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Answer:

Step-by-step explanation:

(x + y)^2 = 144

x^2 + y^2 = 80

----

x + y = 12 ---> y = 12 - x

x^2 + y^2 = 80

x^2 + (12-x)^2 = 80

2x^2 - 24x + 64 = 0

x^2 - 12x + 32 = 0

x = 4, x = 8

y = 8, y = 4

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

x + y = -12 ---> y = -12 - x

x^2 + y^2 = 80

x^2 + (-12-x)^2 = 80

2x^2 + 24x + 64 = 0

x^2 + 12x + 32 = 0

x = -4, x = -8

y = -8, y = -4

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One number is + or -4, the other is + or -8,

and the absolute value of the sum is 12.

Answer:

(4,8);(8,4);(-4,-8);(-8,-4)

Step-by-step explanation:

Ok, let's start writing down the two conditions:

[tex]\left \{ {(x+y)^2 = 144} \atop {x^2+y^2=80}} \right.[/tex]

Mumble.  The second almost look like a square, if only there was the [tex]2xy[/tex] term. Let's add (and subtract, so we aren't creating something new) term to the second:

[tex](x+y)^2-2xy = 80[/tex] But we know what the first term is, it's 144. Let's replace and do some number tricks to get:[tex]144-2xy=80 \rightarrow 72-xy=40\\72-40=xy \rightarrow xy=32[/tex]

At this point, let' stare at it for a while. You can tell that the system is simmetrical (if you replace x with y you still get a solution). Moreover, x and y have the same sign: it means that if (a,b) is a solution, then also (b,a), (-a,-b) and (-b, -a) are solutions, and since it's a 4th degree system (the degree of a system is the product of the degrees of the single equations, and they're both quadratic) there are no other solution.

Let's find one pair then. We're tasked to find two numbers that sum to [tex]\sqrt{144} = 12[/tex] and whose product is 32. that is, the root of the polynomial

[tex]z^2+12z+32= (z+4)(z+8)[/tex] (or if you can't see the factors right away, bruteforce it with quadratic formula, it's always good practice). That tells us that one of the two is -4, and the other is -8. From what we said above, the solutions are by combining them with plus or minus.

[tex](4,8);(8,4);(-4,-8);(-8,-4)[/tex]

Answer:

b/2-15

or

-15+1/2b

or

b:2-15

Step-by-step explanation:

which expression is equivalent to 1/2b-15

b/2-15

or

-15+1/2b

or

b:2-15

Answer:

Perpendicular line: y = ⅕x + 0 or y = ⅕x

Step-by-step explanation:

Given the point, (10, 2), and the linear equation, y = -5x + 7:

In order to find the equation of the perpendicular line that passes through (10, 2), we must first determine the definition of perpendicular lines.

Perpendicular lines have negative reciprocal slopes ⇒ this means that when you take and multiply the slopes of both lines, it results in a product of -1.

                    m₁ × m₂  = -1

                     -5 ×  ⅕  = -1

Now that we have the slope of the other line, m₂ = ⅕, and the given point, (10, 2), substitute these values into the slope-intercept form to solve for the y-intercept, b :

y = mx + b

2 = ⅕(10) + b

2 = 2 + b

Subtract 2 from both sides:

2 -2 = 2 -2 + b

0 = b

Hence, the y-intercept is b = 0.

The linear equation of the perpendicular line that passes through point (10, 2) is: y = ⅕x + 0 or   y = ⅕x

Answer:

Step-by-step explanation:

the varible would be x

29.25 divided by 9 is 3.25. You have to take the total amount of money he made $29.25 and divide it by the amount he gets every hour $9. So 29.25 divided by 9 is 3.25 or 3 hours and 15 minutes.

Answer:

15 cents a minute

Step-by-step explanation:

9 ÷ 60 = $0.15

Answer:

Maybe 34cm

Sana makatulong..

Answer:

Step-by-step explanation:

Answer: y = -10x + 293

Step-by-step explanation:

Since you start with $293, this is your intercept.

Since you withdraw $10 per week, your m is -10. Per in a sentence means rate of change.

Answer:

Yes, it is proportional because the number of gallons filled is always 15 times the number of minutes.

Answer:

The selling price of one striped lanyard

Answer:

Answer is 2,000 option (B)

Answer:

13. C

14. B

Step-by-step explanation:

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

Answer:

where is the graph??

Step-by-step explanation:

i have no picture soooo like

Answer:  16 1/4 minutes

Step-by-step explanation:

Let A be the mowing rate for the first person, and B the rate for the second. X will be the time spent mowing.

We are told that A = 30 min/lawn.  B = 45 min/lawn.  These are conversion factors, so we can invert them to:

A =  1 lawn/30 min.  B = 1 lawn/45 min

If both work together, the amount of lawn that is mowed working togehterwould be the time, X (in minutes), spent times their individual rates:

X*(A + B) = Lawn Mowed

We want to know the time, X, it would take to mow the same 1 lawn together.  [Lawn Mowed = 1].  Use the equation:

X*(A + B) = Lawn Mowed

X*((1 lawn/30 min) + (1 lawn/45 min)) = 1

X/(30 min) + X/(45 min) = 1

X/30 + X/45= 1

X + X(30/35) = 30  {Multiply both sides by 30]

(1 + 30/35)X = 30

(65/35)X = 30

X = 30*(35/65)

X = 30/(7/13)

X = 30*(7/13)

X = 210/13

X =  16 1/4 minutes

Answer:

22w - 18  

Step-by-step explanation:

To find the perimeter we have to add up all the sides

10w-10+w+1+10w-10+w+1

combine light terms

22w - 18 would be our answer

Brainliest please

Answer:

140 inches

Step-by-step explanation:

one decagon has 10 sides

14*10= 140

Answer:

Your answer is in the image linked below.

Step-by-step explanation:

When the shape is moved right 2, down 1, you should have this translation,  hope this helps.

Answer:

x=0

Step-by-step explanation:

2.5^2x = 1

2.5^2x=2.5⁰

2 x = 0

x=0

Answer:

150 + 3x = 369 X= 73

Step-by-step explanation:

X is the amount of days

So 150 minus 369 would be 219

Then take 219/3 and that would mean X equals 73

Answer:

Pretty sure the dimensions are 125.6 meters by 251.2 meters 31,550.72 square meters.

Answer:

the surface area is 180 if u use multiplication

Step-by-step explanation:

the surface is 0.8 if you use devide

the surface is 3 if u use subtract

and the surface is 27 if you use addition

correct me if I'm wrong :)

Answer:

y equals -2x plus 8

Step-by-step explanation:

Answer:

$24

Step-by-step explanation:

First, we round to the nearest tenth.

$120

Now, we calculate the tip amount.

[tex].20 * 120 = 24[/tex]

Answer:

3.1

Step-by-step explanation:

Answer:

The answer is ">"

Step-by-step explanation:

I took the quiz epicly

Answer:

>

Step-by-step explanation:

Answer:

All of the equations seem to have infinitely many solutions.

Step-by-step explanation:

Since the same equations are equal to each other, whatever you replace x with, it will be equal to the other equation's solution since all answers have equations equal to each other.