Malachi took cans to the recycling plant and put them into the can-crusher one at a time. After he had already crushed some of the cans, he started recording the number of cans he crushed per minute. This table shows how many cans Malachi put in the can-crusher at different times. Time (min) 3 5 7 9 Number of cans crushed 49 65 81 97 What is the equation that represents Malachi’s situation, where x represents the time and y represents the number of can crushed? Enter your answer in the boxes yâ’65= (xâ’ ).
Answers
The equation that represents the situation, in point-slope form, is: \(\mathbf{y - 65 = 8(x - 5)}\)
Recall:
If we know the slope and a point (a pair of values), a linear equation can be written in the point-slope form as: \(y - y_1 = m(x - x_1)\).In \(y - y_1 = m(x - x_1)\), m = slope; \((x_1, y_1)\) = a point or pair of values on a table.Using two points or pairs of values, \(slope = \frac{y_2 - y_1}{x_2 - x_1}\)Thus, we are given the table as shown below (see attachment).
The slope, using (3, 49) and (5, 65) is calculated below:
\(slope = \frac{65 - 49}{5 - 3} = \frac{16}{2} \\\\\mathbf{slope (m) = 8}\)
To write the equation in point-slope form, substitute \((x_1, y_1)\) = (5, 65) and m = 8 into \(y - y_1 = m(x - x_1)\).
Thus:\(\mathbf{y - 65 = 8(x - 5)}\)
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Related Questions
Circle O is shown. Secants C A and C E intersect at point C outside of the circle to form an angle with measure 36 degrees. Secant C A intersects the circle at point B, and secant C E intersects the circle at point D. Arc B D is 48 degrees. In circle O, what is mArc A E?
Answers
Answer:
120°Step-by-step explanation:
The external angle <C outside the circle can be expressed in terms of length of arc AE and BD using the formula below.
<C = \(\frac{AE-BD}{2} \\\)
Next is to make the length of arc AE the subject of the formula;
<C = \(\frac{AE-BD}{2} \\\)
cross multiply
\(2<C = AE-BD\)
add BD to both sides of the equation
\(2<C+BD = AE-BD+BD\\2<C +BD = AE\)
\(AE = 2<C +BD\)
Given
<C = 36°
arc BD = 48°
Substitute the given parameters into the formula;
\(AE = 2<C +BD\\AE = 2(36)+48\\AE = 72+48\\AE = 120^0\\\)
Hence mArc is 120°
Answer:
its C, 120
Step-by-step explanation:
got it right on the test
\(3\sqrt[5]{(x+2)^3}+3=27\)
Show all work
Answers
Answer:
Step-by-step explanation:
\(3\sqrt[5]{(x+2)^{3}}+3=27\)
\(3\sqrt[5]{(x+2)^{3}}=27-3\)
\(ln 3\sqrt[5]{(x+2)^{3}}= ln 24\)
\(ln 3 + ln\sqrt[5]{(x+2)^{3}}= ln 3 + ln 8\)
\(ln\sqrt[5]{(x+2)^{3}}= ln 8\)
\(\frac{3}{5} ln(x+2)= ln 8\)
\(ln(x+2)=\frac{5}{3} ln 8\)
x + 2 = \(\sqrt[3]{8^{5}}\)
x = \(\sqrt[3]{8^{5}}\) -2
Consider trying to determine the angle between an edge of a cube and its diagonal (a line joining opposite vertices through the center of the cube). a) Draw a large sketch of the problem and label any relevant parts of your sketch. (Hint: it will simplify things if your edges are of length one, one corner of your cube is at the origin, and your edge and diagonal emanate from the origin) b) Determine the angle between an edge of a cube and its diagonal (use arccosine to represent your answer).
Answers
The angle between an edge of a cube and its diagonal is:
θ = arccos 1/√3
Step-by-step explanation:
Theta Symbol: (θ), Square-root Symbol: (√):
Set up the problem: Let the Cube have Side Lengths of 1, Place the cube so that One Corner is at the Origin (0, 0, 0), and the Edge and Diagonal emanate from the origin.Identify relevant points:Label the Points:
A(0, 0, 0)
B(1, 0, 0)
C(1, 1, 1)
Where A is the Origin:AB is the Edge
AC is the Diagonal
Calculate the lengths of the Edge and Diagonal:The Lenth of the Edge AB is (1) Since it's the side length of the cube.
The length of the Diagonal AC can be found using the Distance Formula:AC = √(1 - 0)^2 + (1 - 0)^2 + (1 - 0)^2 = √3
Use the product formula:The Dot Product Formula:
u * v = |u| |v| cos θ, Where θ is the angle between the vectors:
Calculate the Dot Product of AB and AC:AB = (1, 0, 0 )
AC = (1, 1, 1 )
AB * AC = (1)(1) + (0)(1) + (0)(1) = 1
Substitute the Lengths and Dot Product into the formula:1 = (1)(√3) cos θ
Solve for the angle (θ):Divide both sides by √3
cos θ = 1/√3
Take the arccosine of both sides:θ = arccos 1/√3
Draw the conclusion:Therefore, The angle between an edge of a cube and its diagonal is:
θ = arccos 1/√3
I hope this helps!
Solve the inequality.
6x + 10 + 10x < 4(4x + 3)
Answers
Answer:
X = all #'s
why?
6x+10+10x < 4(4x+3)
Combined liked terms
16x + 10 < 16x +12
you can see that there is X on both sides and the lowest one has a +10 and the highest has a +12 so it will always be greater by 2
Answer:
undeterminate (all real numbers are a solution)
Step-by-step explanation:
1) multiply 4 by 4x and 3
6x + 10 + 10x < 16x + 12
2) added up the terms with x
16x + 10 < 16x + 12
3) add at the two members -16x
10 < 12
4) notice the 10 is ever < 12, so the inhequality is undetermined
—2х + бу = 18
Зу = 15
Answers
Answer:
x =6 y = 5
Step-by-step explanation:
3y = 15
3/3 15/3
y= 5
-2x + 6(5) = 18
-2x + 30 = 18
-30 -30
-2x = -12
-2/-2 -12/-2
x = 6
Please help me!!
Which equation is equivalent to x + 139 = 537
Answers
But where are the equations?
Answer:
You need to give us the answers
Step-by-step explanation:
Celine invests S 800 for 5 months at 3% simple interest per year.
Calculate the interest she receives.
Answers
Answer:
10%
Step-by-step explanation:
-The formula for simple interest is I = PRT
-P= Principle (amount of money invested), R= rate%, T= time in years
-I=PRT/100
-So I = 800 * 3% * (5/12) (convert 5 months to years)
-I = 10%
i hope this helps<3
:)
The amount of interest she receives is $10.
What is Simple Interest?Simple interest is defined as the interest obtained over the principal amount on a certain rate.
Given that,
Amount invested or principal amount = $800
Rate of interest = 3% = 3/100 = 0.03
Period = 5 months = 5/12 year
Amount of interest obtained in a simple interest is calculated as,
Amount of interest = P R T
Here, P is the principal amount, R is the interest rate and T is the time in years.
Interest received = 800 × 0.03 × (5/12)
= 10
Hence the interest received is $10.
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Solve the algebraic equation -4x +2 (x - 1)^2
Answers
Answer:
2x^2 - 8x + 2
Step-by-step explanation:
-4x + 2(x-1)^2
= -4x + 2(x^2 -2x +1)
= -4x + 2x^2 - 4x + 2
= -8x + 2x^2 + 2
=2x^2 - 8x + 2 (usually put the exponent kind of things first)
Which situation can be modeled by the equation 705 – m= 430?
Answers
Please help me I am stressed it is ratio tables
Answers
Answer:
1.
1/2/3/4/5/32
3/6/9/12/15/96
2.
1/2/3/4/5/12
8/16/24/32/96
3.
2/4/6/8/10/12
3/6/9/12/15/18
Step-by-step explanation:
ratios are basically in "#:#" form. then put that in a table. remember that for each one of one thing, it is equivalent to another thing. it might be easy to count it. good luck
HELP ASAP!! SOMEONE DO NUMBER 7 AND 8. ILL GIVE BRAINLIEST
Answers
Answer:
3.6 3/6 3.6 percent 3:6
Step-by-step explanation:
10:9
15:14
20:19
Answer:
7. 3:6, 3/9 (or 6/9), .33..... (or .66......), 33.3......% (or 66.6.....7)
8. 10 roses, 8 daisies, 10:8 ratio
15 roses, 13 daisies, 15:13 ratio
20 roses, 16 daisies, 20:16 ratio
( the 15 roses part was hard so if its wrong im sorry)
A pair of jeans costs $32 at Old Navy. If there is an 11% sales tax, how much will the total price of the jeans be
Answers
Answer:
35.52
$ total for the jeans
Answer:
The price of the jeans will be $28.48
Step-by-step explanation:
11% of $32 is $3.52
Do $32 - $3.52 and you get your answer of $28.48
I hope this answered your question
Using Laplace Transforms, find the solution of the initial value problem: d²y +9y =9. sin(t). U(t - 3), = y(0) = y'(0) = 0 dx²
Answers
The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.
To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:
Take the Laplace transform of the given differential equation.
Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:
s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))
Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:
s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))
Solve for Y(s).
Combining like terms, we have:
Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))
Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:
Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)
Simplifying further, we have:
Y(s) * (s⁴ + 10s² + 9) = 9s² + 9
Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):
Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)
Partial fraction decomposition.
To proceed, we need to decompose the right side of the equation using partial fraction decomposition:
Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)
Multiplying through by (s⁴ + 10s² + 9), we have:
9s² + 9 = A(s² + 9) + B(s² + 1)
Equating the coefficients of like powers of s, we get:
9 = 9A + B
0 = A + B
Solving these equations, we find:
A = 0
B = 0
Therefore, the decomposition becomes:
Y(s) = 0/(s² + 1) + 0/(s² + 9)
Inverse Laplace transform.
Taking the inverse Laplace transform of the decomposed terms, we find:
L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}
The inverse Laplace transform of 0/(s² + 1) is 0.
The inverse Laplace transform of 0/(s² + 9) is 0.
Combining these terms, we have:
Y(x) = 0 + 0
Therefore, the solution to the initial value problem is:
y(x) = 0
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Can somebody help me out ?
Answers
Answer:
The given polynomial is in standard form.
1.There are 4 terms.
2.The coefficient of the second term is 14.
3.The constant is 12.
Step-by-step explanation:
Hope this helps u!!
5/8 divided by 3/4
I'm having a bit of trouble with homework
Answers
Answer:
5/6
Step-by-step explanation:
in decimals it would be 0.83333333333
Answer:
5/6
Step-by-step explanation:
All you have to do is do KCF (Keep, Change, Flip) Keep the first fraction, change the division sign, and flip the second fraction and multiply straight across. Simplify if needed. (Hope this helps)
slope = 2; 3-intercept=-1
Answers
Answer: Slope = 2; 3-intercept=-1
Step-by-step explanation:
What is the slope of the line y=3
Answers
Answer:
m = 0
slope = 0
Step-by-step explanation:
PLEASE HELP ME WITH THIS PROBLEM, SYSTEM OF LINEAR EQUATIONS, 30 POINTS!!!!
Answers
Answer:
You can either use substation or you can use elimination on both of the problems
Step-by-step explanation:
The circumference of a circle is 23.864 inches. What is the circle's radius?
Answers
Answer:
3.8
Step-by-step explanation:
Please help me me with this please actually help me please and thank you
Answers
Answer:
A. (-1, 3)
Step-by-step explanation:
To solve, find which point in the options are in the double shaded region (the region that is shaded the darkest which is the region above the point where the lines cross).
A. (-1, 3) is the correct answer because it falls in the correct region.
B. (-4, 1) is not the correct answer because it does not fall ABOVE both lines like the question says.
C. (0, 1) is not the correct answer because it falls in the 2nd darkest region.
What is the slope of the line that passes through the points (-6, 1) and (-6,-4)?
Write your answer in simplest form.
Answers
Answer:
The slope is undefined
Step-by-step explanation:
a circular pool is surrounded by a brick walkway 3 m wide. find the ra- dius of the pool if the area of the walk- way is 198 m*.
Answers
The radius of the pool is 9.01 m.
Given,
In the question:
A circular pool is surrounded by a brick walkway 3 m wide.
The area of the walk- way is 198 m^2.
To find the Radius of the pool.
Now, According to the question:
"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".
Let R = Radius of the pool
Area of the circle bounded by the outside edge of the walkway is:
\(\pi\)(R +3)^2
Area of the pool is:
\(\pi R^2\)
Now, Our equation is:;
\(\pi\)(R +3)^2 - \(\pi R^2\) = 198
\(\pi\)((R+3)^2 - \(R^2\)) = 198
Open the inner bracket :
\(\pi\)(\(R^2+6R+9-R^2\)) = 198
\(\pi\)(6R +9) = 198
6R+9 = 198/\(\pi\)
6R = 198/\(\pi\) - 9
R = (198/\(\pi\) - 9)/6
R = (198/(3.14) - 9)/6
R = (63.057 - 9)/6
R = 54.057/6
R = 9.01 meters
Hence, The radius of the pool is 9.01 m.
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pls help im stuck in this question
Answers
Based on the number of members and the ratio in which they chose the types of film, the number who chose Action in the second week more than the first week is 6 people.
How many chose Action more in the second week?Assuming that the number of members is 99 members, the number who chose Action on the second week were:
= (7 / (5 + 7 + 6)) x 99
= 39 people
The number who chose Action in the first week:
= (5 / (2 + 5 + 8)) x 99
= 33
The difference is:
= 39 - 33
= 6 people
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Help is needed please
Answers
Answer:
y = 0
Step-by-step explanation:
Let's use the addition method.
2x + y - 10 = 0
x - y - 5 = 0
Write the first equation as is. Write below it the second equation multiplied by -2 on both sides. Then add the equations.
2x + y - 10 = 0
(+) -2x + 2y + 10 = 0
--------------------------------
3y = 0
Divide both sides by 3.
y = 0
Answer: y = 0
Fifteen of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select a DVR that is not defective? The probability is nothing.
Answers
Answer:
17/20Step-by-step explanation:
Fifteen of the 100 digital video recorders (DVRs) in an inventory are known to be defective, the total number of non-defective DVRs will be 100-15 = 85 DVRs.
If 85 DVRs are not defective, the probability that you randomly select a DVR that is not defective can be expressed as:
P(non-defective DVRs) = Total number of non-defective DVRs /Total DVRs
P(non-defective DVRs) = 85/100
P(non-defective DVRs) = 17/20
Answer:
0.85
Step-by-step explanation:
Given;
Number of defective DVRs D = 15
Total number of DVRs T = 100
Number of non defective DVR N = T - D = 100 - 15 = 85
The probability of selecting a non defective DVR P(N) is equal to the number of non defective DVR divided by the total number of DVRs.
P(N) = N/T
Substituting the values;
P(N) = 85/100
P(N) = 17/20 = 0.85
Which statement BEST describes V125? A) between 11 and 12 B) between 1 and 13 between 13 and 14 D) between 14 and 15
Answers
Answer:
Step-by-step explanation:
Answer: A) between 11 and 12
Step-by-step explanation:
Because 125 squared = 11.18033988 …
Bill is looking for the best deal on a television that has a wholesale price of $599. Help him compare the price of the
television at two different stores by completing the following.
(a) Bill looks at the television in a department store that marks up the television's wholesale price 50%. But because of
a customer loyalty program, he would receive a 20% discount off the in-store price. Ignoring tax, how much would
he pay for the television at this store?
(b) Bill then goes to a superstore that marks up the television's wholesale price 30% But he is not a member of the
superstore's customer loyalty program. He must pay the full in-store price. Ignoring tax, how much would he pay
for the television at this store?
Answers
Therefore , the solution of the given problem of percentage comes out to be $239.6 price he will pay on first store and $419.3 on second store.
Define percentage.In mathematics, a percentage is any value that can be written as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," or "pc." However, it is commonly indicated by the "%" mark. The proportional amount is flat and lacks any dimensions. Since percentages have a numerator of 100, they can be thought of as fractions. The percent symbol (%) must come after a number to denote that it is a percentage.
Here,
Given :
Price of television is $599
a)
First store is :
=> 50/100 * 599
=> 299.5
and
additional 20% discount :
=> 20/100 * 299.5
=> 59.9
current price =299.5 -59.9 = $239.6
b)
=> 30/100 * 599
=> 179.7
=> 599 - 179.7
=> $419.3
Therefore , the solution of the given problem of percentage comes out to be $239.6 price he will pay on first store and $419.3 on second store.
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A stack of 1000 sticky notes is in the shape of a square prism. The prism has a volume of 13.5 in3 each sticky note measure 3 in by 3 in what is the height of the stack of sticky notes.
Answers
Answer:
1.5 inches
Step-by-step explanation
Volume of a prism = base area x height
base area = length² (the base in the form of a square)
3² = 9
13.5 = 9 x height
height = 13.5 / 9 = 1.5 inches
The area of a circle is modeled by the equation A = πr^2. Rewrite the equation in terms of the circles radius r. In your final answer, include all of your calculations. (brainliest to best answer)
Answers
Answer:
First off, the area of a circle should be pi times r squared, not r times pi squared. I will do my math using this correction.
If A = (pi)r^2 then first we can devide both sides by pi, leaving
A/pi = r^2
To solve for r, we need to take the square root of both sides, leaving
sqrt(A/pi) = r
or
r = sqrt(A/pi)
Step-by-step explanation:
this would be your answer
r = √(A/π)
Step-by-step explanation:
A = πr²
A/π = r²
±√(A/π) = r
But the only thing is that you can't have a negative radius, so you just have to rewrite the answer as positive.
√(A/π) = r
(0,2), (3,3), (8,7), (2,2), (3,9)
Domain :
Range:
Answers
Answer:
Domain: ( 0, 3, 8, 2 )
Range : (2, 3, 7, 9)
Step-by-step explanation: