Given:
In ΔHIJ, h = 40 cm, ∠J=20° and ∠H=93°.
To find:
The length of j, to the nearest centimeter.
Solution:
According to Law of sine,
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
In ΔHIJ, using law of sine, we get
[tex]\dfrac{j}{\sin J}=\dfrac{h}{\sin H}[/tex]
[tex]\dfrac{j}{\sin (20^\circ)}=\dfrac{40}{\sin (93^\circ)}}[/tex]
[tex]j=\dfrac{40\times \sin (20^\circ)}{\sin (93^\circ)}}[/tex]
On further simplification, we get
[tex]j=\dfrac{40\times 0.34202}{0.99863}[/tex]
[tex]j=\dfrac{13.6808}{0.99863}[/tex]
[tex]j=13.69958[/tex]
Approximate the value to the nearest centimeter.
[tex]j\approx 14[/tex]
Therefore, the length of j is 14 cm.
A middle school took all of its 6th grade students on a field trip to see a ballet. The students filled 4753 seats, which was 97% of the total number of seats in the theater. How many total seats were in the theater?
Answer:
4900
Step-by-step explanation:
3. Solve the following application of a system of linear equations.
Two students in the same Spanish class, Cindy and Ruben, plan to get together after school to make
vocabulary flashcards. Cindy started on the project yesterday and has already made 14 flashcards.
Ruben hasn't started yet so he has none. Since Cindy makes 9 flashcards per minute and Ruben makes
10 flashcards, Ruben will soon have the same number of flashcards.
Which variables will you use and what do they represent?
Write your system of linear equations below.
Solve the system.
How much time will it take for Cindy and Ruben to have the same number of flashcards?
How many flashcards will each student have at that time?
Answer:
Equations:
[tex]y = 14 + 9 x[/tex] --- Cindy
[tex]y = 10 x[/tex] --- Ruben
Solution to equation:
Time they have the same amount: 14 minutes
Number of cards they have at that time: 140 flashcards
Step-by-step explanation:
Solving (a): Variables and what they represent
The variables to use are x and y
Where x represent the minutes and y represents the number of flashcards in x minutes
Solving (b): System of linear equation
Cindy:
[tex]Existing\ Flashcards = 14[/tex]
[tex]Additional = 9[/tex] per minute
Total number of flashcards (y) in x minutes is:
[tex]y = Existing\ Flashcards + Additional * x[/tex]
[tex]y = 14 + 9 * x[/tex]
[tex]y = 14 + 9 x[/tex]
Ruben:
[tex]Rate = 10[/tex] per minute
Total number of flashcards (y) in x minutes is:
[tex]y = Rate * x[/tex]
[tex]y = 10 * x[/tex]
[tex]y = 10 x[/tex]
Solution to Equations:
Time they have the same amount.
To do this, we [tex]equate[/tex] [tex]both[/tex] expressions
i.e.
[tex]10x = 14 + 9x[/tex]
Collect Like Terms
[tex]10x - 9x = 14[/tex]
[tex]x = 14[/tex]
Number of cards they have at that time.
Here, we simply substitute 14 for x in any of the equations.
[tex]y = 10 x[/tex]
[tex]y = 10 * 14[/tex]
[tex]y = 140[/tex]
or
[tex]y = 14 + 9 x[/tex]
[tex]y = 14 + 9 * 14[/tex]
[tex]y = 14 + 126[/tex]
[tex]y = 140[/tex]
24/30 in the simplest form
Answer:
The answer to this question is 4/5.
Answer:
4/5 or 0.8
Step-by-step explanation:
we divide tap and bottom by 6.
Help me pleaseeeeeeeeeeee
Answer:
they first answer or a
Step-by-step explanation:
because if you look at stage direction he is just facing the crowd
Answer:
The stage direction shows how King Frederick looks when he speaks.
Step-by-step explanation:
40 POINTS Geometry homework
[tex]\angle{DBC }[/tex]=(5x+4)°
[tex]\angle{ A }[/tex]=(2x-2)°
[tex]\angle{C }[/tex]=(4x-6)°
we know that,
[tex]\angle{DBC}[/tex]=[tex]\angle{A}[/tex]+[tex]\angle{C}[/tex]
According to the question,
[tex]\tt{ 5x+4=2x-2+4x-6 }[/tex]
[tex]\tt{ 5x+4=6x-8 }[/tex]
[tex]\tt{ 6x-5x=4+8 }[/tex]
[tex]\blue{x=12 }[/tex]
so,
[tex]\angle{C }[/tex]=(4x-6)°=(4×12-6)°=(48-6)°=42°
Need help :) plss will mark brainliest
Answer:
C
Step-by-step explanation:
Solve (x + 3)2 - 5 = 0 using the quadratic formula.
A) x= 3 + 15 , x= 3 - 15
OB) x= 3
C) x= -3
ODx= -3 + 15x= -3 - 15
Answer:
x=−3±√5
Decimal Form:
x=−0.76393202…,−5.23606797
So D would be your answer
Step-by-step explanation:
Sunny made 2 pitchers of strawberry smoothies for the science club. If each person got One-fifth of a pitcher, how many science club members are there?
2 area models. Both models are made up of 5 shaded parts.
Which statements are true?Check all that apply.
The correct division problem is One-fifth divided by 2.
The correct division problem is 2 divided by one-fifth.
The quotient isStartFraction 1 Over 10 EndFraction.
The quotient is 10.
There are 10 members in the science club.
There are StartFraction 1 Over 10 EndFraction members in the science club.
Answer:
tell me what grade u are in and I will try my best to help
Answer:WAIT I HAVE IT
Step-by-step explanation:
If point E is the midpoint of segment AC and point D is the midpoint of segment BC, which expression represents the value of u?
A. u equals p over q
B. u = 1/2s
C. u equals q over p
D. u = 2s
Answer:
last answer D
i took the test
The expression that most effectively represents u's value would be:
D). u = 2s
What is expression?An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
Given that,
In ΔABC, E is the midpoint in the segment AC and D is the midpoint of BC.
Now,
CE = 0.5 × AC(midpoint)
CD = 0.5 × CB (midpoint)
Thus,
CE/AC = CD/CB = ED/AB = 1/2
As ED = s and AB = u
So, u = 2s
Learn more about concept here:
brainly.com/question/13330632
#SPJ2
12) Abhasra invests $5,323 in a savings
account with a fixed annual interest rate of
9% compounded continuously. What will
the account balance be after 5 years?
Answer:
$7,7748.35
Step-by-step explanation:
$5,323$7748.35 + $2,395.35(INTEREST)
MR Collins made a scatter plot to show the relationship between the number of absences a student in her class has the student final exam score
Mental Math A typical tip in a restaurant is 15% of the total bill. If the bill is $60, what would the
typical tip be?
The typical tip would be $1.
Answer:
It would be $9.
Because 60 * 0.15 = 9
Step-by-step explanation:
McDonalds sold 7 boxes of chicken nuggets for $25.90 Burger King sold 3 boxes of chicken fingers for $11.07. Which food item has a higher unit price? (1 Point McDonalds O Burger King.
Answer:
burger king
Step-by-step explanation:
math
A test of a new car results in 300 miles on 10 gallons of gas. How far could you drive on 45 gallons of gas?
Question 5 options:
1350 miles
67 miles
670 miles
135,000 miles
Answer:
1350
Step-by-step explanation:
300x4=1200
300×.5=150
1200+150=1350
y-2=1/4(x-3)
how can i graph this?
Answer:
your anwer is x=4y-5
Step-by-step explanation:
plssss it’s due in 5 min answer plsss
write the fraction of 7/14in it's simple form
Answer:
1/2
Step-by-step explanation:
Divide both parts by 7
1/2
Hope this helps :)
what is 10:40 plus 7:15 in time?
Answer:
5:55
Step-by-step explanation:
just add it up and you'll get the answer which is 5:55
Answer:5:55
Step-by-step explanation: lol
if the number of boys to girls in gym class is 2:3, what could be the number of students in the gym class
Answer:
I think that it is 5
Step-by-step explanation:
There are 2 boys and 3 girls.3+2=5
Please tell me if I'm right.
Jared and Pedro walk 1 mile in about 15 minutes. They can keep up pace for several hours. About how far they walk in 65 minutes
Jared and Pedro walked a total of 4.3 miles
Step-by-step explanation:The equation for distance is speed = distance ÷ time.Rearrange the equation to make distance the subject:(multiply both sides by time)
Distance = Speed × Time
Convert your numbers into suitable units:1 mile ÷ 15 = 0.06m/minute
Finally, substitute the numbers into the equation and solve:Distance = 0.06 × 65 = 4.3miles (rounded to the nearest decimal place)
What is the value of the value below.
4/5+3/5+3.5*5
Answer:
18.9
Step-by-step explanation:
1. What is the place value of the 5 in the number 1,589,302? *
hundreds
O hundred thousands
millions
Answer:
Hundred thousand
Step-by-step explanation:
500,000
Tamara has $42.00 to buy party decorations. She wants to buy 3 packs of party hats, 2 bags of balloons, and a banner
Answer:
Step-by-step explanation:
Add everything together then you get 22.02 and she could buy everything but you gotta figure out the other part b bc I’m stuck on it
help as fast as you can!!!!!! Any living thing is called an organism,no matter if it is one-celled or many-celled. True or False?.
Answer:
true
Step-by-step explanation:
Answer:
TRUE.
Step-by-step explanation:
PLS HELP! URGENT!
The sides of a square are 5 square root of 2 inches long. What is the area of the square? (3 points)
20 in2
10 square root of 2 in2
50 in2
25 square root of 2 in2
Answer:
A
Step-by-step explanation:
Answer: 25 radical 2 in^2 i think
Step-by-step explanation:
Which of the fractions is equivalent to 2/5 ?
5/2
4/25
12/15
4/10
Answer:
4/10
Step-by-step explanation:
4/10 simplifies to 2/5
4/2 = 2
10/2 = 5
The graph below shows where the two functions y = f(x) and y = g(x) intersect. Solve the equation f(x) = g(x).
The solutions of the equation f(x) = g(x) are (4, 8) and (-2, 2).
We have a graphical representation of two functions f(x) and g(x) and where they intersect.
We have to solve the equation f(x) = g(x)
Two functions A(x) and B(x) are plotted on the graph such that these these two functions intersect each other at three different coordinates. The total number of solutions possible for - A(x) = B(x) is ?The total number of solutions can be calculated by counting the points at which these curves intersect each other. Hence, the total number of possible solutions are 3.
In the question given - We have a straight line and a parabola -
Now, we just have to look at the points at which these two graphs intersect each other. It can be seen that - both the graphs cut each other at coordinates - (4, 8) and (-2, 2).
Hence, the solutions of the equation f(x) = g(x) are (4, 8) and (-2, 2).
Alternative Method -
The general equation of straight line is : y = mx + c and that of parabola is : y = [tex]\sqrt{4ax}[/tex]
The solution can be calculated by equating both of the above expressions and solving them.
mx + c = [tex]\sqrt{4ax}[/tex]
To solve more questions on solving the equations, visit the link below -
https://brainly.com/question/1386163
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How many solutions does the equation 2(9x−6)=18x+2 have?
A.Infinitely many
B.No solution
C.Number of solutions cannot be determined
D.One solution
Answer:
no solution
Step-by-step explanation:
first you have expand the equation and so you will get
18x-12=18x+2
after you cancel 18x on both sides and so you will get
-12=2
and since that equation is false you will get
no solution
for algebra 2 please help <3
Answer:
A. 1
Step-by-step explanation:
✔️To find f(g(1)), first find g(1).
From the mapping given for g(x), the corresponding value of x = 1, is 0.
That is,
g(1) = 0
✔️Next is to find f(g(1)) by replacing x with 0 in f(x) = 3√x + 1
Thus:
f(g(1)) = 3√0 + 1
f(g(1)) = 0 + 1
f(g(1)) = 1
Joe has read 20% of a book. He has 16 more pages to finish. How many pages are there in the book?
There are pages in the book.
(Type a whole number.)
Plz answer ASAP
Answer:
20
Step-by-step explanation:
16 is 80% of 20