Mathematics High School

Identify the factors of x2 + 25y2. ...?

Answers

Answer 1

Answer:

(x-5y)^2 or (x-5y)(x-5y).

Step-by-step explanation:

hope this helps have a nice day! :D

Answer 2

Final answer:

To find the factors of x² + 25y², use the properties of complex numbers like i² = -1. The factors are (x + 5yi)(x - 5yi), representing complex conjugates.

Explanation:

The factors of x² + 25y² are (x + 5yi)(x - 5yi).

To factorize the expression, we use the fact that i² = -1, so we can rewrite 25y² as (5y)²

By factoring this expression, we can see that it represents a sum of two squares in the form of complex conjugates.

Related Questions

Farmer tom’s chickens and sheep are all in a jumble. he counts 48 heads and 134 legs, how many sheep does he have?

Answers

Chickens have 2 legs and sheep have 4 legs. If x is the number of chickens and y is the number of sheep, then we have the system of equations: x + y = 48, 2 x + 4 y = 134. We can solve this system : x = 48 - y, then we will put it into the 2nd equation: 2 * ( 48 - y ) + 4 y = 134, 96 - 2 y + 4 y = 134, 2 y = 134 - 96, 2 y = 38, y = 38 : 2, y = 19. Answer: Farmer Tom has 19 sheep.

The intensity I of light bulb varies inversely as the square of the distance d from the light bulb. Suppose I is 250 w/m^2 when the distance is 5 m. How much farther would it be to a point where the intensity is 40 w/m^2? ...?

Answers

Final answer:

The intensity of a light bulb varies inversely as the square of the distance from the light bulb. To find the distance where the intensity is 40 w/m², use the inverse square law formula to solve for the distance.

Explanation:

The intensity of a light bulb varies inversely as the square of the distance from the light bulb. This means that as the distance increases, the intensity decreases.

If the intensity is 250 w/m² at a distance of 5 m, and we want to find the distance where the intensity is 40 w/m², we can use the inverse square law formula:

I₁d₁² = I₂d₂²

Plugging in the values, we get:

250 × (5)² = 40 × (d₂)²

Simplifying, we find that d₂² = 250 × (5)² / 40

d₂² = 312.5

Therefore, d₂ = √312.5 ≈ 17.68

So, it would be approximately 17.68 - 5 = 12.68 meters farther to a point where the intensity is 40 w/m².

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Sure, let's solve it step by step.

First, we know that the initial intensity (I1) is 250 w/m^2 and the initial distance (d1) is 5 m. We are asked to find a distance where the intensity is 40 w/m^2, which would be our final intensity (I2).

According to the inverse square law, the intensity of light is inversely proportional to the square of the distance from the source, i.e., I ∝ 1/d². Therefore, we can say that I1 * d1² = I2 * d2². This equation allows us to find the distance at which the intensity is I2.

So, substituting the given values in the equation, we have 250 * (5)² = 40 * d2².

Now, we can solve for d2. Rearranging terms, d2 = √((250 * (5)²) / 40), which will give us d2 = 12.5 m.

So, the distance at which the intensity of light is 40 w/m^2 is 12.5 m.

However, we have been asked to find the additional distance that needs to be traveled to reach a point where the intensity is 40 w/m^2. This additional distance is the difference between the final distance (d2) and the initial distance (d1), that is, distance_travelled = d2 - d1 = 12.5 - 5 = 7.5 m.

Therefore, you would need to travel an additional 7.5 m to reach a point with an intensity of 40 w/m^2.

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license plates in a particular state display two letters followed by three numbers, such as AT-887 or BB-013. How many different license plates can be manufactured for this state?

Answers

10^3*26^2
10 values 0-9 which can repeat
26 letters which can repeat

Thirteen and eight tenths

Answers

13 8/10

hope this helps you

6-4x verbal expression

Answers

Four multiplied by "x" subtracted from six

Six minus four multiplied by x

Erica went shopping for new clothes for school. She bought a pair of jeans for $70.19 and several shirts for $8.63 each. If x represents the number of shirts she bought, which of the following equations should be used to find y, the total cost of Erica's shopping trip? Explain your choice.

plzzzz helpppp

Answers

it's at least y=$8.63x+$70.19

Y=70.19+(8.63*X)

To find the total she spent all you have to do is add everything together. The cost of the pants was $70.19, to find how much she spent on shirts you take the amount each shirt was, which in this case is $8.63, and multiply it by how many shirts she bought. We don't know how many shirts she bought so we use the varriable of X to represent that number.

(I used the asterisk * to indicate the multiplication)

Solve the inequality 6x - 8 > 4x + 26

x < 9

x < 17

x > 9

x > 17

Answers

6x > 4x+26+8
2x > 34

so,
x > 17

Answer:

The Answer is D. x > 17

Hope This Helps!

Using the 28/36 ratio, determine the maximum allowable recurring debt for someone with a monthly income of $4,850.
a. $388
b. $776
c. $970
d. $1,358

Answers

Answer:

The correct answer is A. $388

Step-by-step explanation:

The 28/36 Rule states that : A household should spend a maximum of 28% of its gross monthly income on total housing expenses and not more than 36% on total debt service.

Maximum expense on housing expense = 28% of 4850

= $1358

Maximum expense on total debt service = 36% of 4850

= $1746

Therefore, the maximum allowable recurring debt with a monthly income of $4,850 = 1746 - 1358 = $388

Hence, The option A is correct.

Answer:

Step-by-step explanation:

got it right on edge

tinku is fond of collecting spiders and insects. He knows spiders have 8 legs and insects have 6 legs. he counted 36 legs. How many of each does he have in hi collection?

Answers

Let, number of spiders = x
number of insects = y

6x + 8y = 36

remember, legs can't be in fraction or decimal.

So, only (3, 2) fits with that.

So, there are 3 spiders & 2 insects in his collection.

Hope this helps!

It takes for three gardeners 90 minutes to weed a garden. If the job is to be done in only 15 minutes, how many more gardeners need to be put on the jobs?

Answers

3 gardeners :90 minutes
? Gardeners : 15 minutes
1 gardener : 270 minutes
? Gardeners : 270/15
18 gardeners

The answer is 15 gardeners.
Thus, 15 gardeners would be needed if the job is to be done in only 15 minutes.

160 percent of 1,825 is? Rounded to nearest tenth
...?

Answers

2920 is 160 percent of 1825

What are the constant terms in the expression? 8m−5n+2+m−148m−5n+2+m−14 Drag and drop the constant terms into the box.

Answers

2

Is is the only integer that is alone.

2, 2, and -14 are the constant terms. They never change. The other terms change when 'm' and 'n' change.

A farmer wishes to enclose a pasture that is bordered on one side by a river (so one of the four sides wont require fencing) She has decided to create a rectangular shape for the area and will use barbed wire to create the enclosure there are 600 feet of wire availible for this project and she will use all the wire. what is the maximum area enclosed by the fence then find the maximum of the function. ...?

Answers

The area enclosed is (2x)(600-2x).(2x)(600−2x)=1200x−4x2
In order to maximize we need the derivative to be equal to 0.y′=1200−8x=0
1200=8x
x=150
Therefore the sides for maximum area are 150*300.
The area is: 45000

Answer:

Area is 45000 square feet.

Step-by-step explanation:

Let x be the length of fenced side parallel to the river side.

Let y be the length of other two sides.

Then,

[tex]x+ 2y 600[/tex]

So, we get [tex]x=600-2y[/tex]

Area of this rectangle = xy

= [tex]y(600-2y)[/tex]

[tex]x=-2y^{2}+600y[/tex]

Now attached is the graph of the area function, which is a parabola opening downward.

We can see ta the maximum area occurs when y=[tex]-600/[2(-2)][/tex] = 150

And [tex]x = 600-2(150)[/tex]

x =[tex]600-300=300[/tex]

Therefore, to maximize the area, the side parallel to the river is to be 300 feet long, and the other two fenced sides should be 150 feet long.

The area is = [tex]300\times150= 45000[/tex] square feet.

Find the slope of the line that passed through points a and d
A) -7/2
B) -2/7
C) 0
D) 2/7

Answers

Simple...

you have: Find the slope of the line that passed through points A and D.

A is located at: (-3,-2)

B is located at (4,0)

Using [tex] \frac{ y_{1}- y_{2} }{ x_{1}- x_{2} } [/tex] to find slope-->>>

[tex] \frac{-2-0}{-3-4} = \frac{-2}{-7} = \frac{2}{7} [/tex]

m=[tex] \frac{2}{7} [/tex]

Thus, your answer.

Answer:

The answer is m=2/7 or answer choice D

Step-by-step explanation:

The first digit in the quotient of 6523÷7

Answers

931.857143 is ur answer. Ok

Four points A, B, C, and D are coplanar, but only two at a time are collinear. Suppose a line is drawn through each pair of points. How many lines can you draw? ...?

Answers

Based on the given details above, the number of lines that can be drawn through each pair of points would be six: Four sides and two diagonals. When we say coplanar points, these are points that lie in the same plane. This is made up of three or more points. Hope this answer helps.

A store is having a clearance sale where merchandise on the sales rack is reduced by 80% from the original price. If a jacket was originally priced at $76, what is the sale price.

Answers

76 - 80% = 15.2
$15.20 is your answer :)

At the grocery store, you buy a carton of milk for $1.95, a loaf of bread for $0.85, and a box of cereal for $2.05. Use mental math to find the total cost of the groceries

Answers

total cost is 4.85 dollars to do this simply add them together

what is a term without a variable

Answers

A term without a variable is called a constant term, and the degree of that term is 0 Hope that helps you I knew this was 0 beciase i study this a long time ago

A ball on a string moves around a complete circle, once a second, on a frictionless, horizontal table. The tension in the string is measured to be 6.0N . What would the tension be if the ball went around in only half a second?

Answers

The tension in the string balances out, and thus equals the centripetal force of the ball

T = mv^2/r

if it only takes half the time to finish one orbit it has to be moving at twice the original speed.

And since v is squared T will increase by 4

T' = m(2v)^2/r

T' = 4mv^/r = 4T

T' = 24.0 N

I hope my answer has come to your help. Have a nice day ahead and may God bless you always!

Final answer:

If the ball went around in half a second, the tension in the string would be 24.0 N.

Explanation:

To find the tension in the string if the ball went around in half a second, we can use the equation for centripetal force. The tension T in the string provides the centripetal force, which is equal to the mass of the ball times the square of its velocity divided by the radius of the circle:

T = (m * v^2) / r

In this case, the mass of the ball and the radius of the circle remain the same, but the velocity changes. Since the ball takes half the time to complete the circle, the velocity is twice as fast. Therefore, the tension in the string would be four times greater:

Tension = 4 * 6.0 = 24.0 N

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An organic farm uses 3/7 of the land to grow potatoes and 2/5 of the land to grow spinach. The remaining land is used to grow tomato plants. What fraction of the land is used to grow tomato plants?

Answers

Fraction of the land is used to grow tomato plants=1-(fraction of the land to grow potatoes + fraction of the land to grow spinach)

Land used for to grow tomato plants=1-(3/7 + 2/5)
=1-(15+14)35
=1-29/35
=(35-29)/35
=6/35

Answer: this organic far uses 6/35 of the land to grow tomato plants.

What is the measure of angle B?

A. 32
B. 62
C. 120
D. 31

Answers

I hope this helps you

so we can narrow it down to a or D .so if 5*31 =155 155-35=120 .180-120=60 60+58=118 180-118=62 31*2=62(answer is 31) and sorry for the long problem.its how I think.if you need more help with answers,m message and follow me .

HELP!!!
what is the value of x in the following equation:
1/4 x + 1/4 x = 4/5 ?
A. 8/5
B.5/8
C.2/5
D.3/5

Answers

the value of x in this equation is 2/5

The slope of a line is 0, and the y-intercept is 6. What is the equation of the line written in slope-intercept form? y = 6 y = 6x y = x + 6

Answers

the answer would be y=0x+6

Answer:

The answer is

y = 6

You travel 2,557 km in 190 days how far did you travel per hour

Answers

You travel 1.78 km per hour. I came up with this by takin 190 and multiplying it by 24(the amount of hours in a day). Then, I divided that by 2557 and came up with 1.78.

What it is asking for is a distance over time in HOURS.
It isn't specific about the distance units so, we can assume km is OKAY to use!

Now we need to convert 190 days to hours. Let's set up some conversion factors.

1 Day = 24 Hours

[tex] \frac{190 days}{1} * \frac{24 hours}{1 day} [/tex]

I recommend setting up conversions like the way I did above. To do so simply make the units cancel out. Similar to how 3/3 cancel out, units also cancel out in the same way. So when you are trying to figure out whether or not you divide or multiply by the conversion factor simply use this method. Say we had 190 hours, the hours unit would need to be on the bottom, and the days on top. It'd be 1/24, thus you would divide by 24.

[tex] \frac{190 days}{1} * \frac{24 hours}{1 day} [/tex] = 4560 hours.

Now what it is asking for his a rate of distance per hour. This rate is also called speed. Remember in the statement it said how far per hour. Meaning when dividing the units should look like this: [tex] \frac{km}{hour} [/tex]

[tex] \frac{2557km}{4560hour} [/tex] = 0.5607[tex] \frac{km}{hour} [/tex]

The answer is:
0.5607[tex] \frac{km}{hour} [/tex]

Solve the system of equations.

5x + y = 9
3x + 2y = 4

Answers

y=-5x+9

3x+2(-5x+9)=4
3x-10x+18=4
-7x=4-18
-7x=-14
x=2

5(2)+y=9
10+y=9
y=9-10
y=-1

The answer is (2,-1) :)

John has 15 more music cds than micheal together they have a total of 55 cds

Answers

Michael has 40 CDs. 40+15=55.

Which arrangement shows 4.09,4 2/3 ,21/4 and 4.7 in order from least to greatest?

Answers

4.09 < 4 2/3 < 4.7 < 21/4

A liquid-filled glass pyramid is being erected as part of a museum attraction. The pyramid is designed to be 15 feet tall with a rectangular base that is 10 feet long and 6 feet wide. What is the total amount of liquid that the pyramid can hold?

Answers

First we calculate surface of base.

10 * 6 = 60 feet^2

The Volume of pyramid is calculated by formula:
V = B*H/3

H- height of pyramid
B- surface of base of pyramid

We have both of those so all we have to do is to finish calculation:

V = 60*15/3 = 300 feet^3

Answer is 300 qubic feets

Answer:

300 cubic feet

Step-by-step explanation:

Is 3.4 a rational or irrational number? Please explain why, thanks.

Answers

Rational, 3.4 can be written as a fraction and is noncontinuous
"An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point."

Answer:

Yes it is a rational number

I just did it and I passed

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