If angle ABC is one degree less than three times angle ABD and angle DBC=47 find each measure
1 answer:
It has not been indicated whether the figure in the questions is a triangle or a quadrilateral. Irrespective of the shape, this can be solved. The two possible shapes and angles have been indicated in the attached image.
Now, from the information given we can infer that there is a line BD that cuts angle ABC in two parts: angle ABD and angle DBC
⇒ Angle ABC = Angle ABD + Angle DBC
Also, we know that angle ABC is 1 degree less than 3 times the angle ABD, and that angle DBC is 47 degree
Let angle ABD be x
⇒ Angle ABC = 3x-1
Also, Angle ABC = Angle ABD + Angle DBC
Substituting the values in the above equations
⇒ 3x-1 = x+47
⇒ 2x = 48
⇒ x = 24
So angle ABD = 24 degree, and angle ABC = 3(24)-1 = 71-1 = 71 degree
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Answer is B. 44
Hope this helps. - M
System of inequalities representing given scenario is as follows
x + y ≤40
5x + 4y ≥ 120
<h3><u>Solution:</u></h3>Given that Sara sells homemade blueberry jelly (b) and strawberry jam (s) at the farmer's market. She has enough berries for no more than 40 jars.
The blueberry jelly sells for $5 per jar,
And the strawberry jam sells for $4 per jar.
Sara's goal is to make at least $120
Need to write system of inequalities for above scenario.
Let’s assume number of jars of blueberry jelly be represented by variable “x”
And assume number of jars of strawberry jam be represented by variable “y”
<em><u>Let’s create first inequality </u></em>
As it is given that Sara has enough berries for no more than 40 jars, so total number of jars cannot be more than 40.
=> Number jars of blueberry jelly + number of jars of strawberry jam ≤40
=> x + y ≤ 40 ------(1)
<em><u>Now let’s create second inequality </u></em>
Selling Price of 1 blueberry jelly = $5
So Selling Price of "x" blueberry jelly
Selling Price of 1 strawberry jam = $4
So Selling Price of "y" strawberry jam =
So amount generated by selling x blueberry jelly and y strawberry jam = 5x + 4y
And as Sara’s goal is to generate at least $120, so amount generated by selling “x” blueberry jelly and “y” strawberry jam must be greater than $120
=> 5x + 4y ≥ 120 ------ (2)
Hence system of inequalities representing given scenario is as follows :
x + y ≤40
5x + 4y ≥ 120