An exponential function with a vertical stretch by a factor of 2 and a translation left 1 unit and up 2 units is given as follows:
y = 2(2)^(x + 1) + 2.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.A vertical stretch by a factor of k means that the definition of the function is multiplied by k.
The parent function in the context of this problem is given as follows:
y = 2^x.
Hence the exponential function with a vertical stretch by a factor of 2 and a translation left 1 unit and up 2 units is given as follows:
y = 2(2)^(x + 1) + 2.
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Question 6(Multiple Choice Worth 1 points) (05.05 LC) Which of the following inequalities matches the graph? Ox≤5 0x25 Oy≤5 Oy25 -6-4 4 6 8 10 ▷
The corresponding inequality for this graph is
0 <= x <= 5
What is inequality?An inequality is a statement that two values are not necessarily equal. In other words, it expresses a relation between two quantities that can be either less than, greater than, less than or equal to, or greater than or equal to each other. Inequalities are typically written using symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), and "≥" (greater than or equal to).
The graph represents a shaded rectangle with sides on the x and y axes, and with one corner at the origin (0,0). The top-right corner of the rectangle is at the point (5,5), and the sides of the rectangle are parallel to the axes.
The corresponding inequality for this graph is 0 <= x <= 5, which can be read as "x is greater than or equal to 0 and less than or equal to 5".
Therefore, the correct answer is:
0 <= x <= 5
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The complete question is:
Which of the following inequalities matches the graph?
Ox≤5
0<=x<=5
What are the coordinates of point P on the directed line
segment from R to Q such that P is the length of the
line segment from R to Q? Round to the nearest tenth,
if necessary.
Hence, point P's coordinates are (6, 3) as the midpoint of the line segment from R to Q, which is the precise halfway point between R and Q.
what is coordinates ?A point's location on a line or in space can be determined using a set of numbers called coordinates. An x-coordinate and a como, which denote the horizontal as well as vertical ranges from a bench mark known as the origin, are the two numbers that make up coordinates in two-dimensional space. Three numbers, the x, y, and z coordinates, which describe the distances from origin in the x, y, and g directions, respectively, might make up coordinates in three-dimensional space. Among other disciplines, coordinates are frequently employed in physics, arithmetic, and geometry.
given
The midpoint of the line segment from R to Q, which is the precise halfway point between R and Q, must be located in order to determine the coordinates of point P.
We can separately aver the x- and y-coordinates to get the middle.
The midpoint's x-coordinate is (4 + 8)/2, which equals 6.
(0 + 6)/2 = 3 is the midpoint's y-coordinate.
Hence, point P's coordinates are (6, 3) as the midpoint of the line segment from R to Q, which is the precise halfway point between R and Q.
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Answer:
(-3.5 , 2.3)
Step-by-step explanation:
I know
Help!! Brandon wants to cut 12 pieces of old rubber in the size shown to make a patio mat. How much rubber will Brandon need for 12triangukar pieces?
Step-by-step explanation:
The area of a right triangle like this is area = 1/2 * base * height
base and height are the LEGS of the right triangle
this one pictured piece area is: 1/2 * 14 in * 11 in = 77 in^2
He needs 12 of them ....so total is then 12 * 77 in^2 = 924 in^2 needed
Two geometric progressions have equal sums to infinity. Their first terms are 25 and 40 respectively. if the common ratio of the first is 1/2 what is the common ratio of the second point?
The common ratio of the second geometric progression is 1/5.
What is Geometric Progression?A geometric progression or a geometric sequence is the sequence, in which each term is varied by another by a common ratio. The next term of the sequence is produced when we multiply a constant (which is non-zero) to the preceding term. It is represented by:
a, ar, ar2, ar3, ar4, and so on.
Equation:Let the common ratio of the second geometric progression be r. Then the sum to infinity of the first progression is:
S1 = a1/(1 - r1), where a1 = 25 and r1 = 1/2
And the sum to infinity of the second progression is:
S2 = a2/(1 - r), where a2 = 40 and r is the common ratio of the second progression
We know that S1 = S2, so we can set the two expressions equal to each other:
S1 = S2
a1/(1 - r1) = a2/(1 - r)
Substituting the given values:
25/(1 - 1/2) = 40/(1 - r)
Simplifying:
50 = 40/(1 - r)
Multiplying both sides by (1 - r):
50 - 50r = 40
Subtracting 50 from both sides:
-50r = -10
Dividing both sides by -50:
r = 1/5
Therefore, the common ratio of the second geometric progression is 1/5.
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PLS HELP! (I need to finish this today because it was due yesterday!)
Answer:
Step-by-step explanation:
Search up the area of both. rectangle is LxW therefore the area is 18. the other is trapezium therefore, ((a+b)xh)/2 therefore the area is 20. trapezium has larger area
Answer trapezoid has greater area
Step-by-step explanation: rec: 6*3= 8, trapezoid [ (6+2) * 5 ]1/2 = 20
please help will give brainliest
Answer:
Option D is the correct answer
D. f(n) = 95 + 60(n - 1)
Step-by-step explanation:
Solution:
f(n) = installation charges + monthly fees x number of months -> f(n) = 35 + 60*n-> f(n) = 35 + 60*n + 60 - 60 (Add and subtract 60)-> f(n) = (35 + 60) + (60*n - 60)-> f(n) = 95 + 60(n - 1)Tamika got a raise in her hourly pay from 15.50 to 17.75 find the percent increase
Answer:
Step-by-step explanation:
14.516129%
Find the surface area of the following figure by approximating pi as 3.14.
a. 314 in2
b. 315 in2
c. 316 in2
d. 317 in2
e. 318 in2
Answer:
A
Step-by-step explanation:
Given:
r (radius) = 5 in
h (height) = 5 in
Find: A (surface area) - ?
.
[tex]a(surface) = a(lateral) + a(2 \: bases)[/tex]
First, we have to find the lateral surface:
[tex]a(lateral) = 2\pi \times r \times h = 2 \times 3.14 \times 5 \times 5 = 157 \: {in}^{2} [/tex]
Then, we have to find the area of the base and multiply it by 2, since the shown figure is a cylinder, which has 2 identical bases:
[tex]a(2 \: bases) = 2 \times \pi {r}^{2} = 2 \times 3.14 \times {5}^{2} = 157 \: {in}^{2} [/tex]
Now, let's add everything together and we'll get the answer:
[tex]a(surface) = 157 + 157 = 314 \: {in}^{2} [/tex]
ANSWER QUICK ILL GIVE BRAINLIEST
(1.) What is the height of the cannon before it is launched, at t=0? Remember to include units.
(2.) A projectile's maximum height is shown by the vertex of the parabola. When does the cannonball reach its maximum height? Round to the nearest whole number and remember to include units.
(3.) What is the maximum height of the cannonball? Round to the nearest whole number and remember to include units.
(4.) How long does it take the cannonball to land on the ground? Round your answer to the nearest whole number and remember to include your units.
(5.) What would the equation be if the initial velocity was changed to 40.5 m/s but the initial height stays the same?
1. The cannonball is at 70 meters before it is launched.
2. The cannonball reaches its maximum height at about 3 seconds.
3. The maximum height of the cannonball is about 115 meters.
4. It takes about 8 seconds for the cannonball to reach the ground.
I don't know the answer to number 5 - sorry :(
I hope the rest are correct
acellus algebra 2. piece wised functions.
find f(-2) for the piece wised function
[tex]f(-2) = -4[/tex] for the given piecewise function by using the equation [tex]f(x) = x - 2[/tex] if [tex]x < 3.[/tex]
What is the piecewise function?A piecewise function is a mathematical function that is defined differently on different parts of its domain.
Instead of having a single formula that applies to the entire domain, a piecewise function has multiple formulas, each applying to a specific interval or subset of the domain.
To find f(-2) for the given piecewise function, we need to determine which piece applies to the input value o [tex]f -2[/tex], which is less than 3. Therefore, we use the first piece of the function, which is[tex]f(x) = x - 2 if x < 3.[/tex]
Substituting x = -2 into this piece, we get:
[tex]f(-2) = (-2) - 2 = -4[/tex]
Therefore, f(-2) = -4 for the given piecewise function.
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need help asap thank youuu
Answer:
11/3
Step-by-step explanation:
2[tex]\frac{1}{5}[/tex] = 11/5
2[tex]\frac{1}{5}[/tex] ÷ [tex]\frac{3}{5}[/tex] = 11/5 · 5/3 = 55/15 = 11/3
the time until recharge for batteryin a laptop computer under common conditions is normally distributed with mean of 275 minutes and standard deviation of 50 minutes. a) what is the probability that battery lasts more than four hours? round the answer to 3 decimal places b) what are the quartiles (the 25% and 75% values) of battery life? 25% value minutes (round the answer to the nearest integer) 75% value minutes (round the answer to the nearest integer:) c) what value of life in minutes is exceeded with 95% probability? integer:) (round the answer to the nearest
a) The probability that the battery lasts more than 4 hours is 0.758 (rounded to 3 decimal places).
b) The 25% value is 240 minutes, and the 75% value is 310 minutes.
c) The value of life in minutes that is exceeded with 95% probability is 357 minutes.
a) To find the probability that the battery lasts more than 4 hours (240 minutes), we first need to convert 240 minutes into a z-score.
z = (X - μ) / σ
z = (240 - 275) / 50
z = -0.7
Now, we'll use a z-table to find the probability that the battery lasts more than 4 hours:
P(Z > -0.7) = 1 - P(Z ≤ -0.7) = 1 - 0.2420 = 0.758
The probability that the battery lasts more than 4 hours is 0.758 (rounded to 3 decimal places).
b) To find the quartiles, we'll use the z-table to find the z-scores corresponding to 25% and 75%:
25%: z = -0.674
75%: z = 0.674
Now, we'll convert the z-scores back into minutes:
Q1 = μ + z * σ = 275 + (-0.674) * 50 = 240 (rounded to the nearest integer)
Q3 = μ + z * σ = 275 + (0.674) * 50 = 310 (rounded to the nearest integer)
The 25% value is 240 minutes, and the 75% value is 310 minutes.
c) To find the value of life in minutes that is exceeded with 95% probability, we first find the z-score corresponding to 95%:
95%: z = 1.645
Now, we'll convert the z-score back into minutes:
X = μ + z * σ = 275 + (1.645) * 50 = 357 (rounded to the nearest integer).
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5. From a stack of 100 paper plates,
42 were used at a picnic. What
portion of the paper plates were
used?
Step-by-step explanation:
42/100 = 21/50 about 42%
f(x)=2x^5−x^4+4x^3−3x^2−31x−5
. Find f(−3/2)
.
Answer:
f(-3/2) = -411/16.
There are 78 Year 9 pupils in a music club, out of a total of 167 pupils.
Write this proportion as a percentage.
Give your answer correct to 1 decimal place when appropriate.
The proportion of Year 9 pupils in the music club is approximately 46.7%.
A ratio or value that may be stated as a fraction of 100 is called a percentage.
To find the proportion of Year 9 pupils in the music club as a percentage, follow these steps:
To get proportion as a percentage divied number of Year 9 pupils by total pupils multiplied by 100.
Proportion as a percentage = [tex]\frac{Year \:9 \:pupils}{total \:pupils} \times 100[/tex]
Divide the number of Year 9 pupils by the total number of pupils.
78 (Year 9 pupils) ÷ 167 (total pupils)
= 0.4671
Multiply the result by 100 to convert the proportion to a percentage.
0.4671 × 100
= 46.71%.
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Solve y3 = 1.
y = −1
y = 1
y = ±1
y = 3
The answer is y = ±1, as well as two complex solutions. The answer y = 3 is not a solution to the equation [tex]y^3 = 1.[/tex]
What is equation?An equation is a statement that asserts the equality of two expressions. It typically contains one or more variables, which are symbols that represent unknown or varying quantities. The expressions on either side of the equals sign can include numbers, constants, functions, and other mathematical operations.
To solve[tex]y^3 = 1[/tex], we can take the cube root of both sides of the equation:
y = ∛1
There are three cube roots of 1, which are 1, -1/2 + √3/2 i, and -1/2 - √3/2 i, where i is the imaginary unit. These three roots form a complex conjugate pair.
Therefore, the solutions to the equation [tex]y^3 = 1[/tex] are:
y = 1
y = -1/2 + √3/2 i
y = -1/2 - √3/2 i
So the answer is y = ±1, as well as two complex solutions. The answer y = 3 is not a solution to the equation [tex]y^3 = 1.[/tex]
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Since spring started, Kareem has been surveying the growth of leaves on his neighborhood trees. He goes out every day and computes the average number of leaves on a sample of trees. He created a scatter plot where the y-axis represents the average number of leaves on the trees, and the x-axis represents the number of weeks since spring started.
Use the 2 given points to write a linear equation that can be used to approximate the data distribution.
A
y = 1566.67x + 1716.67
B
y = 4700x + 1500
C
y = 3x + 2000
D
y = x + 1700
Based on the equation you created, what would be the expected average number of leaves on a tree 8 weeks after spring has started?
Answer:
a
Step-by-step explanation:
A tree should therefore have 38,900 leaves on average by the eighth week of spring.
what is linear equation ?An equation that depicts a linear model on a graph is referred to as a linear equation. This polynomial equation has a factor whose greatest power is one. The formula for a linear equation is y = mx + b, were x and y are factors, m is the line's gradient or slope, and b is the y-intercept, or the place where the line crosses the y-axis. The line's steepness is determined by its slope, and its point of intersection with the y-axis is indicated by its y-intercept. Science and mathematics both frequently model and examine relationships between variables using linear equations.
given
B is the right response for the linear equation y = 4700x + 1500, which can be used to approximate the data distribution.
We may enter x = 8 into the calculation to get the predicted average number of leaves on a tree 8 weeks after spring has begun:
y = 4700(8) + 1500
y = 38,900
A tree should therefore have 38,900 leaves on average by the eighth week of spring.
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solve the equation
1. 4x^2-4x-24=0
2. 3p^2-5p-28=0
Solve using substitution.
y = 5x - 9
y = -2x + 5
Answer:
(2,1) (2,1)
1=5(2)-9 1=-2(2)+5
1=10-9 1=-4+5
Step-by-step explanation:
Hope this helps!!
Mark me brianliest :))
An eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.
Sunglasses Inventory:
Number of Days | Total Amount of Sunglasses
______
2 | 52
5 | 46
7 | 42
10 | 36
______
Which graph shows the relationship given in the table?
A) graph with the x axis labeled number of days and the y axis labeled total amount of
sunglasses and a line going from the point 0 comma 52 through the point 1
comma 50
B) graph with the x axis labeled number of days and the y axis labeled total amount of
sunglasses and a line going from the point 0 comma 56 through the point 1 comma
54
C) graph with the x axis labeled number of days and the y axis labeled total amount of
sunglasses and a line going from the point 0 comma 52 through the point 1
comma 49
D) graph with the x axis labeled number of days and the y axis labeled total amount
of sunglasses and a line going from the point 0 comma 56 through the point 1
comma 53
Therefore, the correct option is C). graph with the x axis labeled number of days and the y axis labeled total amount of
sunglasses and a line going from the point 0 comma 52 through the point (1,49).
What is graph?mathematics, a graph is a data structure that represents a collection of vertices (also known as nodes) and edges between them.
A graph can be used to represent a wide range of real-world systems, such as social networks, transportation networks, and electrical circuits.
In a graph, vertices are usually represented as points or circles, and edges are represented as lines or arrows that connect pairs of vertices. Each edge can be directed (pointing from one vertex to another) or undirected (connecting two vertices without any specific direction).
Graphs can be classified in many ways, such as by their density (the ratio of edges to vertices), their connectivity (how many separate components the graph has), and their degree distribution (the distribution of the number of edges connected to each vertex). Graph theory, which is the study of graphs, has many practical applications in computer science, mathematics, and other fields.
Which graph shows the relationship given in the table?
A) graph with the x axis labeled number of days and the y axis labeled total amount of
sunglasses and a line going from the point 0 comma 52 through the point 1 comma 50.
B) graph with the x axis labeled number of days and the y axis labeled total amount of
sunglasses and a line going from the point 0 comma 56 through the point (1,54)
C) graph with the x axis labeled number of days and the y axis labeled total amount of
sunglasses and a line going from the point 0 comma 52 through the point (1,49)
D) graph with the x axis labeled number of days and the y axis labeled total amount
of sunglasses and a line going from the point 0 comma 56 through the point (1,53)
Based on the given data in the table, the inventory of sunglasses decreases as the number of days since the opening of the eyeglasses store increases. This suggests a negative correlation between the two variables.
To visualize this relationship, we can plot the data points on a scatter plot and draw a line of best fit. Based on the options provided, the closest graph to the relationship given in the table is option C) with the x-axis labeled as number of days, the y-axis labeled as the total amount of sunglasses, and a line going from the point 0,52 through the point 1,49.
Option A) has a decreasing trend, but the line does not pass through all the given data points.
Option B) has a similar decreasing trend, but the values on the y-axis are higher than those in the table.
Option D) has a decreasing trend, but the values on the y-axis are higher than those in the table, and the line does not pass through all the given data points.
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What is the image point of (-2, 10) after the transformation R270° 0 D₁?
PLS HELP ASAP
MAKE A NUMBER LINE AND MARK ALL THE POINTS
A number line that represent the values of x is shown in the graph attached below.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0):
x < - 1 or x > 1
-1 > x > 1
-3 < x ≤ 1
-5 ≤ x ≤ 0
In this scenario and exercise, we would use an online graphing calculator to plot each of the inequality as shown in the graph (number line) attached below.
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increase 15/16 by 3/4 of it. then increase the result by 3/5 of it
Increasing [tex]\frac{15}{16}[/tex] by [tex]\frac{3}{4}[/tex] of it and then increasing the result by [tex]\frac{3}{5}[/tex] of it gives us the fraction of [tex]\frac{45}{32}[/tex].
To increase [tex]\frac{15}{16}[/tex] by [tex]\frac{3}{4}[/tex] of it, we can multiply [tex]\frac{15}{16}[/tex] by [tex]\frac{3}{4}[/tex], which gives us:
[tex]\frac{15}{16}[/tex] × [tex]\frac{3}{4}[/tex] = [tex]\frac{45}{64}[/tex]
Adding this result to [tex]\frac{15}{16}[/tex], we get:
[tex]\frac{15}{16}[/tex] + [tex]\frac{45}{64}[/tex] = [tex]\frac{225}{256}[/tex]
Now, to increase this result by [tex]\frac{3}{5}[/tex] of it, we can multiply [tex]\frac{225}{256}[/tex] by 3/5, which gives us:
[tex]\frac{225}{256}[/tex] × [tex]\frac{3}{5}[/tex] = [tex]\frac{135}{256}[/tex]
Adding this result to [tex]\frac{225}{256}[/tex], we get the final answer:
[tex]\frac{225}{256}[/tex] + [tex]\frac{135}{256}[/tex] = [tex]\frac{360}{256}[/tex]
Simplifying this fraction, we get:
[tex]\frac{360}{256}[/tex] = [tex]\frac{45}{32}[/tex]
The problem involves increasing a fraction by a certain percentage twice. To solve the problem, we first find the increase in the fraction by multiplying it with the given percentage. We then add the result to the original fraction to get the new fraction. This process is repeated for the second increase. Finally, we simplify the resulting fraction if possible. In this specific problem, we are increasing [tex]\frac{15}{16}[/tex] by [tex]\frac{3}{4}[/tex] of it and then increasing the result by [tex]\frac{3}{5}[/tex] of it to find the resulting fraction [tex]\frac{45}{32}[/tex].
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A builder was building a fence. In the morning, he worked for 25 of an hour. In the afternoon, he worked for 910 of an hour. How many times as long as in the morning did he work in the afternoon?
Write a division equation to represent this situation, then answer the question. Use "?" to represent the unknown quantity. Do not use parentheses in your equation.
Answer:
36.4
Step-by-step explanation:
In morning, builder worked for = 25 in a hour.
Let hour be ? hr.
then 25? = Time he worked in morning.
In afternoon,he worked for= 910 of ? hour = 910? hr
Times he worked more = 910?/25? = 36.4 times
25*6 =
the following table contains figures on the monthly volume and unit costs for a random sample of 16 items from a list of 2,000 inventory items. the company classifies products with annual dollar volume of $10,000 or more as a items and products with annual dollar volume of $2,000 or less as c items. a) develop an abc classification for these items. a file labeled abc data.csv is available on t-learn. b) what is the percentage of items stocked in each classification group?
A: 75% of items are classified as C items, 18.75% as B items, and 6.25% as A items.
A-B-C examination is an instrument utilized for stock administration, which orders things into three classifications: A, B, and C, in light of their worth and significance. Classification A things have a high worth however a low volume, and their administration requires close consideration and control. Class B things have moderate worth and volume and require moderate control. Classification C things have a low worth yet a high volume, and their administration can be loose. The reason for the examination is to recognize which things need the most consideration and control, and which things can be dealt with less consideration and cost-actually. The examination assists in streamlining with reviewing levels, decreasing expenses, and expanding benefits.
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Reflect triangle ABC over the line y = 2. Translate the image by the directed line segment from (0,0) to (3,2). What are the coordinates of the vertices in the final image?
The coordinates of the triangle's image in the question serve as an example of transformation and are A(-2,4), B (-3,7), and C (0,6).
The triangle's coordinates are as follows:
(-6,-1), (-5,2) and (-3,0) (-3,0)
The new points are created when the triangle is mirrored over the line y = 2.
(-6,5), (-5,2) and (-3,4) (-3,4)
Then, we use the translation to translate the triangle's picture.
(x,y) -> (x + 3, y +2)
We thus have:
(-6,5) => (-6 + 3, 5 + 2) = (-3,7) (-3,7)
(-5,2) => (-5 + 3, 2 + 2) = (-2,4) (-2,4)
(-3,4) => (-3 + 3, 4 + 2) = (0,6) (0,6)
Hence, the triangle's image's coordinates are A(-2,4), B (-3,7), and C (0,6) respectively.
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For the circle with equation (x-2)² + (y+3)² = 9, what are the center coordinates?
Answer:
[tex]\large\boxed{(2, -3)}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked for the Center Coordinates given a circle.}[/tex]
[tex]\large\underline{\textsf{What is a Circle?}}[/tex]
[tex]\textsf{A Circle is a curved shape that is commonly used to present a equidistant (same}[/tex]
[tex]\textsf{distance apart) from a Center point.}[/tex]
[tex]\textsf{When we create an equation for a circle, we should keep in mind of what the}[/tex]
[tex]\textsf{coordinates of the center point are, and the Radius. For this problem an equation}[/tex]
[tex]\textsf{has been given to us.}[/tex]
[tex]\boxed{\begin{minipage}{20 em} \\ \underline{\textsf{\large Equation of a Circle (Standard Form);}} \\ \\ \tt \tt (x-h)^{2} + (\tt y-k)^{2} = r^{2} \\ \\ \underline{\textsf{\large Where;}} \\ \textsf{h represents the x-coordinate of the center.} \\ \textsf{k represents the y-coordinate of the center.} \\ \tt r^{2} \ \textsf{represents the radius of a circle squared.} \end{minipage}}[/tex]
[tex]\textsf{*Note that if we are given the formula, the radius is already squared, unless}[/tex]
[tex]\textsf{specified in the directions.}[/tex]
[tex]\tt (x-2)^{2} + (y+3)^{2} = 9[/tex]
[tex]\textsf{Our main focus should be h and k. Notice how both point values are negative.}[/tex]
[tex]\textsf{The Center Point is represented as the opposite given to us in the formula.}[/tex]
[tex]\underline{\textsf{Find the Opposite of -2 and 3;}}[/tex]
[tex]\tt -2 \rightarrow \boxed{2}[/tex]
[tex]3 \rightarrow \boxed{-3}[/tex]
[tex]\underline{\textsf{Center Coordinates;}}[/tex]
[tex]\large\boxed{(2, -3)}[/tex]
a chinese restaurant has a large goldfish pond. suppose that an inlet pipe and a hose together can fill the pond in hours. the inlet pipe alone can complete the job in one hour less time than the hose alone. find the time that the hose can complete the job alone and the time that the inlet pipe can complete the job alone.
So, the hose can complete the job alone in approximately 2.62 hours, and the inlet pipe can complete the job alone in approximately 1.62 hours.
Let the time it takes for the hose alone to fill the pond be H hours, and the time it takes for the inlet pipe alone be P hours. According to the given information:
1) P = H - 1 (The inlet pipe alone can complete the job in one hour less time than the hose alone)
2) In one hour, the hose fills 1/H of the pond, and the inlet pipe fills 1/P of the pond. Together, they can fill the pond in one hour, so: (1/H) + (1/P) = 1
Now, substitute the value of P from equation 1 into equation 2:
(1/H) + (1/(H-1)) = 1
To solve for H, first find a common denominator (H*(H-1)):
(H-1) + H = H*(H-1)
Combine the terms on the left:
2H - 1 = H^2 - H
Rearrange to form a quadratic equation:
H^2 - 3H + 1 = 0
Now, solve the quadratic equation using the quadratic formula:
[tex]H = (3 + sqrt(5))/2 or H = (3 - sqrt(5))/2[/tex]
However, since H > 0, the only valid solution is H = (3 + sqrt(5))/2 ≈ 2.62 hours.
Now, find the time it takes for the inlet pipe alone to complete the job:
P = H - 1 = 2.62 - 1 = 1.62 hours
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For the circle with equation (x-2)^2 + (y+3)^2 = 9, what is the radius?
Answer:
The equation of the given circle is (x-2)^2 + (y+3)^2 = 9, which is in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
Comparing the given equation with the standard form, we can see that the center of the circle is (2, -3) and the radius is 3.
Therefore, the radius of the circle is 3 units.
Find the value of $x$ . Two segments start at a point outside the circle intersect the circle at two points that divide the segments. The length of the first segment is 45 units and length of the segment outside the circle is labeled x. The length of second segment is 50 units and length of the segment outside the circle is 27 units. $x\ =\ $
The value of x is 29.5 units. Since the segments inside the circle have the same length, we can set 52.5 - x = 23 and get the value of x.
What is radius?It is half of the diameter of the circle. The radius is used to calculate the area of a circle and the length of an arc or a circular sector.
In order to find the value of x, we need to first determine the radius of the circle.
In this problem, the first shorter side is 45 units, and the second shorter side is 27 units. Thus, we can find the radius of the circle by using the following method,
Radius of the circle = √(45² + 27²)
= √(2754) = 52.5 units
Now that we know the radius of the circle, we can use this information to find the value of x. We know that the total length of the first segment is 52.5 units. This means that the length of the segment outside the circle is x units and the length of the segment inside the circle is 52.5 - x units.
Similarly, the total length of the second segment is 50 units, so the length of the segment outside the circle is 27 units and the length of the segment inside the circle is
50 - 27 = 23 units.
Since the segments inside the circle have the same length, we can set 52.5 - x = 23 and solve for x.
52.5 - x = 23
x = 52.5 - 23
x = 29.5 units
Therefore, the value of x is 29.5 units.
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