Twelve pennies are arranged in a row on a table every other coin is replaced with a nickel then every third coin is replaced with a dime finally every fourth coin is replaced with a quarter what is the total value of the coins on the table?

The value of y is:

           [tex]y=\dfrac{93-qa}{q-67}[/tex]

We are given a expression in terms of three unknowns q,a and y.

Now, we are asked to solve this expression for y.

i.e. we are asked to represent y in terms of other two unknowns.

We will first use the distributive property under multiplication in the left hand side of the equation.

i.e.

[tex]q\times a+q\times y=67y+93\\\\i.e.\\\\qa+qy=67y+93[/tex]

Now, we combine the terms of y at one side of the equation and the other terms to the other side.

i.e.

[tex]qy-67y=93-qa\\\\i.e.\\\\(q-67)y=93-qa\\\\i.e.\\\\y=\dfrac{93-qa}{q-67}[/tex]

Answer:

  not a right triangle

Step-by-step explanation:

The slope of AB is -1/4; the slope of BC is 2. These are not negative reciprocals of one another.

Answer: True.

Step-by-step explanation:

Given: The graph below shows the graphs of the linear function y=7x and the exponential function [tex]y=7^x[/tex]

Both of the function have same value of rate =7

But in linear function y=7x , 7 is the constant of proportionality.

In exponential function [tex]y=7^x[/tex], 7 is the multiplicative rate of change.

For [tex]1\leq x\leq 3[/tex]

For y=7x ,

x    y

1     7

2    14

3    21

For [tex]y=7^x[/tex]

x    y

1    7

2   49

3    343

Thus, we can see the growth rate of  the exponential function exceeds the growth rate of the linear function for [tex]1\leq x\leq 3[/tex].

Answer:

D

Step-by-step explanation:

Just took test on it

The solution for the problem is:

d(S,P) = √(0-0)^2 + √(b-0)^2
d(S,P) = √b^2
d(S,P) = b

so we know that, SP = b

d(P, Q) = √(a-0)^2 + √(b-b)^2
d(P, Q) = √a^2
d(P, Q) = a
so
PQ = a 

SQ = c^2 = a^2 + b^2
SQ = √(a^2 + b^2)

Therefore, the answer is √(a^2 + b^2).

Proof of the congruence of the diagonals of a rectangle involves the distance formula stemming from the Pythagorean theorem and can be shown using specific coordinates. Comparing areas of squares uses the squares of the side lengths which simplifies to ratios.

The lengths of the diagonals of a rectangle can be found using the distance formula, which is derived from the Pythagorean theorem. To prove the diagonals are congruent, coordinates are assigned to the vertices of the rectangle and the distance formula is applied to both diagonals. If the rectangle is placed with one corner at the origin and sides along the axes, then this process is further simplified as one can use the differences in x-coordinates and y-coordinates directly.

If we have a rectangle with vertices at coordinates (0,0), (a,0), (a,b), and (0,b), the diagonal lengths can be found by using the distance formula: the diagonal between (0,0) and (a,b) would have a length of √(a² + b²), and the diagonal between (a,0) and (0,b) would also have a length of √(a² + b²), proving that they are congruent. Additionally, when comparing areas using ratios, one simply needs to compare the squares of the lengths of respective sides, as the area of a square is the square of its side length.

The value of r in a solution of the expression 5 + r - 2 = 9 is,

⇒ r = -6

Given that,

A mathematical expression is,

⇒ 5 + r - 2 = 9

Now, simplify the expression by combining like terms as,

⇒ 5 + r - 2 = 9

⇒ 3 - r = 9

Add r on both sides,

⇒ 3 = 9 + r

Subtract 9 on both sides,

⇒ 3 - 9 = r

⇒ - 6 = r

Therefore, the solution of the expression is,

⇒ r = -6

To learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

CIDR, or Classless Inter-Domain Routing, is tied to IP address aggregation and subnetting, which help in efficient IP address allocation and network management.

Classless Inter-Domain Routing, commonly known as CIDR, is a method for allocating IP addresses and routing Internet Protocol packets.

Two terms often associated with CIDR are IP address aggregation and subnetting. IP address aggregation involves the grouping of multiple networks into a single, larger network, represented as a CIDR block.

Subnetting refers to dividing a larger network into smaller, more manageable sub-networks or subnets. This technique can help reduce the number of routing table entries needed in a network, which improves routing efficiency and conserves the limited supply of IP addresses.

The linear function represents the line given by the point-slope equation y + 1 = –3(x – 5) is f(x) = -3x + 14.

"In a Point-slope form it is likely to be y - y1 = m(x - x1). This form of a linear equation is derived from a equation for finding the slope of a line."

Given

The point-slope equation y + 1 = –3(x – 5)

By solving the above equation

y + 1 = -3x + 15

⇒ y = -3x + 15 - 1

⇒ y = -3x + 14

Replace y with f(x)

⇒ f(x) = -3x + 14

Hence, the linear function represents the line given by the point-slope equation y + 1 = –3(x – 5) is f(x) = -3x + 14.

Learn more about point-slope equation here

https://brainly.com/question/11365604

#SPJ2

If the discriminant of an equation is zero, then the correct statement amongst given statement is:

      a.    It has one real solution

We have three cases of discriminant--

1.      To construct parallel lines, first, you must start with a line segment AB that well copies. Mark another point called C. Set the compass to the point A and adjust the compass to the width of the original line. Then without moving the compass, put it on point C and mark the end and label it D. Use a straightedge to connect the points and now you’ve copied a line segment.

2.      First, you click the line and make a line segment. Then make a separate point anywhere. Then you double-click perpendicular lines and click parallel lines. Click and drag the line segment onto the separate point.

3.      First, you start with a point on a line. Then you put your compass on the point and mark an arc on each side of the line and put points on them. Then you put the compass on one of the points and make an arc above the original point. Do the same for the other side. You should end up with 2 X’s on top and bottom of the original point. Then mark points on the Xs. Finally, use a straight edge to connect the two X’s which will make a bisecting line through the original.

4.      First, you make a line and click perpendicular lines and you will have a straight line cutting through the original.

Answer:

Step-by-step explanation:

The statement "The following sequence is arithmetic. 18, 11, 4, -3, -10, -17 is True.

To determine if a sequence is arithmetic, one must check if there is a common difference between consecutive terms. The common difference (d) can be found by subtracting any term in the sequence from the term immediately following it.

Let's calculate the common difference for the given sequence:

- For the first two terms: (11 - 18 = -7)

- For the next two terms: (4 - 11 = -7)

- For the following two terms: (-3 - 4 = -7)

- And for the last two terms provided: (-10 - (-3) = -10 + 3 = -7)

 Since the difference between each pair of consecutive terms is constant and equal to \(-7\), this confirms that the sequence is indeed arithmetic. Therefore, the statement is True.

By multiplication property of equality, we can eliminate fractions and decimals from equations. Option C is correct.

Given that,
To determine which property justifies the procedure used to eliminate fractions and decimals from equations.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Suppose the equation
1 / 4 = 0.25
Now multiply both sides by 4
4 * 1/ 4 = 0.25 * 4
1 = 1
So, by multiplication property of equality, we can eliminate fractions and decimals from equations.

Thus, by multiplication property of equality, we can eliminate fractions and decimals from equations.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer:

n ≥ 9

Step-by-step explanation:

The lateral surface of a cone is the curved surface that connects the base of a cone to the apex of the cone.

The lateral surface of a cone refers to the curved surface area that connects the base of the cone to its apex (the pointed top).

It forms the sloping sides of the cone.

In a cone shape, the base is a circle, and the lateral surface is the part that wraps around the sides to meet at the apex.

This surface does not include the base or the tip of the cone. It is only the curved part that connects the two.

The lateral surface area of a cone can be calculated using the formula A = πrl, where A represents the lateral surface area, r is the radius of the base of the cone, and l is the slant height, which is the distance from the apex to any point on the edge of the base.

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ6

A cheeseburger contains 290 calories and a small fries contains 230 calories.

Let X be the number of calories in a cheeseburger, and Y be the number of calories in a small fries.

From the given information, we can create two equations:

To solve this system of equations, we can use substitution or elimination. Let's use elimination:

Therefore, a cheeseburger contains 290 calories and a small fries contains 230 calories.

Rounded to the nearest thousandth, it's 0.357. So, the correct answer is: A) 0.357.

To express  5/14 as a decimal, divide 5 by 14 to get 0.357142857. Rounding to the nearest thousandth means considering the third digit after the decimal point. Since the fourth digit is 1, which is less than 5, it doesn't affect the rounding. Therefore, 5/14 as a decimal rounded to the nearest thousandth is 0.357. This approximation maintains three decimal places, with the third digit being 7.

[tex]\frac{5}{14}=0.357142857[/tex]

Complete Question:

Express 5/14 as a decimal number rounded to the nearest thousandth.

A) 0.357

B) 2.8

C) 0.3571

D) 0.28