Suppose that you want to mix two coffees in order to obtain 100 pounds of a blend. If x represents the number of pounds of coffe
1 answer:
Answer:
Therefore, the algebraic exp
Step-by-step explanation:
Given : x represents the number of pounds of coffee A.
The total weight of the mix of coffee A and coffee B = 100 pounds.
Then , we have the following expression to represents the number of pounds of coffee B:-
Therefore, the algebraic expression that represents the number of pounds of coffee B. :-
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Answer:
Options (3) and (6)
Step-by-step explanation:
ΔABC is a dilated using a scale factor of to produce image triangle ΔA'B'C'.
Since, dilation is a rigid transformation,
Angles of both the triangles will be unchanged or congruent.
m∠A = m∠A' and m∠B = m∠B'
Since, sides of ΔA'B'C' = of the sides of ΔABC
Area of ΔA'B'C' =
Area of ΔABC > Area of ΔA'B'C'
Since, angles of ΔABC and ΔA'B'C' are congruent, both the triangles will be similar.
ΔABC ~ ΔA'B'C'
Therefore, Option (3) and Option (6) are the correct options.
Refer to the diagram below.
Because ray NP bisects ∠MNQ, therefore
∠MNP = ∠PNQ = 2x + 1.
Therefore
∠MNQ = 2*∠PNQ = 2(2x + 1) = 4x + 2.
Because ∠MNQ is given as x² - 10, therefore
x² - 10 = 4x + 2
x² - 4x - 12 = 0
(x + 2 )(x - 6) = 0
x = -2, or x = 6
When x = -2,
∠MNQ = 4*(-2) + 2 = -6°
This answer is not acceptablle, therefore x = -2 should be rejected.
When x = 6,
∠MNQ = 4*6 + 2 = 26°
Answer: x = 6, and ∠MNQ = 26°
Because ray NP bisects ∠MNQ, therefore
∠MNP = ∠PNQ = 2x + 1.
Therefore
∠MNQ = 2*∠PNQ = 2(2x + 1) = 4x + 2.
Because ∠MNQ is given as x² - 10, therefore
x² - 10 = 4x + 2
x² - 4x - 12 = 0
(x + 2 )(x - 6) = 0
x = -2, or x = 6
When x = -2,
∠MNQ = 4*(-2) + 2 = -6°
This answer is not acceptablle, therefore x = -2 should be rejected.
When x = 6,
∠MNQ = 4*6 + 2 = 26°
Answer: x = 6, and ∠MNQ = 26°