Among all pairs of numbers with a sum of 149149, find the pair whose product is maximum. Write your answers as fractions reduced to lowest terms.

Answer:

-13/30

Step-by-step explanation:

take 1/6 to other side,

x=-3/5 -1/6

taking LCM of denominators,

-8-5/30

=-13/30

Answer:

X=23/30

Step-by-step explanation:

X + 1/6 = -3/5

X + 5/30 = -18/30

-5/30 -5/30

X = -23/30

I feel like i did something wrong... but im pretty sure its right. Let me know if it's right! Hope it helps.

Answer:

12+x goes to 19

3x+y goes to 25

4y-10 goes to 6

1/2xy goes to 14

x=7 and y=4 all you have to do is substitute for example 12+x substituted it's 12+7 then just do the math. That's it.

Answer:

9+9

Step-by-step explanation:

9+9=18

23-5=18

Answer:

The answer is

Step-by-step explanation:

[tex] \frac{9x + 3}{12x + 4} [/tex]

To solve the rational expression factorize both the numerator and the denominator.

For the numerator

9x + 3

Factorize 3 out

We have

3( 3x + 1)

For the denominator

12x + 4

Factorize 4 out

That's

4( 3x + 1)

So we now have

Reduce the expression with (3x + 1)

We have the final answer as

Hope this helps you

Answer:

42 or 4^2

hope this helps

Answer:

4^12

Step-by-step explanation:

Answer: $51

Step-by-step explanation:

If 15% discount is applied then 85% of the price will be the left to pay.

so 85% * 60   will give you the price of the shirt after the discount.

85% * 60 = 51

Answer:

Step-by-step explanation:51.00$

Answer:

rational numbers

Step-by-step explanation:

They cannot be negative numbers because the product of two negative numbers is positive.

They cannot be prime numbers because the product of two prime numbers is not a prime number.

The product of two complex numbers can be a complex number, but it may also be a real number.

The product of two rational numbers is always rational.

Answer: rational numbers

Answer:12

Step-by-step explanation:

Answer:

Step-by-step explanation:

The standard form of a point slope equation of a line is expressed as shown;

y-y₀ = m(x-x₀) where;

m is the slope of the line

(x₀, y₀) is the coordinate of the point that lies in the line.

Comparing the standard equation given with the equation in question

y - 3 = 4(x + 7) to get the point on the line we will have;

y₀  = 3 and -x₀ = 7

for -x₀ = 7;

multiply both sides with a minus sign

-(-x₀) = -7

x₀ = -7

Hence the coordinate of the point required (x₀, y₀) is (-7, 3).

Answer:

12.5

Step-by-step explanation:

that is to say 20 -15 because it went late =5

then 2.5×5

Answer:

Step-by-step explanation:

y= 0

x + 2(0) = 10

x = 10

(10, 0)

x = 0

0 + 2y = 10

2y = 10

y = 5

(0,5)

In U.S. dollars, the equivalent money will be $100.74

Given is your dinner in London cost 82 British pounds

Then in U.S. dollars, the equivalent money will be equivalent to -

x = 82 pounds = 82 x 1.2286 = $100.74

x = $100.74

Therefore, in U.S. dollars, the equivalent money will be $100.74

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

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#SPJ2

Its conjugate is

7 - i√2

Answer:

b

Step-by-step explanation:

Answer:

y=x-1

is the line equation

Step-by-step explanation:

As we know that general equation of line is given by

y=mx + c

m is the slope and c is is y intercept

Know m = 1 and point (x,y) as (5,4)

So plug in the values and solve for c

4=1*(5)+c

c=-1

So equation of line is

y=x-1

Answer:

Step-by-step explanation:

The domain of any polynomial function, quadratics included, is "all reals."

The graph opens upward, so the y-value of the vertex is the minimum value of the range: y ≥ 2.

Answer:

36

Step-by-step explanation:

Starting with 4, 9.

9 - 4 = 5 then + 2

So forward.

Answer:

1, 4, 9, 16, 25, 36

Step-by-step explanation:

This is because as you see 1 + 3 = 4, then 4 + 5 = 9, then 9 + 7 = 16. So we see that it goes like 3 + 5 + 7 + 9 + 11 + 13  . . .  That is the pattern. Hope this helps!

Answer:

x = -7

Step-by-step explanation:

4x — 3 = —31

Add 3 to each side

4x — 3+3 = —31+3

4x = -28

Divide by 4

4x/4 = -28/4

x = -7

Your answer would be x=-7 or -7!

Answer:

10.5

Step-by-step explanation:

If the recipe is designed for 4 people than you would need 6 eggs for 8 people (8 is twice as many as 4 so you need twice as many eggs.) similarly, 14 is 3.5 times as many as 4 (14/4=3.5) so you would need 3x3.5=10.5 eggs.

Not sure how that works but I hope this helped!

Answer:

49.68

Step-by-step explanation:

you would just plug in 35400 for y so  you get 35400=312x+19900 and then you would subtract 19900 from both sides so you get 15500 and then divide that by 312 which is 49.68

Answer:

The side of the square is 15m

The side of the triangle is 20m

Step-by-step explanation:

P square = 4s  where s is the side length

P triangle = 3 x where x is the side length

x = s+5

The perimeters are equal

4s = 3x

Replace x with s+5

4s = 3(s+5)

Distribute

4s = 3s+15

Subtract 3s from each side

4s-3s = 15

s = 15

The side of the square is 15

x =s+5

  =15+5

   = 20

The side of the triangle is 20

Answer:

[tex]\Large \boxed{\mathrm{square: 15 \ meters}} \\\\ \Large \boxed{\mathrm{triangle: 20 \ meters}}[/tex]

Step-by-step explanation:

The perimeter of a square is [tex]\sf P=4s[/tex], where s is the side length.

The perimeter of an equilateral triangle is [tex]\sf P=3a[/tex], where a is the side length.

The side length of the equilateral triangle is 5 more than the side length of the square.

[tex]\sf a = s+5[/tex]

The perimeter of the square and equilateral triangle are equal.

[tex]\sf 4s=3(s+5)[/tex]

Expanding brackets.

[tex]\sf 4s=3s+15[/tex]

Subtracting 3s from both sides.

[tex]\sf s=15[/tex]

The side length of the square is 15 meters.

[tex]\sf a=15+5 \\\\\\ a=20[/tex]

The side length of the triangle is 20 meters.

Answer:

28 times

Step-by-step explanation:

Create an equation where x represents the number of times the bus is used:

1.75x = 0.5x + 35

Solve for x:

1.75x = 0.5x + 35

1.25x = 35

x = 28

So, the bus has to be used 28 times for the prices to be the same.

Step-by-step explanation:

Let's look at our expression:

[tex]1.7+8.23-3.4+4.7j[/tex]

The numbers without a variable at the end are like terms here. Let's add them up.

[tex]1.7+8.23=9.93\\9.93-3.4=6.53[/tex]

Then, let's add our answer, 6.53, to the term with a variable, 4.7j.

Our final answer: 6.53 + 4.7j

I hope this helps you!

Answer:

[tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

Given that two fair dice are tossed.

Total outcomes as we toss two dice are given as:

{

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

}

Where (a, b) represents a is the outcome of the die rolled for the 1st time and b is the outcome of 2nd toss of the die.

Total number of outcomes = 36

The outcomes with sum = 7 are :

{(1, 6), (2, 5), (3, 4) , (4, 3), (5, 2), (1, 6)}

Number of outcomes = 6

Probability of an event E is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

[tex]P(sum=7) = \dfrac{6}{36}\\\Rightarrow \bold{P(sum=7) = \dfrac{1}{6}}[/tex]

Answer:

5/6 can´t be simplified

Step-by-step explanation:

Answer:

5i/6

Step-by-step explanation:

[tex]\frac{5}{6}i\\\\\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}\\=\frac{5i}{6}[/tex]

Answer:

It will take 5.4 hour to paint 720 square feet

Step-by-step explanation:

The question should be like this"Andy painted 400 square  feet in 3 hours. How long  would it take him to paint  720 square feet?"

In 3 hours = 400 square  feet is painted

1 square feet is painted in [tex]\dfrac{3}{400}\ h[/tex]

To find time to paint 720 square feet multiply the above term by 720 as follows :

[tex]720\ ft^2=\dfrac{3}{400}\times 720\ h\\\\=5.4\ h[/tex]

So, it will take 5.4 hour to paint 720 square feet.

Answer:

Step-by-step explanation:

Hello,

What other numbers are of this form have exactly four factors?

[tex]8=2^3\text{ has 4 factors } 1, 2, 2^2, 2^3\\\\\text{For any prime p, }p^3\text{ has 4 factors } 1, p, p^2, p^3\\\\[/tex]

Do all the perfect cubes have exactly four factors?

[tex]\text{If p is not prime, then it is not true anymore} \\ \\\text{For instance, }8^3\text{ has more than 4 factors } 1, 2^2, 2^3, 2^4, etc..[/tex]

Is it true that all numbers that have exactly four factors are perfect cubes?

6 has 4 factors : 1, 2, 3, 6 but this is not a perfect cube.

Thank you.

We know that any number can be decomposed as a product of prime numbers.

For example:

[tex]8 = 1\cdot 2\cdot 2\cdot 2[/tex]

8 has four factors if we count the 1.

Now we need to answer some questions regarding this:

What other numbers are of this form have exactly four factors?

8 is a cube number.

Remember that all cube numbers X can be written as:

[tex]X = n\cdot n\cdot n \cdot 1[/tex]

Now, if n is prime, then we can say that X is of the form of 8 and also has 4 factors.

But let's see the case:

[tex]8\cdot 8\cdot8= 512[/tex]

512 is a perfect cube, and if we decompose it we get:

[tex]512 = 8\cdot 8\cdot 8 = (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot 1[/tex]

So we found a perfect cube that has 10 factors.

This means that not all perfect cubes have exactly 4 factors.

Now, all numbers that have exactly four factors are perfect cubes?

This is also false, just let's create a counterexample.

[tex]1\cdot 2\cdot 3\cdot 5 = 30[/tex]

the number 30 is not a perfect cube, and we can see that it has exactly 4 factors.

If you want to learn more, you can read:

https://brainly.com/question/832797

Answer:

4

Step-by-step explanation:

Because if you substitute x = 4 and y = 1 in the equation of y = 3x + 1, you'll see that both sides are different.

So if we substitute x = 4 and y = 1 in the equation, we get:

1 = 3(4)+1

1 = 12+1

1 = 13

The equation isn't true though. Also we can explain why (4,1) isn't the solution to the equation by graph (you can go draw the graph of y = 3x + 1 and notice that the line doesn't pass through (4,1) )

Also how about another example? But this time, we use (0,1) which is the solution of y = 3x + 1.

Substitute x = 0 and y = 1 in the equation as we get:

1 = 3(0)+1

1 = 0 + 1

1 = 1

Since the equation is true, that means the (0,1) is one of the solution of y = 3x + 1.

Maybe, you want another example again? How about (1,4) which is also one of the solution of y = 3x + 1.

Again, substitute x = 1 and y = 4.

4 = 3(1)+1

4 = 3+1

4 = 4

Since the equation is true. Therefore (1,4) is also one of the solution of y = 3x + 1.

Also here's why (4,1) is not the solution of y = 3x + 1

Basically, from (x,y), 4 is the x and 1 is the y. If we substitute "x" in any equations, we get the "y". Meaning that the x value can be meant as "input" and we get the output "y" like Function which is it.

If we substitute x = 4 in the equation...

y = 3(4)+1

y = 12+1

y = 13

Meaning that the actual y value is 13, not 1. This explains why (4,1) isn't the right solution.

Maybe, what if we substitute y instead? Well that works. Now let's try substitute both y = 1 and y = 13 to see which is the right value.

(1) For y = 1,

1 = 3x+1

1-1=3x

0=3x

x=0 (Therefore, x = 0 and y = 1)

So the actual order is (0,1).

(2) For y = 13

13 = 3x+1

13-1 = 3x

3x = 12

x = 4 (Therefore, x = 4 and y = 13)

so the actual order for (2) is (4,13).

Basically, (4,1) is false for y = 3x + 1.

Answer:

See below

Step-by-step explanation:

Given the point (4,1) means

(x,y) = (4,1)

So, x = 4 , y = 1

Given the equation y = 3x+1

Put x = 4 and y = 1

=> 1 = 3(4)+1

=> 1 = 12 + 1

=> 1 ≠ 13

Since Left hand side doesn't equal right hand side, (4,1) is not the solution to y = 3x+1