Answers
3x + 60 (-60) = 180 - 60
3x = 120
3x/3 = 120/3
x = 40
Check:
3x + 60 = 180
3(40) + 60 = 180
120 + 60 = 180
The answer is: x = 40
Related Questions
The radius of a sphere is increasing at a rate of 5 mm/s. how fast is the volume increasing when the diameter is 60 mm? evaluate your answer numerically. (round the answer to the nearest whole number.)
Answers
The formula for the radius when the time is x second would be:
r(t)= 30+ 5x
dr/dt= 5
The speed of volume increase of the sphere volume would be derived from sphere volume:
V(r)=4/3* pi * r^3
dV/dt= 4/3 * pi * 3r^2 * (dr/dt) =4/3* pi * 3(30)^2 * 5 = 18000 pi= 56571 mm^3/s
The rate of change of volume of the sphere is [tex]56520\;\rm{mm/sec}[/tex].
According to the question, the radius of a sphere is increasing at a rate of [tex]5 mm/s[/tex] and the diameter is [tex]60 mm[/tex].
The volume of the sphere is, [tex]V=\dfrac{4}{3}\pi r^3[/tex] where, [tex]r[/tex] is the radius of the sphere.
Differentiate the volume of the sphere both sides with respect to [tex]t[/tex] as-
[tex]\dfrac{dV}{dt}=\dfrac{4\pi}{3}\dfrac{dr^3}{dt}\\\dfrac{dV}{dt}=\dfrac{4\pi}{3}\times 3r^2\dfrac{dr}{dt}\\\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}[/tex]
The radius of the sphere is-
[tex]r=\dfrac{60}{2}\\r=30mm[/tex]
Substitute the value of the parameter as-
[tex]\dfrac{dV}{dt}=4\pi\times (30)^2\times 5\\\dfrac{dV}{dt}=62.8\times 900\\\dfrac{dV}{dt}=56520\;\rm{mm/sec}[/tex]
Hence, the rate of change of volume of the sphere is [tex]56520\;\rm{mm/sec}[/tex].
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Bill's new porch is rectangular, with an area of 50 square feet. If the length of the porch is two times the width, what is the perimeter of the porch?
Answers
A=LxW
L: The lenght of the rectangle (L=2W).
W: The width of the rectangle.
2. Let's substitute L=2W into the formula A=LxW:
A=LxW
A=2WxW
A=2W²
3. When we clear "W", we obtain:
W²=A/2
W=√(A/2)
4. We already know the value of "A", so:
W=√(50 ft²/2)
W=√(25 ft²)
W=5 ft
5. Now, we must substitute the value of "W", into L=2W:
L=2W
L=2(5 ft)
L=10 ft
6. The perimeter of a rectangle is:
P=2L+2W
7. We know the value of "L" and "W", therefore:
P=(2x10 ft)+(2x5 ft)
P=20 ft+10 ft
P=30 ft
What is the perimeter of the porch?
The answer is: 30 ft
The width of the porch is 5 feet and the length is 10 feet. The perimeter of the porch is 30 feet.
Explanation:To find the perimeter of the porch, we first need to find the dimensions of the porch. Let's assume the width of the porch is x feet. According to the problem, the length of the porch is two times the width, so the length would be 2x feet. Since the area of the porch is 50 square feet, we can set up the equation: x * 2x = 50. Simplifying this equation, we get 2x^2 = 50. Divide both sides by 2 to isolate x^2: x^2 = 25. Taking the square root of both sides, we find that x = 5. Therefore, the width of the porch is 5 feet and the length is 2 * 5 = 10 feet.
To find the perimeter, we use the formula: perimeter = 2 * (length + width). Substituting the values, we get perimeter = 2 * (10 + 5) = 2 * 15 = 30 feet. So, the perimeter of the porch is 30 feet.
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?
Answers
Answer:
5 roots
Step-by-step explanation:
just did it on edge
without graphing decide whether the system of linear equations below has one solution, no solution, or infinitely many solutions. y=3x-8. 4y=12x-5
Answers
Answer:
B. no solution
Step-by-step explanation:
Multiplying the first equation by 4 gives ...
4y = 12x -32
This is inconsistent with the second equation, ...
4y = 12x -5
There can be no common point on these parallel lines, hence no solution.
Answer:
You will revise your narrative, indicating four instances in which you have added adjectives and/or adverbs.
You will also submit a reflection paragraph.
View the grading rubric as you complete your assignment. This is your guide to a super submission.
Add adjectives and adverbs. Mark your new additions with an (Adj) or (Adv).
Make other revisions suggested in your Discussion-Based Assessment.
Write a reflection paragraph discussing changes you made during the revision process. Explain how you feel these changes improved your narrative.
Submit your (1) final draft and your (2) reflection paragraph.
Save your work to your computer or drive.
Submit your work in 03.10 Kick It Up a Notch.
Step-by-step explanation:
robert ordered 11 pizzas for a pizza party for the softball team. when he ordered the pizzas, he told members they could each eat 3/5 of a pizza. if each person gets 3/5 of a pizza, how many people can eat this much pizza at the party
Answers
Final answer:
18 people can eat 3/5 of a pizza, with a little pizza left over.
Explanation:
To find out how many people can eat 3/5 of a pizza at the party, we need to divide the total number of pizzas by the fraction each person can eat.
Number of people who can consume 3/5 of a pizza = Total pizzas / (3/5)Number of people = 11 / (3/5)Number of people = 11 / (3/5) = 11 * (5/3) = 55/3 = 18.33Therefore, approximately 18 people can eat 3/5 of a pizza at the party.
help!!! 10pts!!
The coordinates of the vertices of triangles are listed in the options below. Which is a right triangle?
D(2, −3), E(−5, 7), F(6, −9)
A(−3, 2), B(−3, −9), C(2, −4)
P(−6, 2), Q(1, 0), R(−3, −2)
X(3, 1), Y(−4, −3), Z(−1, 8)
Answers
The correct choice is the last one, XYZ, with vertex X being where the right angle is located.
_____
Slope of XY is 4/7; slope of XZ is -7/4. The product of these is -1, so those segments are at right angles.
ANSWER FAST 15 PTS
What is the length of PQ?
JKLM : PQRS
12 km
16 km
18 km
20 km
Answers
Answer:
20 KM
Step-by-step explanation:
God bless!!!
Answer: 20 Km
Step-by-step explanation: I did the assignment (Similar Polygons)
The perimeter of a rectangle is 12 inches. If the length and width are whole numbers, what are the least and greatest possible areas?
Answers
Answer:
5in and 9in
Step-by-step explanation:
find the probability of getting a king then an eight. Assume the cards are not replaced?
Answers
To draw the king card, you have 4/52 probability.
To draw the eight card, you have 4/51 probability ( since the king card not replaced).
The total probability would be: 4*4/ 52*51= 4/663
the diagram shows an artificial lake. When Amanda jogged twice around the lake she jogged a distance of 2,700 meters. Find the value of x
Answers
[tex]2 \div 2700[/tex]
Assuming that the attached file is the lake which you are mentioning in the question.
The perimeter is the distance around the lake, we need to set up an equation based on the statement "When Amanda jogged twice around the lake she jogged a distance of 2,700 meters" as below:
[tex] 2(Perimeter \; of\; the\; lake) =2700\\ \\ 2(x+140+x+x+250+x+x+3x)=2700\\ Group \; Like\; Terms\\ \\ 2(x+x+x+x+x+3x+140+250)=2700\\ Combine \; Like\; Terms\\ \\ 2(8x+390)=2700\\ Distribute\; 2\; in\; left\; side\; of\; the\; equation\\ \\ 16x+780=2700\\ Subtract \; 780\; on\; both\; sides\\ \\ 16x+780-780=2700-780\\ Combine \; like\; terms\\\\16x=1920 \\ Divide\; 16 \; on\; both\; sides\\ \\ \frac{16x}{16}=\frac{1920}{16}\\ Simplify\; fraction\; on\; both\; sides\\ \\ x=120 [/tex]
Conclusion:
The value of x is 120 meters
Pierce wishes to purchase a municipal bond with a par value of $500 from Arapahoe County, and he is trying to decide which broker he should employ to purchase the bond. Broker A charges a 3.1% commission on the market value of each bond sold. Broker B charges a flat $24 for each bond sold. If the bond has a market rate of 88.754, which broker will give Pierce the better deal, and by how much?
Answers
Answer:
Since the given problem statement and data is
Manicipal bond with par value=$500
commission rate =3.1%
charges of broker B=$24
bond market rate=$88.754
hence from the given data Broker A charges a 3.1% commission on the market value of each bond sold is a better deal.
A rectangular prism has a volume of 729ft3. The length, width and height are all the same. What is the length of each side of the prism?
Answers
because 9 x 9 x 9 = 729
Tomas created a function table using the equation y = x + 4. Which table is correct?
Answers
1) How to make a table
For the function y = x + 4, the variable x is the input and the variable y is the output.
A table consists of a sequence of pairs x, y.
You choose the x-values and calculate th y-values using the function.
For expample if you choose x = 3 as your input, then the output is given by the function y = x + 4, so you subsititute x = 3 and obtain y = 3 + 4 = 7.
And the table is represented as in the example below.
What you have to do is checking if all the values of the table given satisfy the equation y = x + 4.
2) Table (example):
x y = x + 4
-20 -16
-19 -15
-18 -14
-17 -13
-16 -12
-15 -11
-14 -10
-13 -9
-12 -8
-11 -7
-10 -6
-9 -5
-8 -4
-7 -3
-6 -2
-5 -1
-4 0
-3 1
-2 2
-1 3
0 4
1 5
2 6
3 7
4 8
5 9
6 10
7 11
8 12
9 13
10 14
11 15
Scientist determine that Antarctica average winter temperature was 34.44 Celsius the difference between the temperature and Antartica highest record temperature was 49.44 degrees what was the highest record temperature
Answers
Then the highest recorded temperature is
-34.44 °C +49.44 °C = 15 °C . . . . . . . . . . about 59 °F
A grocer had 40 crates of tomatoes. Each crate contained 124 tomatoes. She threw away 24 rotten tomatoes and repack the rest into bag of 8 tomatoes each. How many bags of tomatoes were there?
Answers
4,960 - 24 = 4,936
4,936 / 8 = 617
There are 617 bags of tomatoes.
124*40=4960 tomatoes
24 are rotten
4960-24=4936
4936/8=617 bags
On top of a hill, a rocket is launched from a distance 80 feet above a lake. The rocket will fall into the lake after its engine burns out. The rocket's height, h, in feet above the surface of the lake, is given by the equation, h = -16t^2 + 64t + 80, where t is time in seconds. The maximum height of the rocket is _______ feet
Answers
The maximum height is the y-coordinate of the vertex. To find the vertex, we first use x = -b/2a. For our information, that is x=-64/2(-16) = -64/-32 = 2.
Now we substitute this into the equation:
y = -16(2²) + 64(2) + 80 = -64 + 128 + 80 = 144
He radius r of a circle is increasing at a rate of 6 centimeters per minute. find the rate of change of the area when r = 35 centimeters. cm2/min
Answers
The rate of change of the area when the radius is 35 centimeters is 420π cm2/min.
Explanation:To find the rate of change of the area, we can use the formula for the area of a circle: A = πr2. We are given that the radius (r) is increasing at a rate of 6 centimeters per minute. We need to find the rate of change of the area when r = 35 centimeters.
First, differentiate the area formula with respect to time (t) using the chain rule:
dA/dt = 2πr(dr/dt)
Substitute the given values into the formula: dA/dt = 2π35(6) = 420π cm2/min.
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The rate of change of the circle's area when the radius is 35 cm is 420π cm²/min.
Explanation:The subject of this question is related to the rate of change in the context of a circle's area, which is a topic in calculus. Given that the radius r of a circle is increasing at a rate of 6 centimeters per minute, we are to find the rate of change of the area when r = 35 centimeters.
The area A of a circle is given by the equation A = πr². If we differentiate this equation with respect to time t, we get dA/dt = 2πr(dr/dt). We know that dr/dt, the rate of change of the radius, is 6 cm/min. Substituting r = 35 cm and dr/dt = 6 cm/min into the derivative equation, we get dA/dt = 2π*35*6 = 420π cm²/min.
So, the rate of change of the circle's area when the radius is 35 cm is 420π cm²/min.
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Formulate a decision model to determine whether there are any arbitrage opportunities with the spot currency rates given in table 1. note that an arbitrage opportunity could involve several currencies. if there is an arbitrage opportunity, your model should specify the exact set of transactions to achieve it. to us dollar pound ffranc dmark yen us dollar - 0.63900 5.37120 1.57120 98.8901 pound 1.56480 - 8.43040 2.45900 154.7733 from ffranc 0.18560 0.11860 - 0.29210 18.4122 dmark 0.63610 0.40630 3.42330 - 62.9400 yen 0.01011 0.00645 0.05431 0.01588 - table 1: cross-currency spot rates
Answers
Final answer:
To determine if there's an arbitrage opportunity, convert an amount through various currencies in the table and see if you end with more than you started. If more is ended up with, there's an opportunity, specifying the currencies and transactions. If not, the market is in equilibrium, and rates will adjust to prevent arbitrage.
Explanation:
To identify an arbitrage opportunity within the given spot currency rates, one must find a sequence of exchanges that results in more currency than initially started with, after accounting for the currency exchange rates in table 1. The decision model for discovering an arbitrage opportunity typically involves converting an amount from one currency to another across several pairs and ending up with more than one started with in the original currency. The following steps outline the process to determine if arbitrage is possible:
Start with a denomination of one currency (e.g., $1).
Convert this amount into another currency using the provided spot rates.
Repeat the conversion process for subsequent currencies.
Finally, convert back to the original currency.
If the final amount is greater than the starting amount, an arbitrage opportunity exists. In such a scenario, the model should indicate the currencies involved and the specific transactions to execute the arbitrage. However, if no sequence of transactions results in profit, then no arbitrage opportunity is present given the rates provided. The absence of arbitrage ensures that the markets are in equilibrium, and the exchange rates will adjust to eliminate any potential for arbitrage as per the efficient market hypothesis.
PLEASE HELP!!!!
Which is the following best describes the graph below?
A. it is many-to-one function
B. it is a function but it is not one to one.
C. it is a one to one function
D. it is not a function
Answers
Solution:
we are given with a graph and we have been asked to find Which of the given options best describes the graph ?
As we know from the vertical line test of a function that a curve reprsents a function , if we draw a vertical line and that line intersect that curve only once.
If that vertical line interscet the given curve more than once it mean that curve does not represent a function.
Here for the given curve if we will draw any vertical line, that line will intersect it more than once.
Hence the given curve does not represent a fimction.
Hence the correct option is D.
A space shuttle orbits earth at a rate of about 4,375 miles in 15 minutes. At the rate, how far does the space shuttle travel around earth in 1 hour?
Answers
Hope this helps
There min in and 1hour so
291.6 times 60= 17,596
The shuttle will go 17,596 miles in an hour.
Please help me with questions 23, 24, and 25
Answers
A = 40
B = 3x+1
C = 3x+1
B and C are congruent, so they have the same angle measure
The three angles of any triangle add to 180 degrees
A+B+C = 180
40+(3x+1)+(3x+1) = 180
6x+42 = 180
6x = 180-42
6x = 138
x = 138/6
x = 23
Answer: B) 23
============================================================
Problem 24
AB is the midsegment parallel to XY
So AB is half that of XY
AB = (1/2)*XY
AB = (1/2)*28
AB = 14
Answer: B) 14
============================================================
Problem 25
Note the ratio of the given rectangle's sides: 7/12 = 0.583 roughly
Divide the answer choices in a similar fashion
A) 5/7 = 0.714
B) 14/36 = 0.389
C) 21/36 = 0.583
D) 21/48 = 0.4375
We get the same result in choice C as we did in the original rectangle
Answer: C) 21 ft x 36 ft
Six different ways to show equal groups of 18
Answers
9+9
Add 1 until you get 18 (18x1)
Add 2 until you get 18 (9x2)
6+6+6
3+3+3+3+3+3
I hope this helped! :-)
Suppose 60% of a graduating class in a certain high school goes on to college. if 240 stuare going on to college, how many students are in the graduating class?
Answers
hope this helps
Lesson 8 homework practice solve percent problems
Answers
To solve percent problems, we can use equivalent fractions, cross-multiply, solve for the unknown, or convert percent to a fraction and simplify. In context, a 24% positive rate among students indicates that 24 out of every 100 students are positive.
Explanation:In mathematics, specifically in percentage calculation, there are several methodologies to solve problems. One very common way, as mentioned in the reference material, is by setting up equivalent fractions with 100 as the denominator, and cross-multiplying. For example, if you have the fraction 9/37 representing some scenario (like 9 successful attempts out of 37), you can set up an equation like 9/37 = x/100, where 'x' is the equivalent percentage. Cross-multiply and solve for 'x' to get x = (9/37) * 100, giving you the percentage.
Also, note that a percent can be converted to a fraction by writing the value of the percent as a fraction with a denominator of 100. Simplify the fraction, if possible.
In context, if 24% of students are positive, that means for every 100 students, 24 would be positive. If only 70 are surveyed, then (24/100)*70 = 16.8 students, but since we can't have a part of a student, we would round it to 17 students are positive for this sample size.
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In playing Monopoly, rolling doubles three times in a row sends you to jail. What is the probability of rolling three consecutive doubles? a. 0.167 b. 0.5 c. 0.00463 d. 18.0
Answers
to roll a double of any number you have to have the same number on a six-sided die that can be represented as 1/6 times 1/6 = 1/36 chance per roll
[tex] \frac{1}{36} * \frac{1}{36} * \frac{1}{36} = \frac{1}{46656} [/tex]
there is a 1 in 46656 chance in rolling doubles 3 times in a row.
Answer:c 0.00463
Step-by-step explanation:
1/6×1/6×1/6=1/216
write each fraction in simplest form. if the fraction is already in simplest form, write simplified
A.
[tex] \ \frac{4}{14} [/tex]
B.
[tex] \frac{15}{20} [/tex]
C.
[tex] \frac{21}{35} [/tex]
Answers
B. 15/20 = 3/4
C. 21/35 = 3/5
Answer:
4/14 = 2/7
15/20 = 3/4
21/35 = 3/5
Step-by-step explanation:
The Gades Foundation and HBM Corporation are eager to donate generously to their favorite charities. The Gades Foundation donated $250 in the first month, and each month afterward their cumulative donation total increases by $100. The HBM Corporation donated $64 in the first month, and each month afterward their cumulative donation total increases by 75 %. In which month will the HBM Corporation's cumulative donation total first exceed the Gades Foundations' cumulative donation total?
Answers
Gades Foundation
donation cumulative total
1st month 250 250
2nd month 100 350
3rd month 100 450
4th month 100 550
5th month 100 650
6th month 100 750
y = 250 + 100(n-1)
y = 250 + 100(6-1) = 250 + 500 = 750
HBM Corp.
donation cumulative total
1st month 64 64
2nd month 48 112
3rd month 84 196
4th month 147 343
5th month 257 600
6th month 450 1,050
y = 64 * (1.75)^(n-1)
y = 64 * (1.75) ⁽⁶⁻¹⁾ = 64 * (1.75)⁵ = 64 * 16.41 = 1,050
Answer:
month 6
Step-by-step explanation:
khan academy
What is the following product?
3 sqrt24 * 3sqrt 45
Answers
The product of 3√24 and 3√45 is approximately 295.77.
Explanation:To find the product, we can first simplify the individual square roots.
√24 = √(4 * 6) = 2√6
√45 = √(9 * 5) = 3√5
Substitute the simplified terms: 3 * 2√6 * 3 * 3√5 = 18√30
Factor out a 9: 18√30 = 9 * 2√(10 * 3)
Simplify the remaining square root: 9 * 2√30 ≈ 9 * 2 * 5.477 = 295.77 (rounded to two decimal places).
Therefore, the product of 3√24 and 3√45 is approximately 295.77.
Find the product of (4x − 3)(2x2 − 7x + 1).
Answers
=(4x − 3)(2x2 − 7x + 1)
=(4x*2x2) + (4x*-7x) + (4x*1) + (-3*2x2) + (-3*-7x) + (-3*1)
multiply each set of parentheses
=8x3 - 28x2 + 4x - 6x2 + 21x-3
combine like terms
ANSWER:
=8x3 - 34x2 + 25x - 3
Hope this helps! :)
In a basic sine curve, where can the zeros NOT be found?
a. middle
b. beginning
c. maximum point
d. end
Answers
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we know that
[tex]f(x)=\sin x[/tex]
It is an odd function.
It has a period of 2π because the sine wave repeats after every 2π units.
It value lies between -1 and 1.
And we know that
[tex]\sin 0^\circ=0^\circ[/tex]
And 0 occurs exactly middle of -1 and 1.
So, the zeroes can be found in the middle, beginning and at the end.
But at maximum point, there will be no zero.
As when it attains its maximum point, it won't touch x-axis.
Hence, Option 'C' is correct.