Answer:
Therefore
1. Vertical Opposite Angle Theorem is used to prove that the triangles are similar.
2. Angle-Angle similarity statement is used.
3. x = 10 unit and y = 7.5 unit.
Step-by-step explanation:
Given:
∠A ≅ ∠E
AB = 8 , DE = 12 , BC = 5 , CE = 15
To Prove:
Δ ABC ~ ΔEDC
To Find :
x = ?
y = ?
Proof:
Vertical Angle Theorem:
The angles opposite each other when two lines cross. They are always equal.
Here vertical opposite angles are,
∴ ∠ACB ≅ ∠ECD
Angle-Angle Similarity :
If in Two triangle Two corresponding angles are congruent then the Triangles are Similar by Angle-Angle Similarity statement.
Now,
In Δ ABC and Δ EDC
∠A ≅ ∠E …………..{ Given }
∠ACB ≅ ∠ECD ……….....{Vertical Opposite Angle Theorem}
Δ ABC ~ Δ EDC ….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
On Substituting the given values we get
Therefore,
Therefore
1. Vertical Opposite Angle Theorem is used to prove that the triangles are similar.
2. Angle-Angle similarity statement is used.
3. x = 10 unit and y = 7.5 unit.
Answer:
x = 29°, y = 61°
Step-by-step explanation:
x + 61 = 90
Because of the right angle symbol
x = 90 - 61
x = 29°
x + y = 90
Because vertically opposite angles are equal
29 + y = 90
y = 90 - 29
y = 61°
Answer:
Total number of quarters=10
Total number of nickels=19
Step-by-step explanation:
The expression for the total value of money you have is;
Quarters have a value of= $0.25
Nickels have a value of= $0.05
Total value=(value of quarters×number of quarters)+(value of nickels×number of nickels)
where;
Total value=$3.45
Value of a quarter=$0.25
number of quarters=x
Value of a nickel=0.05
number of nickels=y, but y=x+9
replacing;
3.45=(0.25×x)+0.05(x+9)
3.45=0.25 x+0.05 x+0.45
3.45=0.3 x+0.45
0.3 x=3.45-0.45
0.3 x=3
x=3/0.3
x=10
y=x+9=10+9=19
Total number of quarters=10
Total number of nickels=19
<span>Let be A =a3b +9a2b2-4ab5, and B=a3b-3a2b2+ab5,so the difference can be defined as A - B =a3b +9a2b2-4ab5 -(a3b-3a2b2+ab5), when there is negative sign in front of the parathesis, all the inside signs must change: that is as follow: A- B= a3b +9a2b2-4ab5 - a3b + 3a2b2 - ab5= a3b-a3b +9a2b2+3a2b2-4ab5- ab5= 12a2b2 -5ab5, the fist term has 2+2=4, as a degree,the second term has 1 +5 =6, so the true answer : The difference is a binomial with a degree of 6</span>
Answer:
point D
Step-by-step explanation:
think about it....y = x.....this is saying that x and y are equal
now look at point D. (-3,-3)...x = -3 and y = -3
therefore, y = x
the rest of them dont work
because on A, 1 does not equal -1
because on B, 4 does not equal 2
because on C, -3 does not equal 3
