Answer:
30.6
Step-by-step explanation:
The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The length of the side j is 30.6 cm.
What is Sine rule?The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}[/tex]
where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,
Sin B is the angle and β is the length of the side of the triangle opposite to angle B,
Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.
Given the length of i is 53 cm, while the measure of the ∠I is 120°. Also, the measure of ∠J is 30°. Therefore, the length of the side j is,
[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ A}{\beta} =\dfrac{Sin\ A}{\gamma}\\\\\dfrac{Sin\ I}{i} =\dfrac{Sin\ J}{j} \\\\\dfrac{Sin\ 120^o}{53} =\dfrac{Sin\ 30^o}{j} \\\\j = \dfrac{Sin\ 30^o \times 53}{Sin\ 120^o}\\\\j = 30.5995 \approx 30.6\rm\ cm[/tex]
Hence, the length of the side j is 30.6 cm.
Learn more about Sine Rule:
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PLEASE IM BEGGING YOU please answer i’ll do anything i need in 10 minutes please
Answer:
1. 2.
-3, 4 -3, 2
-1, 2 0, 1
0, 1 3, 0
4, -3 6, -1
Step-by-step explanation:
What is the product of -5/8 and -6/7
Answer:
-1 27/56
Step-by-step explanation:
Using the given fractions,
−58+−67
Applying the fractions formula for addition,
=(−5×7)+(−6×8)8×7
=−35+−4856
=−8356
Simplifying -83/56, the answer is
=−12756
James determined that these two expressions were equivalent expressions using the values of x - 4 and x - .6
Which statements are true? Check all that apply.
7x+4 and 3x+5+4x-1
When x = 2, both expressions have a value of 18.
The expressions are only equivalent for x = 4 and x = 6.
The expressions are only equivalent when evaluated with even values.
The expressions have equivalent values for any value of x.
The expressions should have been evaluated with one odd value and one even value.
When x = 0, the first expression has a value of 4 and the second expression has a value of 5.
The expressions have equivalent values if x = 8.
Answer:2 4 and 5
Step-by-step explanation:
A tank contains 5,000 L of brine with 11 kg of dissolved salt. Pure water enters the tank at a rate of 50 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. (a) How much salt is in the tank after t minutes? y = ___________kg (b) How much salt is in the tank after 20 minutes? () y = ________ kg
Answer:
a
[tex]y(t) = 11e^{-\frac{t}{100} }[/tex]
b
[tex]y(20) = 9 \ kg[/tex]
Step-by-step explanation:
From the question we are told that
The volume of brine in the tank is [tex]V_L = 5000 \ L[/tex]
The mass of the salt is [tex]y(0)= 11 \ kg[/tex]
The rate at which water enters that tank is [tex]\r V = 50 \ L / min[/tex]
Generally the rate at which salt enters the tank is mathematically represented as
[tex]z = \frac{0}{V_L} * \r V[/tex]
=> [tex]z = \frac{0}{5000} * 50[/tex]
Here the zero implies that there is no salt entering the tank
Generally the rate at which salt leaves the tank is mathematically represented as
[tex]u = \frac{y(t)}{V_L} * \r V[/tex]
=> [tex]u = \frac{y(t)}{5000} * 50[/tex]
=> [tex]u = \frac{y(t)}{100}[/tex]
Generally the rate of salt flow in and out of the tank is
[tex]\frac{dy}{dt} = z - u[/tex]
=> [tex]\frac{dy}{dt} = - \frac{y(t)}{100}[/tex]
=> [tex]\frac{dy}{y} = -\frac{dt}{100}[/tex]
=> [tex]ln(y(t)) = -\frac{t}{100} + c[/tex]
at time t = 0 y(0) = 11
=> [tex]ln(11) = -\frac{0}{100} + c[/tex]
=> [tex]c = ln (11)[/tex]
So
[tex]ln(y(t)) = -\frac{t}{100} + ln (11)[/tex]
taking exponent of both sides
[tex]y(t)=e^{ -\frac{t}{100} + ln (11)}[/tex]
=> [tex]y(t) = e^{-\frac{t}{100} } * e^{ln(11)}[/tex]
=> [tex]y(t) = 11e^{-\frac{t}{100} }[/tex]
Generally at t = 20 minutes
The amount of salt in the tank is mathematically represented as
[tex]y(20) = 11e^{-\frac{20 }{100} }[/tex]
=> [tex]y(20) = 9 \ kg[/tex]
Example of a balance point
a home's loss of heat is equal to heat created in the home or when both sides of a seesaw are at an equal level.
Write a mathematical sentence that expresses the information given below. Use s as your variable name If necessary : type to mean If you need to show multiplication , do not use the letter x. Use the asterisk (*) symbol instead, or simplify your answer. Mr. Jones's algebra class has too many students in it. If the class were split exactly in equal parts to form 3 new classes, each class would have no more than 14 students in it.
Answer:
s*3=42
Step-by-step explanation:
s= no. of students
* is used for multiplication sign
s*3=42
s=42/3
s=14
Answer:
ˢ⁄₃ ≤ 14
s ≤ 42
Step-by-step explanation:
This question requires you to apply your algebra knowledge to create an equation (in this case, an inequality) using variables and information. We need to translate the phrases into basic operations.
S would represent the number of students in Mr. Jones's Algebra class.
The info says "if the class were split exactly in equal parts to form 3 new classes." The words 'split' and 'in equal parts' indicate that we need to use the division operator (or a fraction). The "3 new classes" tell us by how many to divide by (the denominator of the fraction). So we write
ˢ⁄₃
The next part forms the inequation. "each class would have no more than 14 students in it"
The "no more than 14" tells us each class can either be 14 or less, so we should use the lesser or equal to sign (≤). So now we join the parts together:
ˢ⁄₃ ≤ 14
Since we now have an equation/inequation and have enough information, we can solve for s (the number of students in Mr. Jones's algebra class).
s ≤ 42
What we have done here is translate the given information into a mathematical sentence
ill give brainliest please help.
Answer:
A = 5
Step-by-step explanation:
hhhhhhhhhhhhhhhhhelp hhhhhhhhhhhhhhhhhelp hhhhhhhhhhhhhhhhhelp hhhhhhhhhhhhhhhhhelp hhhhhhhhhhhhhhhhhelp
Answer:
B is the answer
Step-by-step explanation:
What's the range in the question below. Please answer one of the answer choices.
Answer:
yo I'm doing the same thing
Zoey wants to use her iPad throughout a 6-hour flight. Upon takeoff, she uses the iPad for 2 hours and notices that the battery dropped by 25%, from 100% to 75%. How many total hours can Zoey expect from the iPad on a full battery charge?
Answer:
6 hours more
Step-by-step explanation
When Zoey started the flight the battery was 100%, then it dropped to 75% in 2 hours. So each 25% will last 2 hours and there is 75% remaining which if you divide by 3 it will give 1. And each 25% will last 6 more hours until the battery dies.
Solve one fourth plus ten sixteenths
Answer:
The answer is 0.875
Answer:
13
Step-by-step explanation:
Please help me I need help?!!!
Answer:
B
Step-by-step explanation:
At Clean Cut Manufacturing, Jethro made a graph representing the number of riding lawn mowers manufactured, y, based on the number of hours the assembly line is operating, x. The graph is a straight line that passes through the origin and the point (1, 13). Which of the following graphs and statements fit the situation? The assembly line manufactures 13 riding lawn mowers per hour of operation. The slope of the graph is 1. The y-intercept of the graph is 13. It takes 13 hours of operation for the assembly line to manufacture each riding lawn mower.
Answer:
The assembly line manufactures 13 riding lawn mowers per hour of operation. And the graph that the line is vertical but slightly tilted.
Step-by-step explanation:
How do you say 9.876?
Answer:
nine point eight hundred seventy six....hope u got, babes...
PLEASE HELP ME ASAP
Answer:
The answer is Option D
Step-by-step explanation:
Supplementary angles are angles that sum up to 180 °
I need a girl and yes I understand I’m on the wrong website please don’t report smh
Answer:
lol, what for?
Step-by-step explanation:
Answer:
So the answer would be B.
Step-by-step explanation:
This is not the right site like you said also no one knows your age or what you look like so good luck buddy.
Which step will get you closest to the solution of this equation?
5.2 – 2)=7
(Imagine math)
Answer:
I'm pretty sure it's the to right one
Step-by-step explanation:
Find the volume of the sphere. Sorry the pic isn’t the best! I tried lol!
Answer:
4,186.6 repeated (just round to .7 if it asks for it)
Step-by-step explanation:
The volume of a sphere is 4/3 pi r^3
plug in the radius and simplify that expression
What do you call a female bug that floats?
Answer:
A buoyant girl ant
Step-by-step explanation:
I wil I give the BRAINIEST!
Please explain :)
What is the best description of the relation?
Rochelle received a $15 gift card to an online music store. She downloaded 12 songs that each cost the same price. After the gift card was applied, her total was $8.88. Which equation can be used to find , the price of each song?
Answer:
15 + 18.88 ÷ 12 = p
if p were price of each song
p= 1.99
4n + 1= 25 how do I solve this and show my work?
Answer:
n=6
Step-by-step explanation:
4n + 1= 25
Move constant to the right
4n=25-1
Calculate
4n=25-1
Then divide on both sides
Answer:
Today: Friday, 06 November 2020
Hour: 09.44 WIB (Indonesia)
_______________________________
4n + 1 = 25
4n = 25 - 1
4n = 24
n = 24/4
n = 6
Enter the ordered pair for the vertices for Rx-axis(QRST).
The graph with X-coordinate marks -4, -2, 0, 2, 4 and Y-coordinate marks -4, -2, -1, 0, 2, 4, 6. There is a polygon QRST with coordinates T at (-2, 3), Q at (1, 5), R at (3, -1) and S at (0, 0).
Given:
The vertices of a polygon QRST are T(-2, 3), Q(1, 5), R(3, -1) and S(0, 0).
To find:
The vertices for [tex]R_{x-axis}(QRST)[/tex].
Solution:
The rule [tex]R_{x-axis}(QRST)[/tex] represents refection of polygon QRST across the x-axis.
If a figure is reflected across the x-axis, then
[tex](x,y)\to (x,-y)[/tex]
Using this rule, we get
[tex]T(-2,3)\to T'(-2,-3)[/tex]
[tex]Q(1,5)\to Q'(1,-5)[/tex]
[tex]R(3,-1)\to R'(3,1)[/tex]
[tex]S(0,0)\to S'(0,0)[/tex]
Therefore, the vertices for [tex]R_{x-axis}(QRST)[/tex] are T'(-2, -3), Q'(1, -5), R'(3, 1) and S'(0, 0).
Rx-axis means that the polygon QRST is reflected across the x-axis.
The ordered pair after Rx-axis is Q'(1,5), R'(3,1), S'(0,0) and T'(2,3)
The points are given as:
[tex]\mathbf{Q = (1,5)}[/tex]
[tex]\mathbf{R = (3,-1)}[/tex]
[tex]\mathbf{S = (0,0)}[/tex]
[tex]\mathbf{T = (-2,3)}[/tex]
The rule of reflection across the x-axis is:
[tex]\mathbf{(x,y) \to (x,-y)}[/tex]
So, we have:
[tex]\mathbf{Q' = (1,-5)}[/tex]
[tex]\mathbf{R' = (3,1)}[/tex]
[tex]\mathbf{S' = (0,0)}[/tex]
[tex]\mathbf{T' = (-2,-3)}[/tex]
Hence, the ordered pair after Rx-axis is Q'(1,5), R'(3,1), S'(0,0) and T'(2,3)
Read more about reflections at:
https://brainly.com/question/938117
You are in charge of food shopping for a party. You need to buy snacks and soda. A bag of snacks costs $2 and a pack of soda $3.5. If your mom gives you $25 to buy groceries and you buy 8 bags of snacks, how many packs of soda can you buy?
Answer:
2 bags
Step-by-step explanation:
Answer: 2
Step-by-step explanation:
2x8=16
25-16=9
3.5+3.5=7
kala is saving money to buy a bike that cost $125. She has $60 and will save an additional $5 each week. In how many weeks will she have enough money to buy the bike?
Explain how multiplying fractions and dividing fractions are alike and how they are different.
Answer:
Multiplying and dividing fractions are essentially the same process which you multiply the numbers straight across and no need for common denominators. Except in division of fractions, the second fraction is flipped so that the denominator is on the top and the numerator is on the bottom (reciprocal).
Step-by-step explanation:
Example:
[tex]\frac{3}{4} * \frac{1}{5} = \frac{3}{20}[/tex]
[tex]\frac{3}{4}[/tex] ÷ [tex]\frac{1}{5} = \frac{3}{4} * \frac{5}{1} = \frac{15}{4}[/tex]
Help!!I will give BRAINLIEST
Answer:
3.125
Step-by-step explanation:
Hope this helps!! :)
Answer:
3.05
Step-by-step explanation:
Two pounds of cashews costs $19. Which table best represents y, the total cost of the cashew for x pounds?
9. Which expression is equivalent to 14(8x−36)+2x? (1 point)
a. 10x - 36
b. 30x
c. 4x - 9
d. 4x - 36
Answer:
Step-by-step explanation:
14(8x-36)+2x
112x -504 +2x
114x-504
What is the coefficient of 4x^2 ?
