Ages of Dan and Cary are 29 and 33 respectively.
<u>Step-by-step explanation:</u>
Step 1:
Form equations out of the given details. Let the age of Dan be x, then age of Cary is x + 4.
In 7 years, sum of their ages = 76
⇒ (x + 7) + (x + 4 + 7) = 76
⇒ 2x + 18 = 76
⇒ 2x = 58
⇒ x = 29
Step 2:
Calculate age of Cary.
⇒ x + 4 = 33
Brady studied for 4.5 hours that week
How we determine the total study hours?
The total study hours for Brady is the sum of the hours used in studying on Monday, Tuesday, Wednesday and Thursday.
He studied for 1.5 hours on Monday
He studied for 0.75 hours on Tuesday
He studied again for 1.25 hours on Wednesday
Lastly, he studied for 1 hour on Thursday, the last day
Total number of study hours=1.5+0.75+1.25+1
Total number of study hours=4.50
Find out more about study hour on: brainly.com/question/876733
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DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.
<h3>
Congruent shape</h3>
Two shapes are said to be congruent if they have the same shape, all their corresponding angles and sides are congruent to one another.
Given that DE = AB and BC = EF.
In right triangle DEF, using Pythagoras:
DF² = DE² + EF²
Also, In right triangle ABC, using Pythagoras:
AC² = AB² + BC²
But DE = AB and EF = BC, hence:
AC² = DE² + EF²
AC² = DF²
Taking square root of both sides, hence:
AC = DF
Since DE = AB, EF = BC and AC = DF, hence triangle ABC is congruent to triangle DEF.
Find out more on Congruent shape at: brainly.com/question/11329400
sin α = opposite leg/ hypotenuse
For ΔABC,
sin A = |BC|/|AB|
sin A = 12/37
Y=6.75x
He charges $6.75 per hour
