Lucy has to run two errands. She starts from home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. Then, from the gas station, she travels 5 miles to return home. The entire trip forms a triangle. What was the smallest angle made in her trip?
Answers
Answer:
Smallest angle = [tex]36.87^\circ[/tex]
Step-by-step explanation:
Given that:
Let the home be at the point A.
Lucy travels 3 miles south to reach point B.
Then 4 miles to east to reach point C and then
returns to home traveling 5 miles making it a triangle for the whole journey.
This travel is nothing but forms a right angled [tex]\triangle ABC[/tex], right angled at point B.
To find:
Smallest angle in the travel.
Solution:
In a triangle, the smallest angle is the angle opposite to the smallest side.
Therefore, the [tex]\angle C[/tex] will be the smallest.
We can use tangent trigonometric ratio here:
[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan C = \dfrac{AB}{BC}\\\Rightarrow tan C = \dfrac{3}{4}\\\Rightarrow \angle C=tan^{-1}{0.75}\\\Rightarrow \angle C=36.87^\circ[/tex]
Therefore, the answer is:
Smallest angle = [tex]36.87^\circ[/tex]
Related Questions
What is the simple Intrest to 1,250 at 4.5% for 2 years
Answers
Answer:
1,362.50 Dollars
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 4.5%/100 = 0.045 per year.
Solving our equation:
A = 1250(1 + (0.045 × 2)) = 1362.5
A = $1,362.50
Then You Get 1362.50 Dollars
Glen is making accessories for the soccer team. He uses 536.25 inches of fabric on headbands for 37 players and 2 coaches. He also uses 325.97 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
Answers
Answer:
For Headband
Each player used 13.75 inches of fabric
For Wristband
Each player used 8.81 inches of fabric
Step-by-step explanation:
Glen is making accessories for the soccer team.
For head bands :
He uses 536.25 inches of fabric on headbands for 37 players and 2 coaches.
Let the inches of fabric used be represented by x
536.25 = 37 x + 2x
536.25 inches = 39x
x = 536.25 inches/39
x = 13.75 inches of fabric.
For Wristbands
He also uses 325.97 inches of fabric on wristbands for just the players.
Let y represent the inches of fabric used for players
We have 37 players
Hence:
325.97 = 37y
y = 325.97 inches/37
y = 8.81 inches
Therefore:
For Headbands
Each player used 13.75 inches of fabric
For Wristbands
Each player used 8.81 inches of fabric
There are 7 fourth-grade classes at Grant Elementary. Each class has 28 students. About how many students are in the fourth grade at Grant Elementary?
28 students
140 students
О 210 students
• 280 students
Answers
Answer:
by inuv6gh8vig
Step-by-step explanation:
rydyctcyvuvubig8g
Answer:
210
Step-by-step explanation:
because you multiply 7 and 28 to get 196, and 210 is the closest thing to that. Hope this helped
: )
Which of these statements is true for f(x) = (9/10)X?
O A. It is always decreasing.
B. The domain of f(x) is x > 0
C. The range of f(x) is y > 9/10
D. The y-intercept is (0,1)
Answers
PLEASE HELP, DUE TODAY AND IM STUCK, ITS TWO QUESTIONS, WILL GIVE BRAINLIEST ♥
Drop down options for #4:
13
4x
-4x
3
-3
Answers
Answer:
#4: Blank 1: 4x, Blank 2: 3; #5: A) or D)
Step-by-step explanation:
Question 4: 4x, 3
Divide using the rules of synthetic divison (see Khan Academy)Blank 1: 4xBlank 2: 3Question 5: A) or D)
B) and C) are automatically out- they have the wrong notationIt's either A) or D) - don't know for sure7b−15=5b−3 solve for b
Answers
Step-by-step explanation:
7b-5b=-3+15
2b=12
b=12/2
b=6
Answer:
[tex]b = 6[/tex]
Step-by-step explanation:
1.) We need to manipulate the equation to get b by itself.
2.) Subtract 5b from each side. Combine like terms. Add 15 to each side. Combine like terms. Divide each side by 2. Simplify.
Ruben brought 2 large popcorn buckets and 4 small drins for 20. Lucia bought 2 large popcorn buckets and 2 small drinks for 14.What was the cost of the large popcorn and the small drinks
Answers
Answer:
Cost of large popcorn = 4
Cost of small drinks = 3
Step-by-step explanation:
Given that :
Let cost of large popcorn = x
Cost of small drinks = y
Cost of 2 large popcorn and 4 small drinks
2x + 4y = 20
2x + 2y = 14
x + 2y = 10 - - - (1)
x + y = 7 - - - (2)
Subtract :
2y - y = 10 - 7
y = 3
Substitute y = 3 into (2)
x + 3 = 7
x = 7 - 3
x = 4
Hence,
Cost of large popcorn = 4
Cost of small drinks = 3
5 1/5 + 4 3/5 please help
Answers
Answer:
9 4/5
Step-by-step explanation:
5 1/5+4 3/5
26/5+23/5
lcm of the denominator is 5
26+23 everything all over 5
49/5
9 4/5
Answer:
9
Step-by-step explanation:
5 1/5 + 3 3/5 =
26/5 + 18/5 =
45/5 =
9
8One fifth of a number plus three times the number is equal to twice the
number plus 42. What is the number?
Show your work
Answers
Answer:
x=-7
Step-by-step explanation:
Set up an equation: 1/5x+3x=2x+42 This is the equation. Now solve.x+3x=10x+42 4x=10+42 6x=-42 x=-7 Hope this helps :D
an oil company fills 1/12 of a tank in 1/3 hour. At this rate, which expression can be used to determine how long it will take for the tank to fill completely?
A) 1/12 • 3 hours
B) 1/3 • 12 hours
C) 1/3 • 1/12 hour
D) 3 • 12 hours
Answers
Answer:
It's C
Step-by-step explanation:
Correct me if i'm wrong.
But it seems to make sense with my calculations....
Sue is shopping for a turkey. At Stater Bros., she found an 18 lb turkey for $21.42. At Ralphs, she found a 20 lb turkey for $24.20. At Food for Less, she found a 17 lb turkey for $18.36. Tasks: Find the price per pound of each turkey. Stater Bros.: Ralphs: Food for Less: Which store has the best price? Store name:
Answers
Answer: See explanation
Step-by-step explanation:
At Stater Bros., she found an 18 lb turkey for $21.42. The cost per pound will be:
= $21.42 / 18
= $1.19 / lb
At Ralphs, she found a 20 lb turkey for $24.20. The cost per pound will be:
= $24.20 / 20
= $1.21 / lb
At Food for Less, she found a 17 lb turkey for $18.36. The price per pound will be:
= $18.36 / 17
= $1.08 / lb
Based on the explanation, Food for Less has the best price as it's cheaper than others.
Como se resuelve un circuito en serie matemáticamente?
Answers
Answer:
Step-by-step explanation:
En un circuito en serie, toda la corriente pasa a través de cada uno de los resistores, uno a la vez. Esto significa que cada resistor contribuye su resistencia completa al circuito. Si conoces el valor individual de cada resistencia, solo súmalos para encontrar la resistencia total del circuito.
In a series circuit , all of the current passes through each of the resistors, one at a time. This means that each resistor contributes its full resistance to the circuit . If you know the individual value of each resistor, just add them together to find the total resistance of the circuit .
A poster board was cut into equal pieces, and 3 pieces were used for
drawings. The fraction below shows how much of the poster board is left.
According to the fraction, how many pieces were not used for drawings?
8/11
A. 11
B. 8
C. 3
D. 5
Answers
Answer: 8. There were 11 pieces and 3 were used, so 8 are left.
Tammy, Kelley, and Jim love reading books. Tammy read 7.75 hours last month. Kelley read 7.69 hours. Jim read 7.075 hours. Who spent the most time reading
Answers
Answer:
Tammy
Step-by-step explanation:
Tammy read 7.75 hours last month. Kelley read 7.69 hours
Jim read 7.075 hours.
We would arrange the hours of reading from smallest to the highest
7.075, 7.69, 7.75
The person who spent the most time reading is the person with the highest number of hours that was spent reading. This person is Tammy.
Therefore, person who spent the most time reading is Tammy because she read for 7.75 hours.
The person who spent the most time reading is Tammy.
Tammy read 7.75 hours last month reading.Kelley read 7.69 hours reading.Jim read for 7.075 hours.Therefore, from the decimals given, we can see that the highest is 7.75 hours that was used by Tammy.
Learn more about time on:
https://brainly.com/question/2972832
segment QS bisects m
Answers
Answer:
ok
What is your question?
Put your question in the replies to this answer and I'll gladly help you
May I have brainliest please? :)
what is the value of x
Answers
Answer:
11
Step-by-step explanation:
3x+2
3(11)+2
33+2
35
Alright here me out...
if Pinocchio said his nose grows when he lies he would be telling the truth and lying at the same time since his nose didn't grow. So what would happen....
Answers
Answer: Well he didn't lie so his nose wouldn't grow. Can i have brainliest?
Step-by-step explanation:
Hope this helps!!
Engineering=120+22x; Business=105-4x;Biology=98+6x; how many years will it be before Engineering has twice as many students as Business; how many years will it be before Engineering has twice as many students as Biology.
Answers
Answer:
Step-by-step explanation:
Given
Engineering=120+22x;
Business=105-4x;
Biology=98+6x;
If Engineering has twice as many student as biology then,;
120+22x = 2(98+6x)
Expand
120+22x = 196+12x
Collect like terms
120-196 = 12x-22x
-76 = -10x
x = -76/-10
x = 7.6
Hence it will take like 7 and a half years before engineering has twice as many student as biology
find the measure of the missing angles in the kite.
Answers
Angle 1 = 90 degrees
Angle 2 = 63 degrees
Angle 3 = 63 degrees
A car dealer has 120 cars in stock, all either four-door or two-door. There are 4 times as many four-door
cars as two-door cars. How many two-door cars are in stock?
O 24
O 30
0 36
0 40
Answers
Answer:
40
Step-by-step explanation:
can someone help me
Answers
Cody has a bag of 28 pencils. Each pencil is 18 centimeters long. What is the combined length of the pencils in meters?
The total length of all 28 pencils is __ meters.
Answers
Answer:
504
Step-by-step explanation:
A baby grows 4 inches every 6 months. What is his rate of change?
Answers
Answer:
4:6 but if you reduce it is 2:3
Step-by-step explanation:
Find the slope of the line that passes through (10,9) and (5,11)
Answers
Answer:
-2.5
Step-by-step explanation:
Divide: 5 divided by 5/6
Answers
the watch bee would like to buy costs $10 less then 2 times the amount she has saved the watch costs $50. how much money does bee have saved?
Answers
Answer:
20$
Step-by-step explanation:
50 - (2x - 10) = x
50 + 10 = x + 2x
60 = 3x
60/3 = x
20 = x
Mom has ⅘ quart of strawberries. She needs to fill ¼-quart jars. How many jars will she be able to fill?
Answers
Challenge You have 2 different savings accounts. For Account A, the simple interest earned after months is $. For Account B, the simple interest earned after months is $. If the interest rate is % for Account A and % for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer.
Answers
Answer and Step-by-step explanation:
The computation is shown below;
As we know that
The simple interest is
Simple interest = Principal × rate × time
For Account A, the principal would be
2 = Principal × 3.2% × 3
So, the principal is $20.83
For account B, the principal would be
38.50 = Principal × 2.2% × 30
So, the principal is $58.33
Now the interest for both the accounts are as follows
For account 1
= $20.83 × 3.2%
= $0.67
And, for the account 2
= $58.33 × 2.2%
= $1.28
As it can be seen that the account 2 has the highest interest
The same is to be considered
PLEASE HELP ITS DUE AT nov 17 at 11:59
Answers
Suppose the price of admission to the state fair is $9.50, and each ride costs an additional $2.25.
Karen is going to the state fair. If she can spend at most $50, which inequality can be used to solve for r, the number of rides Karen can go on?
A) 9.50 + 2.25r ≥ 50
B) 9.50r + 2.25 ≥ 50
C) 9.50 + 2.25r ≤ 50
D) 9.50r + 2.25 ≤ 50
Answers
Answer:
C
Step-by-step explanation:
You need to multiply the variable by how much each ride costs.