Answer:
x=43°
Step-by-step explanation:
The angles are adjacent and create a straight line so their sum is 180°.
(x+6)°+(3x+2)°=180°
x°+6°+3x°+2°=180°
4x°+8°=180°
4x°=172°
x=43°
Answer:
Therefore the value of x is 5.
Step-by-step explanation:
Given:
△ABC ≅ △DEF,
EF = x 2 - 7, and
BC = 4x - 2.
To Find:
the values of x. = ?
Solution:
△ABC ≅ △DEF ........Given
If two Triangles are congruent then the Corresponding Parts of Congruent Triangles are Congruent.
∴ BC ≅ EF ...................CPCTC
Substituting the values we get

Now By Factorizing we get

Therefore the value of x is 5.
Answer: I think that the answer is D
Step-by-step explanation:
Steps to simplify:
(2x + 3)(x - 7)
~Use FOIL to multiply
(2x * x) + (2 * -7) + (3 * x) + (3 * -7)
~Simplify
=2x² - 14x + 3x - 21
~Combine Like Terms
2x² + (-14x + 3x) - 21
~Simplify
2x² - 11x - 21 (Option 2)
Best of Luck!
A good place to start is to set
to y. That would mean we are looking for
to be an integer. Clearly,
, because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since
is a radical, it only outputs values from
, which means y is on the closed interval:
.
With that, we don't really have to consider y anymore, since we know the interval that
is on.
Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval
, which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:

Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.