there are two routes to solve this, Substitution or elimination, I'll go for the 2nd one because I can see that the y values are a multiple of each other :)

6 *( −5x−3y−9=0 )

Eq. 3) -30x -18y =54

subtract Eq. 2 from Eq. 3 :)

-30x -18y =54

-( 4x−18y=54)

-34x = 0

so according to the equations then x =0 but, that's not really a full answer, so now we should go back and try the other method, substitution,

then:

-5x = 9 +3y

x = - 9/5 + (-3/5)y

now plug that into Eq. 2

4( - 9/5 + (-3/5)y ) - 18y = 54

-36/5 + (-12/5)y -18y = 54

(-12/5)y - (90/5)y = 54+36/5

-(102/5)*y =270/5+36/5

-(102/5)y = 306/5

y = (-5/102)*(306/5)

y = -306/102

y = -3

then plug in for either equation

-5x-3( -3) = 9

-5x + 9 = 9

-5x = 0

x = 0

now we have the full answer

check it by plugging in both x and y into the 2nd equation

4(0) - 18(-3) = 54

54= 54

this seems good

3 0

3 years ago

One leg of a 45°-45°-90° triangle measures 9sqrt2 inches. What is the length of the hypotenuse?

stiv31 [10]

We know that
a=9√2
b=9√2
a=b---------- for having both angles of 45
c²=a²+b²-------> (9√2)²+(9√2)²------>(324)-----------> c=√324=18

the answer is the option A 18 inches

8 0

3 years ago

When a number is added to six times its square, the result is twelve. Find the number.

7nadin3 [17]

Let's represent our number as x.
x is being added to 6 * x², and it equals 12
$x + 6x^{2}=12\\6x^{2}+x-12=0$
Factor:
$6x^{2}+x-12=0\\(2x+3)(3x-4)=0$
Solve for x:
$(2x+3)=0\\2x=-3\\x=\frac{-3}{2}\\\\(3x-4)=0\\3x=4\\x=\frac{4}{3}$

Therefore, x = -3/2 and 4/3.

6 0

2 years ago

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