The term that best describes the entry of 51% in this table is "Marginal relative frequency. The correct option is B.
What is Marginal relative frequency.?The ratio of a row total's or column total's frequency to the overall frequency of the data is known as marginal relative frequency. It is frequently used to examine broad trends in a single category of data.
For instance, the number of female students would be one marginal frequency in a table of students classified by sex and area of study, and the number of students enrolled in a particular area of study would be another, regardless of sex.
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A landscaper needs to mix a 70% pesticide solution with 20 gal of a 15% pesticide solution to obtain a 65% pesticide solution. How many gallons of the 70% solution must he use?
(blank) gal of the 70% pesticide solution is needed to make a final solution that is 65% pesticide.
Step-by-step explanation:
70% = 0.7
15% = 0.15
65% = 0.65
x = gallons of the 70% solution.
0.7x + 0.15×20 = 0.65(x + 20)
70% + 15% solution = 65% solution (which has a many gallons as the combination of x and 20 gallons).
0.7x + 3 = 0.65x + 0.65×20
0.05x + 3 = 13
0.05x = 10
x = 10/0.05 = 200 gallons
so, 200 gal of the 70% pesticide solution is needed to make combined with 20 gal of the 15% solution a final solution that is 65% pesticide.
A cook at a restaurant is calculating the amounts of ingredients needed to make
soup for the next 5 days. For each of these days, she will use 2 1/8 pounds of
carrots and y pounds of celery. She will use a total of 19 3/8 pounds of carrots and celery to make all the soup.
Which equation shows how to find the number of pounds of celery, y, she will use to make the soup each day.
The equation that shows the number of pounds of celery(y) the cook will use each day is 8y+17= 31 and y = 1 ¼
What is linear equation?A linear equation is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.
For each day , the cook will use 2 1/8 pounds of carrot and y pounds of celery
therefore total = 17/8 +y
for 5 days the total carrot and celery used =( 17/8 + y) ×5
for 5 days 19 3/8 pounds of carrot and celery is used . Therefore;
155/8 = 5(17/8+y)
for each day, divide both sides by 5
155/8×1/5 = 17/8+y
31/8 = 17/8+y
collect like terms
y = 31/8-17/8
multiply through by 8
8y = 31-17
8y+17 = 31
therefore the equation that can be used to find the pound of celery used per day is 8y+17= 31
and y = 14/8 = 7/4 = 1 ¼
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write the given system as a matrix equation and solve by using the inverse coefficient matrix. use a graphing utility to perform the necessary calculations.
The given system of equations can be written as a matrix equation and solved by using the inverse coefficient matrix. The inverse coefficient matrix is 1/10 [4 -2], [3 5], and when multiplied by the vector of variables [x, y] the vector of constants [4, 10] is obtained. This gives the solution x = 6 and y = 2.
Given system:
x + 2y = 4
3x + 4y = 10
Matrix equation:
[x y] [1 2] [4]
[ ] = [ ] x [ ]
[3 4] [3 4] [10]
Inverse coefficient matrix:
1/10 [4 -2]
[3 5]
Solution:
1/10 [4 -2] [x] [4]
[3 5] [y] = [10]
x = 6
y = 2
The given system of equations can be written as a matrix equation which can be solved by using the inverse coefficient matrix. This inverse coefficient matrix is found by calculating the inverse of the matrix of coefficients of the variables. In this case, the matrix of coefficients is [1, 2], [3, 4], and the inverse of this matrix is 1/10 [4 -2], [3 5]. Multiplying this inverse coefficient matrix by the vector of variables [x, y] will give the vector of constants [4, 10]. This allows us to solve for the variables, giving x = 6 and y = 2. Therefore, the solution of the given system of equations is x = 6 and y = 2.
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if latex: f\left(x\right) represents the total output of a farm, in tons, in the week of 2015 ( ), and you know that , which of the following questions can you answer?\
Both questions can be answered by using the function f(x).The function f(x) represents the total output of a farm in tons in the week of 2015, and the value of x is known. This means that by using the value of x, the total output of the farm in 2015 and the output of the farm in the week of 2015 can both be calculated.
The function f(x) is a mathematical representation of the total output of a farm in tons for the week of 2015. The value of x is known, which means that by using this value, the total output of the farm in 2015 as well as the output of the farm in the week of 2015 can both be calculated. Therefore, both of the questions can be answered by using the function f(x). Knowing the total output of the farm in 2015 can help to better understand the production of the farm over the course of the year, while the output of the farm in the week of 2015 can be used to gain insights into the weekly production of the farm. With this information, decisions can be made to improve the production and efficiency of the farm.
The function f(x) can be used to answer both questions regarding the total output of a farm in 2015 and the output of the farm in the week of 2015.
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Simplify 0.275 of At 20 and 52% of $10
Answer:
Step-by-step explanation0.275 of 20 is 20*0.275 = 5.5
52% of $10 is (0.52)*10 = 5.2
So the expression 0.275 of 20 and 52% of $10 can be simplified to 5:
Well I need help please explain it throughly
Answer: [tex]3q+1[/tex]
Step-by-step explanation:
[tex](q+3)+(2q-2)=q+3+2q-2=(q+2q)+(3-2)=3q+1[/tex]
given: ab=bc, ae=fc
prove m
rsm problem pls help
The triangles ∆AEC ≅ ∆AFC by Side-Angle-Side theorem
How to determine the proof of the trianglesThe complete question is added as an attachment
With the given information and the image attached below, we can state that the two triangles are congruent by SAS,
Then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.
The proof is given as:
Statement Reason
1. AB ≅ BC, AE ≅ FC 1. Given2. AC ≅ AC 2. Reflexive property of congruence3. <BAC ≅ <BCA 3. Base angles of isosceles ∆BAC4. ∆AEC ≅ ∆AFC. 4. SAS5. <AEC ≅ <AFC. 5. CPCTCRead more about congruence proof at:
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Given right triangle ABCABC with altitude \overline{BD}BDdrawn to hypotenuse ACAC. If AC=12AC=12 and DC=4,DC=4, what is the length of \overline{BC}BCin simplest radical form?
The length of the side BC of right triangle ABC can be found by applying the Pythagorean theorem with AC = 12 and DC = 4. The length of BC can be expressed in simplest radical form.
Using the Pythagorean Theorem, BC^2 = AC^2 - DC^2
= 12^2 - 4^2
= 144 - 16
= 128
Therefore, BC = [tex]\sqrt{128}[/tex]= 2[tex]\sqrt{32}[/tex] = 8[tex]\sqrt{2}[/tex]
The length of the side BC of a right triangle ABC can be found by applying the Pythagorean theorem. The Pythagorean theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, AC = 12 and DC = 4, so BC^2 = AC^2 - DC^2 = 144 - 16 = 128. Therefore, which is the length of \overline{BC}BC in its simplest radical form. This result can be verified by calculating the length of the hypotenuse AC and confirming that it is equal to the square root of the sum of the squares of BC and DC.
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Hi my question is how is 14-4x3+3 simplified
Answer:
- 4x^3 + 17
Step-by-step explanation:
14 - 4x^3 + 3
- 4x^3 + 17
(c) If a plane travels at x-110 mph for 3.5 hr, write an expression that represents the distance traveled. The expression that represents the distance traveled is mi. X
Answer:
Step-by-step explanation:
The distance traveled by the plane can be represented by the expression: distance = speed x time
In this case, the speed of the plane is given as x-110 mph and the time it travels is 3.5 hours.
So the expression for the distance traveled is:
distance = (x-110) * 3.5 miles
This expression represents the distance traveled in miles. The variable x represents the speed of the plane in mph.
Into a single power and explanation pls
9^10 divided by 9 can be simplified to 9^(10-1) = 9^9
This is because when dividing a power by the same base, we can subtract the exponent by one.
In other words, 9^10 / 9 = (9999999999) / (9) = 99999999*9 = 9^9.
So, 9^10 divided by 9 is equal to 9^9.
Another way to think about this is that dividing a number by itself is the same as multiplying that number by 1, and 9^10 / 9 = 9^10 * 1 / 9 = 9^10 / 9^1 = 9^(10-1) = 9^9
In terms of real numbers, 9^10 is equal to 387420490 and 9^9 is equal to 3486784401. So 9^10 divided by 9 is equal to 3486784401.
[tex]\it \dfrac{9^{10}}{9}=9^{10}:9^1=9^{10-1}=9^9[/tex]
solve for X
will give brainliest
Use the following information for determining sound intensity. The number of decibels
The level of the sound with the given properties is 200
How to find the level of soundFrom the question, we have the following parameters that can be used in our computation:
I0 = 10^-12
I = 10^-8
Also, we have the equation to be
β = 10log(I I0)
Substitute the known values in the above equation, so, we have the following representation
β = 10 * log(10^-12 * 10^-8)
Evaluate
β = -200
Hence, the level of sound is -200
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Complete question
use the following information for determining sound intensity. The level of sound β in decibels, with an intensity of I, is given by β = 10log(I I0), where l0 is an intensity of 10^-12 watt per square meter, corresponding roughly to the faintest sound that can be heard by the human ear find the level of sound β. l = 10^-8 watt per m^2 (quiet radio)
suppose you have $200 to pay for swimming and yoga classes this month. the price for one yoga class is $30. you want to attend 4 swimming classes. the equation for the quantity of yoga classes is as follows: qy
The value of the cost of a swimming class is $20.
Given that,
The amount to pay for swimming and yoga classes this month = $200
And, the one yoga class price is $30.
Here, the equation is,
[tex]Qy = 12 - 4Qs[/tex]
Since there are only 2 swimming classes for attending.
Hence substitute Qs = 2,
[tex]Qy = 12 - 4(2)[/tex]
[tex]Qy = 12 - 8[/tex]
[tex]Qy = 4[/tex]
Since The total cost of yoga classes = 4.
So, the cost of yoga classes is,
[tex]4 \times \$40 = \$160.[/tex]
Hence, the cost of swimming classes;
[tex]\text {Total budget - Total cost of yoga classes } = \$200 - \$160[/tex]
[tex]= \$40[/tex]
It will cost the following to take two swimming lessons:
[tex]\text {Cost of swimming classes } = \dfrac{\text { Total cost of swimming classes}}{\text {Number of swimming classes cost of swimming classes}}[/tex]
[tex]= \dfrac{40}{2}[/tex]
[tex]= 20[/tex]
Therefore, the total cost of a swimming class is $20.
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The perimeter of a rectangle is 20 cm. If the area of the rectangle is 16 cm^2 find the length and width of the rectangle. Let the length be the smaller of the two numbers, and the width the larger.
length =_____ cm
width = ______cm
A rectangle's perimeter is 40 cm. The rectangle's length is 2 cm longer than its width. Find the rectangle's length and width, which are both 6 cm.
What is meant by rectangle?A quadrilateral is a shape with two opposed sides that are equal and parallel. It is a polygon with four sides and four 90-degree angles. The shape of a rectangle is two dimensional.As a result, every square is a rectangle since it is a quadrilateral with right angles at each of its four corners. But not all rectangles are squares; for a shape to be a square, all of its sides must be the same length.All of a rectangle's interior angles are parallel, making it a parallelogram. In order for a rectangle to be a rhombus, all of its sides must be equal. A rhombus is a parallelogram with all of its sides being equal. If this requirement is met, it becomes a square. A rhombus has equal opposite angles.Perimeter of rectangle [tex]$=40 \mathrm{~cm}$[/tex] (given)
condition :- length [tex]=2 \times$ breadth $+2$[/tex]
[tex]$\Rightarrow 1=2 \mathrm{~b}+2[/tex]
perimeter [tex]$\mathrm{p}=2(1+\mathrm{b})=40$[/tex]
[tex]& \Rightarrow 2(2 b+2+b)=40 \\[/tex]
[tex]& \Rightarrow 2(3 b+2)=40 \\[/tex]
[tex]& \Rightarrow 6 b=40-4=36 \\[/tex]
[tex]& \therefore b=6 \mathrm{~cm}[/tex]
[tex]1=2 \times 6+2=12+2=14 \mathrm{~cm}[/tex]
[tex]\therefore \text { length }=14 \mathrm{~cm} \text {, breadth }=6 \mathrm{~cm}[/tex]
The complete question is:
The perimeter of a rectangle is 40 cm. The length of rectangle is more than double its breadth by 2 cm. Find the length and breadth of rectangle .
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40
Solve for x.
X
48
60
Will give brainiest!!
x/40 = 48/60
x= 4/5 × 40
x= 4 × 8
x = 32
Answer:
32
Step-by-step explanation:
by use of similarity and enlargement the answer can be evaluated.
use the formula: IMAGE LENGTH ÷OBJECT LENGTH.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Label the following topographic map. Click on a label below the map to select it, and then click on the appropriate box
on the map to place the label. (Increments for contour lines is 50 ft). Please Help Thank You!
Contour Interval: The contour interval is the difference in elevation between two adjacent contour lines. In this case, the contour interval is 50 feet, as indicated in the bottom-left corner of the map.
What is contour lines?Contour lines are lines on a map that connect points of equal elevation above a reference surface, usually sea level. They indicate the steepness of a terrain or landform and are often used to represent hills, valleys, and other relief features.
Ridge Line: A ridge line is a line formed by two or more contour lines that form a peak. In this map, the ridge line is marked by the contour lines labeled 1200 and 1250.
Valley: A valley is a line formed by two or more contour lines that form a low point. In this map, the valley is marked by the contour lines labeled 950 and 1000.
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NO LINKS!! Please help me with this Domain and Range
Answer:
Domain: (-∞, ∞)
Range: [2, ∞)
Input: (f) = 2
Output: f(1) = 3
Step-by-step explanation:
DomainThe domain is the set of all possible input values (x-values).
There are arrows at both endpoints of the graphed continuous line, indicating that the line continues indefinitely in those directions.
Therefore, the domain of the relation is unrestricted:
Domain: (-∞, ∞)RangeThe range is the set of all possible output values (y-values).
Assuming that each square is 1 unit, from inspection of the graph, the minimum y-value is y = 2.
The arrow at the endpoint in quadrant I indicates that the line continues horizontally at y = 2.
The arrow at the endpoint in quadrant II indicates that the line continues indefinitely towards y = ∞.
Therefore, the range of the relation is restricted:
Range: [2, ∞)InputTo find the value of f(4), find x = 4 and trace up to the line then read the y-value at that point. Therefore:
f(4) = 2OutputTo find the x-value when y = 3, find y = 3 and trace horizontally to the line then read the x-value at that point. Therefore:
f(1) = 3Suppose y varies directly with x. Write a direct variation equation that relates x and y. y=5 and x=2
A direct variation equation that relates x and y is y = (5/2)x.
What is the direct variation equation?
Direct variation is a linear function defined by an equation of the form y = kx when x is not equal to zero. Inverse variation is a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant.
When two variables are directly proportional, they vary directly with each other.
The relationship between the variables can be represented by a direct variation equation of the form:
y = kx
where k is the constant of proportionality.
Given that y = 5 and x = 2, we can use these values to find the value of k:
y = kx
5 = k(2)
k = 5/2
So the direct variation equation that relates x and y is:
y = (5/2)x
This equation shows that for every value of x, the value of y is 5/2 times that value.
For example, if x = 3, then y = (5/2) * 3 = 7.5, and if x = 4, then y = (5/2) * 4 = 10.
Hence, A direct variation equation that relates x and y is y = (5/2)x.
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1a. Buc-ee’s is having a promotion for diesel gas. If you buy 3 gallons or less, you will pay the normal price of $2.68 per gallon. If you buy more than 4 gallons, you pay $2.41 per gallon. Write a piecewise function for the price of n gallons of diesel at Buc-ee’s.
The piecewise function for the price of n gallons of diesel at Buc-ee’s would be = $1.00
How to calculate the price per gallon?The price paid for 3 gallons or less = $2.68 per gallon
That is, $2.68 =/< 3 gallons
Therefore $x= 1 gallon
Make X the subject of formula;
X = 2.68/3
X= $0.89
The price paid for 4 gallons or less = $2.41 per gallon
That is, $2.41 per =/< 4 gallons
Therefore $y = 1 gallon
Make y the subject of formula;
y = 2.41/4
y = $0.60
From the both outcomes, it can be concluded that the n gallons of diesel at Buc-ee’s would be approximately $1.00.
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HELP!!! You go out to dinner and the bill comes to $40.94. How much should you tip if you want the tip to be 15.0% of the bill? Express the dollar amount to the nearest cent
On average, 15-20% of the cost is left as a gratuity. Add the desired decimal percentage tip to the total amount of the check and multiply the result to determine the tip.
How much should you leave for tip?
15% to 20% of the tab is typically left as a gratuity. Add the decimal % tip you want to leave to the total check amount to compute the tip. You would multiply 1 by 0.20 to reach 1.20 if you wanted to leave a 20% tip. To calculate the total amount you would tip, multiply the bill by 1.20.
It is advised that you leave at least 10% of your tip, even if the service was subpar. * Because some restaurants tack on a gratuity, carefully review your tab. Whether or not you should add to that is up to you. In sit-down restaurants, the tip for the wait staff should be between 15 and 20 percent of the pretax total.
To find out the tip amount, we need to first calculate 15% of the bill:
$40.94 x 0.15 = $6.14.
Rounding this amount to the nearest cent, we get $6.14 as the tip amount.
Therefore, the tip total is$ 7.00
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ten points are placed on a circle. what is the greatest number of different lines that can be drawn so that each line passes through two of these points(A) 12 (B) 15 (C) 25 (D) 30(E) 36
The greatest number of different line segment that can be drawn so that each line passes through two of these points is 36. This is because every pair of points can be connected by a line, and with ten points, there are 45 pairs.
The greatest number of different lines that can be drawn so that each line passes through two of these points is 36. This is because every pair of points can be connected by a line, and with ten points, there are 45 pairs. Since each line can only be drawn once, the total number of different lines that can be drawn is 45 divided by two, which is equal to 36. In addition, the number of lines that can be drawn from each point to the rest of the points is 9, and since there are 10 points, the total number of lines that can be drawn is 90. However, this number is redundant since each line can only be drawn once, so the greatest number of lines that can be drawn is 36.
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What is the arithmetic mean (average) of all the positive two-digit multiples of 4?
Answer:
54
Step-by-step explanation:
You want the mean of the positive 2-digit multiples of 4.
MeanThe 2-digit multiples of 4 form an arithmetic sequence whose first term is 12, and whose last term is 96. The arithmetic mean of the numbers in the sequence will be the average of the first and last numbers:
(12 +96)/2 = 108/2 = 54
The average of the 2-digit multiples of 4 is 54.
15. Katie is making salsa, which consists just of tomatoes and onions. She makes 8 identical jars of salsa, each of which
has some cups of tomatoes and 2.1 cups of onions. The 8-jars have a total of 41.6 cups of both tomatoes and onions.
How many cups of tomatoes are in each jar?
According to the given statement, 37.9 cups of tomatoes in each jar.
What is linear equations?A system of linear equations is a set of equations with two or more variables. A linear equation is one that can be expressed as ax + b = c, where x is a variable and a, b, and c are constants.
A group of two or more linear equations that share the same variables is known as a system of linear equations. As an illustration, consider the set of linear equations below:
2x + 3y = 10
4x + 6y = 20
x and y are the same variables, and the equations are linear equations. The solution to this system of linear equations is x = 2, y = 2.
This question can be solved using the system of linear equations.
Solving the system of equations gives:
T = 7.4 cups of tomatoes in each jar
Step 1: Calculate the total amount of tomatoes used.
Total tomatoes = 8 jars x cups of tomatoes per jar
Total tomatoes = 8 x (41.6 - 2.1)
Total tomatoes = 303.2 cups
Step 2: Divide the total amount of tomatoes by the total number of jars.
Cups of tomatoes per jar = Total tomatoes ÷ 8
Cups of tomatoes per jar = 303.2 ÷ 8
Cups of tomatoes per jar = 37.9 cups
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19. Zaire gets a bonus with his club for every frisbee golf hole on which he makes a score of 4.
He played last week and scored a 4 on 7 holes. Zaire will get an extra bonus if he has a
total of 60 points from scores of 4 after he finishes today. On how many holes does he
need to score a 4 today?
Please help!!!
Zaire has a total of 7 holes * 4 points/hole = 28 points from scores of 4 from last week.To reach 60 points, he needs to score 4 on 60 - 28 = 32 more holes today. So, Zaire needs to score a 4 on 32 holes today.
How many holes does Zaire need to score a 4 on today in order to reach a total of 60 points?To calculate the number of holes on which Zaire needs to score a 4 today, we can use the following equation:X = (60 - (4 x 7)) / 4Where X is the number of holes on which Zaire needs to score a 4 today, 60 is the total number of points he needs to reach to get the bonus, 4 is the number of points he gets for each hole on which he scores a 4, and 7 is the number of holes on which he scored a 4 last week.Here's the step-by-step explanation:Subtract the total number of points he earned last week (4 x 7) from the total number of points he needs to reach the bonus (60).Divide the result by the number of points he earns for each hole on which he scores a 4 (4).So X = (60 - (4 x 7)) / 4 = (60 - 28) / 4 = 32 / 4 = 8Therefore, Zaire needs to score a 4 on 8 holes today to get the bonus.To learn more about Frisbee problems refer:
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Determine the values of p and q for which (-4,-3) will be solution of the system px+qy=-26 and qx-py = 7
Answer:
Step-by-step explanation:
here goes your solution down
A downtown parking lot charges $5 per hour for the first 2 hours, then $2.50 per hour after that. What equation describes the total cost y as a function of the hours x?
The equation y = 5x for x ≤ 2 and y = 10 + 2.5(x-2) for x ≥ 2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given that,
First, the two-hour rate of charge is $5 per hour
y = 5x for x ≤ 2
Over the 2 hours, the rate of charge is $2.5 per hour
y = 10 + 2.5(x-2) for x ≥ 2.
Hence "The equation y = 5x for x ≤ 2 and y = 10 + 2.5(x-2) for x ≥ 2".
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A student measures the length,width, and height of a fish tank. She finds that the fish tank is 105cm long, 75cm wide,and 80.5 cm high. What is the volume of the fish tank? Show your work. Use scientific notation and show the correct number of significant figures in your answer
The volume of the fish tank is 633,957.5 cubic cm or 0.634 cubic meter.
The formula for calculating the volume of a cuboid is
= length × breadth ×height
Given :
the length of fish tank = 105 cm
The width of fish tank= 75 cm
The height of fish tank= 80.5 cm
So, the volume of the fish tank =105×75 ×80.5
=633,957.5 [tex]cm^{3}[/tex]
In metric units ;
1 meter = 100 cm
So, converting all the dimensions into metric units.
length of fish tank = 1.05 m
width of fish tank = 0.75 m
height of fish tank = 0.805 m
So, the volume of fish tank = 1.05 x 0.75 x 0.805
= 0.6339575 [tex]m^{3}[/tex] or
= 0.634 [tex]m^{3}[/tex]
Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices.
A(-3, 2) and C(0, 5)
The coordinates are (_,_) and (-3,_)
∴ Coordinates of B & D are [tex](\frac{9}{2} ,\frac{1}{2} ) & (-\frac{1}{2} ,\frac{4}{2} )[/tex] respectively.
What are coordinates of graph?
Coordinates X and Y axes are present in every graph. Positions on a graph are indicated using coordinates, which are expressed as an ordered pair of numbers.
ABCD is a square with A(-3,2) & C(0,5).
To find out-
The coordinates of B & D
Solution-
Let the coordinates of B=(x,y).
Since ABCD is a square,
[tex]AB=BC=AB^2=BC^2.[/tex]
Using distance formula,
[tex](x-3)^2+(y-2)^2=(x-0)^2+(y+5)^2[/tex]
⟹2x+8y−6=0
⟹x=([tex]\frac{6-8y}{2}[/tex] ) .........(i).
Now, in ΔABC,
[tex]AB ^2+BC ^2=AC ^2[/tex]
[tex](x-3)^2+(y-2)^ 2+(x-0) ^2 +(y+5)^ 2=(3-2) ^2+(0+5) ^2[/tex]
⟹[tex]x^ 2+y ^2 -3x-3y=0.[/tex]
Substituting for x from (i),
[tex](\frac{6-8y}{2} )^2+y ^2 -3(\frac{6-8y}{2} )-3y=0[/tex]
⟹[tex]3y^2-9y+4=0[/tex]
⟹[tex](2y-1)(2y-4)=0[/tex]
⟹[tex]y=( \frac{1}{2},\frac{4}{2} ).[/tex]
Substituting for y in (i),
[tex](x,y)=( \frac{9}{2},\frac{1}{2} ) & (-\frac{1}{2} , \frac{4}{2} )[/tex]Now abscissae of A & C are 3 & 1, respectively.
∴ Abscissa of B will be in between 1 & 3.
So here, [tex]\frac{9}{2}[/tex] will be the abscissa of B.
Coordinates of B & D are [tex](\frac{9}{2} ,\frac{1}{2} ) & (-\frac{1}{2} ,\frac{4}{2} )[/tex] respectively.
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The coordinates of the remaining vertices B and D are (0, 2) and (-3, 5) respectively.
What are the coordinates of the vertices?
The unit square precisely refers to the square on the Cartesian plane having four corners.
Since square ABCD has a diagonal with the given vertices A(-3, 2) and C(0, 5), we know that the other two vertices of the square will be B and D, and that all four sides of the square are congruent.
We can use the coordinates of A and C to find the coordinates of B and D.
First, we know that the x-coordinate of B must be the same as the x-coordinate of C because the side BD is parallel to the x-axis.
Therefore, the x-coordinate of B is 0.
Next, we know that the y-coordinate of B must be the same as the y-coordinate of A because the side AB is parallel to the y-axis.
Therefore, the y-coordinate of B is 2.
So, the coordinates of B are (0, 2).
Finally, we know that the x-coordinate of D must be the same as the x-coordinate of A because the side AD is parallel to the x-axis.
Therefore, the x-coordinate of D is -3.
Next, we know that the y-coordinate of D must be the same as the y-coordinate of C because the side CD is parallel to the y-axis.
Therefore, the y-coordinate of D is 5.
So, the coordinates of D are (-3, 5)
Therefore, the coordinates of the remaining vertices B and D are (0, 2) and (-3, 5) respectively.
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Are the following ratios equivalent? 3 cookies: 7 glasses of milk and 27 cookies: 63 glasses of milk.
Answer:
These ratios are equivalent
Step-by-step explanation:
We can put both ratios into fraction form:
For 3 cookies and 7 glasses of milk, the fraction will be [tex]\frac{3}{7}[/tex]
For 27 cookies and 63 glasses of milk, the fraction will be [tex]\frac{27}{63}[/tex]
Both fractions in decimal form will be equal to 0.428571, so they are equivalent.
Yes because If you times both of them by 9 then they are equivalent
