Answer:
x = 7
Step-by-step explanation:
Given:
∠DEF = 117°
∠DEG = (12x + 1)°
∠GEF = (5x - 3)°
Find:
value of x
Computation:
∠DEF = ∠DEG + ∠GEF
117° = (12x + 1)° + (5x - 3)°
117° = 17 x - 2
x = 7
Lines j and k are intersected by line m. At the intersection of lines j and m, the uppercase left angle is 93 degrees. At the in
tersection of lines k and m, the bottom right angle is 93 degrees. Given the information in the diagram, which theorem best justifies why lines j and k must be parallel? a) alternate interior angles theorem b) alternate exterior angles theorem c) converse alternate interior angles theorem d) converse alternate exterior angles theorem
2 answers:
Answer:
b) alternate exterior angles theorem
Step-by-step explanation:
When two lines are cut by a transversal, the alternate exterior angles are congruent. In the first diagram:
- x and y are congruent
- a and b are congruent
Comparing with our given lines, j, k and m.
We can see that the two given angles are in the same position as in the first image. Therefore, lines j and k are parallel by the alternate exterior angles theorem.
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It is recommended that adults consume at least 1,000 mg of calcium every day.
Step-by-step explanation:
Let, x be the quantity of milk in ounces and y be the quantity of cheddar cheese in ounces.
A person meets the recommendation, if
For option A,
Substitute x=50 and y=2 in the given inequality.
This statement is true. So, option A is correct.
Similarly,
For option B,
Substitute x=0 and y=4.5 in the given inequality.
This statement is false. So, option B is incorrect.
For option C,
Substitute x=10 and y=3 in the given inequality.
This statement is false. So, option C is incorrect.
For option D,
Substitute x=39 and y=0 in the given inequality.
This statement is false. So, option D is incorrect.
Therefore, the correct option is only A.
The fraction which produce an equivalent fraction with a rational denominator is
Explanation:
The equation is
To find the rational denominator, let us take conjugate of the denominator and multiply the conjugate with both numerator and denominator.
Rewriting the equation, we have,
Multiplying, we get,
Simplifying the denominator, we get,
Subtracting, the values of denominator,
Dividing the numerator and denominator,
Hence, the denominator has become a rational denominator.
Thus, the fraction which produce an equivalent fraction with a rational denominator is