer:

[tex](-∞,1) , (0,\frac{7}{4})[/tex]

Step-by-step explanation:

Factor:

x(4x³-3x-7)<0

A carpenter has less than 120 minutes to spend painting furniture each day. Today, he has spent 30.5 minutes painting a desk. Now he will paint x chairs, each of which takes 12.5 minutes. What is the maximum number of chairs the carpenter can paint?

Answers

Answer:

Maximum number of chairs is 7.

Step-by-step explanation:

We are told he has less than 120 minutes to spend painting furniture each day.

Now he has spent 30.5 minutes painting a desk.

Also, he wants to paint "x" number of chairs with each chair taking 12.5 minutes.

Thus, we have;

30.5 + 12.5x < 120

Subtract 30.5 from both sides to get;

12.5x < 120 - 30.5

12.5x < 89.5

x < 89.5/12.5

x < 7.16

Thus, maximum number of chairs he can paint is 7

Frederick is training for a triathlon and wants to focus on swimming this week. He can swim 25 yards in 23 seconds. He set up a proportion to determine how long it would take him to swim 175 yards at this rate. Which proportions can be used to determine how long it would take him to swim 175 yards?

Answers

Answer:

161secs

Step-by-step explanation:

If Frederick can swim 25 yards in 23 seconds, then:

25 yards = 23 seconds

To determine how long it will take him to swim 175yards, we will say:

175 yards = x

Equating both expression:

25 yards = 23 seconds

175 yards = x

Cross multiply

25x = 23*175

25x = 4025

Divide both sides by 25

25x/25 = 4025/25

x = 161 secs

This means that it will take Frederick 161 secs to swim 175 yards

Tehara has read 115 pages of a 305 page book she reads 10 pages each day how many days will it take to finish

Answers

It would take her 20 or 19 days

Abraham has visited country somebody he has a cold or visiting at least 50 countries he plans to choose a school by visiting five new countries per year (Y) for the next several years which inequality and solution shows the amount of years they will take for Abraham to meet his goal

Answers

Question:

Abraham has visited at least 50 countries; he plans to visit five new countries per year (Y) for the next several years. Which inequality and solution shows the amount of years they will take for Abraham to meet his goal.

Answer:

[tex]Countries \geq 50 + 5y[/tex]

[tex]y \leq 29[/tex]

Step-by-step explanation:

Given

[tex]Countries = 50[/tex] ------ at least

[tex]Yearly =5[/tex]

Required

Represent as an inequality

"at least" means [tex]\geq[/tex]

So the countries he has visited can be represented as thus;

[tex]Countries \geq 50[/tex]

If

1 year = 5 countries

y years would be 5y countries

So, in y years; he'd have visited

[tex]Countries \geq 50 + 5y[/tex]

To determine the value of y.

We have that

[tex]Countries = 195[/tex] in the world

Substitute 195 for Countries

[tex]195 \geq 50 + 5y[/tex]

Collect Like Terms

[tex]195 - 50 \geq 5y[/tex]

[tex]145 \geq 5y[/tex]

Divide through by 5

[tex]145/5 \geq y[/tex]

[tex]29 \geq y[/tex]

Reorder

[tex]y \leq 29[/tex]

This means that; he'll visit all countries in at most 29 years' time

If f(x)=ax²+bx+c and f(1)=6,f(2)=11,f(3)=18 find the value of a,b,c​

Answers

Given:

f(x) = ax² + bx + c

f(1) = 6

f(2) = 11

f(3) = 18

Find:

value of a,b,c​

Solution:

Substitute x = 1 , 2 , 3 in the given polynomial.

★ f(1) = a(1)² + b(1) + c

⟹ 6 = a + b + c -- equation (1)

Similarly,

★ f(2) = a(2)² + b(2) + c

⟹ 11 = 4a + 2b + c -- equation (2)

★ f(3) = a(3)² + b(3) + c

⟹ 18 = 9a + 3b + c -- equation (3)

Subtract equation (1) from (2).

⟹ 4a + 2b + c - (a + b + c) = 11 - 6

⟹ 4a + 2b + c - a - b - c = 5

⟹ 3a + b = 5 -- equation (4).

From equation (3) ,

⟹ 18 - c = 9a + 3b

⟹ 18 - c = 3(3a + b)

Substitute the value of 3a + b from equation (4).

⟹ 18 - c = 3 * 5

⟹ 18 - 15 = c

⟹ 3 = c

substitute the value of c in equation (1).

⟹  6 = a + b + 3

⟹ 6 - 3 = a + b

⟹ 3 = a + b -- equation (5)

Subtract equation (5) from equation (4).

⟹ 3a + b - (a + b) = 5 - 3

⟹ 3a + b - a - b = 2

⟹ 2a = 2

⟹ a = 1

Substitute a value in equation (5).

⟹ 1 + b = 3

⟹ b = 3 - 1

⟹ b = 2

Therefore,

a = 1

b = 2

c = 3.

I hope it will help you.

Regards.

Consider the graph of the sixth degree polynomial f. Replace the values b, c and d to write function f.

f(x) = (x-b)(x-c)^2(x-d)^3

Answers

Answer:

f(x) = (x - 2)(x + 1)²(x - 4)³

Step-by-step explanation:

Multiplicity of a polynomial:

1). If the multiplicity is odd, the graph will cross the x-axis at that zero.

2). If the multiplicity is even, the graph will touch the x-axis at that zero.

Since the given graph is just touching the x-axis at x = -1 multiplicity for the zero (at x = -1) will be even.

Similarly, graph is crossing the x-axis at x = 2 and x = 4, multiplicity for the zero will be odd.

So, the function will be,

f(x) = (x - 2)(x + 1)²(x - 4)³

Answer:Answer : f(x)= (x-1)(x+1)^2(x-4)^3

Step-by-step explanation:

TILE Mark is purchasing new tile for his bathrooms. The home improvement store charges $48 for each box of tiles when three or fewer boxes are purchased, $45 for each box when 4 to 8 boxes are purchased, $42 for each box when 9 to 19 boxes are purchased, and $38 for each box when more than nineteen boxes are purchased a. Write a piecewise-defined function describing the cost of the boxes of tile. b. What is the cost of purchasing 5 boxes of tile? What it is the cost of purchasing 19 boxes of tile?​

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

3 boxes or less = Cost of tiles = $48

4 - 8 boxes ;  cost = $45

9 - 19 boxes ; cost = $42

> 19 boxes ; cost = $38

Cost of purchasing 5 boxes of tiles :

$45 * 5 = $225

Cost of purchasing 19 boxes :

$42 * 19 = $798

PLEASE HELP!!!! I HAVE TO TURN THIS IN IN 5 MIN!!!
ARE THE IMAGES IN THE CORRECT GROUPS????
(They have to be in groups of 3!)

Answers

Answer:

Orange with pink, Yellow with red, Purple with blue. Yellow should be 1x instead of 3x. Swotch the table under red with green aswell.

Can anyone do this question? ​

Answers

Answer:

its simple 5.90

Step-by-step explanation:

7+root 3 divided by 7-root 3

Answers

7 + root3 = 8.73
7 - root3 = 5.26
Thus
8.73/5.26 = 1.659

Two pounds of raw materials are needed to produce one product. The desired ending balance of raw materials is 10% of the of the next month's production needs. (Refer to your answer in Activity Sheet 05). The beginning inventory of raw materials is 4,000 pounds and raw material cost per unit is P 0.50/per pound.

Answers

Answer:

Purchases= production + desired ending inventory - beginning inventory

Step-by-step explanation:

Giving the following information:

Two pounds of raw materials are needed to produce one product.

The desired ending balance of raw materials is 10% of the next month's production needs.

The beginning inventory of raw materials is 4,000 pounds.

The raw material cost per unit is $0.50 per pound.

To calculate the direct material purchase required for a given month, we need the production for each month. I will provide the formula and a small example to guide an answer.

To calculate the purchase required, we need to use the following formula:

Purchases= production + desired ending inventory - beginning inventory

For example:

Production:

January= 5,000 units

February= 4,500 units

Direct material purchases January:

Production= 5,000*2= 10,000

Desired ending inventory= (4,500*2)*0.1= 900

Beginning inventory= (4,000)

Total purchase in pounds= 6,900

Total direct material cost= 6,900*0.5= $3,450

The lowest temperature ever recorded on Earth was $-89.2\degree\text{C}$ at Soviet Vostok Station in Antarctica. The highest temperature ever recorded was $56.7\degree\text{C}$ at Greenland Ranch in California. What is the difference between the highest and lowest recorded temperatures?

Answers

Answer:

145.9°C

Step-by-step explanation:

Given that :

Lowest temperature recorded (Soviet Vostock station Antarctica) = - 89.2°C

Highest temperature recorded (Greenland Ranch California) = 56.7°C

Difference between the highest and lowest recorded temperature :

(Highest temperature - lowest temperature)

(56.7°C - (-89.2°C))

= 56.7°C + 89.2°C

= 145.9°C

Can someone help me on questions 10-15

Answers

Answer:

10. Supplementary

11. Congruent

12. Congruent.

13 . congruent

14 supplement

15 supplementary

Hope this helps you Do mark as brainliest!

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