8x-2=-9+7×
Answer:
Step-by-step explanation:
To find the measure of angle DBC, we can use the angle bisector theorem, which states that in a triangle, if a line bisects one of the angles, it divides the opposite side into segments proportional to the other two sides. In this case, BD bisects angle ABC, so:m∠ABD / m∠DBC = AB / BCWe are given:
m∠ABC = 8x
m∠ABD = 2x + 30So, we have:(2x + 30) / m∠DBC = AB / BCNow, we need to express AB / BC in terms of x. To do that, we'll use the fact that angles in a triangle add up to 180 degrees:m∠ABC + m∠ABD + m∠DBC = 180Substitute the given angle measures:8x + (2x + 30) + m∠DBC = 180Combine like terms:10x + 30 + m∠DBC = 180Now, isolate m∠DBC:m∠DBC = 180 - 10x - 30
m∠DBC = 150 - 10xNow, we can substitute this expression for m∠DBC back into our proportion:(2x + 30) / (150 - 10x) = AB / BCNow, you can solve for m∠DBC:Cross-multiply:(2x + 30)(BC) = (150 - 10x)(AB)Now, you would need more information about the relationship between AB and BC or additional angle measures to solve for the exact value of m∠DBC. Without that additional information, you can't determine the specific angle measure.
|x| < -1
|x| = -1
|x| > -1
The solution sets is all real numbers in case of:
|x| > -1
We know that modulus is a function with the property such that:
if a<0 then |a|= -a
that is the modulus of a negative number is positive and if a≥0
then |a| =a
and modulus of a positive value is also positive.
i.e. modulus function always gives positive value.
Hence,
1)
|x|<-1
This is not possible as modulus function always gives a value ≥0 for all real numbers.
2)
|x|= -1
This is also not possible as modulus of any number can't be negative.
3)
|x| > -1
The modulus of any number will definitely be greater than or equal to zero.
Hence, the solution set contain all the real numbers.
n + (n + 1) + (n + 3) = 36
n + (n + 1) + (n + 2) = 36
n + (n − 1) + (n − 3) = 36
Let
n--------> the first integer
n+1------> the second consecutive integer
n+2-----> the third consecutive integer
we know that
the numbers are
therefore
the answer is
The equation is