Step-by-step explanation:
answer is (a,s) = (14,8)
Please help
The water is 7 meters deep 2 meters from the shore.
How deep is the water 45 meter from
the shore?
Answer: 157.5
Step-by-step explanation:
-20 equals the the difference of 28 and a number x
What is the solution and the equation?
Answer: The solution of the equation is x = 48. The equation is 20 = x - 28.
Step-by-step explanation:
-20 is like having -20 dollars, and you want to know how much you have to add to it to get to 28 dollars. So we add 20 to -28 and we get the number x = 48, so 48 dollars is what we need to add to -20 dollars to get to 28 dollars.
15. Rahj owns a hardware store. For every increase of 10¢ in the price A of a package of batteries, he estimates that sales decrease by 10 packages per day. The store normally sells 700 packages of batteries per day, at $5.00 per package. a) Determine an equation for the revenue, y, when x packages of batteries are sold. b) What is the maximum daily revenue that Rahj can expect from battery sales? How many packages of batteries are sold when the revenue is at a maximum? also,how to get the zeros and the equation
Answer:
a) To determine an equation for the revenue, y, when x packages of batteries are sold, we need to know the price of each package of batteries.
Since the price of a package of batteries is $5.00, the revenue, y, when x packages of batteries are sold is given by y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.
b) To find the maximum daily revenue that Rahj can expect from battery sales, we need to find the value of x that maximizes y = 5x.
Given that for every increase of 10¢ in the price A of a package of batteries, sales decrease by 10 packages per day. And the store normally sells 700 packages of batteries per day, at $5.00 per package.
It means that the store will sell a maximum number of batteries when the price is at $5.00
And the maximum daily revenue will be $5 * 700 = $3500.
So the maximum daily revenue that Rahj can expect from battery sales is $3500. And the number of packages of batteries sold when the revenue is at a maximum is 700.
The equation is y = 5x, where x is the number of packages of batteries sold and y is the revenue in dollars.
The zeroes of the equation are the points at which the function crosses the x and y-axis.
The x-intercept is the point at which the function crosses the x-axis. It happens when y = 0. So the x-intercept of this equation is (0,0)
The y-intercept is the point at which the function crosses the y-axis. It happens when x = 0. So the y-intercept of this equation is (0,0)
Step-by-step explanation:
To order tickets online to a hockey game, there is a processing fee plus the cost per ticket. The cost for 5 tickets is $174.45. The cost for 8 tickets is $271.95. Write and solve a linnear equation to find the total cost to order 12 tickets.
The linear equation for this situation is ax + y = Total cost, where is no. of ticket, x = $32.5, is cost of ticket and y = $11.9 is processing fee.
What is linear equation?A linear equation is an algebraic equation where the highest exponent of the variable is one. There are linear equations with one, two, or three variables, but not all linear systems have three equations. Typically, a system of linear equations has a single solution, but occasionally there is no solution or an infinite number of solutions.
A relationship in which the value of one variable, say "x," depends on the value of the other variable, say "y," is described by a two variables linear equation. A linear equation's graph will be a straight line if there are only two variables.
Given that cost for 5 tickets is $174.45
Let x be the cost of each ticket and y be the processing fee
5x + y = 174.45
And for the cost for 8 tickets is $271.95
8x + y = 271.95
Subtract the terms
8x + y = 271.95
- 5x + y = 174.45
3x + 0 = 97.5
If 3x = 97.5
Then,
x = 97.5/3
x = 32.5
Each ticket costs $32.5 then processing fees
5(32.5) + y = 174.45
y = 174.45 - 162.5
y = 11.95
8(32.5) + y = 271.95
y = 271.95 - 260
y = 11.95
Thus, The linear equation for this situation is ax + y = Total cost, where is no. of ticket, x = $32.5, is cost of ticket and y = $11.9 is processing fee.
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need help asap help help help help help help!!!!!!!!!!!
Answer:
Step-by-step explanation:
What is the following quotient?
2-√√√8
4+√12
The quotient of these two expressions is not a finite value.
What is the quotient?A quotient is a result obtained by dividing one quantity by another. It is the number that results from dividing one number by another.
Here,
Given : The quotient of
2-√√√8
and
4+√12
is not a finite value.
Explanation:
The square root of 8 is 2, so the first square root is 2, the second one is also 2, the third one is 2 again.
So the expression inside the first square root becomes 8, and the whole first square root becomes 2.
So the final expression would be:
2 - (2) = 0
On the other hand, √12 = √(223) = 2*√3
So the final expression would be:
4+2*√3
Hence, the quotient of these two expressions is not a finite value.
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A textbook store sold a combined total of 447 sociology and math textbooks in a week. The number of math textbooks sold was 57 less than the number of sociology textbooks sold. How many textbooks of each type were sold?
If a textbook store sold a combined total of 447 sociology and math textbooks in a week. The number of textbooks of each type that were sold is: 195 Math textbooks, 138 Sociology textbooks.
How to find the number of textbook that were sold?Let x represent the number of math textbooks
Let y represent the number of sociology
Altogether bookseller sold 447 math and sociology textbooks
Hence,
x + y = 447
Since the number of sociology textbooks sold was 57 less than the number of math books sold.
So:
y = x - 57
Substitute for y in the equation
x + y = 447
x + (x - 57) = 447
2x - 57 = 447
Combine like terms
2x = 447 -57
2x = 390
Divide both side by 2x
x = 390/2
x = 195 (Math textbooks)
y = x - 57
y = 195 -57
y = 138 ( Sociology textbooks)
Therefore 195 and 138 textbooks were sold.
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A small city has a population of 34000 in 1994. The population growth after 1994 is modeled by the following function where is the number of years after 1994.
P(t)=34000e 0.04t
During what year will the population reach 68000?
[tex]P(t)=3400e^{0.04t}\implies 68000=3400e^{0.04t}\implies \cfrac{68000}{3400}=e^{0.04t} \\\\\\ 20=e^{0.04t}\implies \log_e(20)=\log_e(e^{0.04t})\implies \log_e(20)=0.04t \\\\\\ \ln(20)=0.04t\implies \cfrac{\ln(20)}{0.04}=t\implies 74.89\approx t[/tex]
that's about 74 years and 325 days more or less.
based on the exponential equation which is really a continuously compounding equation with an initial value of 34000 in 1994, so 74 years later that'd be 1994 + 74 = 2068, then we add the 325 days to that, well, that's pretty much in November in 2069.
help with this please
Answer:
C, E and F
Step-by-step explanation:
A student is taking a multiple choice test that has 30 questions. She needs to answer at least 20
questions to submit her test. In order to earn a passing grade, she needs to get at least as many
questions correct as she got incorrect (not left blank). In order to qualify for a scholarship, she
needs to score at least 100 points, where correct answers are worth 15 points each, and each
incorrect response is 7 points off
Understanding the meanings of words and phrases helps translate into algebraic expressions.
Example: 6 multiplied by the absolute value of 7 less than the cube of a number
6 · |n³ – 7|
? Question
What algebraic expression belongs with each verbal description?
the square root of the ____
of the ____ of a ____ and 11 → √x2² - 11 the ____ of __ times a number and -11 → -2x/11
the __ of the ____ ___ of two times a number and 11 → √2x + 11
The correct statement is- the square root of the __difference__ of a _the polynomial x²_ and 11 → √x² - 11 the __product__ of _-2x_ times a number and reciprocal of -11 → -2x/11 the sum_ of the __square root__ of two times a number and 11 → √2x + 11.
What is a polynomial expression?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11
Given here, [tex]\sqrt{x^2-11}[/tex] , This in word phrase can be written the square root of the difference between a square of a number and 11.
-2x/11 can be written as twice the number multiplied by the reciprocal of -11
√2x + 11 can be written as sum of square root of twice the number and 11
Hence, The correct statement is- the square root of the __difference__ of a _the polynomial x²_ and 11 → √x² - 11 the __product__ of _-2x_ times a number and reciprocal of -11 → -2x/11 the sum_ of the __square root__ of two times a number and 11 → √2x + 11.
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Three candy bars and one soda costs $5.63.
At the same price, one candy bar and four sodas
cost $4.81. How much does a candy bar cost?
The cost of a candy bar is equal to $1.61.
How to determine the cost of a candy bar?In order to write an equation that model this situation, we would assign variables to the cost of candy bars and the cost of soda respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the cost of candy bars.Let the variable y represent the cost of soda.Next, we would translate the word problem into an algebraic equation based on the fact that three (3) candy bars and one (1) soda costs $5.63 as follows;
3x + y = 5.63 ...equation 1.
Additionally, one candy bar and four sodas cost $4.81 at the same price;
x + 4y = 4.81 ...equation 2.
x + 4(5.63 - 3x) = 4.81
x + 22.52 - 12x = 4.81
11x = 22.52 - 4.81
x = 17.71/11
x = $1.61
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During a review game, Mr. Pai's class correctly answered 67 questions on the first try. If there were 74 questions in the game, at what rate were questions answered correctly on the first try? Express your answer as a decimal. Round to the nearest thousandth.
A. 0.905
B. 0.095
C. 1.104
D. 0.091
Answer:
The answer is option A.
Step-by-step explanation:
To find the rate at which the questions were answered correctly on the first try, we can divide the number of questions answered correctly by the total number of questions.
Let's call the rate of correct answers on the first try as R
R = (number of questions answered correctly) / (total number of questions)
Substituting the given values:
R = 67 / 74
R = 0.905
So, the rate of correct answers on the first try is 0.905.
Answer:
Step-by-step explanation:
The question answered correctly in fraction will be 67/74.
67/74 equals 67÷74, which is 0.9054054054...
0.9054054054... round to the nearest thousand is 0.905.
So the answer is A, 0.905.
Solve each equation. 2 1/3(2x-3)=2 1/3
Answer: x = 2
Step-by-step explanation:
Multiply each term between the parentheses by 2 1/3.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}(2x-3)=2\frac{1}{3} \iff \ 2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]
We calculate the expression of the multiplication.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \ \frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]
We calculate the multiplication and division of rational numbers.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \frac{14x}{3}-7=2\frac{1}{3} } \end{gathered}$} }[/tex]
We convert the mixed fraction to improper.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}-7=2\frac{1}{3} \iff \dfrac{14x}{3}-7=\dfrac{7}{3} } \end{gathered}$} }[/tex]
We eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\dfrac{14x}{3}-7=\dfrac{7}{3} \iff \ 14x-21=7} \end{gathered}$} }[/tex]
We move the constant to the right side and change the direction of the sign.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x-21=7 \iff 14x=7+21=28, and \ remains \ 14x=28} \end{gathered}$} }[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x=28 \iff \ we \ divided \ x=\frac{28}{14}=x; \Rightarrow x=2. } \end{gathered}$} }[/tex]
Find the value of X that satisfies the two equations y = 2x + 2 and y = 4x - 4 simultaneously.
Answer:
x=3
Step-by-step explanation: I'm not 100% if this is it because it's been awhile but I believe that you write 2x+2=4x-4 to solve for x since they're both y=mx+b equations. After solving it you would get 3
Write the equation of the line that is parallel to the line 5x- 4y = 4 and passes through one point (-8, 2).
Answer:
y = 5/4x - 8
Step-by-step explanation:
first you convert the equation to y = mx + b
then you add the the -8 into the x and the 2 into the y and solve for b
b = -8 and since it is parallel same slope.
hope this helps :)
EXTRA 30 POINTS IF U GET THEM RIGHT!!!!!!!!!!!!!1
1. What is the surface area of a rectangular prism with dimensions 15.5 inches by 6 inches by 4 inches?
2. The list represents the ages of students in a gymnastics class.
10, 10, 11, 12, 12, 13, 13, 14, 14, 15
If another student of age 15 joins the class, how is the mean affected?
3.What is the distance from (−5, −19) to (−5, 32)?
4.What is the perimeter, in centimeters, of a rectangle with vertices located at (−20, 14), (4, 14), (−20, −5), and (4, −5)?
5.What is the area of a right triangle with a base of 7 feet and a height of 16 feet?
6.A swimming pool in the shape of a rectangular prism has dimensions of 17.5 feet by 13 feet by 6 feet. What is the maximum amount of water that the pool can hold?
Answer:
what is this i do not know sorry so no 30 points right
For a dinner taste testing event, a total of cases of forks and cases of spoons were ordered. Each case of forks contains packages each containing forks. Each case of spoons contains packages each containing spoons. It is planned that each guest will receive forks and spoons at the beginning of the event. At the end of the event, forks and spoons were not given out to guests. Which question about the event can be answered from the given information?
A How many dinners were offered for tasting at the event?
B How many people attended the event?
C How much was earned from the tickets sales for the event?
D How much silverware was used?
It is possible to find out the number of people who attended the event. Hence option B is correct.
What is the system of equations?
System of equations, also known as simultaneous equations, Two or more equations to be solved together in algebra (i.e., the solution must satisfy all the equations in the system). The number of equations must equal the number of unknowns for a system to have a unique solution.
Given that, a total of 24 cases of forks and each case of forks contains 36 packages each containing 12 forks.
Form about information, calculate the number of forks.
A total of 24 cases of spoons and each case of spoons contains 45 packages each containing 12 spoons.
Form about information, calculate the number of spoons.
Given that at the end of the event, 12 forks and 18 spoons were not given out to guests.
Form these we can get information that how many spoon used.
Since each guest will receive 2 forks and 3 spoons at the beginning of the event.
Using this information we can get the number of people who attend the event.
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All of the employees at the acmesoft company are either programmers or salespeople. The programmers are always tell the truth, the salespeople always lie. Threes Acmesoft employees - A, B, and C-were standing together in the hallway. A visitor passed by and asked A. "Are you a programmer or a salesperson?" A mumbled an answer that the visitor could not hear clearly. The visitor then asked B, "what did A say?" B replied. "A said that he is a salesperson."At this point, the third employee, C, said ,"Don't believe B; he is lying! What are B and C?
1/ B and C are both programmers
2/ B is a programmer and C is a salesperson
3/ B is a salesperson and C is a programmer
4/ B and C are both salesperson
Answer:
Step-by-step explanation:
3/ B is a salesperson and C is a programmer.
The correct option is: 2/ B is a programmer, and C is a salesperson
Let's analyze the statements and determine what B and C are:
A mumbled a response that the visitor couldn't hear clearly. We don't have any information from A's response.
B said, "A said that he is a salesperson." Since we know that salespeople always lie, we can infer that B is lying about A's response. Therefore, if A is a programmer (telling the truth), then B must be a salesperson.
C said, "Don't believe B; he is lying!" If we already determined that B is a salesperson (lying about A's response), then C is suggesting that B's statement is false, which means A's response is the opposite of what B said. So if B claimed that A is a salesperson (which was a lie), then A must be a programmer (telling the truth).
Based on the above analysis:
A is a programmer.
B is a salesperson.
C is a programmer.
So, the correct option is: 2/ B is a programmer, and C is a salesperson.
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Some IQ test are standardized to a normal model, with a mean of 100 and a standard deviation of 15
(a) in what interval would you expect the central 95% of IQ scores to be found
(b) About what percent should have IQscores above 115
(c) About what percent of people should have IQ scores between 70 & 85
(d) About what percent should have IQ scores above 130%
Answer:
(a) The central 95% of IQ scores in a standardized test would be found in the interval from 85 to 115. This is because a normal distribution is symmetric around the mean, and 95% of the data falls within two standard deviations of the mean. So, the interval would be mean - 2standard deviation to mean + 2standard deviation i.e. 100 - 215 to 100 + 215 = 85 to 115
(b) About 2.5% of people should have IQ scores above 115. This is because the IQ scores follow a normal distribution and IQ scores above 115 are considered to be in the top 2.5% of the distribution.
(c) About 16% of people should have IQ scores between 70 and 85. This is because the IQ scores follow a normal distribution, and IQ scores between 70 and 85 fall within one standard deviation of the mean (85 is one standard deviation below the mean and 70 is one standard deviation below that)
(d) About 0.1% of people should have IQ scores above 130. This is because IQ scores above 130 are considered to be in the top 0.1% of the distribution.
Step-by-step explanation:
Is 17/4 an mixed number an improper fraction
Answer:
improper fraction
Step-by-step explanation:
A mixed number has a whole number and a fraction.
An improper fraction is a fraction with a numerator bigger than the denominator.
Since 17 > 4 and there is no whole number, this is an improper fraction.
It can be changed to a mixed number by dividing the numerator by the denominator
17 ÷4 = 4 and there is a remainder of 1. The remainder goes over the denominator
4 1/4
Answer: It's an improper fraction
Step-by-step explanation: It's an improper fraction because an improper fraction is a fraction where the numerator is greater than the denominator, whereas a proper fraction is the opposite. A mixed number is when there is a whole number and then a regular (proper) fraction beside it. Here's an example:
[tex]5\frac{1}{7}[/tex]
Since 17 is greater than 4, 17/4 is an improper fraction. Now, if you wanted to find 17/4 as a fraction, you would divide the 17 by the 4, so the whole number (4 in this case) would be the whole number, and the faction would be 1/4
So, [tex]\frac{17}{4}[/tex]= [tex]4\frac{1}{4}[/tex]
To check, you can multiply the 4 by the 4, which is 16, and add the numerator (1) to it, which would be 17/4. I hope this helps.
.J(-4, 4), K(-3, 4), L(-1, 1), M(-4,1) Reflect in the x-axis, and then rotate 180° about the origin.
The quadrilateral's new coordinates will be J(4, 4), K(3, 4), L(1, 1), and M (4,1) when the procedure is applied.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given coordinates of a quadrilateral J(-4, 4), K(-3, 4), L(-1, 1), M(-4,1)
Reflect in the x-axis
Since,
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).
thus new coordinates will be,
J(-4, -4), K(-3, -4), L(-1, -1), M(-4,-1)
Rotate 180 degrees about the origin
Since,
When we rotate a figure of 180 degrees about the origin either in the clockwise or counterclockwise direction, each point of the given figure has to be changed from (x, y) to (-x, -y) and graph the rotated figure.
Thus new coordinates will be
J(4, 4), K(3, 4), L(1, 1), M(4,1)
Therefore, After applying the given operation the new coordinates of the quadrilateral will be J(4, 4), K(3, 4), L(1, 1), and M(4,1).
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PLEASE IF U GET THE ANSWER SHOW UR WORK write the equation for the line that passes through the given point, and is parallel to the given line.
(-3,-1); x-2y = 5
Answer:
y = 5x - 4
Step-by-step explanation:
1. Parallel have the same slope (equation)
- Standard form of an equation of a line: y=mx + b
m = slope
x = x-coordinate
b = y-intercept
y = y-coordinate
SLOPE = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1}}[/tex]
Given that x-2y = 5
and the line has the point:
(-3,-1)
We need to find another point to find the slope
x - 2y = 5
Let's say x = 7 and y = 1
(7, 1)
Now plug it into the slope equation
[tex]\frac{-3-7}{-1-1} = \frac{-10}{-2} = 5[/tex]
Plug the slope into the standard form of an equation of a line
y = 5x + b
Plug in (7,1)
1 = 5 + b
b = -4
The answer is: y = 5x - 4
Hope this helps :)
Have a great day!
Greg washes cars on Saturdays at his dad’s car dealership. His dad pays him $50 plus $5 for each car that he washes. Greg washed 11 cars last Saturday. Use function notation to write an equation that gives the total amount Greg earns as a function of the number of cars he washes. Use the equation to find how much he earned last Saturday.
(SHOW WORK)
Answer:
605
Step-by-step explanation:
11x55=605
Graph the function m(x) = x + 1
When the function, m ( x) = x + 1 is graphed, the result is shown attached.
How to graph a function ?When graphing a function, you need to remember that x is the independent variable. This means that you need to come up with the values of x and then use these values to come up with the corresponding values of y or m (x ) using the function.
Assuming you have values of x which are -3, -2, -1, 0, 1, 2, 3, the values of y would be:
x = - 3:
= x + 1
= - 3 + 1
= -2
x = - 2
= - 2 + 1
= - 1
x = - 1
= - 1 + 1
= 0
x = 0:
= 0 + 1
= 1
x = 1 :
= 1 + 1
= 2
x = 2 :
= 2 + 1
= 3
x = 3 :
= 3 + 1
= 4
The points would then be:
( - 3, - 2) , ( - 2, - 1) , ( - 1 , 0 ) ( 0, 1 ) ( 1, 2 ) ( 2, 3 ) ( 3, 4 )
The graph would be shown as attached.
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this is confusing to me can you help me
Area of figure 1 is 468 cm² and figure 2 is 45 cm².
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
In these given figure for calculating the area of them we need to divide them into two or more shape like rectangle, triangle or square. For example, I will take Figure 1 and 2
For figure 1
Length of base = 16 + 14 = 30 cm
Length of right rectangle whose side is 14 and 14(smaller one)
Thus, its area = 14 * 14 = 196
Area of left rectangle whose side is 16 and 17 = 16 * 17 = 272
Total area of the figure = 272 + 196 = 468 square cm
For figure 2
If we split them into two shape they will become a square and a triangle
Area of triangle = 1/2 base * height = 1/2 * 6 *3 = 9
Area of square = side * side = 6*6 = 36
Thus, total area = 9 + 36 = 45 square cm
Therefore, Area of these given figures(in unit square) are:
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Can anyone here solve for smiley face on this?
The value of the expression - 9(18 - 9 + 12) + 12(- 9 + 18 + 18) is 135.
What are the types of solutions a system of linear equations have?If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.
Let, The rectangle be x, the triangle by y, and the star be z.
Therefore,The three linear equations are,
x + 3y + z = 57...(i)
12x + 5y = 234...(ii)
8x - 6x + 3x = 60...(iii)
5x = 60.
x = 12.
Putting the value of x in eqn(ii) we have,
12(12) + 5y = 234.
144 + 5y = 234.
5y = 90.
y = 18.
Now, Putting the value of x and y in eqn(i) we have,
12 + 3(18) + z = 57.
12 + 54 + z = 57.
z = - 9.
So, The value of the expression z(y + z + x) + x(z + y + y) is,
= - 9(18 - 9 + 12) + 12(- 9 + 18 + 18).
= - 9(21) + 12(27).
= - 189 + 324.
= 135.
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b Write a description of the circuit diagram below.
A4
L
A₁
A3
A₂
Answer:
the circuit a1 and a3 are parallel to each other
rest of them must be in series
Dalton has $3.05 in dimes and quarters. He has 13 more dimes than quarters. How many quarters does he have?
The number of quarters Dalton has is 5.
How to find the number of quarters?Dalton has $3.05 in dimes and quarters. He has 13 more dimes than quarters. Therefore, the number of quarters he has can be calculated as follows:
Hence, using system of equation,
Therefore,
let
x = number of quarters
y = number of dimes
y = x + 13
0.25x + 0.1y = 3.05
using substitution method,
0.25x + 0.1(x + 13) = 3.05
0.25x + 0.1x + 1.3 = 3.05
0.35x = 3.05 - 1.3
0.35x = 1.75
x = 1.75 / 0.35
x = 5
Therefore,
number of quarters = 5
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Dilate the figure by the scale factor. Then enter new coordinates.
The new coordinates after dialting using scale factor are , A ' ( -21, 14 ) ,
B ' ( 28, 14 ) and C ' ( -7, -7 ) .
What is a graph ?
Graph can be defined as the visual representation which is used to represent the data.
The scale factor is k = 7. This tells us to multiply each coordinate, of each point, by the scale factor to get the dilated points.
For example, point A is at (-3, 2) and moves to A ' (-21, 14) after multiplying the x,y coordinates by 7. The same applies for points B and C as well.
The dilation rule can be written as (x, y) -> (7x, 7y)
As a result of the dilation, triangle A'B'C' has sides that are 7 times longer compared to the corresponding sides of triangle ABC.
Example: side AB = 7 units, side A'B' = 49 units
Hence, The new coordinates after dialting using scale factor are , A ' ( -21, 14 ) , B ' ( 28, 14 ) and C ' ( -7, -7 ) .
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