To determine the price for each board game on the stores, we need to divide the total price by the number of board games bought.
[tex]\begin{gathered} \text{board 1}=\frac{22.96}{4}=5.74 \\ \text{board 2}=\frac{33.74}{6}=5.79 \end{gathered}[/tex]The price online is higher, because it is $5.79 per board game.
Describe a series of transformations Matt can perform to device if the two windows are congruent
We can generate congruent shapes by combining the three types of transformations: rotations, reflections, and translations. Actually, using a combination of one or more of these three transformations, any pairs of congruent shapes can be matched to one another.
What are transformations?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given Data
We now understand that the size and shape of the figures are preserved during stiff transformations (reflections, translations, and rotations). Pre-image and image are always congruent with one another.
Series of transformation Matt can perform:
Reflection (Flip)
Because the equivalent points from the pre-image to the image remain at the same distance from the line of reflection, a reflection maintains its original shape.
Rotations as a Transformation of Congruence
A rotation is when a figure turns. Although the figure is the same size and shape, it appears to have fallen over. A clock is a fantastic example of a rotation in the real world. Every hour or every day, the connecting arms of a clock revolve around its central point. The degree of rotation is used to characterize a rotation; popular rotations include 90 degrees, 180 degrees, and 270 degrees. The figure returns to its original position after a full 360-degree spin. A rotation must additionally include the direction, either clockwise or counterclockwise. A rotation's degree amount and direction can be computed using this information.
Congruence transformation through translation
When we move an object or shape from one location to another without changing its size, shape, or orientation, we call that movement a translation. A translation, often known as a slide, involves moving each point on an object or shape by the same amount and in the same direction.
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I-intercept: C y-intercept y 7+ 5+ 3+ 2+ ... Leveled up to Familiar!
The x intercept is (-7.5,0).
The y intercept is (0,5.5).
Sara wants to borrow money from her mother, and she is offered a five-year, simple interest loan of $7,000, with a 3% annual interest rate. What is Sara’s total repayment amount?
a.
1050
Answer: 1050 is the answer trust me i took the quiz and it was correct pls give me brainliest and friend request me ur welcome :)
Step-by-step explanation:
Find the perimeter of the rectangle. Then, Find area of the rectangle. Round your answer to the nearest tenth
Answer:
To find the perimeter of the rectangle, simply add all sides of the rectangle together to get the answer. For finding the area, you have to multiply the length and width together.
Step-by-step explanation:
math.
Suppose you have a monthly entertainment budget that you use to rent movies and purchase cds. You currently use your income to rent 5 movies per month at a cost of 5.00 per movie and to purchase 5 cds per month at a cost of 10 per cd. Your marginal utility from the fifth movie is 30 and your marginal utility from the fifth cd is 70
Total utility of movies and cds will be $160
What is Budget?
A spending plan based on income and costs is called a budget. In other words, it's a projection of your income and expenses for a specific time frame, like a month or a year. (Or, if you're keeping track of the money coming in and going out of your home as a whole, that's a family budget.)
The cost of 1 movie = $5
The cost of 1 CDS = $10
The marginal utility from fifth movie = 30
The marginal utility from fifth CDS = 70
Total cost spent in month for movies = 5+5+5+5+30
= $50
Total cost spent in month for CDS = 10+10+10+10+70
= $110
The total monthly entertainment budget will be
= 50 + 110
= $160
Hence, The total monthly entertainment budget is $160
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What two numbers are located 5/8 of a unit from 1/6 on a number line?Show your work.
ANSWER
[tex]\frac{19}{24}\text{ and }\frac{-11}{24}[/tex]EXPLANATION
To find the two numbers that are located 5/8 of a unit from 1/6 on the number line, we have to first understand that for a number on a number line, there are numbers both ahead and behind the number.
So, the numbers that are 5/8 from 1/6 on the number line will be:
=> one number that is +5/8 from 1/6
=> one number that is -5/8 from 1/6
Therefore, the two numbers are:
[tex]\begin{gathered} \frac{1}{6}\text{ + }\frac{5}{8}\text{ and }\frac{1}{6}\text{ - }\frac{5}{8} \\ \Rightarrow\text{ }\frac{19}{24}\text{ and }\frac{-11}{24} \end{gathered}[/tex]Those are the two numbers.
assume a pool measuring 26 meters by 12 meters is surrounded by a path of uniform width as shown in the figure Express the area in the past A in Square meters as a function of its width X in meters
We know that
• The dimensions of the pool are 26 meters by 12 meters.
,• The uniform surrounding path has a width of ,x, meters.
To find a function of x to express the whole area, we have to define the width and length including the path.
The width would be-
[tex]w=26-2x[/tex]The length is
[tex]l=12+2x[/tex]The total area is
[tex]\begin{gathered} A=w\cdot l \\ A(x)=(26-2x)(12+2x) \end{gathered}[/tex]We use the distributive property to show the function in the simplest form.
[tex]A(x)=312+52x-24x-4x^2[/tex]Then, we reduce like terms. So, the function is
[tex]A(x)=-4x^2+28x+312[/tex]A solution must be 14% Insecticide. To make 5 gallons of this solution how much insecticide must you use? A) 0.028 gallon B) .36 gallon C) .7 gallon D) 2.8 gallons
Insecticides = 14/100 x 5 = 0.7
3(x+4) -4 = 2(x+4) + x
Answer: Infinite Solution
Step-by-step explanation:
3x+12-4=2x+8+x
3x+8=3x+8
Answer:
All real numbers
The answer to this equation is 0=0
Step-by-step explanation:
3(x+4)-4= 2(x+4)+x
3x+12-4= 2x+8+x
3x+8=3x+8
3x-3x=8-8
0=0 Answer
22. After an article is discounted at 25%, it sells for $112.50. The original price of the article was:
A. $28.12
B. $84.37
C. $150.00
D. $152.00
Answer:
the answer is C
Step-by-step explanation:
25% of 150 is 37.5 so 150-37.5 is 112.5
Given the diagram, classify the bolded line as a perpendicular bisector, angle bisector, median or alritude. I chose angle bisector. Am I right?
we have that
the answer is the option First
perpendicular bisector
because, is perpendicular to the segment at its midpoint
A personal trainer offers two different plans. Plan A costs $25 per session and Plan
B costs $50 per session. If the trainer coaches 18 sessions this week and earns $625
dollars, how many sessions of each type did he coach?
The personal trainer took 11 plan A and 7 plan B classes.
Let the number of sessions of plan A be x. So, the number of sessions of plan B be (18 - x). Now forming the equation as per the mentioned information.
25×x + 50 (18 - x) = 625
Performing multiplication on Left Hand Side of the equation
25x + 900 - 50x = 625
Rearranging the equation
900 - 625 = 50x - 25x
Performing subtraction on both the sides of the equation
275 = 25x
Shifting 25 to other side of equation
x = 275/25
Performing division to find the value of x
x = 11
Number of plan A classes = 11
Number of plan B classes = 18 - 11
Number of plan B classes = 7
Thus, the number of plan A classes is 11 and plan B classes is 7.
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What is the length of segment SR?
____ units
The value of the length of the segment SR is; 12 units.
What is a line segment?A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
According to the diagram at point it makes the angle of 90° with both triangles, thus;
SR = SQ
2x + 8 = 8x - 4
And to find the value of x, we will find the value of line segment SR
8x -2x = 8+4
6x = 12
x = 12/6
x = 2
Then we will put the value of x in SR ;
SR = 2x + 8 = 2(2) + 8 = 4 + 8 = 12
SR = 12
Hence, The value of the length of the segment SR is; 12 units.
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evaluate the expression 2(8-4)^2-10÷2
option 1 11
option 2 27
option 3 56
option 4 59
please help quick
I have a time limit
[tex] = 2(4)^{2} - (10 \div 2) \\ = 2(16) - 5 \\ = 32 - 5 \\ = 27[/tex]
THE ANSWER IS OPTION 2. 27
HOPE THIS HELPS
Answer:
Answer is 27
♬
⚫
Overnight the price of gasoline increased by 15% to settle at a price of $4.90 per gallon. What was the price before the 15% increase?
The price of gasoline before the 15% increase is $4.75/gallon.
What is gasoline?
Petroleum-derived clear flammable liquid known as gasoline or petrol is the primary fuel for the majority of spark-ignited internal combustion engines (also known as petrol engines). It mostly comprises of organic compounds made from petroleum fractional distillation that have been improved with various additions. In the United States, refineries typically create 19 to 20 gallons of gasoline, 11 to 13 gallons of distillate fuel, the majority of which is sold as diesel fuel, and 3 to 4 gallons of jet fuel from a barrel of crude oil. The crude oil test and oil refinery processing determine the product ratio. 42 US gallons, or around 159 litres or 35 imperial gallons, is the standard measurement for the volume of an oil barrel.
How can we calculate the price before the 15% increase?
Overnight the price of gasoline increased by 15% to settle at a price of $4.90 per gallon.
15÷100+x = $4.90/gallon
0.15+x = $4.90/gallon
Therefore, x = $4.90/ gallon - 15÷100
x = $4.90/gallon - 0.15
x = $4.75/gallon.
Hence , the price of gasoline before the 15% increase is $4.75/gallon.
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3.50 : 1.50 ratio as a fraction
Answer:
7/3
Step-by-step explanation:
You want the ratio 3.50 : 1.50 written as a fraction.
RatioA ratio can be written 3 ways. Any of them can be reduced to a ratio of mutually prime integers:
3.50 : 1.50 = 3.50/1.50 = 3.50 to 1.50
Here, the fraction can be made to be a ratio of integers by multiplying both numerator and denominator by 2:
3.50/1.50 = (2·3.50)/(2·1.50) = 7/3
The ratio 3.50:1.50 is equivalent to the fraction 7/3.
A random number generator is used to select an integer from 1 to 50 (inclusively). What is the probability of selecting the integer 361?
The probability of selecting the integer 361 from the random generator is 0.
What is probability?It should be noted that probability simply has to do with the likelihood that a particular thing will take place.
In this case, a random number generator is used to select an integer from 1 to 50 .
The probability of selecting the integer 361 from the random generator will be 0. This is because the numbers given are from 1 to 50.
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C Dorothy drew a rectangle with length of 14.3 centimeters and width of 13.9 centimeters. Find its area (nearest tenth).
Area of rectangle = Length x Width
. = 14.3 x 13.9
. = (13.9+ 0.4) x 13.9
. = 13.9^2 + 5.56
. = 13•14 +( 1.4)•8 + 5.56
. =198.77 cm2
Simplify the expression √112x10y13. Show your work. pls help
Answer: [tex]4x^{5} y^{6} \sqrt{7y}[/tex]
Step-by-step explanation:
1) Separate the radicals
sqrt(112x^10y^13) = sqrt(112)*sqrt(x^10)*sqrt(y^13)
2) For sqrt(112), rewrite it as the product of a perfect square and some other number.
sqrt(112) = sqrt(16) * sqrt(7)
= 4*sqrt(7)
3) For sqrt(x^10), rewrite it in terms of it being raised to a fraction
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]
n = 2, so x^(10/2), and when simplified you have x^5
4) For sqrt(y^13), do the same thing.
y^(13/2) = sqrt(y)*(y^6)
5)Combine everything
4x^5y^6sqrt(7y)
Can you help me understand the steps to solve this?
a)36 is 75 % of 48
b)18 is 25% of 72
Explanation
when we have the percentage and the number , the easiest way to find the value is by applying this formula:
[tex]\text{value}=origial\text{ value}\frac{\text{ \% percentage}}{100}[/tex]hence
Step 1
a)
what percet of 72 is 18?
let
100 % = 72, ( the number)
x %, = 18
so
replace
[tex]\begin{gathered} \text{18}=72\frac{\text{ x\% percentage}}{100} \\ 18=\frac{72}{100}x \\ \text{Multiply both sides by 100/72} \\ 18\cdot\frac{100}{72}=\frac{72}{100}x\cdot\frac{1}{0072} \\ 25=x \end{gathered}[/tex]therefeore,
18 is 25% of 72
Step 2
b) 36 is 75 % of what,so
let
100%= x=original value
75%=36
so
[tex]\begin{gathered} \text{value}=origial\text{ value}\frac{\text{ \% percentage}}{100} \\ 36=x\frac{75}{100} \\ \text{Multiply both sides by 100/75} \\ 36\cdot\frac{100}{75}=x\frac{75}{100}\cdot\frac{100}{75} \\ 48=x \end{gathered}[/tex]therefore, 36 is 75 % of 48
I hope this helps you
What are the solutions of the equation (x + 2)2-2(x + 2)-15 = 0? Use u substitution to solve.
O x=-7 and x = 1
O x = -5 and x = 3
O x=-3 and x = 5
O x= -1 and x = 7
The solution for the given equation is x = -5 and x = 3.
How to solve a quadratic equation by substitution?
The equation is first transformed into a more familiar form. Replace the substitutions with the original variables after factoring the problem. The difference of squares equation is used to finish the factorization and locate the answers for x.
Given, the equation for solving is: (x + 2)² - 2(x + 2) - 15 = 0 --(i)
Let in the equation, y = x + 2 --(ii)
Equating (i) and (ii), we get:
y² - 2y - 15 = 0 ⇒ y² - 5y + 3y - 15 = 0 ⇒ y(y - 5) + 3(y - 5) = 0
⇒ (y + 3)(y - 5) = 0 ⇒ y = -3, 5 (by solving the equations)
Thus, from (ii) and value of y obtained above, we get,
x + 2 = -3 ⇒ x = -3 -2 = -5 and x + 2 = 5 ⇒ x = 5 - 2 = 3
Thus, (b) x = -5 and x = 3 is the correct answer.
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A bicycle has a listed price of $522.95 before tax. If the sales tax rate is 7.75%, find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.
$_____
If a bicycle has a listed price of $522.95 before tax and the sales tax is 7.75%, then the total cost of the bicycle with sales tax included is $563.47
The listed price of bicycle = $522.95
The sales tax percentage = 7.75%
We know
C = p(t×p)
Where C is the total cost
p is the listed price
t is the sales tax percentage
Substitute the values in the equation
C = 522.95+((7.75/100)×522.95)
= 522.95+40.53
= $563.47
Hence, if a bicycle has a listed price of $522.95 before tax and the sales tax is 7.75%, then the total cost of the bicycle with sales tax included is $563.47
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At a dinner party, every 3 guests were served a dish of rice to share, every 4 guests were served a dish of greenbeans and every 2 guests were served a dish of meat. There were 17 dishes in all. How many guests were in attendance?"
The number of guests that were at the party is 16.
How many guests were at the party?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 1/2. 1 is the numerator and 2 is the denominator.
The equation that would be formed from the available information in this question is:
[tex]\frac{x}{3} + \frac{x}{4} + \frac{x}{2} = 17[/tex]
Where x represents the number of guests that are in the party.
[tex]\frac{x}{3} + \frac{x}{4} + \frac{x}{2} = 17[/tex]
Add the fractions:
[tex]\frac{3x + 4x + 6x}{12}[/tex] = 17
[tex]\frac{13x}{12}[/tex] = 17
Multiply both sides of the equation by 12
13x = 12 x 17
13x = 204
Divide both sides of the equation by 13
x = 204 / 13
x = 15.7 ≈ 16
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Alexandria a car dealer, earns 1/25 commission of her luxury vehicle sales. Last year, her sales were $480,000. What was the total dollar amount of her commission last year?
The total dollar amount of her commission last year equals to $19,200.
What is a sales commission?This refers to the percentage of the value of a sale that a sales associate or representative may earn.
To start, we must analyze the data we have. Given that Alexandria's total sales were $ 480000, and the commission received is 1/25 of that sales.
The commission earned from the sales:
= 1/25 * $480000
= $19,200
Therefore, the total dollar amount of her commission last year equals to $19,200.
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NO LINKS!! Describe the domain and range (in BOTH interval and inequality notation) for each function shown.
Answers:
Domain as an inequality: [tex]\boldsymbol{-\infty < \text{x} < \infty}[/tex]
Domain in interval notation: [tex]\boldsymbol{(-\infty , \infty)}[/tex]
Range as an inequality: [tex]\boldsymbol{-3 \le \text{y} \le 3}[/tex]
Range in interval notation: [-3, 3]
=================================================
Explanation:
The domain is the set of allowed x inputs. This graph goes on forever in both directions, so we can plug in any real number for x. There are no restrictions to worry about.
As an inequality, we write [tex]-\infty < \text{x} < \infty[/tex] to basically say "x is between negative infinity and infinity". In other words, x is anything on the real number line.
That inequality condenses into the interval notation of [tex](-\infty , \infty)[/tex]
Always use curved parenthesis for either infinity, because we can't ever reach infinity. It's not a number on the number line but rather a concept.
----------------------
Now onto the range.
Recall the range is the set of possible y outputs. We look at the lowest and highest points (aka min and max) to determine the boundaries for the range.
In this case, the smallest y can get is y = -3
The largest it can get is y = 3
The range is any value of y such that [tex]-3 \le \text{y} \le 3[/tex] which in word form is "any value between -3 and 3, inclusive of both endpoints".
That inequality condenses to the interval notation [-3, 3]
We use square brackets to include the endpoints as part of the range.
Answer:
[tex]\textsf{Domain}: \quad (-\infty, \infty) \quad -\infty < x < \infty[/tex]
[tex]\textsf{Range}: \quad [-3,3] \quad -3\leq y\leq 3[/tex]
Step-by-step explanation:
The domain of a function is the set of all possible input values (x-values).
The range of a function is the set of all possible output values (y-values).
Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.[ or ] : Use square brackets to indicate that the endpoint is included.Inequality notation
< means "less than".> means "more than".≤ means "less than or equal to".≥ means "more than or equal to".From inspection of the given graph, the function is continuous and so the domain is not restricted.
Therefore, the domain of the function is:
Interval notation: (-∞, ∞)Inequality notation: -∞ < x < ∞From inspection of the given graph, the minimum value of y is -3 and the maximum value of y is 3. Both values are included in the range.
Therefore, the range of the function is:
Interval notation: [-3, 3]Inequality notation: -3 ≤ y ≤ 3At store A, 3 pounds of apples cost $12. At store B, the cost is given by y = 2x where y is the cost in dollars and x is the number of pounds of apples. The cost of apples at store C is shown in the graph. Answer the questions to find out which store's apples are the least expensive. 1. What is the unit price of apples at store A? Explain how you found this unit price. (2 points) 2. What is the unit price of apples at store B? How did you use the equation to find the unit price? (2 points) 3. What is the unit price of apples at store C? How did you use the graph to find the unit price? (3 points) 4. Which store has the lowest unit price for apples? (3 points)
1. Store A's unit price = $4 per pound
2. Store B's unit price = $2 per pound.
3. Store C's unit price = $3 per pound.
4. Store B's unit price is the lowest.
How to Find the Unit Rate of a Relationship?The unit rate of the relationship between variables x and y, is given as:
Unit rate, m = y/x.
In a given equation, y = mx, the value of m represents the unit rate of the relationship.
In the scenario given, y represents cost in dollars while x represents the number of pounds of apples.
1. The unit rate = unit price of apples. For store A, we are given 3 pounds of apples will cost $12, therefore:
Unit price = y/x = 12/3
Unit price = $4 per pound
2. For store B, the "2" in the equation, y = 2x, represents the unit price.
Unit price for store B = $2 per pound.
3. Using one point on the graph for Store C, say, (2, 6):
Unit price = y/x = 6/2
Unit price = $3 per pound.
4. The lowest unit price is $2 per pound, therefore, Store B has the lowest unit price for apples.
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thirty-thousandths in decimal
Thirty thousandths in decimal is written as ;
[tex]0.3000[/tex]Note that numbers after the decimal point begin from tenths, hundredths, thousandths, tens of thousandths, and so on.
Thirty-thousandths therefore is four digits after the decimal point, starting from the digit 3.
4. Solve the equation 3x + 2 = 17 using the bar diagram.17ххХ2
Given that 3x+2=17
3x=17-2
3x=15
x=15/3
x=5
so,the numbers we end up using are 17,3,15,5,2
Derive the formular to find the area of the moon and state the assumption taken clearly, physically and mathematically, without defying Keplars laws
Answer:
Area = 4πr²
Step-by-step explanation:
- We know that a moon revolves around its orbit as per Keplar. The moon is not a perfect sphere, so we shall take an assumption;
Assume the moon is a perfect and regular sphere
[tex]{ \tt{volume \: of \: moon = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \boxed{ \tt{ \: v = \frac{4}{3} \pi {r}^{3} }}}[/tex]
- From engineering mathematics (rates of change), we know that volume is first order integral of area and area is the first order derivative of volume;
[tex]{ \tt{area = \frac{d(volume)}{dr} }} \\ \\ { \tt{volume = \int area \: dr}}[/tex]
- So, from our formular;
[tex]{ \tt{area = \frac{dv}{dr} = \frac{4}{3}\pi ( \frac{d ({r}^{3} )}{dr} ) }} \\ \\ { \tt{area = \frac{4}{3}\pi(3 {r}^{2}) }} \\ \\ { \boxed{ \rm{area = 4\pi {r}^{2} }}}[/tex]
r is radius of the moon[tex]{ \boxed{ \mathfrak{DC}}}{ \underline{ \mathfrak{ \: delta \: \delta \: creed}}} \\ [/tex]
i need help asap!!! im bad at graphing
Answer:
Step-by-step explanation:
eq. of any line with slope -1/2 and through (-1,-5) is
y+5=-1/2(x+1)
2y+10=-x-1
2y=-x-11
x+2y=-11
y=0
x=-11
point is (-11,0)
draw a line through (-11,0) and (-1,-5)