If $a$ and $b$ are positive integers such that $\gcd(a,b)=210$, $\mathop{\text{lcm}}[a,b]=210^3$, and $a

Answers

Answer 1

Answer:

[tex]a * b = 210^4[/tex]

Step-by-step explanation:

Given

[tex]a,b>0[/tex]

[tex]gcd(a,b) = 210[/tex]

[tex]lcm(a,b) = 210^3[/tex]

Required

The product of a and b --- missing from the question

To do this, we make use of the following formula:

[tex]a * b = gcd(a, b) * lcm(a, b)[/tex]

So, we have:

[tex]a * b = 210 * 210^3[/tex]

Using the product law of indices, we have:

[tex]a * b = 210^4[/tex]

This means that the product of a and b gives [tex]210^4[/tex]


Related Questions

Find the equation of a line perpendicular to y = (75)x - 1 and has a y-
intercept of 1.

Answers

Answer:

6y = -5x + 6

y = -5/6 x + 1

Step-by-step explanation:

y = -5/6 x + b

1 = b

Evaluate x^4 • x^-1 when x = 4

Answers

Answer:

64

Step-by-step explanation:

4^4*4^-1      

4^4*1/4

256*1/4

256/4

64

Solve 2x + 3y = C, for y

Answers

Answer:

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

Step-by-step explanation:

2x+3y=C

isolate y

3y=C-2x

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

If this trapezoid is moved through the
translation (x+3, y-2), what will the
coordinates of Abe?
5
B
С
4
3
D
A
1
2.
1
3
4
-7 6 5 4 3 2 -10
-1
-2
A' = ([?], [ 1)

Answers

Hi! I'm happy to help!

We can see that A's coordinates currently are -6 for x and 2 for y.

When we move x+3, it moves the x coordinate to the right 3 units. This changes it from -6 to -3. When we move y -2, we move the y coordinate down 2 units. This changes it from 2, to 0.

To sum it up: The final coordinates of A will be -3 for x and 0 for y, also written as (-3,0).

I hope this was helpful, keep learning! :D

Find the number of gallons of sulferic acid in 50 gallons of solution in a tank, if the percent of sulfuric acid is 50%.

Answers

Answer:

25 gallons of sulfuric acid

Step-by-step explanation:

Find how much sulfuric acid is in the tank by finding 50% of 50 (the total gallons of solution):

50(0.5)

= 25

So, there are 25 gallons of sulfuric acid.

Consider the equation 5(10)^(z/4)=32 Solve the equation for z, express the solution as a logarithm in base-10

Answers

Answer:

[tex]\displaystyle z = 4\, \log_{10} \left(\frac{32}{5}\right)[/tex].

Step-by-step explanation:

Multiply both sides by [tex](1/5)[/tex] and simplify:

[tex]\displaystyle \frac{1}{5} \times 5\, (10)^{z/4} = \frac{1}{5} \times 32[/tex].

[tex]\displaystyle (10)^{z/4} = \frac{32}{5}[/tex].

Take the base-[tex]10[/tex] logarithm of both sides:

[tex]\displaystyle \log_{10}\left(10^{z/4}\right) = \log_{10} \left(\frac{32}{5}\right)[/tex].

[tex]\displaystyle \frac{z}{4} = \log_{10}\left(\frac{32}{5}\right)[/tex].

[tex]\displaystyle z = \log_{10}\left(\frac{32}{5}\right)[/tex].

Sand and gravel are mixed in the ratio 5:3
form ballast
a) How much gravel is mixed with 750kg of
sand?
b) How much sand is mixed with 750kg of
gravel?

Answers

Answer:

a) 450 gravel   b)1250 sand

Step-by-step explanation:

:)

                           

Given three consecutive odd integers whose sum is 369, find the smallest of the three integers.

Answers

Answer:

Step-by-step explanation:

369 = x + (x+2) + (x+4)

369 = 3x + 6

363 = 3x

121 = x

now that we know that x = 121, we can solve the equation by plugging in the variable

369 = x + (x+2) + (x+4)

369 = 121 + 123 + 125

369 = 369

The smallest three integers are 121,123 and 125.

Let, the smallest odd integers be n

Then according to the given condition,

[tex]n+(n+2)+(n+4)=369\\3n+6=369\\3n=363\\n=121[/tex]

So, the numbers are,

[tex]n=121\\n+2=121+2=123\\n+4=121+4=125[/tex]

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A function() is graphed
What is the slope of the function?
m
What is the intercept of the function?
Which equation represents the graph of the function?

Answers

Y=mx+b use that formula

Help anyone can help me do this question,I will mark brainlest.​

Answers

Answer:

but what to do in do I have to find the area of the particular Region or a length of that

What we have to do in this question
You have to post this question again with full explanation!


0_____ is
than all negative numbers.

Answers

Answer:

is whole number

Step-by-step explanation:

plz mrk me brainliest

Answer:

0 is larger than all negative numbers.

Step-by-step explanation:

When dealing with negative numbers, the number closer to zero is the bigger number. Zero (0) has the unique distinction of being neither positive nor negative.

Find the real or imaginary solutions by factoring.
X^4 -3x^2 = -2x^2

Answers

Look in the images it is solved.

Find the rare of change for the situations , You run 7 miles in one hour and 14 miles in two hours

Answers

The rate of change is 7 because its 7 miles per hour

Amazon hires you as their data analysist. You have to make a presentation
to their board of directors about which shipping method they should invest
an additional $10 million in. The data they provide you is below.

Please help due today

Answers

Answer:

standard= 21.333%

prime= 42.666%

expedited= 6.666%

locker= 29.333%

How do you simplify the following problem?: 9−4d≥−3

Answers

Answer:

d ≤3

Step-by-step explanation:

9−4d≥−3

Subtract 9 from each side

9-9−4d≥−3-9

−4d≥−12

Divide by -4, remembering to flip the inequality

-4d/-4 ≤ -12/-4

d ≤3

Two similar polygons have areas of 4 square inches and 64 square inches.

The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .
The ratio of a pair of corresponding sides is .

Answers

Answer:

4

Step-by-step explanation:

The ratio of the area of similar figures is the ratio between corresponding sides squared. This means that 64/4 or 16 is the square of the ratio of corresponding sides. By taking the square root of 16, we get that ratio is 4.

m + 3n =7 help me solve m

Answers

Answer:

m = 7 - 3n

Step-by-step explanation:

subtract 3n from both sides of the equation

The radius of a circle is 16 ft. Find its area in terms of pi

Answers

Step-by-step explanatio

Which of the following numbers are irrational numbers? Please choose all that apply.

Question 2 options:

−67−−√

13

0.6

π

Answers

Pie it has no ending

Evaluate the expression for c = 11.
-1 - C=

Answers

Answer:

c=-12

Step-by-step explanation:

place 11 in for C > -1-11=

subtract 11 from -1. -12

Solve the equation for all values of x.
- 2x(x − 8)(10x + 1) = 0
From deltamath.com

Answers

Answer:

x=0       x=8          x = -1/10

Step-by-step explanation:

- 2x(x − 8)(10x + 1) = 0

Using the zero product property

-2x =0   x-8 = 0    10x+1= 0

x= 0    x= 8             10x = -1

x=0       x=8          x = -1/10

Which of the following statements is true of the function ? Question 2 options: A) g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x right by 3 units and downward by 5 units. B) g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x left by 3 units and downward by 5 units. C) g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x right by 3 units and downward by 5 units. D) g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x left by 5 units and downward by 3 units.

Answers

Transformations are operators that can act on functions, modifying them in different ways. In this particular problem, we see the translations.

The correct option is B:

g(x) can be graphed by translating the basic rational function ƒ(x)=  1∕x left by 3 units and downward by 5 units.

Let's describe the transformations:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

If N is positive, the shift is to the left.

If N is negative, the shift is to the right

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

If N is positive, the shift is upwards.

If N is negative, the shift is downwards.

Now that we know this, let's see the problem.

We have:

[tex]g(x) = \frac{1}{x + 3} - 5[/tex]

So, the original function is:

[tex]f(x) = \frac{1}{x}[/tex]

Now from f(x) we can apply translations to create g(x).

If first, we apply a translation of 3 units to the left, we get:

[tex]g(x) = f(x + 3) = \frac{1}{x + 3}[/tex]

If now we apply a translation of 5 units downwards, we get:

[tex]g(x) = f(x + 3) - 5 = \frac{1}{x + 3} - 5[/tex]

So we can conclude that the correct option is B:

g(x) can be graphed by translating the basic rational function ƒ(x) 1∕x left by 3 units and downward by 5 units.

If you want to learn more about translations, you can read:

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PLEASE HELP ITS URGENT!! PLEASE

1.) you are looking at your power bill for the month, you pay 12 cent per kilowatt hour. Running a 60 watt lightbulb for one hour is .0 6 KWH, if you leave a light on all the time that has 3 lightbulbs in it how much would that cost a 30 day month

2.) you were looking at your power bill for the month you pay .11 per kilowatt. Your power bill came out to $80.48 how many KWH of energy were using your house this month

3.) you plan to cut the board into three pieces to repair part of a railing. You are going to cut the two ends of the board into two equal pieces that are 2.6 feet long if the remaining piece needs to be 0.86 times longer than each of the first two cats what length boards did you buy round to the nearest tenth

Answers

1. Electrical energy consumption is measured at kilowatt-hour (KWh). Thus the cost of energy consumed for the month is $31.104.

2. The amount of energy used in the house for the month is 731.634 KWh.

3. The length of the board equals the sum of each length of the pieces. The length of the board to buy is 8.70 feet.

1. The rate of consumption of energy is measured in kilowatt-hour.

In the given question,

12 cent is paid per kilowatt-hour.

60 watts of light for 1 hour = 0.06 KWh

3 light bulbs of 60 Watts each for 1 hour = 3 x  0.06

                                           = 0.18 KWh

But,

30 days = 30 x 24 hours

                        = 1440 hours

The total energy consumed for the month = 1440 x 0.18

                                      =  259.20 KWh

The total cost for the month = 0.12 x 259.20

                                               = $31.104

Thus, the total cost for the month is $31.104.

2. Charge per kilowatt-hour = $0.11

Total power bill = $80.48

So that,

Total cost on bill = amount charge per kilowatt x total energy consumed in KWh

Which implies;

$80.48 = $0.11 x total energy consumed in KWh

total energy consumed = [tex]\frac{80.48}{0.11}[/tex]

                               = 731.634 KWh

Therefore, the amount of energy used in the house for the month is 731.634 KWh.

3. Each length of the two end pieces = 2.6 feet each

Given that the remaining piece needs to be 0.86 times longer than each of the first two. Then;

the length of the remaining piece = 2.6 + 0.86

                                                         = 3.46

The length of the remaining piece = 3.46 feet

The length of the board to buy = 2.6 + 2.6 + 3.46

                                                   = 8.66

Thus, the length of the board to buy is 8.70 feet.

Related link: 1, 2. https://brainly.com/question/13988193

                     3. https://brainly.com/question/16046083

Sonia works at a bakery. The function f(x) represents the amount of money Sonia earns per loaf, where x is the number of loaves she makes. The function g(x) represents the number of bread loaves Sonia bakes per hour, where x is the number of hours she works. Show all work to find f(g(x)), and explain what f(g(x)) represents.

f(x)=9x^2+1
g(x)=square root 2x^3

Answers

Answer:

18x^3+1

Step-by-step explanation:

since g(x)=√2x^3 and f(x)=9x^2+1 then

f(g(x))= 9(g(x))^2 +1 = 9(√2x^3)^2 +1 = 18x^3+1

this represents the amount of money Sonia earns baking loaves in x hours

The equation of f(g(x)) is [tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex], and it represents the amount of money Sonia makes when she bakes for x hours

The functions are given as:

[tex]f(x) = 9x^2 + 1[/tex]

[tex]g(x) = \sqrt{2x^3}[/tex]

Recall that:

[tex]f(x) = 9x^2 + 1[/tex]

Substitute g(x) for x

[tex]f(g(x)) = 9(g(x))^2 + 1[/tex]

Substitute [tex]g(x) = \sqrt{2x^3}[/tex]

[tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex]

Hence, the equation of f(g(x)) is [tex]f(g(x)) = 9(\sqrt{2x^3})^2 + 1[/tex]

Read more about composite functions at:

https://brainly.com/question/10687170

x= 3/4 , y= - 2/5 then x+ y =

Answers

Step-by-step explanation:

Given

x = 3/4

y = -2/5

Now

X + y = 3/4 - 2/5

[tex] \frac{3 \times 5 - 2 \times 4}{20} [/tex]

[tex] = \frac{15 - 8}{20} [/tex]

[tex] = \frac{7}{20} [/tex]

Answer:

7/20

Step-by-step explanation:

x=3/4

y= -2/5

x+y=?

to get the sum, plug in x=3/4 into the x and y= -2/5 into the y

1. x + y = ?

2. 3/4 + (- 2/5) = ?

3. 3/4 - 2/5 =?

4. find the lcm of 4 and 5 to get the common denominator (in this case, the lcm of 4 and 5 is 20)

5. multiply 3/4 by 5 (numerator and denominator) and 2/5 by 4 (numerator and denominator)

6. 15/20 - 8/20 = 7/20

the answer is 7/20

9x+5y=34
8x-2y=-2
What are the values of x and y? Please explain the steps.​

Answers

Answer:

x = 1 and y =5

Step-by-step explanation:

[tex]8x -2y= -2\\Divide by -2\\-4x+y = 1\\add 4x\\y= 1+4x\\[/tex]

Substitute this value of y in the next equation.

[tex]9x+5(1+4x) = 34\\9x+5+20x=34\\29x+5=34\\29x=29\\x=1[/tex]

Solve for y using x.

[tex]y=4x+1\\y=4(1)+1\\y=5[/tex]

What are the zeros of f(x) = x2 - 8x+16?
O A. x= 4 only
B. x = -4 and x = 4
C. X=-2 and x = 8
D. x=-4 only

Answers

Answer:

x=4

Step-by-step explanation:

f(x) = x^2 - 8x+16

Set equal to zero

0 = x^2 -8x +16

Factor

what 2 numbers multiply to 16 and add to -8

-4*-4 = 16

-4+-4 = -8

0= (x-4)(x-4)

Using the zero product property

x-4 = 0  x-4 =0

x=4  x=4


The rules for two lines are y=x+2 and y=5 - 2x. At what point do they intersect?

Answers

Answer:

(1,3)

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

The population of a city is currently 45,000 and is declining at a rate of 2% each year. Give a formula for determining the total population after a period of t years.
Question 4 options:

A)

A = (45,000)e–0.02t

B)

A = 45,000 + e–0.02t

C)

A = (45,000)e0.02t

D)

A = 45,000 + e0.02t

Answers

Answer:

Step-by-step explanation:

The general form of this equation is

[tex]A=Pe^{rt}[/tex] where P is the initial population, e is Euler's number (a constant), r is the rate of decay, and t is the time in years.

Therefore, filling in:

[tex]A=45000e^{-.02t[/tex]

there are nickels, dimes, and quarters in a piggy bank. altogether, the coins are worth $3.65. the number of dimes is three times greater than the number of nickels, and the number of quarters is one greater than double the number of nickels. how many quarters, nickels, and dimes are there?

Answers

This question is solved using a system of equations, and doing this, we get that: There are 9 quarters, 4 nickels and 12 dimes.

I am going to say that:

x is the number of nickels.

y is the number of dimes.

z is the number of quarters.

In all, they are worth $3.65.

A nickel is worth $0.05, a dime is worth $0.1 and a quarter is worth $0.25, so:

[tex]0.05x + 0.1y + 0.25z = 3.65[/tex]

Dimes: 3 times greater than nickels:

This means that:

[tex]y = 3x[/tex]

Quarters: One greater than double the number of nickels:

This means that:

[tex]z = 2x + 1[/tex]

Value of x:

We have y and z as function of x, so we can replace into the equation and find the value of x, so:

[tex]0.05x + 0.1y + 0.25z = 3.65[/tex]

[tex]0.05x + 0.1(3x) + 0.25(2x+1) = 3.65[/tex]

[tex]0.05x + 0.3x + 0.5x + 0.25 = 3.65[/tex]

[tex]0.85x = 3.4[/tex]

[tex]x = \frac{3.4}{0.85}[/tex]

[tex]x = 4[/tex]

y and z:

[tex]y = 3x = 3(4) = 12[/tex]

[tex]z = 2x + 1 = 2(4) + 1 = 9[/tex]

There are 9 quarters, 4 nickels and 12 dimes.

A similar question is found at https://brainly.com/question/17096268

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