We subtract 8 from the x-coordinate and add 20 to the y-coordinate of the original point.
What do you mean by translation?In mathematics, translation refers to the process of moving an object from one location to another, without rotating or scaling it. The movement is described by a vector, which is a directed line segment that specifies the direction and distance of the movement.
In two-dimensional geometry, a translation can be represented by a shift of an object along the x- and y-axes. For example, if a point is translated by a vector (a, b), its new position will be (x + a, y + b), where (x, y) is the original position of the point.
Translations can also be performed on shapes, such as lines, polygons, or curves. The effect of a translation on a shape is to create a new shape that is identical to the original shape, but located in a different position.
A translation is a transformation that moves a figure in a certain direction and by a certain distance without rotating or reflecting it. To find the rule for a translation, we need to find the vector that represents the displacement between the original point and the translated point.
Given two points A (2, -5) and A' (-6, 15), the translation vector is given by:
Translation vector = A' - A = (-6, 15) - (2, -5) = (-6 - 2, 15 - (-5)) = (-8, 20)
So, the rule for the translation is:
(x, y) -> (x - 8, y + 20)
This means that to apply the translation, we subtract 8 from the x-coordinate and add 20 to the y-coordinate of the original point.
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The ratio of the number of fiction books to the number of non-fiction books is 5:2 if there are 1421 book fiction and non-fiction books altogether how many fiction books more than nonfiction books are there in the library
Answer:
306
Step-by-step explanation:
Let's call the number of fiction books "f" and the number of non-fiction books "n". From the given information, we know that the ratio of fiction books to non-fiction books is 5:2 and the total number of books is 1421, so we can write the following equation:
f + n = 1421
Since the ratio of fiction books to non-fiction books is 5:2, we can write:
f/n = 5/2
We can cross-multiply to solve for f:
f = (5/2) * n
Substituting this expression for f into the first equation:
(5/2) * n + n = 1421
Expanding the left side:
(5/2 + 2/2) * n = 1421
Simplifying the left side:
(5 + 2)/2 * n = 1421
(7/2) * n = 1421
Dividing both sides by (7/2):
n = 1421 * 2/7
n = 204
So there are 204 non-fiction books and 5/2 * 204 = 204 * 5/2 = 102 * 5 = 510 fiction books.
The difference between the number of fiction books and non-fiction books is 510 - 204 = 306. So there are 306 more fiction books than non-fiction books in the library.
Step-by-step explanation:
If the ratio of fiction and non-fiction books are 5:2. Therefore that means that the total books were divided into 7 parts and the fiction books took 5 parts while the non-fiction books took two parts.
To get the number of fiction and non-fiction books we first add the ratio
[tex]5 + 2 = 7[/tex]
So that means that 7 = 1421
After adding the ratio we now take
The total parts that the books took as the numerator and the total of the ratio as the denominator, and multiply the fraction by the total number of books which is 1421
[tex] \frac{5}{7} \times 1421 = number \: of \: fiction \: books[/tex]
[tex] \frac{2}{7} \times 1421 = number \: of \: non - fiction \: books[/tex]
let's work out each fraction separately
[tex] \frac{5}{7} \times 1421 = \frac{7105}{7} [/tex]
[tex] \frac{7105}{7} = 1015[/tex]
1015 = Number of fiction books[tex] \frac{2}{7} \times 1421 = \frac{2842}{7} [/tex]
[tex] \frac{2842}{7} = 406[/tex]
406 = number of non-fiction booksTo get the answer to the question we subtract the number of non-fiction books from the number of fiction books
[tex]1015 - 406 = 609[/tex]
Answer:609ple Interes How much simple interest would be earned on a savings account of $4,500 at 5.5% interest per year after 24 months? I=(4,500)(055)(2)
4500(1+0.055)^24
4500(1.055)^24
= 16,265.65456755
When my wife and I drove to Boston from Chicago (a trip of about 1170 miles), the trip took a total of 20 hours. The first part of the trip, I drove at an average speed of 55 mph. The second part of the trip was driven by my wife, who drove at an average speed of 65 mph. For how many hours did each of us drive?
Let's call the time you drove "x" and the time your wife drove "y". We know that the sum of the two times is 20 hours:
x + y = 20
We also know the distance traveled during each part of the trip. The first part of the trip was 55x miles, and the second part of the trip was 65y miles. The total distance of the trip was 1170 miles:
55x + 65y = 1170
We can use the first equation to solve for x in terms of y:
x = 20 - y
We can then substitute this expression for x in the second equation:
55(20 - y) + 65y = 1170
Simplifying and solving for y:
1100 - 55y + 65y = 1170
10y = 70
y = 7
So your wife drove for 7 hours. We can use the first equation to find your driving time:
x + 7 = 20
x = 13
So you drove for 13 hours.
Answer:
13 hours
Step-by-step explanation:
02: Pretest CR Algebra 2 A / 2:Equations and Functions
option B is correct, the equation or function of the graph is y≥3/4x-3.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The line passing through points (4,0) and (0,3)
Slope=3/-4=-3/4
Now let us find y intercept
0=-3/4(4)+b
0=-3+b
b=3
Hence, option B is correct, the equation or function of the graph is y≥3/4x-3.
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the length of a rectangle is 4 times the width. if the length is decreased by 5cm and the width is increased by 2cm, the perimeter will be 74. Find the dimensions of the original rectangle.
Answer:
w=6, L=24
Step-by-step explanation:
let the width be x,
then, L=4x
Perimeter=2(l+w)
=2(4x+x)
the new dimensions,
perimeter=2(l+w)
74 =2(4x+5+x+2)
=2(5x+7)
=10x+14
10x=74-14
10x=60
x=60/10
x=6
Therefore, The width is 6 cm
L=4x
=4(6)
=24
Therefore the length is 24 cm
what pattern would you observe if everyone in the class were to bias their results to 5 heads and 5 tails?
In a coin flip experiment, you would see a pattern of 50/50 heads and tails if every student in the class skewed their findings to show 5 heads and 5 tails.
This is due to the fact that each participant purposefully altered their results to display an equal number of heads and tails.
It is crucial to remember that this pattern does not accurately reflect the chances of either getting heads or tails in a fair coin flip. The results cannot be taken as a representative sample of a fair coin flip because everyone purposefully slanted their findings. It is crucial to conduct experiments with appropriate controls and prevent results bias in order to acquire reliable findings.
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i need help pls rn like dang
Answer:
Step-by-step explanation:
I gotchu.
sinP = 5/14
= 0.36
P = sin^-1(5/14)
P = 20.92
there exists a number , such that when is revolved abut the line , the resulting solid has the same volume as the solid in question . write but do not solve, an equation involving an integral expression that can be used to find the value of
The equation involving an integral expression that can be used to find the value of k is π integration [(k - x²)² - (k - 4)²] dx.
We need to perform integration to find the value of k which will have same volume. Thus, tos over the question the clarity of concepts of volume of any area and integration is required.
The graph representing the mentioned situation is attached in the picture. So, now, writing the expression -
π integration [(k - x²)² - (k - 4)²] dx
Remember tha the integration limit in the mentioned equation will be -2 to 2.
On solving we will get the volume 256π/5.
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The comp question is -
The shaded region, R, is bounded by the graph of y = x² and the line y = 4, as
shown in the figure.
There exists a number k, k 4 , such that when R is revolved about the line y = k , the resulting solid has the same volume as the solid in part (b).
Write, but do not solve, an equation involving an integral expression that can be used to find the value of k.
pls help and give me a good answer pls
Answer:
y-intercept: 5
slope: -1
equation: y = -x + 5
Step-by-step explanation:
The y-intercept is when x is 0, and it is shown on the table as 5.
The slope can be found by doing [tex]y_1-y_2/x_1-x_2[/tex], which is 6-5/-1-0 = 1/-1 = -1.
The equation is y = mx + b, so we can write it as y = -x + 5
Write the standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point. Use a graphing utility to verify your result.
Vertex:
(−4, −1);
Point:
(−2, 4)
The standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point is 1/36(x +4)² - 1.
What is Quadratic function?Equation of a quadratic function in the vertex form is given by;
f(x) = a(x - h)² + k
Here, (h, k) is the vertex of the parabola representing the quadratic function;
Given;
Vertex of the quadratic function (−4, −1);
Parabola passes through a point (−2, 4);
Substitute the vertex in the quadratic function;
f(x) = a(x +4)² - 1
Because, this parabola passes through a point (7, 0),
0 = a(-2- 4)² - 1
0 = 36a - 1
a = 1/36
Equation of the quadratic function will be;
f(x) = 1/36(x +4)² - 1
Therefore, equation of the quadratic function will be f(x) = 1/36(x +4)² - 1;
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Please solve in 20 mins
The table should be completed as follows;
Coordinate Key feature Does the coordinate Justification
make sense ___________________
(-7.565, 0) it is a key feature yes it is a zero (root).
(0, 37) it is a key feature yes it is the y-intercept.
(6, 46) it is a key feature yes it is the vertex.
A reasonable constraint for the context in set builder notation is {y|y ∈ R ≤ 46}.
What is a quadratic function?In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two or more variable on a graph, with a maximum exponent of two (2).
What is y-intercept?In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).
In this scenario, the y-intercept of this quadratic function can be calculated as follows;
G(x) = -1/4(x²) + 3x + 37
G(0) = -1/4(0²) + 3(0) + 37
G(0) = 37.
In conclusion, the vertex (maximum point) of this quadratic function is given by the ordered pair (6, 46).
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Audrey is getting a hoverboard, it is on sale for 35% off, it is originally $89. 95. What is the discount amount? Round to the nearest penny. Audrey is getting a hoverboard, it is on sale for 35% off, it is originally $89. 95. What is the discount amount? Round to the nearest penny
The discount amount based on 35% discount offered on $89.95 is $31.5.
The discount amount can be calculated by the formula -
Final amount = original price - discount percentage × original price
The method of solving this formula will be to first multiply followed by subtraction according to PEMDAS rule.
Now, keep the values in formula
Final amount = 89.95 - 35/100 × 89.95
Performing multiplication and division on Right Hand Side of the equation
Final amount = 89.95 - 31.48
Now performing subtraction on Right Hand Side of the equation
Final amount = $58.47
Here we see that that the discount amount is $31.48
Round to nearest penny = $31.5
Thus, the discount amount is $31.5.
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17 Problem-solving Orla drove 155 km in 2 hours. Then she drove 48 km at a speed of 60 km/h. 48 Work out Orla's average speed for the whole journey.
The average speed for the whole journey is 72.5 km/h. The result is obtained by using the formula for the average speed.
What is average speed?Average speed is the overall speed of a moving object during a given amount of time. It can be expressed as
Avg speed = Total distance covered / Total time taken
The speed itself is
v = s/t
Where
v = speeds = distancet = time takenOrla drove 155 km in 2 hours. Then, she drove 48 km at a speed of 60 km/h. Find the average speed for the whole journey!
We have
s₁ = 155 kmt₁ = 2 hourss₂ = 48 kmv₂ = 60 km/hThe time taken in the second journey is
v₂ = s₂/t₂
60 = 48/t₂
t₂ = 48/60
t₂ = 0.8 h
The average speed will be
= total distance covered / total time taken
= (s₁ + s₂)/(t₁ + t₂)
= (155 + 48)/(2 + 0.8)
= (203)/(2.8)
= 72.5 km/h
Hence, the whole journey will have the average speed of 72.5 km/h.
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What is Y=2x+1 I can’t find it
Y=2x+1 is an equation used in mathematics to calculate the relationship between two variables, X and Y.
What is equation?An equation is a physical and mathematical statement that describing physical phenomena are describe the relationship between different physical quantities it typically consists of two or more variable which are simple representing physical quantity and then equal sign the variable may be quantity such as force velocity or energy.
This equation is a linear equation, meaning it is a straight line when graphed. It is a very basic equation and one of the most commonly used equations.
To use this equation, you will need to know the value of X. Once you have determined the value of X, you can plug it into the equation to calculate the value of Y. For example, if X=3, then the equation would look like this: Y=2(3)+1, which equals 7. Therefore, when X=3, Y=7.
The equation Y=2x+1 is often used in a variety of math problems, such as determining the slope of a line, calculating the area of a triangle, and finding the equation of a circle. It is also used in physics to calculate velocity or acceleration. As you can see, this equation is quite versatile and can be used in a variety of situations.
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What is the product?
(3a^2b^7)(5a^3b^8
8a^5b^15
8a^6b^56
15a^5b^15
15a b^56
Answer/Solution:
15a^5b^15
Explanation:
First, multiply the numbers, then combine the exponents until you get the answer.
Which expression to represents the phrase: "6 times a number plus 3."
Question 2 options:
6 x 3
6 x 3 + n
6n + 3
6n = 3
The expression to represent the phrase "6 times a number plus 3" is:
"6n + 3".
"n" represents an unknown number, and "6" and "3" are constants. The expression means that 6 is being multiplied by "n" to get an intermediate result, and then 3 is being added to that result to get the final answer.
For example, if n = 2, then the expression would evaluate to 6 * 2 + 3 = 12 + 3 = 15. So, the expression "6n + 3" represents the mathematical relationship between the unknown number "n" and the final result.
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8 − 1 − (18 − 2) ÷ 8
Answer: 5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
First do 18-2 which is 16
Then do 16 divided by 8 which is 2
Right now the equation is 8 - 1 - 2
Then we minus 8 by 1 which is 7
and then 7 - 2 which is 5
So then our final answer is 5
Susan Marciano invested part of her $32,000 bonus in a fund that paid a 9% profit and invested the rest in stock that suffered a 3% loss. Find the amount of each
investment if her overall net profit was $2,040.
The amount invested at 9% is $.
The amount invested in stock is $
Let x be the amount of money invested in the 9% fund. Then the amount invested in the stock is $32,000 - x. The profit from the 9% investment is 0.09x and the loss from the stock investment is -0.03(32000 - x).
What exactly does compounding mean?
Compounding is the method through which interest is added to both the principle balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."
The overall net profit was $2,040, so we can set up the following equation to solve for x:
0.09x - 0.03(32000 - x) = 2040
Expanding the second term,
0.09x - 9600 + 0.03x = 2040
Combining like terms,
0.12x - 9600 = 2040
Adding 9600 to both sides,
0.12x = 1640 + 9600
Simplifying,
0.12x = 11240
Dividing both sides by 0.12,
x = 93, 666.67
So, the amount invested in the 9% fund is $93,666.67 and the amount invested in the stock is $32,000 - $93,666.67 = $-61,666.67.
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Subtract ab-2a+3b from 5a-3ab+6b
Answer:
7a - 4ab + 3b
Step-by-step explanation:
5a - 3ab + 6b - (ab - 2a + 3b)
=5a - 3ab + 6b - ab + 2a - 3b
=7a - 4ab + 3b
if a triangle is other side is 7m and other side is 12m what is the other side going to be
The value of the other side is 9. 7 m
How to determine the length of the sideUsing the Pythagorean theorem stating that the square of the hypotenuse side is equal or equivalent to the sum of the squares of the other two sides.
From the information given, we have that;
One side is 7mThe other side is 12mThis is represented as;
12² = 7² + x²
Find the value of the squares, we get;
144 = 49 + x²
collect like terms. we get;
x² = 144 - 49
subtract the values, we have;
x² = 95
Find the square root of both sides
x = 9. 7 m
Hence, the value is 9. 7 m
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The Smith family will drive 240 miles round-trip to visit a relative. Mr. Smith, Mrs. Smith, and their 20 -year old son, James, will share the driving. Determine whether each statement is correct by selecting True or False. A If Mrs. Smith and Mr. Smith drive 80 miles each, then James will drive for 13 of the round-trip distance. True False B If Mrs. Smith and Mr. Smith drive 90 miles each, then James will drive for 12 of the round-trip distance. True False C If Mrs. Smith drives 90 miles and Mr. Smith drives 50 miles, then James will drive for 512 of the round-trip distance. True False D If Mrs. Smith drives 60 miles and Mr. Smith drives 120 miles, then James will drive for 712 of the round-trip distance. True False
Answer:
Your answer should be: TRUE FALSE TRUE FALSE
The shortest side of a triangle similar to XYZ is 20 units long. Find the other side lengths of the triangle. The sides to XYZ is 13,12,10
The other side lengths of the triangle will be 24 and 26 units.
How to calculate the side?
It should be noted that based on the information, it's important to write a proportion for the side length.The sides of a triangle are straight lines that are joined by the three vertices of the triangle. In other words, we can say that the sides of a triangle are line segments that meet each other at the vertices of the triangle.The shortest side of a triangle similar to triangle XYZ is 20 units long and the shortest side on the other. triangle is 10. This means the proportion is [tex]\frac{20}{10}[/tex]=2
The other sides will be:
⇒12 × 2 = 24
⇒13 × 2 = 26
Therefore, the sides are 24 and 26 respectively.
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Pls po i really need this help. I'll mark brainliest who answered po.
The table is filled as follows
x P(x) x P(x) (x - μ)²
3 3 9 961
4 7 28 900
5 22 110 841
6 60 360 784
7 85 595 729
8 32 256 676
9 8 72 625
mean, μ = 34.05
variance = 919.33
standard deviation = 30.32
How to solve for the meanThe mean is calculated using the information provided as follows
= summation of (x P(x) ) / summation of x
= 1430 / 42
=34
The variance is solved by the formula
= summation of (x - μ)² / (n - 1), where n = 7
= 5516 / (7 - 1)
= 5516 / 6
= 919.33
the standard deviation is solved using the formula
= √variance
= √919.33
= 30.32
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2. Seth’s father is thinking of buying his son a six-month movie pass for $40. With the pass, matinees cost $1.00. If matinees are normally $3.50 each, how many times must Seth attend in order for it to benefit his father to buy the pass?
Answer: The savings per movie with the pass is $3.50 - $1.00 = $2.50. For the pass to benefit Seth's father, Seth must attend enough movies such that the total savings is equal to or greater than $40.
Let's call x the number of times Seth must attend for the pass to benefit his father. Then:
$2.50x >= $40
Solving for x:
$2.50x/$2.50 >= $40/$2.50
x >= 16
So Seth must attend at least 16 movies in order for the pass to benefit his father.
Oleg is training for a triathlon. One day, he jogged for 2 hours at x miles per hour. Then he bicycled for 2 hours at y miles per hour. Finally, he swam a distance of 2 miles. The total number of miles did not exceed 30 miles.
What is the greatest possible speed that Oleg could have bicycled that day?
The greatest possible speed that Oleg could have bicycled that day is 13 miles per hour.
How did we get the value?Let's call the total distance that Oleg jogged z. Then z = 2x.
The total distance that Oleg bicycled was 30 - z - 2. Let's call this distance w. Then w = 30 - 2x - 2.
Since Oleg bicycled for 2 hours, the speed that he bicycled was w / 2. So, w / 2 = y.
Substituting the expressions for z and w, we have:
y = (30 - 2x - 2) / 2.
Since y must be the greatest possible speed that Oleg could have bicycled that day, x must be the smallest possible value.
Since Oleg jogged for 2 hours, the minimum value of x is 2 / 2 = 1.
Substituting x = 1 into the expression for y, we have:
y = (30 - 2 * 1 - 2) / 2 = (26) / 2 = 13.
So, the greatest possible speed that Oleg could have bicycled that day is 13 miles per hour.
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isaiah and juanita are picking apples to make an apple pie. isaiah picks 3 apples a minutes and janita picks 5 apples every two minutes, If they need 40 apples for a pie, how long will it take both of them to pick enough apples? round your answer to the nearest minute
The time it will take both of them to pick enough apples is 7.27 minutes.
What is the time taken for them to pick the apples?
The time it will take both of them to pick enough apples is calculated as follows;
Let the time = t ( minutes )
3t + (5/2)t = 40
3t + ( 5t / 2 ) = 40
multiply through by 2
6t + 5t = 80
11t = 80
divide through by 11
t = 80 / 11
t = 7.27 minutes
Thus, the time to pick enough apples depends on the rate at which they are picking the apples.
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how do we solve systems of equations by substitution
Step-by-step explanation:
Step One→ Solve one equation for either x or y.
Step Two→ Substitute the expression from step one into the 2nd equation.
Step Three→ Solve the second equation for the given variable.
Step Four→ Plug you solution back into the first equation.
Step Five→ Write your solution as a point.
In the interval 0° ≤ x ≤360°, find the values of x for which tan x =0. 8645 Give your answers to the nearest degree
The inverse tangent function [tex]tan^{-1}[/tex] can be used to find the values of x for which tan x = 0.8645 in the interval 0 degrees < x < 360 degrees. The inverse tangent function gives us the angle that has a tangent equal to the input value.
The function can be expressed as:
[tex]x = tan^{-1 (0.8645)}[/tex]
Using a scientific calculator or trigonometry tables, we can find that the value of [tex]tan^{-1 (0.8645)}[/tex] is approximately 47.5 degrees.
So, in the interval 0 degrees < x < 360 degrees, there is one value of x that satisfies the equation tan x = 0.8645, and it is approximately 47.5 degrees. It's important to remember that the inverse tangent function is a one-to-one function and its range is restricted to the interval -90° < x < 90°, so the value found represents the smallest angle in the interval 0° < x < 360° that has a tangent equal to 0.8645.
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Melissa bought some books for each and received a discount of off of her total purchase. She spent after the discount. How many books did she buy?
(a) Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers , , and . Let represent the number of books.
(b) Solve the equation in part (a) to find the number of books.
The equation that represents the number of books will be 6x - 8 = 58. And the number of books will be 11.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Melissa bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6.
Let 'x' be the number of books. Then the equation is given as,
6x - 8 = 58
Simplify the equation, then we have
6x - 8 = 58
6x = 66
x = 11
The equation that represents the number of books will be 6x - 8 = 58. And the number of books will be 11.
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i need help please :o
Answer:
10.8s
Step-by-step explanation:
120÷11.1= 10.8s (to 3 s.f.)