Answer:
1. 8.85 quarts
2. 44.25%
Step-by-step explanation:
In 15 quarts of a solution with percentage of antifreeze = 35%
Amount of antifreeze = 35% × 15
= 0.35 × 15
= 5.25 quarts
that solution is mixed with 5 quarts of a solution with percentage of antifreeze = 72%
Amount of antifreeze = 72% × 5
= 0.72 × 5
= 3.6 quarts
Total amount of mixture = 15 quarts + 5 quarts = 20 quarts
1. Now we will calculate the total amount of antifreeze in the resulting mixture.
= 5.25 + 3.6 = 8.85 quarts
2. The percentage of the resulting mixture is antifreeze
= 
= 44.25%
1. total amount of antifreeze is 8.85 quarts
2. the percentage of antifreeze is 44.25%
angle AOB = 132 and is also the sum of angles AOD and
DOB. Hence
angle AOD + angle DOB = 132° ---> 1
angle COD = 141 and is also the sum of angles COB and BOD. Hence
angle COB + angle DOB = 141° ---> 2
Now we add the left sides together and the right sides of equations 1 and 2
together to form a new equation.
angle AOD + angle DOB + angle COB + angle DOB = 132 + 141 ---> 3
We should also note that:
angle AOD + angle DOB + angle COB = 180°
Therefore substituting angle AOD + angle DOB + angle COB in equation 3 by 180
and solving for angle DOB:
180 + angle DOB = 132 + 141
angle DOB = 273 - 180 = 93°
Answer:
97,99,101,103
Step-by-step explanation:
Let x = first odd integer
x+2 = 2nd odd integer
x+4 = 3rd odd integer
x+6 = 4th odd integer
Sum of 4 odd integers is 400
x+ (x+2) + (x+4)+(x+6) = 400
Combine like terms
4x +12 = 400
Subtract 12 from each side
4x+12-12 = 400-12
4x = 388
Divide by 4 on each side
4x/4 = 388/4
x=97
The first integer is 97
The 2nd is 97+2 =99
The third ix 97+4 = 101
The 4th is 97+6 = 103
Answer:
Yes, △ABC ∼ △FED by AA postulate.
Step-by-step explanation:
Given:
Two triangles ABC and FED.
m∠A = m∠B
m∠C = m∠A + 30°
m∠E = m∠F = 
m∠D = 
°.
Now, let m∠A = m∠B = 
So, m∠C = m∠A + 30° = 
Now, sum of all interior angles of a triangle is 180°. Therefore,
m∠A + m∠B + m∠C = 180
Therefore, m∠A = 50°, m∠B = 50° and m∠C = m∠A + 30° = 50 + 30 = 80°.
Now, consider triangle FED,
m∠D+ m∠E + m∠F = 180
Therefore, m∠F = 50°
m∠E = 50° and
m∠D = 
So, both the triangles have congruent corresponding angle measures.
m∠A = m∠F = 50°
m∠B = m∠E = 50°
m∠C = m∠D = 80°
Therefore, the two triangles are similar by AA postulate.
