Which equation will yield the time it takes for the candles to burn down to the same height?
How much time will it take for the candles to burn down to the same height?
Answers
Answer:
(i) Equation is
[tex]12 - \displaystyle {\dfrac{3}{4}x = 18-3x\\\\[/tex]
This would be choice C
(ii) 2 hours and 40 minutes which is Choice A
Step-by-step explanation:
Let the time taken for both candles to burn down to the same length be x hours
[tex]\textrm{The rate at which the 12 inch candle burns } = \dfrac{3}{4} \textrm{ inches per hour}\\\\[/tex]
In time x hours, this candle would have burnt
[tex]\displaystyle {\dfrac{3}{4}x \;}\textrm{inches}[/tex]
Height of 12" candle after x hours =
[tex]12 - \displaystyle {\dfrac{3}{4}x \;}\textrm{inches}[/tex]
The 18" candle burns at the rate of 3" per hour
So height of candle after x hours = 18 - 3x
Both these quantities must be equal
[tex]12 - \displaystyle {\dfrac{3}{4}x = 18-3x\\\\[/tex]
Solving for x:
1. Multiply both sides by 4
48 - 3x = 72 - 12x
2. Add 3x to both sides:
48 = 72 - 12x + 3x
48 = 72 - 9x
3. Subtract 72 from both sides:
48-72 = - 9x
==> -24 = -9x
4. Switch sides
-9x = -24
5. Multiply by -1
9x = 24
6. Divide by 9 to get
x = 24/9 = 2 2/3 hours
2/3 hour = 2/3 x 60 = 40 minutes
So total time taken for both candles to reach the same height is
2 hours and 40 minutes (Choice A)
1- 12- 3/4 x = 18 - 3x
(C)
2- 2 hours and 40 minutes
(A)
Related Questions
Carter made a scale drawing of the auditorium. The scale of the drawing was 1 inch : 9 feet. The stage is 5 inches long in the drawing. How long is the actual stage?
feet _____
Answers
29 feet and I need 2 more Brainleist before I get expert can you help?
Answer:
29
Step-by-step explanation:
All of the following statements describe the relation shown except _____.
The inputs are {-1, 0, 3, 4}.
The diagram represents a function.
This relation could also be represented as {(-1, 1), (0, -2), (3, 1), (4, -1)}.
The outputs are {-2, -1, 1}.
Answers
Answer:
the answer is The imputs are {-1,0, 3,4}
Answer:
-1,0, 3,4
Step-by-step explanation:
Expand the expression -12(4c - 3d) using the Distributive Property
Answers
Answer:
-48c - 37d
Step-by-step explanation:
Multiply both numbers by -12.
The expanded form of the expression is -48c+36d
What is Distributive Property?According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Given that, we have to expand the expression -12(4c - 3d) using the Distributive Property,
We know that the rule for distributive property is :
a(b+c) = ab+ac
Therefore,
-12(4c - 3d)
= -12(4c)+12(3c)
= -48c+36d
Hence, the expanded form of the expression is -48c+36d
Learn more about Distributive Property, click;
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#SPJ2
Which of the following statements is always true?
Select the Hint button to view a hint.
Answers
A number that end in 5 is divisible by 10.
Carlos is buying movie tickets for a group. He wants to have at least 20 tickets and spend no more than $300.
Adult tickets cost $15 and child tickets cost $8. Write a system of inequalities that can be used to find the number of each type of ticket Carlos could buy?
Answers
Answer: hope this helps ♡
13 Adults = $210
11 Children = $88
Step-by-step explanation:
x = Adults
y = Children
x + y ≥ 20
$15x + $8 ≤ $300
let's take 13 adults and 11 children
14 + 11 ≥ 20 $15*14 + $8*11 ≤ $300
= 25 ≥ 20 ✓ = $210 + $88 ≤ $300
= $298 ≤ $300 ✓
Please help asap! Also explain how you did it... Tys m!♡♡
Answers
Answer:
A" (-3, 0)
B" (9, 9)
C" (9, 0)
Step-by-step explanation:
The hint explains how to get the final coordinates.
The original figure ABC has vertices
A (-3, -1)
B (1, 2)
C (1, -1)
There are two separate transformations for this triangle, so let's take it one step at a time
The first transformation is a translation by the vector <2, 1>, This means we get a new figure A'B'C' where we add 2 to each of the x coordinates of the original figure and 1 to the y coordinates of the original figure
For A which is (-3,-1) the transformed coordinate becomes:
A -> A' -> A' (-3 + 2, -1 + 1) => A'(-1, 0)
Similarly
B(1, 2) -> B' is B'(1 + 2, 2 + 1) => B'(3, 3)
C(1, -1) -> C'(1 + 2, -1 + 1) or C'(3, 0)
So the first transformation results in a triangle A'B'C' with the following coordinates:
A'(-1, 0)
B'(3, 3)
C'(3, 0)
The second transformation is a dilation of A'B'C' which results in an expansion or compression of the image depending on the scale factor. Here the scale factor is 3 so the image is expanded by a factor of 3
Dilation simply requires you to multiply both x and y coordinates oof A'B'C' by 3
A' (-2 , 0) -> A"(-1 x 3, 0 x 3) => A"(-3, 0)
B'(3, 3) -> B"(9, 9)
C'(3, 0) -> C"(9, 0)
I have attached two images showing each of the transformations separately to give you a better idea
Is 4/5 divided by 1/3 greater than 1
Answers
Answer:
Yes
Step-by-step explanation:
It's 12/5 or also 2.4
Answer:
yes
Step-by-step explanation:
remember how to do fraction operations :
a/b / c/d = a×d / b×c
that is why you can also say it is the same as the multiplication with the upside-down fraction
a/b / c/d = a/b × d/c = a×d / b×c
in your case here
4/5 / 1/3 = 4/5 × 3/1 = 12/5
and that is definitely greater than 1.
The measure of ∠1 is 111°. What is the measure of ∠S ?
Answers
Answer:
Wow, it genuinly is 69
Step-by-step explanation:
it has to add up to 360 degrees
so 111 + 111 = 222 since those two angles are the same
then 360 - 222 so you get the sum of the two smaller angles
which is 138
and 138/2 is 69
Answer: 69
Step-by-step explanation: 111 + 111 = 222
360 - 222 = 138
138 / 2 = 69
Joey made a scale drawing of an Italian restaurant. The restaurant's kitchen is 63 millimeters long in the drawing. The actual kitchen is 28 meters long. What is the scale of the drawing?
9 millimeters : _______meters
Answers
Answer: 4 meters
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Jackson bought a pair of sunglasses online for $29. He used a coupon code to get a 40% discount. The website also applied a 5% processing fee to the price after the discount. How much was the discount, in dollars and cents?
Answers
40% off $29 is $17.40 and after adding the 5% fee it adds 87 cents
Answer:
$18.27 is the answer
40% off $29 is $17.40 and after adding the 5% fee it adds 87 cents
Step-by-step explanation:
Find x, the missing side length of the right triangle.
Answers
Answer:
17
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
2. A. use this function to answer questions a-d f(x)=3x^3-7x^2-14x+24 using the fundamental theorem of algebra. how many possible complex roots with this polynomial have? explain.
B. Using descartes rule determine how many possible positive roots and how many possible negative roots this function will have
C. Use the same function
f(x)=3x^3-7x^2-14x+24
using the rational roots theorem list all the possible rational roots for the function
D. using possible roots you found on the previous question find all the possible zeros for this function (hint: you will use remainder theorem and synthetic division)
Answers
Answer: I'm confused by the question... MORE DETAIL "-d f(x)=3x^3-7x^2-14x+24"
Step-by-step explanation:
please helppp find c
Answers
Answer:
76°
Step-by-step explanation:
Use the Exterior Angle Property. The Exterior Angle Property states that an exterior angle of a triangle is equal to the sum of it's two opposite non adjacent interior angles.
In this case, set the exterior angle equal to the sum of the two given interior angle measurements:
(c) + (c - 26) = c + 50
First, simplify, combine like terms. Like terms are terms that share the same amount of the same variable:
c + c - 26 = c + 50
(2c) - 26 = c + 50
Next, isolate the variable, c. Note the equal sign, what you do to one side, you do to the other. Subtract c and add 26 to both sides of the equation:
2c (-c) - 26 (+26) = c (-c) + 50 (+26)
2c - c = 50 + 26
c = 76
76° is your answer.
~
Learn more about the Exterior Angle Theorem, here:
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Answer:
c = 76 degrees
Step-by-step explanation:
A number increased by twenty-two is less than fourteen. What value must the number be less than?
7
-8
8
-7
Answers
Answer:
-8
Step-by-step explanation:
x + 22 < 14
Subtract 22 from both sides.
x < -8
Answer:
-8
Step-by-step explanation:
-7 +22 is 15 and the only one less is -8 and -8+22 is 14 so it has to be less then -8
1.Mike’s age is 5 more than 3 times Sam’s age. The sum of their ages is 72. How old are Mike and Sam?
2.The difference between two numbers is 12. Find the two numbers if the larger number is 5 times the smaller number.
3.Sue and Tom collect baseball cards. Sue has 8 more than 4 times as many cards as Tom. The total number of cards they both have is 276. How many cards do they each have?
please let it be correct please please please!
Answers
Answer:
1. Mike's age is 53 and Sam's age is 19.
2. The first number is 3 and the other is 15.
3. Tom has 66 cards and Sue has 210.
Step-by-step explanation:
Sam is 19
2. 1 number is 3
2 number is 15
3. Tom has 56
Sue has 210
PLEASE HELP ADDED FILE Which letter represents the colony of Maryland on this map?
Responses
C
G
J
L
Answers
Answer:
I guess G is Maryland
Each week, Robbie earns $x mowing lawns and receives $15 as his allowance.
To find how much he will earn in total over 3 weeks, Robbie writes the following expression: x + 15 + x + 15 + x + 15
What are some other ways Robbie can write the above expression? Check all that apply.
A. 3x + 45
B. x + 15
C. 3x + 15
D. 3(x + 15)
Answers
Answer:
A. 3x + 45
D. 3(x + 15)
Step-by-step explanation:
x + 15 + x + 15 + x + 15 = (x + 15) + (x + 15) + x + 15) = 3(x + 15) = 3x + 45
Answer:
A. 3x + 45
D. 3(x + 15)
A works because he gets payed “x” 3 times, making 3x. He gets payed $15 3 times so that makes $45.
D works because when you use the distributive property to solve you get 3x+45
Jordan opens an account with a deposit of $300 that earns 6% interest annually. She makes no other deposits or withdrawals. Based on this information, circle the correct answer to each question given below.
A. Which function can be used to model this situation?
Linear/ Quadratic/ Exponential
B. By how much money will Jordan’s account grow each year?
$18/ $6/ $318
C. After 3 years, Jordan would have earned how much in Interest?
$54/ $354/ $318
Answers
help asap please its due today
__________________________
tomas is planning out a rail trail using a map with a marked grid. The head of the trail, which has an information kiosk, is located at (3, 0). He moves 1 unit east and 3 units north and places a pin at (4, 3) to represent the location of another information kiosk. He continues to move 1 unit east and 3 units north twelve more times, placing a pin each time. Where will the last pin be placed?
theres a picture aswell!
Answers
Kiosks only occur when the y-coordinate is a multiple of 3. The closest to the 40 units of northern land would be at 39. 39 divided by 3 would mean Tomas placed an additional 13 kiosks after the first. With the x-coordinate incrementing 1 unit east each time, the x-coordinate of the last kiosk endpoint is 3+13 or 16. Thus the foot of the trail ends at (16,39).
Answer:
The last pin will be placed at (16,39).
Explanation:
I used an answer double checker.
are -(-12) and -12 opposites
Answers
[tex]-(-12)[/tex] and [tex]-12[/tex] are opposites because the negative before the parentheses of [tex]-(-12)[/tex] multiplies.
[tex]-1\times-12=12\neq -12[/tex]
So therefore, [tex]-(-12)[/tex] is not equal to [tex]-12[/tex]
Mark starts with $100 in his bank account. He deposits $15 each month from his allowance.
Can someone please tell me what order to put it in.
Answers
X+15
y=115
Esa es la opción correcta
Claudia wants to replace the carpet in her living room and hallway. How many square meters of carpet are needed? If carpet costs $3.50 per square meter, how much will the carpet cost? Is this are or perimeter?
Answers
Please I need help ASAP
I WILL GIVE BRAINLIEST
Answers
Answer:
11.5
Step-by-step explanation:
7 / 1.4 = 5
5 * 2.3 = 11.5
2.3x5
11.5
You just make a part over whole… cross multiply
you are running a ten mile race. The function d(t) = 1-8 |t-40| represents the distance in miles you are from the water stop after t minutes. interpret the intercepts. Explain what each represents in this context
Answers
The y-intercept of the graph represents the distance in miles that you are from the water stop at time t = 0. In this case, the y-intercept is d(0) = 1 - 8|0 - 40| = 1 - 8|-40| = 1 - 8(-40) = 1 + 320 = 321. This means that at time t = 0, you are 321 miles from the water stop.
In summary, the x-intercepts represent the times at which you are exactly one mile from the water stop, and the y-intercept represents the distance in miles that you are from the water stop at time t = 0.
Please help ASAP
I WILL GIVE BRAINLIEST
Answers
Answer:
12 inches
Step-by-step explanation:
What is the x and y coordinates that define the location of a point?
Answers
Answer: The x and y coordinates that define the location of a point are the coordinates of that point in a two-dimensional coordinate system.
In a two-dimensional coordinate system, a point is represented by an ordered pair of numbers (x, y). The first number, x, represents the point's position along the horizontal axis, and the second number, y, represents the point's position along the vertical axis.
For example, if a point is located at the position (3, 4) in a two-dimensional coordinate system, this means that the point is 3 units to the right of the vertical axis and 4 units above the horizontal axis.
The x and y coordinates of a point can be used to plot the point on a graph or to find the distance between two points using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
Explanation: yes
Please I need help ASAP
I WILL GIVE BRAINLIEST
Answers
Answer: It's D, 11.5.
Step-by-step explanation:
To find how many times QRST is bigger that ABCD, we can use the equation
1.4*x=7
or
7/1.4=5.
Since we now know QRST is 5 times bigger, we can multiply 2.3 by 5 to get the length of RS.
2.3*5=11.5
Use the diagram to determine which statement is true.
Answers
Answer:
Choice C
Area(DEFG) + Area(GHIA) = Area(ABCD)
Step-by-step explanation:
This is solved using the Pythagorean theorem which states states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides(Wikipedia)
Area of the square on the hypotenuse = Area(ABCD)
Sum of the areas on the other two sides = Area(DEFG) + Area(GHIA)
So we get
Area(ABCD) = Area(DEFG) + Area(GHIA)
which can be re-written as
Area(DEFG) + Area(GHIA) = Area(ABCD)
which is choice C
(24,3),(8,1)(16,2)(40,5)
Answers
Answer: y= 1/8x
Step-by-step explanation:
I think
Which fractions have a LCD of 45?
Answers
Answer:
I think it’s B
Step-by-step explanation:
