There are total of 7 terms in the formula of intersection of 3 sets.
What is intersection?In set theory, the intersection of two sets A and B, denoted {A,B}, is the set containing all the elements of A that also belong to B, or all the elements that also belong to B.A cut operation is represented by the symbol ∩.The set A ∩ B - pronounced "intersection B" or "intersection of A and B" - is defined as the set consisting of all elements that belong to both A and B.A controlled intersection has signs, signals, and lane markings that tell drivers and others what to do.The most common controlled intersections are stop sign controlled intersections.Stop signs and traffic lights are also used depending on the flow of traffic passing through that particular intersection.The formula of the given sets is,
n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C).
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Proportion question
y is directly proportional to the cube of x
y = 20h when x = h
Answer:
see explanation
Step-by-step explanation:
(a)
given y is directly proportional to x³ then the equation relating them is
y = kx³ ← k is the constant of proportion
to find k use the condition y = 20h when x = h
20h = kh³ ( divide both sides by h³ )
[tex]\frac{20h}{h^3}[/tex] = k , then
k = [tex]\frac{20}{h^2}[/tex]
y = [tex]\frac{20}{h^2}[/tex] x³ = [tex]\frac{20x^3}{h^2}[/tex]
(b)
when y = 67.5h , then
67.5h = [tex]\frac{20x^3}{h^2}[/tex] ( multiply both sides by h² to clear the fraction )
67.5h³ = 20x³ ( divide both sides by 20 )
3.375h³ = x³ ( take cube root of both sides )
[tex]\sqrt[3]{3.375h^3}[/tex] = x , that is
x = 1.5h
The formula for y in terms of x and h will be y = (20 / h²)x³ and y = 20h. The x in terms of then y = 67.5 h will be x = 1.5h.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
y is directly proportional to the cube of x. Then we have
y ∝ x³
y = kx³
We have y = 20h when x = h, then
20h = k(h)³
k = 20 / h²
The formula for y in terms of x and h is given as,
y = (20 / h²)x³
y = (20 / h²) (h³)
y = 20h
If y = 67.5 h, then we have
67.5 h = (20 / h²)x³
3.375 h³ = x³
x = 1.5h
The formula for y in terms of x and h will be y = (20 / h²)x³ and y = 20h. The x in terms of then y = 67.5 h will be x = 1.5h.
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consider a new dam where the height is doubled and the width is only one third of the original value. the ratio of the total force exerted on the new dam to that on the original dam fnew f is given by
the total force exerted on the new dam to that on the original dam f new is given by F = 624010000 lb.
What is Pascal's Principle.?
Consider a flat surface that is immersed vertically in a fluid whose weight density is p, according to Pascal's Principle.
A flat surface experiences fluid force (F) which is
F = ∫ph(x)w(x) dx
where h(x) is the height of the point x in the x-axis' vertical direction and w(x) is the surface's width.
to determine fluid force applied
Assume that x is equal to the height of the water. At height x on the dam, width of the dam is w(x) = 200 ft (given), and height is h(x) = x ft.
F = ∫ph(x)w(x) dx
F =0→100 ∫62.4 x 200 dx
F = 12480* 0 →100∫ x dx
F = 12480* 0 →100(x²/2)
F =
F = 6240((100)²- (0)²)
F= 6240(10000)
F = 624010000 lb
Hence the total force exerted on the new dam to that on the original dam f newf is given by F = 624010000 lb.
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Jack raied 45 dollar. He raied 3 time more than Tamara. How much did Tamar raie?
Tamar raise $15
What is division ?
One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.
A group is divided into equal portions when it is divided. For a game or activity, division can be used to divide a class into equal groups. It can also be used to divide a pizza among friends in equal pieces. Divided into partitive and quotative, there are two forms of division.
There are 2 ways one by writing equation and the other by using logic
1. by using equation
3*x=45
x=45/3
= 15
2. Logically
If Jack has $45 which is 3 times Tamara's we can reverse the statement:
45/3
=15
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Simon eats 3/8 of a pizza. Eira and Martin eat an equal share of the pizza that is left. How much pizza do they each eat?
The amount of pizza ate by Simon, Eira and Martin is
Simon = 3/8 pizzaEira = 5/16 pizzaMartin = 5/16 pizzaHow to find the amount of pizza each ateSimon eats 3/8 of a pizza = 3/8
The amount of pizza left after Simon ate
= 1 - 3/8
= 5/8
Eira and Martin eat an equal share of the pizza that is left
that is the amount left was shared into 2
= 5/8 ÷ 2
= 5/16 each for both of them
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The line graph below displays the average value of a 2000 Toyota Camry since the year 2000. A trendline has been added to the data. V represents value in dollars of the car and t represents the time in years since 2000.
a. Consider the variables “Value” and “time”. Which variable is the independent variable and which variable is the dependent variable?
b. Find an equation for the value as a function of the number of years since 2000.
c. Write a sentence that identifies and interprets the y intercept of the trendline. Use
appropriate units.
d. Write a sentence that identifies and interprets the slope of the trendline. Use
appropriate units.
e. Use the equation of the trendline to predict the value of the car in 2017. Use your
appropriate units. Show your work.
The evaluation of the trendline in line graph of the trendline displaying the value of a 2000 Toyota Camry since the year 2000 are as follows;
a. Independent variable; Time
Dependent variable; Value
b. The equation is; V = 22,500 - 1,166.[tex]\overline 6[/tex]·t
c. The y-intercept is at the point (0, 22,500), which indicates that the value of the 2000 Toyota Camry in the year 2,000 is $22,500
d. The slope of the trendline is -1,166.[tex]\overline {6}[/tex], which indicates that the annual reduction in the price of the 2000 Toyota Camry is $1,166.[tex]\overline 6[/tex]
e. The value of the car in 2017 based on the trendline is $2,666.[tex]\overline{6}[/tex]
What is a trendline in a graph or chart?A trendline is a line drawn through a scatterplot, minimizing the distances between the points in the chart and the line itself, and shows the trend of the scatterplot.
a. The independent variable is the variable that is the input variable of the function, which the researcher can vary or the value that is controlled.
Therefor;
The independent variable is the ''time''The dependent variable is the value under study, therefore;
The dependent variable is the ''Value''b. The points on the line graph are; (0, 22,500), and (15, 5,000), the slope is therefore;
m = (5,000 - 22,500)/(15 - 0) = -3,500/3
The equation is therefore;
V - 22,500 = -3,500/3·t
V = -3,500/3·t + 22,500
The equation for the value is; V = (22,500 -(3,500/3)·tc. The y-intercept of the trend line is (0, 22,500), which indicates that in the year 2,000, the price of the 2,000 Toyota Camry was $22,500
d. The slope of the trend line is -3,500/3 = -1,166.[tex]\overline 6[/tex], which indicates that the value of the Toyota Camry, 2000, reduces at a rate of $1,166.[tex]\overline 6[/tex], each year.
e. In the year 2017, t = 17, therefore;
V = 22,500 - (3,500/3) × 17 = 2,666.[tex]\overline {6}[/tex]
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read questions A and B... Must give 2 answers
For a student with a shoe size of 9, the student's height is equal to 65 inches.
For a student with a height of 60 inches, the student's shoe size is equal to 6.5.
How to determine the approximate of a student?From the information provided, an equation for the line of best fit that represents or models the heights x (in inches) and shoe sizes y of several student is given by this mathematical expression:
y = 0.50x - 23.5
Where:
x represents the height of a student.y represents the shoe size of a student.For a student with a shoe size of 9, the student's height is given by:
y = 0.50x - 23.5
0.50x = y + 23.5
Student's height, x = (y + 23.5)/0.50
Student's height, x = (9 + 23.5)/0.50
Student's height, x = 32.5/0.5
Student's height, x = 65 inches.
For a student with a height of 60 inches, the student's shoe size is given by:
y = 0.50x - 23.5
y = 0.50(60) - 23.5
y = 30 - 23.5
y = 6.5
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Under his cell phone plan, liam pays a flat cost of $69. 50 per month and $5 per gigabyte. He wants to keep his bill under $90 per month. Write and solve an inequality which can be used to determine xx, the number of gigabytes liam can use while staying within his budget.
The inequality given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
Let the number of gigabytes consumed be x,
The total cost per month will be 69.50 + 5x
accoding to the question the bill would not exceed $90.
So the inequality,
69.50 + 5x ≤ 90
Simplification for the maximum gigabyte he can buy,
5x ≤ 90 - 59.90
5x ≤ 20.5
x ≤ 4.1
Hence, the required inequality is given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.
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A man bought a car for $60,320. After uing it for 2 year, he decided to trade-in the car. The company etimated a depreciation of 15% for the firt year of it ue and a further 15% on it reduced value for the econd year. A) Calculate the value of the car after 2 year. B) Expre the value of the car after two year a a percentage of the original value
c) Expre the depreciation after the 2 year period a a percentage of the original value
The value of car after 2 years is $17,008.8, as percent it is 28.2% and depreciation is 27.75%
Value of car after two years will be calculated by calculating the depreciation each year.
Depreciation after first year = 60,320 - 15%×60,320
Depreciation after first year = 60,320 - 9,048
Depreciation after first year = $51,272
Depreciation after second year = 51,272 - 15%×51,272
Depreciation after second year = 51,272 - 7690.8
Depreciation after second year = $43,311.2
Value after depreciation = 60,320 - 43,311.2
Value after depreciation = $17,008.8
Value of car as percentage = 17008.8/60320×100
Value of car as percentage = 28.2%
Depreciation after two years period = 9048 + 7690.8
Depreciation after two years period = 16,738.8
Depreciation as percentage = 16738.8/60320×100
Depreciation as percentage = 27.75%
The correct answers are a) $17008.8, b) 28.2% and c) 27.75%.
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Read and try to solve the problem below.
Are -(-3m +6 - 12 + 15m) and 2(1 − 2m) equivalent expressions?
Show why or why not.
The given expressions are equivalent.
What is equivalent expression?
Expressions that function identically despite having different appearances are called equivalent expressions. If two algebraic expressions are equivalent, then when we enter the same value(s) for the variable, the two expressions have the same value (s).
Consider the given expressions,
-(-3m + 6 - 12 + 15m) and 2(1 - 2m)
First simplify the expression -(-3m + 6 - 12 + 15m)
= 3m - 6 + 12 - 15m
= -12m + 6
Divide the expression by 3,
= -4m + 2
= 2 + 4m ..(1)
Now, consider the expression, 2(1 - 2m)
Simplifying this,
2(1 - 2m) = 2 - 4m ..(2)
From (1) and (2) we can see that the expressions are equivalent.
Hence, the given expressions are equivalent.
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The mean and standard deviation of a population are 200 and 20, respectively. What is the probability of selecting 25 data values with a mean less than 190?.
The probability of selecting 25 data values with a mean less than 190 is 0.6%.
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.What is mean?
The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset.Why do you use the word deviation?
The deviation is a metric used in statistics and mathematics to determine the discrepancy between an observed value and an expected value of a variable.Population mean = 20
Standard deviation = 20
Sample size= 25
Sample mean= 190
z = 190-200/20/5
Square root of 25 -10/4 = 2.
Corresponding term is 0.4938 P(X<190) = 0.500-0.4938
P(X<190) = 0.0062 or 0.62
P(X<190) = 0.6%
Hence, the probability of selecting 25 data values with a mean less than 190 is 0.6%.
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PLEASE HELP ME
...This is my homework and I don't understand how to do it.
The probability that a point chosen at random lies in the shaded region is 0.28
Calculating the area of a shaded region and probabilityFrom the question, we are to find the probability that a point chosen at random lies in the shaded region.
The shaded region is a triangle.
The probability that a point chosen at random lies in the shaded region = Area of the triangle / Area of the circle
First, we will calculate the unknown side of the triangle
Let the unknown side be x.
Then, from the Pythagorean theorem, we can write that
12² = 6² + x²
144 = 36 + x²
x² = 144 - 36
x² = 108
x = √108
x = 6√3
From formula,
Area of a triangle = 1/2 × base × height
Area of the triangle = 1/2 × 6 × 6√3
Area of the triangle = 18√3 square units
Now, we will determine the area of the circle
Area of a circle = πr²
Where r is the radius
From the given information,
Diameter of the circle = 12
But,
Radius = Diameter / 2
Therefore,
r = 12/2
r = 6
Thus,
Area of the circle = 3.14 × 6²
Area of the circle = 113.04 square units
Now,
The probability that a point chosen at random lies in the shaded region = 18√3 / 113.04
The probability that a point chosen at random lies in the shaded region = 0.2758
The probability that a point chosen at random lies in the shaded region ≈ 0.28
Hence, the probability is 0.28
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Factorise this equation + workings out!! Please help!!!!
Answer:(2x+1)(3x-4)
Step-by-step explanation:Factor the expression out first by getting 6x^2+3x-8x-4. From there, factor again to 3x(2x+1)-4(2x+1) to get the answer (2x+1)(3x-4)
Answer:
(3x - 4)(2x - 1)
Step-by-step explanation:
6x^2 - 5x - 4
When factoring, we want to first find the GCF. In this case, the GCF is one so we leave it as that. Next, we want to try and find the sum and the product. Additionally, we have a leading coefficient. We will multiply the leading coefficient by the last term, which is -4. (You will need to remember this to continue on later.)
x^2 - 5x - 24
Now, we can find the sum and the product. To do this, we need to list the factors of 24. (Remember negatives as well!)
24: 1 and 24, 2 and 12, 3 and 8, 4 and 6.
As -24 is also a negative, that means it will have one positive and one negative factor. This must also add up to -5.
One pair that does this is -8 and 3. They multiply together to -24 and add up to -5.
Now, since we multiplied the leading coefficient in the beginning, we must bring it back down into the parenthesis.
(6x - 8)(6x - 3)
We must divide out and try to simplify this as much as we can to match the leading coefficient. The divisors must multiply up to 6.
(6x - 8)/2 and (6x - 3)/3. 3*2 = 6
(3x - 4)(2x - 1)
Jackson and his children went into a movie theater and where they sell bags of popcorn for $6.50 each and candies for $4 each. Jackson has $75 to spend and must buy no less than 15 bags of popcorn and candies altogether. If Jackson decided to buy 2 candies, determine the maximum number of bags of popcorn that he could buy. If there are no possible solutions, submit an empty answer
Answer:6
Step-by-step explanation:
In an Arithmetic Progression (AP), the first
term is 3, and the sum of the first and the sixth
terms is 20. What is the 8th term
Answer:
The 8th term of the AP= 113/5 or 22.6
Answer:
22.6
Step-by-step explanation:
Given:
a = 3a + a₆ = 20Find the value of a₆:
[tex]\implies a+a_6=20[/tex]
[tex]\implies a_6=20-a[/tex]
[tex]\implies a_6=20-3[/tex]
[tex]\implies a_6=17[/tex]
Therefore:
a = 3a₆ = 17General form of an arithmetic sequence:
[tex]\boxed{a_n=a+(n-1)d}[/tex]
Where:
[tex]a_n[/tex] is the nth term.a is the first term.d is the common difference between terms.n is the position of the term.Substitute a = 3 and a₆ = 17 into the formula and solve for d:
[tex]\begin{aligned}\implies a_6=3+(6-1)d&=17\\3+5d&=17\\5d&=14\\d&=2.8\end{aligned}[/tex]
Therefore, the equation for the nth term is:
[tex]\implies a_n=3+(n-1)2.8[/tex]
[tex]\implies a_n=3+2.8n-2.8[/tex]
[tex]\implies a_n=2.8n+0.2[/tex]
To find the 8th term, substitute n = 8 into the equation for the nth term:
[tex]\implies a_8=2.8(8)+0.2=22.6[/tex]
State all integer values of x in the interval 1 ≤ x ≤ 6 that satisfy the following
inequality:
2x - 4 ≥1
The value of x≥2 are: 2,4,5,6
What is meant by inequality ?Inequality—the state of not being equal, particularly in status, rights, and opportunities1—is central to social justice theories. However, it is prone to misunderstanding in public debate because it means different things to different people. Some distinctions, however, are universal.
An inequality compares two values to determine whether one is less than, greater than, or simply not equal to the other. a b indicates that a is not equal to b.
Given ,
2x - 4≥1
State the values of x within 1 and 6
2x - 4≥1
2x ≥ 1 +4
2x ≥ 5
Divide both sides by 2
2x/2 ≥ 5/2
x = 2
(1,6) is an open interval which means that 1 and 6are not inclusive of the values of x.
So:
therefore the values of x≥2 are: 2,4,5,6
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The volume of a regular hexagonal prism is 2800 cm³. The height of the prism is 14 cm. Find the side of the hexagonal base in cm.
The side of the hexagonal prism is 8.77 cm
What is a hexagonal prism?
A hexagonal prism has 8 faces, 18 edges, and 12 vertices. Out of the 8 faces, 6 are parallelograms, and 2 are hexagons, and that's why it is called a hexagonal prism. These hexagons are at the base and the top as the opposite faces of a prism are the same.
Given data ,
Let the volume V of the hexagonal prism be V = 2800 cm³
Let the height of the hexagonal prism be H = 14 cm
Now , let the side of the hexagonal prism be = A cm
The volume of the hexagonal prism be V = ( ( 3 √3 / 2 ) ) a²h
where a is the side of the hexagonal base
h is the height of the hexagonal prism
Substituting the values in the equation , we get
The volume of the cube be V = ( ( 3 √3 / 2 ) ) a²h
V = ( ( 3 √3 / 2 ) ) a²h
2800 = ( 3 √3 / 2 ) x a² x 14
200 = ( 3 √3 / 2 ) x a²
Multiply by 2 on both sides of the equation , we get
400 = 3√3 x a²
Divide by 3√3 on both sides of the equation , we get
a² = 76.98
Taking square roots on both sides of the equation , we get
a = 8.77 cm
Therefore , the value of a is 8.77 cm
Hence , The side of the hexagonal prism is 8.77 cm
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Clip 136 Rearranging Simple Formulae - Question 4
Standard Questions
Question Progress
Make r the subject of x=e+r/d
Answer:
r = d(x-e)
or r = dx - de
Step-by-step explanation:
x = e + [tex]\frac{r}{d}[/tex] subtract e from both sides.
x - e = [tex]\frac{r}{d}[/tex] Multiply both sides by d
d(x -e) = r
or
dx -de = r
25.92x +5.15²* = 12.25²* ;
2-10 how do you solve this?
idddddddddddddddkkkkkkkkkkkkkkkkkkkkkkkk annnnthinggggggg
Quick Someone Help!!! Please!
The endpoints of line segment AB are A (9,4) and B (5,-4). Then endpoints of its image after dilation are A' (6,3) and B' (3,-3). Find the scale factor and explain step by step
The image with line segment AB is dilated from (6, 3) and (3, 3) with scale factor of 1.8
DilationDilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor.
In this case, the image with endpoints of line segments AB which are (9, 4) and (5, -4) and dilated to become (6, 3) and (3, 3) would have a scale factor of;
scale factor = 9 * x = 5
x = 9 / 5 = 1.8
The scale factor is 1.8
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find the area of the region that lies inside both curves. r2 = 50 sin(2θ), r = 5
The area under the curve r²=50sin2Θ is (15.71)unit square
How to find the area under the parabola?A parabola is defined as a plane curve that is mirror-symmetrical and approximately U-shaped.
The given parabola is r²=50sin2∅,
where r=5
Where r=radius of the circle of the parabola
Substitute r=5 in the parabola
5²=50sin2∅
Simplifying the equation to find the value of ∅25=50sin2∅[tex]\frac{25}{50}[/tex]=sin2∅
Finding the sine inverse, we havesin[tex]^{-1} 0.5=2[/tex]∅30⁰=2∅∅=15⁰
The angle made by the parabola is 15⁰
note r=5
Area = 22/7 × 5
Area = 15.71 unit²
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Gianna is going to use a computer at an internet cafe. The cafe has an initial charge of $10 to use a computer and an additional charge of $0.60 for every minute of use. Make a table of values and then write an equation for C , C, in terms of t , t, representing the total cost of using a computer for t t minutes at the internet cafe.
A table of values and an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the internet cafe are as follows:
C t
$10.60 1
$11.20 2
$11.80 3
C = 0.60t + 10.
How to write an equation for the total cost?In order to write an equation for the total cost, we would assign variables to the amount of time used and the total cost of using a computer, and then translate the word problem into algebraic equation as follows:
Let the variable C represent the total cost in dollars.Let the variable t represent the amount of time in minutes.Since the cafe has an initial charge of $10 to use a computer and an additional charge of $0.60 for every minute of use, an equation for the total cost is given by:
C = 0.60t + 10
When t = 1, we have:
Total cost, C = 0.60(1) + 10
Total cost, C = $10.60.
When t = 2, we have:
Total cost, C = 0.60(2) + 10
Total cost, C = $11.20.
When t = 3, we have:
Total cost, C = 0.60(3) + 10
Total cost, C = $11.80.
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(1.5x10^-5) divided (3.0x10^4)
Answer:
1/2 x 1/10^-9
Step-by-step explanation:
(1.5x10^-5)/(3.0x10^4)
=> 1.5/3 x 10^-5/10^4
=> 1/2 x 10^-9
Answer:
= 5
Step-by-step explanation:
(1.5*10⁵) / (3.0*10⁴)
1.5*10⁵ = 15*10⁴
Then:
(1.5*10⁵) / (3.0*10⁴) = (15*10⁴) / (3*10⁴) = 15/3
= 5
A Pharmacist needs 100 gallons of 50% solution. She has available a 30% solution and an 80%. How much of each should she use? (Step-by-step answer)
Answer:
look below
Step-by-step explanation:
Step 1: Determine the amount of pure solvent needed.
100 gallons x 0.5 (50%) = 50 gallons of pure solvent
Step 2: Determine the amount of each solution to use.
30% solution: 50 gallons of pure solvent / 0.3 = 166.67 gallons of 30% solution
80% solution: 50 gallons of pure solvent / 0.8 = 62.5 gallons of 80% solution
Step 3: Total the amount of solution used.
166.67 gallons of 30% solution + 62.5 gallons of 80% solution = 229.17 gallons total
Put the following equation of a line into slope-intercept form, simplifying all fractions.
6x + 4y = 16
Answer:
y = - [tex]\frac{3}{2}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
6x + 4y = 16 ( subtract 6x from both sides )
4y = - 6x + 16 ( divide through by 4 )
y = [tex]\frac{-6}{4}[/tex] x + [tex]\frac{16}{4}[/tex] , that is
y = - [tex]\frac{3}{2}[/tex] x + 4 ← in slope- intercept form
Triangle abc was dilated using the rule do,4. Triangle a'b'c' is the result of the dilation. Point o is the center of dilation. Triangle a b c is dilated to create triangle a prime b prime c prime. The length of o b is three-fourths. What is ob'?.
The length of OB' after dilation 3 units.
What is dilation of triangle?
Dilation is a method for producing similar figures. By increasing distances by the scale factor, each point is extended outwards from the center point.
Dimensions of the new shape = Dimensions of the original shape × Scale factor.
in a given triangle,
Dilation is using the rule d o,4, it means is that triangle was enlarged by a scale factor of 4 with point O as the center of dilation.
[tex]ob = \frac{3}{4}[/tex]
[tex]o'b' = 4 * \frac{3}{4}[/tex]
[tex]o'b' = 3 units[/tex]
The length of OB' after dilation 3 units.
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VYing Ying wants to buy some petunias. The table compares the number of petunias Ying Ying could buy and the money that would remain in her wallet (in dollars). Petunias Money (dollars) 2 2 6. 5 0 6. 50 8 8 5. 0 0 5. 00 1 4 14 3. 5 0 3. 50 How many Petunias can Ying Ying buy at most?
The most petunias Ying Ying will ever purchase is 28.
Given data;
Using x as the total amount of money in her wallet and m as the price per petunia
The money remaining in the wallet after buying 2 petunias equals $6.50 according to the provided table.
Now,
6.50 = x - 2m ⇒ (I)
In addition, $5 was left in the wallet after the purchase of 8 petunias,
5 = x - 8m ⇒ (II)
Here, (I) - (II);
6.50 - 5 = x - 2m - x + 8m
1.50 = 6m
m = 0.25
One petunia costs $0.25.
Therefore, the total number of petunias Ying Ying buys at most is,
When 14 petunias brought money left in the wallet is $3.50.
Now,
→ 3.50/0.25 = 14
The total number of petunias Ying Ying buys at most is 14 + 14 = 28
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In five years Angela will be the age that Khalil is now. In three years, Khalil will be twice as old as Angela. How old are they now?
The current age of Angela and Khali by the formation of the equation will be 2 and 7 years old.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Suppose the current age of Angela is A while Khali is K.
In 5 years,
A + 5 = K
In 3 years,
K + 3 = 2(A + 3)
K + 3 = 2A + 6
K + 3 = 2(K - 5) + 6
K + 3 = 2K - 10 + 6
2K - K = 3 + 4
K = 7 years old,
A = 7 - 5 = 2 years old.
Hence "The current age of Angela and Khali by the formation of the equation will be 2 and 7 years old".
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JE
Write an equation for a line perpendicular to y = 3a + 3 and passing through the point (-6,6)
Answer:
Step-by-step explanation:
A line that is perpendicular to another will have the opposite slope.
y = [tex]-\frac{1}{3}[/tex]a + b
To find b, substitute y and a with the given values
6 = [tex]-\frac{1}{3}[/tex](-6) + b
6 = 2 + b
-2 -2
4 = b
thus
y = [tex]-\frac{1}{3}[/tex]a + 4
The speed of a space shuttle orbiting the earth is 17{,}600\,\text{mph}17,600mph17, comma, 600, start text, m, p, h, end text.
The graph below shows the distance ddd (in thousands of miles) traveled in ttt hours by a weather satellite orbiting the earth.
Which orbits the earth at a greater speed, the space shuttle or the weather satellite?
Answer: the space shuttle
Step-by-step explanation:
What does y equal?
Will Give Brianlest!
Answer:
[tex]\boxed{\tt y=48}[/tex]
Step-by-step explanation:
[tex]\tt \cfrac{3}{16}=\cfrac{9}{y}[/tex]
Cross multiply:-
[tex]\tt 3 \times y=(9)\times (16)[/tex]
[tex]\tt 3y=144[/tex]
Divide both sides by 3:-
[tex]\tt \cfrac{3y}{3}=\cfrac{144}{3}[/tex]
Simplify:-
[tex]\tt y=48[/tex]
_________________
Hope this helps!
Answer:y=48 I hope this is helpful good luck have a good day
Step-by-step explanation:
3/16 = 9/y
Determine the defined range
3/16=9/y y=0 cross out the equal sign y=0
Simplify the equation using cross-multiplication
3y=144
Divide both sides of the equation by 3
y=48
Check if the solution is in the defined range
