Answer:
The exact volume of an oblique cylinder is [tex]V=2,000\pi\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The Cavalieri's principle states that if two or more figures have the same cross-sectional area at every level and the same height, then the figures have the same volume
so
The volume of the oblique cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]h=20\ cm[/tex]
[tex]r=10\ cm[/tex]
substitute
[tex]V=\pi (10)^{2} (20)[/tex]
[tex]V=2,000\pi\ cm^{3}[/tex]
Answer:
the volume of an oblique cylinder is V=2,000\pi\ cm^{3}
How many terms are in the expression shown below?
2x3 - 10x2 +Z
2
3. 4. 5
Answer:
3 terms. All of the numbers are considered terms.
Step-by-step explanation:
If it asked for variables, it would be 2.
The sum of all but one interior angle of a heptagon is 776°. The final angle must have a measure of degrees.
Answer:
The final angle is 124°
Step-by-step explanation:
1. Getting the total sum of all angles:
The general rule to get the sum of all interior angles is as follows:
sum of interior angles = (n-2)*180
where n is the number of sides
We know that a heptagon has 7 sides, therefore:
sum of interior angles of a heptagon = (7-2)*180 = 5 * 180 = 900°
2. Getting the missing angle:
We know that the total sum of all 7 angles is 900°
We also know that the sum of 6 of those angles = 776°
This means that:
measure of the last angle = 900 - 776
measure of last angle = 124°
The final angle is 124°
Hope this helps :)
Answer:
124 degrees
Step-by-step explanation:
Find the area of a regular hexagon with an apothem 11.4 yards long and a side 13 yards long. Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
area=6×11.4×13÷2=444.6 yd²
Final answer:
The area of a regular hexagon with an apothem of 11.4 yards and a side of 13 yards is approximately 444.6 square yards when rounded to the nearest tenth.
Explanation:
To find the area of a regular hexagon with a given apothem and side length, you can use the formula for the area of a regular polygon:
Area = (1/2) × Perimeter × Apothem
In this case, the perimeter of the hexagon can be calculated by multiplying the length of one side by 6 (since a hexagon has 6 sides). Therefore, the Perimeter = 13 yards × 6 = 78 yards.
Now, plug the values into the area formula:
Area = (1/2) × 78 yards × 11.4 yards
Area = (1/2) × 889.2 square yards
Area = 444.6 square yards
So, the area of the regular hexagon is approximately 444.6 square yards, when rounded to the nearest tenth.
In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that the test has a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the university?
Answer:
1329
Step-by-step explanation:
A suitable calculator can tell you the minimum score is 1329.
Using the concept of z-scores and normal distributions, the lowest possible SAT score a student needs to qualify for acceptance into a top university, that requires top 5% of SAT scores, is approximately 1328.
Explanation:The subject of your question falls under Mathematics, particularly statistics. The problem involves understanding SAT scores and how they apply to scholarships. The problem also asks for the understanding of z-scores and how they apply to normal distributions.
In this case, the SAT score requirement is stated to be within the top 5% of all test-takers. In terms of z-scores, this requirement matches with a z-score of approximately 1.64, since z-scores of this value represent the cut-off for the top 5% in a normal distribution.
To calculate the corresponding SAT score, we use the formula for z-score which is Z = (X - μ) / σ, where X is the SAT score, μ is the mean and σ is the standard deviation. We rearrange the formula to find X, where X = Z * σ + μ. Since we know the mean (μ = 1000), standard deviation (σ = 200), and Z (Z = 1.64), we can substitute these values to get X = 1.64 * 200 + 1000 = 1328.
Therefore, the lowest possible score a student needs to qualify for acceptance into the university is approximately 1328.
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The soccer team collected $800 at a car wash fundraiser. They charged $5.00 for small vehicles and $10.00 for larger vehicles. The amount collected can be modeled by the equation. What is the equation?
Answer:
The equation is 5x + 10y = 800
Step-by-step explanation:
* Lets explain what is the equation and how can we make one
- The equation is a mathematical statement that two things are equal.
- It consists of two expressions, one on each side of an equal sign (=).
* Lets solve the problem
- There are two types of vehicles, large one and small one
- The cost of washing the small vehicle is $5
- The cost of washing the larger vehicle is $10
- They collected from washing both is $800
- To make an equation for the amount collected let the number of the
small vehicles is x and the number of the large vehicles is y
∵ x is the number of the small vehicles were washed
∵ y is the number of the large vehicles were washed
∵ The cost of washing the small vehicle is $5
∵ The cost of washing the larger vehicle is $10
∴ The money collected from the small vehicles = 5 × x = 5x
∴ The money collected from the large vehicles = 10 × y = 10y
- find the total money collected from both
∴ The amount of money collected from both = 5x + 10y
∵ The amount of money collected is $800
- Equate the two expressions above
∴ 5x + 10y = 800
* The equation is 5x + 10y = 800
Where do you find sculptures of great baseball sluggers math worksheet answers?
The sculptures of great baseball sluggers are found in famous places of the city.
Here,
The sculptures of any famous personalities are installed in the places that are frequently visited by the public , so that the it will gain traction.
Thus,
The sculptures of famous baseball players will be available in city malls , museums , parks or baseball stadium.
The players coming to play baseball will be motivated by seeing their idols.
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According to this partial W-2 form, How much money was paid in FICA taxes?
FICA taxes on a W-2 form include Social Security and Medicare taxes, summed up at a standard rate of 7.65% of gross wages. To know the total FICA taxes paid, one must multiply the gross wages by 7.65% based on the provided rates.
Explanation:The question is asking for the total FICA taxes paid, which includes both Social Security and Medicare taxes. The information provided indicates that the employee pays 6.2% for Social Security and 1.45% for Medicare, which are standard rates for FICA tax deductions. To calculate the total amount of FICA taxes, add these percentages together to get a combined rate of 7.65%. If you know the gross wages, you multiply this amount by 7.65% to find the total FICA tax contribution on your W-2 form. If the actual gross wages earned are unknown, the calculation cannot be completed without this figure.
It is important to note that your employer also matches the FICA tax contributions, and some economists argue that this employer contribution effectively reduces employees' wages, meaning that employees might bear the total cost of these taxes indirectly.
I have a model motorcycle that is all metal parts and is 18" long. Since the size all the models online are given in a scale, What scale to an actual motorcycle do I have and where do I look to find a value?
Answer:
See below.
Step-by-step explanation:
The model may have the scale written somewhere. Try looking for it.
If you can't find it, then you can calculate this way.
Search online for the real motorcycle's length.
Then divide the scale model's length, 18 inches, by the real length. Express that as a ratio. That is the scale.
Let's say the length of a real motorcycle of this type is 90 inches.
Divide 18 inches by 90 inches.
18/90 = 1/5
The scale, then, is 1:5.
The number –1,000 can be used to indicate a(n) A. increase in inventory of 1,000 units. B. harvest of 1,000 bushels of wheat. C. withdrawal of $1,000 from a checking account. D. receipt of $1,000.
Answer:
C. withdrawl of $1000 from a checking account
Step-by-step explanation:
When you withdraw money from a checking account, you lose the amount of money which you withdraw. In this situation, you are withdrawing $1000, which means you have -1000 dollars in your checking account
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For more questions or more information, please comment below!
Please answer this multiple choice question for 27 points and brainliest!!
Answer:
A
Step-by-step explanation:
The equation will be in the form
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (2.5, 0) ← 2 points on the line
m = [tex]\frac{0-5}{2.5-0}[/tex] = - 2
The line crosses the y- axis at (0, 5) ⇒ c = 5
y = - 2x + 5 or
y = 5 - 2x → A
Rosana is tracking how many customers she can serve in a morning. She listed the number of customers served per hour in the following table:
Hour (x) Number of Customers f(x)
1 3
2 5
3 7
Determine if these data represent a linear function or an exponential function, and give the common difference or ratio.
A. This is a linear function because there is a common difference of 2.
B. This is an exponential function because there is a common ratio of 2.
C. This is a linear function because there is a common difference of 3.
D. This is an exponential function because there is a common ratio of 3.
Answer:
A. This is a linear function because there is a common difference of 2
Step-by-step explanation:
Differences are ...
5 - 3 = 27 - 5 = 2The differences of 2 are common, so this is an arithmetic function.
Option: A is the correct answer.
A. This is a linear function because there is a common difference of 2.
Step-by-step explanation:Linear function--
A function is said to be linear if the rate of change is constant.
i.e. the function is increasing by a fixed constant.
Here the table is given by:
Hour (x) Number of Customers f(x)
1 3
2 5
3 7
From the table of values we observe that as the value of increasing by 1 the value of y is increasing by 2.
i.e. the rate of change is constant i.e. 2.
Also, the common difference is 2.
since,
5-3=2
and 7-5=2
Hence, the table represents a linear function.
What does the graph of an equation reveal about the solutions to the equation? How do you solve a system of equations approximately using graphs and tables?
Final answer:
The graph of an equation reveals all possible solutions, and a system of equations can be solved graphically by finding the intersection points of their lines. Changing the slope or intercept allows manipulation of these lines, and growth rates show the rate of increase as perce
Explanation:
The graph of an equation illustrates the relationship between two variables and reveals the set of all possible solutions that satisfy the equation. When graphing a line, the slope dictates the direction and steepness of the line, while the intercept indicates where the line crosses the y-axis. To manipulate a line on a graph, you can change the slope or the intercept, altering its position and angle.
To solve a system of equations using graphs, plot each equation on the same set of axes. The point where the lines intersect represents the solution to the system, which is the set of values that satisfies all equations simultaneously. If using tables, input different values for one variable and solve for the other to find ordered pairs. When the pairs from different equations match, you've found an approximate solution. A growth rate can be determined by calculating the percentage change and can be interpreted as the rate at which a quantity increases over time.
Learning how to read and manipulate a graph is critical to interpret and express equations visually. Graphs not only convey solutions but also the behavior of equations, such as trends and growth rates, which are essential in understanding and communicating mathematical concepts effectively.
A farmer wants to plant peas and carrots on no more than 200 acres of his farm. If x represents the number of acres of peas and y represents the number of acres of carrots for solution (x, y), then which is a viable solution?
A.(−50, 160)
B.(80, 160)
C.(75, −200)
D.(60, 135)
Answer:
Option D.(60, 135)
Step-by-step explanation:
Let
x -----> the number of acres of peas
y ----> the number of acres of carrots
we know that
The inequality that represent the problem is equal to
[tex]x+y\leq 200[/tex]
so
Verify each case
case A) (-50,160)
substitute the value of x and the value of y in the inequality and then compare the result
[tex]-50+160\leq 200[/tex]
[tex]110\leq 200[/tex] ----> is true
The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number
case B) (80,160)
substitute the value of x and the value of y in the inequality and then compare the result
[tex]80+160\leq 200[/tex]
[tex]240\leq 200[/tex] ----> is not true
therefore
The point is not a solution
case C) (75,-200)
substitute the value of x and the value of y in the inequality and then compare the result
[tex]75-200\leq 200[/tex]
[tex]-125\leq 200[/tex] ----> is true
The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number
case D) (60,135)
substitute the value of x and the value of y in the inequality and then compare the result
[tex]60+135\leq 200[/tex]
[tex]195\leq 200[/tex] ----> is true
therefore
The point is a viable solution
two lengths of a triangle are show
I can't give you the correct answer but you can guess for it, cause I can give you the the scop of the length of KL.
So, as we know this;
The sum of the two sides of a triangle is greater than the third and the difference between the two sides is less than the third.
10+5 >= KL >= 10-5
15 >= KL >= 5
based on your option, the answer should be:
9 in
Given the equation 6/x=3/k+2, and the constraints x ≠ 0 and k ≠-2, what is x in terms of k?
A) x=2k+4
B) x=2k+12
C) x=2k-1/4
D) x=1/4+12
Answer:
A) 2k+4
Step-by-step explanation:
To solve for terms of x, we need to. she sure that x is on its own side while every other term is on the other side.
To start, we will cross multiply. If we have a/b=c/d, then ad=bc
We can perform the same calculation here,
6/x=3/(k+2)
6(k+2)=3x
Divide both sides by 3
2(k+2)=x
x=2k+4
What is the solution to this system of equations?
x + 2y = 4
2x + 4z = 8
3y − z= 10
A. (-6, 5, 5)
B. (2, -4, 1)
C. no solutions
D. (1, 8, -2)
E. infinite solutions
Answer:
A. (-6, 5, 5)
Step-by-step explanation:
A suitable calculator can reduce the augmented matrix for the system.
Which of the following equations is of the parabola whose vertex is at (4, 3), axis of symmetry parallel to the y-axis and focus at (4, -3)?
A.) y+3=1/24 (x+4)^2
B.)y-3=-1/24 (x-4)^2
C.)x-4=-1/24 (y-3)^2
Answer:
B.
Step-by-step explanation:
First thing to determine is how this parabola opens. Up or down? Or left or right?
*We see that the axis of symmetry is a line parallel to the y-axis; therefore, the axis of symmetry is an x = line, making this an up or down parabola. Now we need to determine how everything else all fits in.
The standard form of this type of parabola is
[tex]4p(y-k)=-(x-h)^2[/tex]
where p is the distance between the vertex and the focus. If the vertex has a y coordinate of 3, and the focus has a y coordinate of -3, the vertical distance between those 2 numbers is 6. Therefore, p = 6. Filling in then:
[tex]4(6)(y-3)=-(x-4)^2[/tex]
and [tex]24(y-3)=-(x-4)^2[/tex]
Dividing both sides by 24 gives you what you are looking for:
[tex]y-3=-\frac{1}{24}(x-4)^2[/tex]
The equation of the parabola is:
⇒ y - 3 = -(1/24)(x - 4)²
What is Parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.
We can use the standard form of the equation of a parabola with vertex (h, k) and axis of symmetry parallel to the y-axis, which is given by:
(x - h)² = 4p(y - k)
where (h, k) is the vertex and p is the distance between the vertex and the focus.
In this case, the vertex is (4, 3) and the focus is (4, -3).
Therefore, We get;
p = 3 - (-3)
p = 6.
Substituting the values of h, k, and p, we get:
(x - 4)² = 4(6)(y - 3)
Simplifying, we get:
(x - 4)² = 24(y - 3)
Now, we can simplify the equation to match it with the given options:
(x - 4)² = 24y - 72
(x - 4)² + 72 = 24y
y = (1/24)(x - 4)² + 3
Therefore, the equation of the parabola is:
B.) y - 3 = -(1/24)(x - 4)²
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I need Help!!!! Please Solve and show WORK!!!
3(x+2)=15
Answer: x=3
Step-by-step explanation: First we do distributive property in the parentheses. Next we subtract both sides by 6. Lastly we divide both sides by 3. Algebraic Rules!!!
Work:
3(x+2)=15
3x+6=15
3x+6-6=15-6
3x=9
3x/3=9/3
x=3
Multiply the bracket by 3
3x+6=15
3x+6-6=15-6
3x=9
divide by 3 for 3x and 9
3x/3=9/3
x=3
Check answer by using substitution method
3(x+2)=15
3(3+2)= 15
Multiply the bracket by 3
9+6= 15
15= 15
Answer is x= 3
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what is the exact value of cos 90degrees as found on the unit circle?
Answer:
it is 0 because cosine is the x and sine is the y. Sin is 1 and cos is 0
Write the equation of the graph shown in factored form.
let's take a peek at the graph.
the graph of the equation touches the x-axis at 1, 2 and 3, at 1 it crosses it, at 2 it crosses it, at 3 is doesn't cross it, it simply bounces off of it.
on the roots/solutions the graph crosses the x-axis, they have ODD multiplicity, on the solutions it bounces off of it, they have EVEN multiplicity, so then.
x = 1 => x - 1 = 0 <------ one factor
x = 2 => x - 2 = 0 <------ another factor
x = 3 => x - 3 = 0 <------ another factor, BUT with even multiplicity
(x-1)¹(x-2)¹(x-3)² = f(x)
(x-1)(x-2)(x-3)² = f(x).
Analyze the zeros of f(x) =x^4 - 3x^3 - 2x^2 + 3x + 5.
Determine the number of possible positive real zeros and the number of possible negative real zeros
a. positive 1; negative 3 or 1
b. positive 1; negative 2 or 1
c. positive 3 or 1; negative 1
d. positive 2 or 1; negative 1
Answer:
c
Step-by-step explanation:
c. positive 3 or 1; negative 1
A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle.
The first step in solving by factoring is to write the equation in standard form, setting one side equal to zero. What is the equation for the situation, written in standard form?
Choose one of the best answers.
A. x² – 99 = 0
B. x² – 99x = 0
C. x² + 5x + 104 = 0
D. x² + 5x – 104 = 0
Please explain your answer?
If your answers is wrong, it's going mark your answer report and it's called "improper answer."
No need to spam answers, if your answer is spam is going to be report.
Don't copied or paste answers with someone else answers from other sites. If you copied and paste answers from other websites and it mark your answer report and it's called "plagiarism."
Thank you!
-Charlie
Answer:
D
Step-by-step explanation:
(x + 5)x = 104
Distribute:
x² + 5x = 104
Subtract 104 from both sides:
x² + 5x − 104 = 0
Matthew earned $325 giving haircuts. He charged $25 for each haircut. How many haircuts did he give? PLEASE ANSWER AS SOON AS POSSIBLE (nvm i got it)
Answer: 13
Step-by-step explanation:
Divide 325 by 25
Taylor fires a toy rocket from ground level. The height of the rocket with respect to time can be represented by quadratic function. If the toy rocket reaches a maximum height of 34 feet, 3 seconds after it was fired, which of the following functions could represent the height, h, of the rocket t seconds after it was fired?
A) h(t)=-16(t-3)²+34
B) h(t)=-16(t+3)²+34
C) h(t)=16(t-3)²+34
D) h(t)=16(t+3)²+34
Answer:
The function in choice
A) [tex]h(t) = -16(t - 3)^{2} + 34[/tex]
could possibly represent this relationship.
Step-by-step explanation:
Consider the vertex form of parabolas with a local extrema at [tex](x_{0}, y_{0})[/tex].
[tex]y = a(x - x_{0})^{2} + y_0[/tex].
Note the minus sign in front of [tex]x_0[/tex] in this expression.
The coefficient [tex]a[/tex] cannot be zero. The value of [tex]a[/tex] depends on the direction and width of the parabola's opening:
[tex]a > 0[/tex] if the parabola opens upwards, and[tex]a < 0[/tex] if the parabola opens downwards.The width of the opening decreases as the value of [tex]a[/tex] increases.For this parabola,
[tex]a < 0[/tex] since the parabola opens downwards: the height of the rocket will eventually decrease as the rocket falls back to the ground;[tex]t_0 = 3[/tex], and[tex]h_0 = 34[/tex].Among the four functions, only the function in A) meets the requirements.
I
f point A is located at (–15, –7) and JKL has vertices at J(–22.5, –10.5), K(19.5, –3.0), and L(–4.5, 15.0), find the scale factor ABC to JKL of the dilation from
Answer:
1.5
Step-by-step explanation:
The coordinate values of point J are 1.5 times those of point A, so if dilation is about the origin, the scale factor is 1.5.
If the dilation is about some other point, this problem statement does not contain enough information to tell what the scale factor might be.
Solve for x.
5(2x - 1) = 6
x = 1/10
x = 11/10
x = 1/2
Answer:
Distributive Law : x= [tex]\frac{11}{10}[/tex]
Step-by-step explanation:
5(2x - 1) = 6
Using Distributive law on right hand side we get
5*2x - 5 * 1 = 6
10x - 5 = 6
Now we add 5 on both hand sides
10x-5+5=6+5
10x= 11
Now we divide both sides by 10
[tex]\frac{10x}{10} = \frac{11}{10}[/tex]
Hence we get
x= [tex]\frac{11}{10}[/tex]
Solve the 3 × 3 system shown below. Enter the values of x, y, and z. X + 2y – z = –3 (1) 2x – y + z = 5 (2) x – y + z = 4 (3)
[tex]\boxed{x=1, \y=-1, \ z=2}[/tex]
Step-by-step explanation:We will use the Gaussian elimination method to solve this problem. To do so, let's follow the following steps:
Step 1: Let's multiply first equation by −2. Next, add the result to the second equation. So:
[tex]\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\~~ x&-~~~~~ y&+~~~~ z&~=~4\end{array}[/tex]
Step 2: Let's multiply first equation by −1. Next, add the result to the third equation. Thus:
[tex]\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&-~~~3~ y&+~~2~ z&~=~7\end{array}[/tex]
Step 3: Let's multiply second equation by −35, Next, add the result to the third equation. Therefore:
[tex]\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\&-~~~5~ y&+~~3~ z&~=~11\\&&+~~\frac{ 1 }{ 5 }~ z&~=~\frac{ 2 }{ 5 }\end{array}[/tex]
Step 4: solve for z, then for y, then for x:
[tex] \frac{ 1 }{ 5 } ~ z & = \frac{ 2 }{ 5 } \\ \\ \boxed{z & = 2}[/tex]
[tex]-5y+3z &= 11\\-5y+3\cdot 2 &= 11\\ \\ \boxed{y &= -1}[/tex]
By substituting [tex]y=-1 \ and \ z=2[/tex] into the first equation, we get the [tex]x[/tex]. So:
[tex]x+2(-1)-2=-3 \\ \\ x-2-2=-3 \\ \\ \boxed{x=1}[/tex]
Answer:
X= 1, y= -1, z= 2
Step-by-step explanation:
jackson bought 555 ounces of raisins for \$4$4dollar sign, 4. How much do raisins cost per ounce? \$$dollar sign How many ounces of raisins can be bought for \$1$1dollar sign, 1? ounces
Answer:
$.80 and 1.25
Step-by-step explanation:
hope this helps
If carol travels 30 miles and her car averages 48 miles per hour, how long will it take carol to complete the distance?
[tex]\bf \begin{array}{ccll} miles&hours\\ \cline{1-2} 48&1\\ 30&x \end{array}\implies \cfrac{48}{30}=\cfrac{1}{x}\implies \cfrac{8}{5}=\cfrac{1}{x}\implies 8x=5 \\\\\\ x=\cfrac{5}{8}\qquad \textit{37 minutes and 30 seconds}[/tex]
Twenty-five blue and twenty-five yellow marbles are placed in a jar. Thirty-four marbles are removed from the jar and put in a second jar. What is the positive difference between the number of blue marbles in the second jar and the number of yellow marbles remaining in the first jar?
Answer:
a) Let b represent the number of blue marbles placed in the second jar. Then 34-b is the number of yellow marbles in the second jar, and 25 - (34-b) is the number of yellow marbles remaining in the first jar. That value simplifies to b-9. The positive difference between b and (b-9) is 9.
b) Let n, d, p represent the numbers of nickels, dimes, and pennies, respectively.
.. (5n + 10d + p)/(n + d + p) = 7 ... the average value of the collection is 7 cents per coin
.. (5(n-1) + 10d + (p+5))/((n-1) + d + (p+5)) = 6 ... replacing one nickel with pennies changes the average to 6 cents per coin
Multiplying by the denominator and subtracting the right side of each resulting equation gives
.. 10d + 5n + p = 7d + 7n + 7p
.. 10d + 5n + p = 6d + 6n + 6p + 24
Subtracting the second equation from the first gives
.. 0 = d + n + p - 24 ... tells us the total number of coins is 24. This tells us the total value is $1.68 = 24*$0.07.
This sum will consist of at least 3 pennies. If that is all the pennies, then the remaining 21 nickels and dimes must add to $1.65. If all were nickels, the value of the 21 coins would be $1.05. We have $0.60 more than that. For each nickel traded for a dime, we gain $.05, so 12 of the 21 nickels must be traded for dimes to raise the total coin value to $1.65.
Alternatively, you can write two equations in the two unknowns:
.. d + n = 21
.. 10d + 5n = 165
Subtracting 5 times the first equation from the second gives
.. 5d = 60 ... which gives the same answer as reasoned above.
There are 3 pennies, 9 nickels, 12 dimes. (If there are 8 pennies to start, then the number of nickels is zero, so it is impossible to trade one for 5 pennies. The solution shown is the only one.)