a. x = 50, the measure of ∠A = 170°.
b. y = 7, the measure of FE = 14, AB = 14.
In the question, we are given that ΔABC ≅ ΔEFG, that is, triangle ABC is congruent to triangle EFG.
As we know that corresponding parts of congruent triangles are also congruent,
we can write that:
∠A = ∠E,
∠B = ∠F,
∠C = ∠G,
AB = EF,
BC = FG, and
CA = GE.
Now,
a. We are asked to solve for x.
We know that:
∠A = ∠E,
or, 3x + 20 = 5x - 80,
or, 3x - 5x = -80 - 20,
or, -2x = -100,
or, x = -100/-2 = 50.
Also, we are asked to find the measure of ∠A.
∠A = (3x + 20)° = (3*50 + 20)° = 170°.
b. We are asked to solve for y.
We know that,
AB = EF,
or, y + 7 = 3y - 7,
or, y - 3y = - 7 - 7,
or, -2y = -14,
or, y = -14/-2 = 7.
Also, we are asked to find the measure of FE and AB.
FE = 3y - 7 = 3*7 - 7 = 14.
AB = y + 7 = 7 + 7 = 14.
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Answer:
3
Step-by-step explanation:
As with any other addition fact problem, you can isolate the unknown term by subtracting the unwanted constant.
5/7 +x/6 = 51/42
x/6 = 51/42 -5/7 . . . . . subtract 5/7 from both sides
x/6 = 51/42 -30/42 = 21/42 = 1/2 . . . . . complete the subtraction
x = 6(1/2) = 3 . . . . . . . . multiply by 6
The missing numerator is 3.
_____
<em>Alternate solution</em>
Multiply the equation by 42:
30 +7x = 51
7x = 51 -30 = 21 . . . . . subtract 30
x = 21/7 = 3 . . . . . . . . divide by the coefficient of x
Using a system of equations, the amount of solution a and b required to make the required gallons of the solution are 29.41 and 20.59 respectively.
Let :
- Solution with 24% acid = a
- Solution with 41% acid = b
a + b = 50 - - - - (1)
0.24a + 0.41b = 50 × 0.31
0.24a + 0.41b = 15.5 - - - - (2)
From (1) :
a = 50 - b - - - - (3)
<em>Substituting</em><em> </em><em>(</em><em>3</em><em>)</em><em> </em><em>into</em><em> </em><em>(</em><em>2</em><em>)</em>
0.24(50 - b) + 0.41b = 15.5
12 - 0.24b + 0.41b = 15.5
0.17b = 15.5 - 12
0.17b = 3.5
b = 20.588
From (3) :
a = 50 - 20.588
a = 29.412
Therefore, about 29.41 gallons of solution a and 20.59 gallons of solution b is required.
Learn more : brainly.com/question/25449918
Answer: 8/12
Step-by-step explanation:
1/4 times 3 will give you 3/12 and add 5/12
