There are many ways to solve this problem. All you have to do is simple algebraic manipulation. Solve for b and h with the two simpler equations:
2b = 12; divide 2 on both sides to get b = 6
h - x = 2; add x to both sides to get h = (2 + x)
Plug this stuff into the first equation to solve for x. Once we solve for x, we can plug that x value into the equation for h. Because you can see we didn’t get an actual numerical value for h. So:
x + (2+x) + 6 = 14
Subtract 6 from both sides and distribute that plus sign to get rid of the parenthesis. Then combine the like terms to get:
2x + 2 = 8
Subtract 2 from both sides and divide by 2 to get x = 3
Finally plug it into the equation for h:
h = 2+3 = 5
Where's the sample space? I need it to answer this question.
Step-by-step explanation:
20.
In each proof, start by looking at what you're trying to prove. We want to prove that two triangles are congruent. To do that we use one of the following: SSS, SAS, ASA, or AAS.
To decide which one to use, look at the information given. We're given two pairs of congruent sides, so we can narrow the strategy down to either SSS or SAS. We aren't told anything about the third pair of sides, but we <em>can</em> see that ∠JNK and ∠MNL are vertical angles. We'll use this to show the triangles are congruent by SAS.
1. JN ≅ MN, Given
2. ∠JNK ≅ ∠MNL, Vertical angles
3. NK ≅ NL, Given
4. ΔJNK ≅ ΔMNL, SAS
21.
Repeat the same steps as 20. Again, we're trying to prove two triangles are congruent, so we have 4 strategies to choose from. Just like before, we're given two pairs of congruent sides, so we'll use either SSS or SAS. And again, we aren't told anything about the third pair of sides, but we can see that both triangles are right triangles. So we'll use SAS again.
1. MN ≅ PQ, Given
2. ∠LMN ≅ ∠NQP, Right angles are congruent
3. LM ≅ NQ, Given
4. ΔNML ≅ ΔPQN, SAS
Answer:
<h2>30</h2>
Step-by-step explanation:
<h3>to understand the steps</h3><h3>you need to know about:</h3>
- system of linear equation
- word problems
- PEMDAS
first step
let's create the equation word problem
<h3>my mother's current age is four times the sum of the ages of my two sisters. After 5 years, my mother's age will be double the sum of the ages of my two sisters. What is the current age of my mother? (imaginary problem)</h3>
let's solve
let my mother's and sister's age be x and y respectively
according to the first condition,x=4y....(I)
according to the 2nd condition,x+5=2(y+5×2).....(ii)
so the system of linear equations is
x=4y
x+5=2(y+5×2)
gets from the second equation
x+5=2(y+10)
x+5=2y+20
4y+5=2y+20 (as x=4y)
2y=15
y=7.5
so the age of mother is
x=4.(7.5)
x=30
