Answer:
Step-by-step explanation:
Eq. 1 ) −5x−3y−9=0
Eq. 2) 4x−18y−54=0
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
<u>-( 4x−18y=54)</u>
-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
Answer:
I, II and III
Step-by-step explanation:
Two sides of a triangle have length 6 and 8.
the maximum possible area occurs in the right angle .
To find maximum area we use the area of the triangle formula
So maximum possible area is 24 units^2
all the given possible values are less than and equal to 24
so all the three options are correct
I, II and III
Step-by-step explanation:
step 1
Two triangles are similar if the only difference between them is the size, this means that their internal angles must be the same. If we look at the picture the first triangle has one angle equal to 40 degrees, one equal to 80 degrees and the third one is unkown (x). The second triangle has one angle equal to 40 degrees, one equal to 60 degrees and the third one is unkown (y). The sum of the internal angles of a triangle must be equal to 180 degrees, with this information we can find the values of the missing angles. We have:
Therefore the internal angles of the first triangle are (40,80,60) and the angles of the second triangle are (40,80,60) as well, therefore they are similar.
Two triangles are congruent if they have sides with the same length. Which is not the case, because the sides of one triangle is (8, 10, 6) while the other is (4,3 and unkown). Therefore they are not congruent.
Let me express the equation clearly:
lim x→-9 (x²-81)/(x+9)
Initially, we solve this by substituting x=-9 to the equation.
((-9)²-81)/(-9+9) = 0/0
The term 0/0 is undefined. This means that the solution is not see on the number line because it is imaginary. Other undefined terms are N/0 (where N is any number), 0⁰, 0×∞, ∞-∞, 1^∞ and ∞/∞. One way to solve this is by applying L'Hopitals Rule. This can be done by differentiating the numerator and denominator of the fraction independently. Then, you can already substitute the x=-9.
(2x-0)/(1+0) = 2x = 2(-9) = -18
The other easy way is to substitute x=-8.999 to the original equation. Note that the term x→-9 means that x only approaches to -9. Thus, you substitute a number that is very close to -9. Substituting x=-8.999
((-8.999)²-81)/(-8.999+9) = -18
