Answer:
m < S = 40°
Step-by-step explanation:
According to the Triangle Exterior Angle Postulate, the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
The exterior angle is m < R = 140°. In reference to the Triangle Exterior Angle Postulate, the sum of the measures of < T and < S must equal 140°.
Given m < T = (8x + 4)°
m < S = (3x + 4)°
We can set up the following equality statement to solve for the value of x:
m < R = m < T + m < S
140° = (8x + 4)° + (3x + 4)°
Combine like terms:
140° = 11x + 8
Subtract 8 from both sides:
140° - 8 = 11x + 8 - 8
132° = 11x
Divide both sides by 11:
132°/11 = 11x/11
12 = x
Substitute the value of x into the equality statement to verify whether it is the correct value:
140° = (8x + 4)° + (3x + 4)°
140° = [8(12) + 4]° + [3(12) + 4]°
140° = (96 + 4)° + (36 + 4)°
140° = 100° + 40°
140° = 140° (True statement. Therefore, the correct value for x = 12).
Therefore, m < S = (3x + 4)° = [3(12) + 4]° = 40°
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Answer:
The least number of calories possible in a package is 129 calories.
Step-by-step explanation:
We can write equations to representeach requirement of the snack.
Fruit:0 protein
2 carb
1 fat
18 cal
Nuts: 3 prot
1 carb
2 fat
28
The amount of protein contained in the final snack will be: the sum of the amount of ounces of fruit (and nuts) times the amount of protein pero ounce of fruit(and nuts). So for N, M integers or decimals:
Protein=N*0 carbs+M*3 carbs , this means that fruit doesn't affect protein content.
Similarly we write the other requirements as inequalities:
a.Protein≥9 → N*0+M*3≥9
b.Carbs≥8 → N*2+ M*1≥8
c.Fat≤9 → N*1+M*2≤9
d. Cal=N*18+M*28
From a we get M≥3
Replacing M in b, N≥2.5.
And finally we replace in c to have a maximum amount.
2.5+2*3≤9
8.5<9 so this is the least amount of ounces in a package, avaluating how many calories each component contributes:
Least amount of calories: 18*2.5+28*3=129cal
Answer:
The solution is obtained by adding the two equations.
The solution is: (x, y) = (
, 
)
Step-by-step explanation:
We are given two equations with two variables. The strategy is to eliminate one variable and solve for both the variables.
The two equations are:
Adding both the equations, we get:
Substituting the value of 'x', we get the value of y.
We substitute in (2). [Can be substituted in any equation].
We get: y = 2x - 1
So, we get the corresponding values of x and y which is the solution of the two equations.
Answer:
bc= 7
Step-by-step explanation:
Answer:
99-7a^2=36 when a =3
Step-by-step explanation:
99-7a²
99-7(3)²
99-7(9)
99-63
36
