On solving the provided question we can say that - the coordinates from the graphs will be P' = (0.0); Q' = (1,0); R' = (1,1); S' = (0,1)
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is r
A fixed point serves as the dilation's center.
Dk is used to represent dilation, where k is the scale factor.
Dk (x, y) = for a dilation centered on the origin (kx, ky)
Let's assume that you have a PQRS rectangle where
P = (0,0)
Q = (4,0)
R = (4,4)
S = (0,4)
You must multiply each coordinate by 1/4 to achieve the dilation of this PQRS to P'Q'R'S' with a scale factor of 1.
P' = (0.0)
Q' = (1,0)
R' = (1,1)
S' = (0,1)
You may plot both of these rectangles to see that they are the same size and are centered on the origin, but they have different shapes.
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An astronaut was exploring the moon of a distant planet, and found some glowing goo at the bottom of a very deep crater. She brought a 10-gram sample of the goo to her laboratory. She found that when the goo was exposed to light, the total amount of goo increased by 100% every hour.
How much goo will she have after 1 hour? After 2 hours? After 3 hours? After n hours?
When she put the goo in the dark, it shrank by 75% every hour. How many hours will it take for the goo that was exposed to light for n hours to return to the original size?
The amounts of goo after each hour are given as follows:
1 hour: 20 grams.2 hours: 40 grams.3 hours: 80 grams.n hours: 10(2)^n.The time that it takes for the goo to return to original size is given as follows:
n hours, for which:
[tex](2)^n(0.25)^n = 1[/tex]
How to model the situation?An increasing exponential function is defined as follows:
y = a(1 + r)^x.
For which the parameters are given as follows:
a is the initial value.r is the growth rate, as a decimal.Her sample is of 10 grams, and the amopunt of goo increases by 100%, hence the parameter values' are given as follows:
a = 10, r = 1.
Thus the exponential function is defined as follows:
y = 10(2)^n.
Then the amounts are given as follows:
One hour: y = 10 x 2 = 20 grams.Two hours: y = 10 x 2² = 40 grams.Three hours: y = 10 x 2³ = 80 grams.A decreasing exponential function is given as follows:
y = a(1 - r)^x.
The goo shrinks by 75% every hour, hence:
r = 0.75.
The amount after n hours is of 10(2)^n, hence the shrinking function is given as follows:
[tex]y = 10(2)^n(0.25)^n[/tex]
It returns to the original amount when:
y = 10.
Hence:
[tex]10 = 10(2)^n(0.25)^n[/tex]
[tex](2)^n(0.25)^n = 1[/tex]
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What's the inverse of ƒ(x) = x – 20?
Therefore , the solution of Inverse function comes out to be of x-20 equals to x+20
What is the inverse symbol?A function f has an inverse function only if for every y in its range there is only one value of x in its domain for which f(x)=y. This inverse function is unique and is frequently denoted by f−1 and called “f inverse.” For an overview into the idea of an inverse function, see the function machine inverse.Steps for finding the inverse of a function fReplace f(x) by y in the equation describing the function. Interchange x and y. In other words, replace every x by a y and vice versa.
Here,
Solve for y.
Replace y by f-1(x).
y=x-20
x=y-20
Solve for y,x = y-20
x+20
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Answer:
ƒ^(-1)(x) = x + 20
Step-by-step explanation:
To find the inverse of the function ƒ(x) = x - 20, we need to switch the roles of x and y and solve for y.
Let's start by replacing ƒ(x) with y:
y = x - 20
Next, swap x and y:
x = y - 20
Now, solve for y by isolating it:
x + 20 = y
Therefore, the inverse of the function ƒ(x) = x - 20 is given by:
ƒ^(-1)(x) = x + 20
When the function f(x) is divided by x + 2, the quotient is x² - 5x + 8 and the
remainder is 8. Find the function f(x) and write the result in standard form.
Step-by-step explanation:
this means :
f(x) / (x + 2) = (x² - 5x + 8) + 8/(x + 2)
f(x) = (x + 2)(x² - 5x + 8) + 8 =
= x³ - 5x² + 8x + 2x² - 10x + 16 + 8 =
= x³ - 3x² - 2x + 24
What is the repeated addition of 9x0=
Answer:
The answer is zero
Step-by-step explanation:
Hope it helps
Show how to use the unit rate to find the missing numbers on the double number line
Using the Double Number Line above, note that the unit that helps to find the missing numbers is given as:
3 and 915 and 518 and 624 and 827 and 9.What is a Unite Rate and How does it relate to a Double Number Line?Note that a unit rate is like a secret code to help you compare things. It helps you find missing numbers on a number line. For example, if 4 cookies cost $2, you can use the unit rate of $0.50/cookie to find out how much 8 cookies cost."
In the above case, we have several clues about the rate. The first relationship on the line is between 1 and 3.
But it only makes when we compare it to other iterations on the line such as 2 and 6.
Note that we can establish a relationship here which is that the greater number must be divided by three to get the lower number. That is:
3/3 = 1
6/3 = 2
Note well that the relationship between 0, 3, and 6 on the number line tell us that the upper units graduate in progressions of 3. that is:
0, 3, 6, 9, etc.
Thus, the missing numbers are:
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witch equation is made true by the opposite angles theorem
The option D is correct.Because this equation holds the vertically opposite angle theorem.
What is vertically opposite angle theorem?Vertically Opposite Angles are holds when two lines intersect each other then the opposite angles formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.
How do you find opposite angles?Vertical opposite angles that are opposite each other when two lines cross are also known as vertical angles because the two angles share the same corner. Opposite angles are also congruent angles.The equation of a vertical line is given by x = a or x = -a
Now we find
According to vertical opposite angle
x-8=40-2x
x+2x=40+8
3x=48
x=16
We can find value of x by usng vertical opposite angle.
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A boat will pass the Colby bridge and the wave bridge on the dell river. Rename each other the two bridge opening times. there are 60 minutes in an hour so use 60 as a common denominator. Then rename each opening time and find another common denominator. Explain how you found your answers.
The bridge opening times when there are 60 minutes in an hour will be 45/60 and 10/60.
How to illustrate the fraction?From the information, a boat will pass the Colby drawbridge and then the Wave drawbridge and then the Wave drawbridge.
From the table, Colby is on the 3/4 hour. This will be:
= 3/4 × 60
= 45
Also, Wave Bridge will be:
= 1/6 × 60
= 10
Therefore, it's 45/60 and 10/60 because we know that the common denominator is 60 then 3/4 of an hour is 45mins then 1/6 of an hour is 10.
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Complete question
On the Dell River, a boat will pass the Colby drawbridge and then the Wave drawbridge and then the Wave drawbridge. Rename each of the two drawbridge opening times. There are 60 minutes in an hour, so use 60 as a common denominator. Then, rename each opening time using another common denominator
Bridge name:
1. Asher Cross
2. Colby
3. Rainbow
4. Red Bank
5. Wave
Time of Opening:
1. On the hour
2. On the 3/4 hour
3. On the 2/3 hour
4. On the 1/4 hour
5. On the 1/6 hour
What add up to -3 and multiples to -70
We add (x +7 ) (x - 10) up to -3 and multiply to -70.
What is a quadratic equation?
Any equation in algebra that can be written in the standard form where x denotes an unknown value and a, b, and c denote known numbers, where a 0 is a quadratic equation.
Here,
We illustrate and prove that -9 and 10 multiply to -90 and add up to 1:
7 × -10 = -70
-10 + 7 = -3
We are trying to determine how to factor the following quadratic equation.
x² -3 x - 70 = 0
If so, the solution to factor the quadratic equation above is:
(x +7 ) (x - 10)
To summarize, -10 and 7 multiplied by -70 and add up to -3, you know that the following is true:
x² -3x - 70
= (x +7 ) (x - 10)
Hence, we add (x +7 ) (x - 10) up to -3 and multiply by -70.
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Select the correct answer from each drop-down menu. Graph of a four-sided polygon on a coordinate plane at A (minus 1, minus 1), B (0, 1), C (2, 2), and D (2, minus 1). In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation. Point A′ is at (-2, -2) , and point D′ is at (4, -2) .
The coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:
A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The vertices of the original polygon for this problem are given as follows:
A(-1,-1), B (0, 1), C (2, 2), and D (2, -1).
The scale factor for the dilation in this problem is given as follows:
k = 2.
Hence the coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:
A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).
(as each coordinate of each vertex was multiplied by the scale factor of 2).
Missing InformationThe problem is incomplete, hence the coordinates of the vertices of the image after the dilation were obtained to show how the dilation works.
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For a long distance person-to-person telephone call a telephone company charges $.89 for the first minute and $.31 for each additional minute and $1.23 service charge at the cost of the avocado is six hours and $.15 how long did the person talk
So the person talked for 6 minutes.
Define Unitary Method.The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.
Define ratio and proportion.Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.
To solve this problem, we can use the following equation:
Cost = (Number of minutes x $0.31) + $0.89 + $1.23
We know that cost is $6.15 and the call lasted 6 hours. Since there are 60 minutes in an hour, we can convert the time in hours to minutes by multiplying 6 hours by 60 minutes/hour
So the number of minutes is 6 hours * 60 minutes/hour = 360 minutes
Now we can substitute the values into the equation:
Cost = (360 minutes x $0.31) + $0.89 + $1.23
Cost = $111.6 + $0.89 + $1.23
Cost = $113.72
The equation does not match the $6.15 cost, which means that the person talked for 6 minutes
So the person talked for 6 minutes.
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Solve for x and show your steps. Is the solution extraneous? Check your work to show how you extraneous or not.
1 1x + 5 = 7
For the given issue, x has a value of 4. The offered solution is the solution extraneous .
What does the mathematical concept of superfluous mean?When we solve equations, we often obtain values that aren't actually the answer to the equation.
What makes an equation unnecessary?A root of a transformed equation that isn't a root of the previous iteration because it was left out of the original equation's domain is known as a extraneous solution.
According to the given information:√(11x + 5) = 7
(11x + 5) = 7²
11x + 5 = 49
11x = 49 - 5
11x = 44
x = 4
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The density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume. Express this density in pounds per cubic foot. Round your answer to the nearest whole number.
The density of the material is 1533.3 grams per quarts.
What is density?Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.
Given that, the density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume.
The formula to find the density is Density=Mass/Volume
Density =6900/4.5
Density= 1533.3 grams per quarts
Therefore, the density of the material is 1533.3 grams per quarts.
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PLEASE HELP!!
I’m rlly struggling with my hw rn
There you have it, your answer
Step-by-step explanation:
Easy
Need with this … substitution method..
Answer:
The solution is the point (-3,2)
Step-by-step explanation:
x + 2y = 1 Subtract 2y from both sides
x + 2y - 2y = 1 - 2y
x = 1 - 2y Substitute 1 - 2y in for x in the second equation and solve for y.
5x -4y = -23
5(1 - 2y) -4y = -23 Distribute the 5
5(1) - 5(2y) - 4y = -23
5 -10y - 4y = -23 Combine like terms
5 -14y = -23 Subtract 5 from both sides
5 -5 - 14y = -23 -5
-14y = -28 Divide both sides by -14
[tex]\frac{-14y}{-14}[/tex] = [tex]\frac{-28}{-14}[/tex]
y = 2
Solve for y
x + 2y = 1 Substitute in 2 for y and solve for x
x + 2(2) = 1
x + 4 = 1 Subtract 4 from both sides
x + 4 - 4 = 1 - 4
x = -3
The solution is the point (-3,2)
Check:
2 + 2y = 1
-3 + 2(2) = 1
-3 + 4 = 1
1 - 1 checks
5x - 4y = -23
5(-3) - 4(2) -23
-15 - 8 = -23
-23 = -23
Guys, how much triangles this picture has?
Answer:
6 for the number of triangles or 7 because all the triangles form a hole triangle
Step-by-step explanation:
Answer: The answer is 6. If you add the triangle that all the small triangles are within, then you would get 7.
Write an expression with 5 terms where one of the terms is a constant of 3
Answer:
Since the term "3" contains no variables, "3" IS a constant term. In the expression 2x - 5 the constant term is -5.
4. The Jerico family went ice skating on the
frozen lake. The 2 parents and 4 children each
had ice skates. They brought an extra pair of
ice skates in case anyone else wanted to join
them. How many ice skates did the family
bring?
Answer:
10
I wish you luck in your assignments.
Water flows at 2 feet per second through a pipe with a diameter of 8 inches. A cylindrical tank with a diameter of 15 feet and a height of 6 feet collects the water.
a. What is the exact volume, in cubic inches, of water flowing out of the pipe every second? Leave your answer in terms of π.
The volume is
cubic inches.
Question 2
b. What is the height, in inches, of the water in the tank after 5 minutes?
The height in the tank is about
inches.
Question 3
c. How many minutes will it take to fill 75% of the tank?
It will take about
minutes.
a. The exact volume, in cubic inches, of water flowing out of the pipe every second is 32π cubic inches.
b. The height, in inches, of the water in the tank after 5 minutes is 600 feet.
c. It will take 0.132 minutes to fill 75% of the tank
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
Given, Water flows at 2 feet per second through a pipe with a diameter of 8 inches so it is a cylindrical shape.
Therefore, The exact volume, in cubic inches, of water flowing out of the pipe every second is,
= π(4)²×2.
= 32π cubic inches.
The volume of the cylindrical tank is,
= π(7.5)²×6.
= 337.5π cubic inches.
The height, in inches, of the water in the tank after 5 minutes would be
= (32π×300)/π×16).
= 600 feet.
Now, 75% of 337.5π cubic inches is (0.75×337.5π) = 253.125π cubic inches.
Therefore the time required to fill 75% of the tank is,
= [(253.125π/32π)]/60 minutes.
= 7.91/60 minutes.
= 0.132 minutes.
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4. Torrie has $430 and Sonia has $760. John has the same number of dollars more than Torrie as he has less than Sonia. How much money does John have?
To solve this problem, we can set up the following equation:
Torrie + John = Sonia - John
This equation represents the fact that John has the same number of dollars more than Torrie as he has less than Sonia. We can then substitute the given values for Torrie, Sonia, and John to solve for John:
430 + John = 760 - John
Combining like terms, we get:
2 * John = 330
Dividing both sides of the equation by 2, we get:
John = 165
Thus, John has $165.
Which of the following is most likely the next step in the series?
ООО
О А.
B.
О с.
O D.
The next step in the series is, shown in Option C.
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
There are three steps are shown.
Now, In first step, only one line shown.
In second line the line is left to first line.
And, So on.
Hence, The next step in the series is, shown in Option C.
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Your are filling your rectangular hot tub with water. The base is 76 inches by 64 inches. The hot tub hole allons of water. If the hot tub is one-fourth full, what is the approximate height of the water? (5d- Zlinou are filling your rectangular hot tub with water. The base is 76 inches by 64 inches. The hot tub hold allons of water. If the hot tub is one-fourth full, what is the approximate height of the water?
Answer:
1216 inches
Step-by-step explanation:
First you multiply ¼ by 76 times 64
which gives you 1216 inches
Need help solving this please
Answer:
30 students
Step-by-step explanation:
First, we need to find exactly how many students went to school by car and how many went on the bus.
To do this, we simply multiply the fraction of students that used each transportation method by the total number of students.
[tex]\# \textrm{ of students by car} = \dfrac{3}{8} \times 240 = \dfrac{3 \times 240}{8} = \dfrac{720}{8} = 90 \textrm{ students}[/tex]
So, 90 students went to school by car.
[tex]\# \textrm{ of students on bus} = \dfrac{6}{12} \times 240 = \dfrac{1}{2} \times 240 = \dfrac{240}{2} = 120 \textrm{ students}[/tex]
So, 120 students went to school on the bus.
The number of students that walked to school is the same as the number of students who didn't go in a car or on the bus, so to find the number of students that walked to school, we can subtract the number of students that went by car and on the bus from the total number of students.
[tex]\# \textrm{ of students that walked} = 240 - 90 - 120 = 30 \textrm{ students}[/tex]
Suppose f is a function. If f(6) = -9, give an ordered pair of numbers that is a solution of the function.
The ordered pair solution to the function f(x) is (6, -9) because f(6) = -9,
What is an equation?An equation is an expression relating numbers and variables.
A function is a rule that defines the relationship between the dependent and independent variable. Dependent variables are variables that depends on others variable while independent variables are variables that does not depends on others variable
A solution to a function is the values of the variable that makes the equation true.
Given the function f(x) have solution of f(6) = -9. The ordered pair is (6, -9)
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A triangle has dimensions 9ft by 12ft if you wanted to increase the size of the triangle by a scale factor of 10/3 what would the area of the new triangle be?
Answer:
The area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2
Step-by-step explanation:
To increase the size of a triangle by a scale factor of 10/3, you can multiply each side length of the triangle by 10/3.
The new dimensions of the triangle would be (10/3) * 9ft = 30ft and (10/3) * 12ft = 40ft.
The area of a triangle is given by the formula A = (1/2) * b * h, where b is the length of the base and h is the height of the triangle.
Using the new dimensions of the triangle, the area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2.
Identify the range of the function shown in the graph. 10 . 0 <= y <= 5 B. y > 0 . y is all numbers D - 5 <= y <= 5
The range of the absolute function will be from 0 to 9. Then the correct option is A.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
If the vertex of the absolute function is at (h, k). Then the absolute function is given as
f(x) = | x - h| + k
The domain means all the possible values of x and the range means all the possible values of y.
From the graph, the range of the absolute function will be from 0 to 9.
Then the correct option is A.
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The complete question is attached below.
PLEASE HURRY BE FAST
A fishing map is laid out on a coordinate plane with each unit equal to 1 mile. The boat is launched from the point (−3, 0) and goes to point (−3, 3) to fish. From there, the boat travels to (0, 0) to fish and then goes back to the launch point.
Determine the total number of miles traveled. Round to the nearest mile.
3 miles
6 miles
10 miles
24 miles
Answer:
24 miles
Step-by-step explanation:
each distance between points is 6.
6+6+6+6=24 miles
Mili has 5 rocks in his rock collection .he finds 40 rocks outside that he wants to put in his collection . If he places the rocks into boxes of 9 how many boxes of rocks will he have in his collection
Answer:
40 + 5 = 45
45 ÷ 9 = 5
Therefore, he will have 5 boxes of rocks.
There are 100 marbles in a jar
There are 9 times as many red marbles
as there are blue marbles. How many
blue marbles are in the jar?
Answer:
Step-by-step explanation:
take 9 divided by 5 wich = 1.8
A tree that is 30 tall casts a 40 shadow. What is the distance from the top of the tree to the end of the shadow?
The distance from the top of the tree of height 30 tall to the end of the shadow is 50.
What is distance?Distance is the length between two point.
To calculate the distance from the top of the tree to the end of the shadow, we use the formula below.
Note: The tree and the shadow form a right angle.
Formula:
a = √(b²+c²)................. Equation 1Where:
a = Distance of from the top of the tree to the end of the shadowb = Height of the treec = Length of the shadowFrom the question,
Given:
b = 30 c = 40Susbtitute these values into equation 1
a = √(30²+40²)a = √(900+1600)a = √2500a = 50Hence, the distance from the top of the tree to the end of the shadow is 50.
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The table shows the types and numbers of prizes at a carnival game what is the ratio of stuffed animals to posters
Answer:
Step-by-step explanation:
3