If l is parallel to m, find the value of each missing variable
1 answer:
Answer:
x = 18
y = 5
Step-by-step explanation:
From the figure attached,
'l' and 'm' are the parallel lines and two transversal lines are intersecting these parallel lines at points A, B and C.
Since, m∠ABC + (7x - 23)° = 180° [Supplementary angles]
m∠ABC = 180° - (7x - 23)°
m∠BCA = (11y - 1)° [Vertical angles]
m∠BAC = 49°
In ΔABC,
m∠ABC + m∠BAC + m∠CAB = 180°
180° - (7x - 23)° + 49° + (11y - 1) = 180°
-7x + 11y = -71
7x - 11y = 71 ------(1)
Since, sum of consecutive angles is 180°
Therefore, m(∠ABC) + (3x + 49)° = 180°
180° - (7x - 23)° + (3x + 49)° = 180°
-4x = -72
x = 18
From equation (1),
7(18) - 11y = 71
11y = 55
y = 5
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The apprentice needs 6.25 hours to complete the job using the brush
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While his apprentice can paint 85 square feet of surface area per hour with a brush
Together they are painting a building with a surface area of 5100 square feet.
After painting for hours , the master painter lets the apprentice Finish the job.
Now, they worked for hours
Then, area painted = area painted by master + area painted by apprentice
Now, the remaining area to be painted = total area – painted area
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So, apprentice has to paint 531.25 square feet alone.
Hence, the apprentice needs 6.25 hours to complete the job
Answer:
See attachment
Step-by-step explanation:
The mapping for a dilation with a scale factor k, about the origin is given by:
From the graph, the coordinates of B are (1,1) and the scale factor is k=4.
We substitute into the rule to get
The image of point B is plotted on the graph in the attachment.
