Answer:
Step-by-step explanation:
(Let the point where the altitude from 
intersects 
be called as point 
.) First, let's find the area of parallelogram 
. The area of a parallelogram is simply 
, where 
is the parallelogram's base and 
is the parallelogram's height. If we let and 
be the base and height respectively, since we are already given their lengths, we know that the area of parallelogram will be 
.
Now, how does this information matter, you might ask? Well, we can take either <em>or </em>
to be the base and either or 
to be the height. In this case, let's take the latter two options, as we are looking to find the length of .
Therefore, we know that the area of parallelogram can also be found by calculating 
. Since we know the values of the area and , we can write the following equation to solve for :
(Substitute 
and 
into the equation)
(Divide both sides of the equation by 
to get rid of 's coefficient)
(Simplify)
(Symmetric Property of Equality)
Hope this helps!
Answer:
19,12
Step-by-step explanation:
Answer:
x = 31
Step-by-step explanation:
The given angles are supplementary and their sum is 180 degrees
5x - 16 + x + 10 = 180 add like terms
6x - 6 = 180 add 6 to both sides
6x = 186 divide both sides by 6
x = 31
The solution (-4,2) satisfies for the system of linear equations 3x + 13y = 14; 6x + 11y = -2
<u>Step-by-step explanation:</u>
Step 1:
Given detail is the solution of the equations (-4, 2) ie, x= - 4 and y = 2
This implies that this solution should satisfy the given linear equations.
Step 2:
Substitute values of x and y in the equations and verify whether the right hand side equals the left hand side.
System 1 Eq(1) ⇒ LHS = 3(-4) + 13 (2) = -12 + 26 = 14 = RHS
System 1 Eq(2) ⇒ LHS = 6(-4) + 11(2) = -24 + 22 = -2 = RHS
Therefore, the first system of linear equations satisfy the condition.
Answer: She has 21 lira coins.
Step-by-step explanation:
Given, Laura collects old foreign coins. She has 83 coins in total. She has 53 lira and drachma coins. She has 51 lira and peseta coins.
Let x = the number of lira coins.
y= the number of drachma coins.
z= the number of peseta coins.
Then, as per given, we have
x+y+z=83 (i)
x+y=53 (ii)
x+z=51 (iii)
From (ii) and (iii)
y=53-x
z=51-x
Put these values in (i) , we get
x+(53-x)+(51-x)=83
⇒ x+53-x+51-x=83
⇒ 104-x=83
⇒104-83=x
⇒x= 21
Hence, she has 21 lira coins.
