Triangle MNO is similar to triangle PRS. Find the measure of side RS. Round
answer to the nearest tenth if necessary. Figures are not drawn to scale.

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

-------------

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:

Step-by-step explanation:

the varible would be x

Yes it is possible.

- BRAINLIEST answerer

Answer:

13. C

14. B

Step-by-step explanation:

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

2.5 is the scale dilation.

Kinda Logic

Answer:

x=0

Step-by-step explanation:

2.5^2x = 1

2.5^2x=2.5⁰

2 x = 0

x=0

Answer:

3:10

Step-by-step explanation:

Disposal time=1:15PM

Choir ending time:-

[tex]\\ \sf\longmapsto 1:15-0:40=12:35PM[/tex]

Answer: 4k^2 - 9k - 9 = 0

Step-by-step explanation:

lmk if i was right please and ty

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:

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:

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:

Answer is 2,000 option (B)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Time in travel:

Average speed is 5 mph

Distance travelled:

Correct choice is A

Total time taken

Distance

Option A

Answer:

The selling price of one striped lanyard

Answer:

a+b+2

Step-by-step explanation:

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:

4.2

Step-by-step explanation:

All sides are proportional, so choose a pair and find the proportion

Ex: AB and JK = 7/5=1.4

so each side is multiplied by 1.4 to get the larger figure

So 3*1.4=4.2

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.

Answer:

1/3 is less than 1

Step-by-step explanation:

3/3=1

1/3<1

I think you have to put all the fractions on one side of the equation and the x-terms on the other side. But I don't see an option for that...

Answer:

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

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] - 4x + [tex]\frac{7}{2}[/tex] = - 9x + [tex]\frac{5}{6}[/tex]

Multiply through by 6 ( the LCM of 3, 2 and 6 ) to clear the fractions

4 - 24x + 21 = - 54x + 5 , that is

25 - 24x = - 54x + 5 ( add 54x to both sides )

25 + 30x = 5 ( subtract 25 from both sides )

30x = - 20 ( divide both sides by 30 )

x = [tex]\frac{-20}{30}[/tex] = - [tex]\frac{2}{3}[/tex]

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:

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

Answer:

[tex]\frac{400}{(10\sqrt{2} + 14\sqrt{3}) }= h[/tex]   or  10.42 = h

Step-by-step explanation:

The area of a trapezoid is [tex]A = \frac{1}{2}h(b_{1} + b_{2} )[/tex].

[tex]200 = \frac{1}{2}h(10\sqrt{2} + 14\sqrt{3})[/tex]

[tex]400 = { h(10\sqrt{2} + 14\sqrt{3} )[/tex]             Multiply both sides by 2

[tex]\frac{400}{(10\sqrt{2} + 14\sqrt{3}) }= h[/tex]

 [tex]\frac{400}{38.39} = h[/tex]

10.42 = h  

Answer:

1.

Step-by-step explanation:

Answer:

The graphs that could be this function are the third one and the last one.

C and E

Hope this helps!

Step-by-step explanation:

Other than C and E, all of the other functions start out by decreasing starting from -5.

They both also have the straight part from -3 - 0 where the function neither increases nor decreases.

They also have the part where from 2 increases to 5.