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Let  n  be the number of nickels in the jar  and let  d  be the number of dimes.

There are  22  coins in the jar, so we can make this equation:

n + d  =  22     Let's subtract  d  from both sides of this equation

n  =  22 - d

The total value of the coins is  $1.60,  so we can make this equation:

0.05n  +  0.10d  =  1.60

                                              We can multiply both sides of the equation through by  10

5n  +  10d   =   160

                                              Since  n = 22 - d  we can substitute  22 - d  in for  n

5(22 - d)  +  10d   =  160

                                              Distribute  5  to each term in parenthesees

110 - 5d  +  10d   =   160

                                              Combine  -5d  and  10d  to get  5d

110 + 5d   =   160

                                              Subtract 110  from both sides of the equation

5d   =   50

                                              Divide both sides of the equation by  5

d   =   10

Now that we know  d  =  10   we can find  n  by substituting  1  for  d  in the first equation.

n   =   22 - d   =   22 - 10   =   12

So there are  12  nickels and  10  dimes.

1.  Yes, △LMN is similar to △WXY because  21/30  =  7/10  =  28/40  and the included angles are equal because they are both 90°, so by the SAS similarity theorem, the two triangles are similar.

2. The one with the larger base, which is the one with △WXY as the base, will have the greater volume.

volume of smaller prism  =   (area of base) * (height)

volume of smaller prism   =   (1/2 * 30 * 21) * (height)

volume of smaller prism   =   (315) * (height)

volume of smaller prism   =   315h        ,  where  h  is the height of the prism

volume of larger prism   =   (area of base) * (height)

volume of larger prism   =   (1/2 * 40 * 28) * (height)

volume of larger prism   =   (560) * (height)

volume of larger prism   =   560h

The larger prism is how many times greater than the smaller prism? That is,  560h  is how many times greater than  315h  ?

560h/315h   =   16/9         so...         560h  =  (16/9) * 315h

In other words,  560h  is  16/9  times  315h ,  which means the volume of the larger larger prism is  16/9  times the volume of the smaller prism.

The angle sum of a triangle is  180 degrees.

(3 sides -2) *180  = 180

Let the number of sides of a polygon be n

The angle sum will be  (n-2)*180

So what is the angle sum of  a six-sided polygon (hexagon) ?

Can you take it from there?

the degree of f(x) is 4

the degree of g(x) is  also 4

so the degree of the product will be 8

Jose kaufte 9 Filmtickets für insgesamt 54 Dollar. Erwachsene Tickets kosten jeweils 8 Dollar und Kindertickets kosten jeweils 3,50. Wie viele Eintrittskarten für Erwachsene hat er gekauft?

Hallo Gast!

\(8e+3.5k=54\\ e+k=9\\ e=9-k\\ 72-8k+3.5k=54\\ 18=4.5k\)

\(k=4\\ \color{blue}e=5\)

Jose hat 5 Eintrittskarten für Erwachsene gekauft.

  !

Finden Sie den Wert von Segment DC

Hallo Gast!

3x-1=x+9

2x=10

x=5

\(\color{blue}\overline{DC}=5\)

  !

f(x)=x-4-3x-2+2 und g(x)=2x-4-6x-2+2x-1. Wie hoch ist der Grad der f(x)*g(x)

Hallo Gast!

\(f(x)\times g(x)=(x-4-3x-2+2)\times (2x-4-6x-2+2x-1)=\color{blue}4x^2+22x+28\)

Es ergibt sich eine Funktion zweite Grades.

  !

CD = sqrt((2√10)² - 2²) = 6 cm

[ABCD] = CD * AB = 30 cm²

[DEF] = [ABCD] - {1/2(4*5) + 1/2(2*3) + 1/2(2*6)} = 11 cm²

the little one is 4' by 9'

the side lengths of the big one are 5 times that so    20 by 45 feet

You can that it from there. 

Angle ZTV = 43 degrees

Hey there!

Here I am going to assume that the kitchen table doesnt have legs so that way we dont have to worry about them!

After assuming this, we can find the diagonal of the door opening and compare this to the diameter of the table to see if it will fit through. This is where we can use Pythagoras (\(c=\sqrt{a^2+b^2}\))! Lets let \(a\) be the height of the door and \(b\) the width of the door, then plug it into the formula to get the diagonal \(c\):

\(a=200\)

\(b=80\)

\(c=\sqrt{200^2+80^2}\)

\(\therefore c\approx215cm\)

Since we know that the diagonal of the door is 215cm, and the table is only 210cm, it is known that the table will infact be able to fit through the front door!

Let me know how this went :)

BC = 36

I wrote a computer program

i = 0

for (a = 1..6)

for (b = 1..6)

for (c = 1..6)

for (d = 1..6)

for (e = 1..6)

  if a*b*c*d*e = 300 then i++

write(output,i)

output = 480

The x-coordinate of the center of the hyperbola is 11 - 3*sqrt(2).

16 is wrong

please help

This is $3/4$ of a circle, so there answer is the area of the full circle $*3/4$
$π*4^2*3/4$

$π*16*3/4$

$π*12$

$\boxed{12pi}$

(x² - k)(x + k) = x³ + k(x² - x - 5)

x³ - kx + kx² - k² = x³ + k(x² - x - 5)

x³ + k(x² - x - k) = x³ + k(x² - x - 5)

Comparing both sides, 

 k = 5

What are the x^2 terms?    kx^2  that is no help

What about the x terms?   -kx     that is no help either

what about the constant ?      -k^2    =  -5k    So what must k be? 

No Cal, you took the answer that was given and effectively checked that it was right.

You did not show how you could have got the answer for yourself.

You do not have enough maths knowledge to do that yet.  Maybe you will have one day  

Does this just depend on reasoning perhaps? I don't think there's anything complex, I simply got the answer by playing around but obviously that's not the correct way to solve it.

Hi Cal,

You have done some excellent expanding.  Good work.

But

I was not asking anyone to show that the answer was correct.  

I was asking for someone to explain how the answer could be arrived at, if I did not already know it.

I'm pretty sure that is what grs75 wants too.   

i see, thank you! 

well, angle 1 would be 180 - 43 = 137, since it is on that straight angle. 

angle 2 is 180 - (90 + 43) = 47.

angle 3 is 180 - 137 - 26 = 17.

hope this helped! sorry if my explanations weren't too clear.