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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hello i need help with question 5 please
5a) The total cost of buying the car, including the harmonized sales tax (HST) of 13%, is $36,160.
5b) Under the lease, the customer saves $14,760.
5c) The lessee after returning the car has the following lease options:
Lease buyoutLease extensionNew lease contractBuying out the vehicle and then reselling it.6a) The after-tax cost of the car that Jordan wants to buy is $32,199.35.
6b) The part of the Honda Civic that needs to be financed after the down payment is $26,199.35.
6c) The monthly payment will be $567.26.
6d) After four years, the total amount Jordan had paid for the vehicle is $33,228.48.
Car Financing Options:A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.
A car purchase can also be financed through loans, like home mortgages.
Value of the car = $32,000
Harmonized Sales Tax (HST) = 13%
Cost of the car with HST = $36,160 ($32,000 x 1.13)
Lease Arrangement:Down payment = $1,000
Financing part = $35,160 ($36,160 - $1,000)
Installment payments = 48
Periodic payments = $425
Total lease cost = $21,400 ($1,000 + 48 x $425)
Savings from leasing = $14,760 ($36,160 - $21,400)
Jordan's Car:The value of the Honda Civic = $28,495
Harmonized Sales Tax (HST) = 13%
After-tax cost = $32,199.35 ($28,495 x 1.13)
Annual interest rate = 1.9% compounded monthly
Down payment = $6,000
Financing part = $26,199.35 ($32,199.35 -$6,000)
Financing period = 4 years
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 1.9%
PV (Present Value) = $26,199.35
FV (Future Value) = $0
P/Y (# of periods per year) = 12
C/Y (# of times interest compound per year) = 12
Results:
Monthly Payments (PMT) = $567.26
Sum of all periodic payments = $27,228.48
Total Interest $1,029.13
Total amount paid by Jordan after 4 years = $33,228.48 ($27,228.48 + $6,000)
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5. Jackson purchased a pack of game cards that was on sale for 22% off. The sales tax in his county is 6%. Let y represent the original price of the cards. Write an expression that can be used to determine the final cost of the cards.
The decimal value is exact without any rounding.
==========================================================
Explanation:
If Jackson saves 22%, then he pays the remaining 100% - 22% = 78%, which leads to the decimal value 0.78
An increase of 6% leads to 100%+6% = 106% and that converts to 1.06
Multiply those decimal values: 0.78*1.06 = 0.8268; this trick is useful to chain together multiple discounts and/or tax increases.
Therefore, the final cost expression is 0.8268y where the variable y is the original price before the discount and taxes.
---------
Extra info:
The expression 0.8268y tells us that Jackson is paying 82.68% of the original price. Note how 100% - 82.68% = 17.32%
This means Jackson is getting a real discount of 17.32% after the taxes have been considered.
Which rectangle has side lengths of 7 units and 8 units?
The rectangle that has side lengths of 7 units and 8 units is (a) a rectangle that has an area of 56 square units
How to determine the rectangleFrom the question, we have the following parameters that can be used in our computation:
Side lengths of 7 units and 8 units
These parameters can be represented as
Length = 7 units
Width = 8 units
Using the options in the question as a guide, we have the following computations
We start by calculating the area of the rectangle
The area of the rectangle can be calculated using the following area formula
Area = length * width
Substitute the known values in the above equation, so, we have the following representation
Area = 7 * 8
Evaluate
Area = 56
Hence, the rectangle is (a)
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Complete question
Which rectangle has side lengths of 7 units and 8 units?
(a) a rectangle that has an area of 56 square units
(b) a rectangle that has a perimeter of 56 square units
(c) a rectangle that has an area of 65 square units
(b) a rectangle that has a perimeter of 6 units
Find the circumference of a circle with a diameter of 50 centimeters
Answer:
157.08 is the circumference. Hope it helps you
Step-by-step explanation:
The perimeter of a rectangle is 408cm and the length is 134cm. Find the rectangle’s width.
Answer: 70 cm
Step-by-step explanation: perimeter = 2*width + 2*length
408 = 2*width + 2*134
408 = 2*width + 268
Subtract 268 from both sides.
140 = 2*width
DIvide both sides by 2
Width = 70 cm
Answer:
The width of the rectangle is 70 cm
Step-by-step explanation:
Given,
The perimeter of a rectangle is 408 cmThe length is given as 134 cmTo Find : The width of the rectangle
As we know, the formula to find the Perimeter of the rectangle is
[tex]P = 2(l+b)[/tex]
Now the Perimeter is given and the length
[tex]408 = 2(134 + b)[/tex]
Now using distributive property
[tex]408 = 268 + 2b[/tex]
[tex]408 - 268 = 2b[/tex]
[tex]140 = 2b[/tex]
[tex]\frac{140}{2} = b[/tex]
[tex]70cm = b[/tex]
Hence, the width of the rectangle is 70 cm
7 time a number , increased by 4
Answer:
7 times a number increased by 4 times the number
Let a number and the number be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces:
7 times a number: 7x
4 times the number: 4x
The phrase increased by means we add 4x to 7x:
7x + 4x
Simplifying, we get: (7 + 4)x
11x
Step-by-step explanation:
Customary American Units of Capacity
1 cup = 8 ounces
1 pint = 2 cups or 16 ounces
1 quart = 2 pints, 4 cups, or 32 ounces
1 gallon = 4 quarts, 8 pints, 16 cups, or 128 ounces
5 quarts 4 pints =____ pints
Answer:
14
Step-by-step explanation:
5 quarts = 10 pints
10 pints + 4 pints = 14 pints
hey any help? (please make sure this is correct i'd appreciate it)
Answer:
Below
Step-by-step explanation:
Line AB is of the form y = mx + b where m is the slope = 2
Line BC is perpendicular to this and will have slope - 1/m = - 1/2 and includes the point C (0,6)
The point slope form of line BC will then be
( y-6) = - 1/2 ( x - 0) which can be re-arranged to
y = - 1/2x + 6 < ==== equation for line BC
evaluate - [tex]6^{2}- 2(5+1+3[/tex]
The expression 6² - 2(5 + 1 + 3) after evaluation gives 18.
What is BODMAS rule?BODMAS rule is rule for operation of numbers in a specific order when more than one type of operations is involved.
BODMAS is the abbreviated form for Brackets, Order including powers and exponents, Division, Multiplication, Addition and Subtraction.
Given expression is, 6² - 2(5 + 1 + 3).
First we should do the operation in brackets.
6² - 2(5 + 1 + 3) = 6² - 2 (9)
Now we should do the power operations.
6² - 2 (9) = 36 - 2 × 9
Now we do multiplication.
36 - 2 × 9 = 36 - 18
Now we do subtraction.
36 - 18 = 18
Hence the answer of the expression given is 18.
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Help
A shade of green paint is made by mixing `2` cups of yellow with `3.5` cups of blue.
Write a recipe for a mixture that will make the same shade of green but a larger amount.
A recipe for a mixture that will make the same shade of green but a larger amount is =4 Cups of Yellow + 7 Cups of Blue
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Here, we have,
A shade of green paint is made by mixing `2` cups of yellow with `3.5` cups of blue.
Now,
2 Cups of Yellow + 3.5 Cups of blue
Multiply all by 2
=4 Cups of Yellow + 7 Cups of Blue
Hence, a recipe for a mixture that will make the same shade of green but a larger amount is =4 Cups of Yellow + 7 Cups of Blue
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Find C. Give your answer in the simplest form.
Using the pythagoras theorem in the given figure, the required length of c is [tex]49\sqrt{6}[/tex].
What is pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean Theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides.
Who is pythagoras theorem named after?The pythagoras theorem is named after the Greek mathematician-philosopher Pythagoras.
To solve for c, first taking the small triangle in the left of the figure,
since one of the angle is 45 degree and another is 90 degree, the unlabelled angle is 45 degree. Which makes this triangle a isosceles triangle, hence the sides a and b are equal in length. i.e a = b
Using pythagoras theorem in this triangle,
[tex](7\sqrt{2} )^{2} = \sqrt{a^{2}+\ a^{2} }[/tex]
Therefore, a = 49[tex]\sqrt{2}[/tex]
Now Taking the small triangle in the right of the given figure,
tan 30 = a/c
or, [tex]\frac{1}{\sqrt{3} }[/tex] *c = 49[tex]\sqrt{2}[/tex]
Therefore , c = 49[tex]\sqrt{6}[/tex]
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1.171875 as a fraction
false
it is a decimal not a fraction
The market research department of a Company recommends that the Company to manufacture and market a new transistor radio after suitable test. The marketing department also presents the following demand equation.X=5,000-500P i.e. P=10-X/500
Furthermore, the financial department provides the following cost equation: C(X) = 7, 000 + 2x
Using derivatives Find Marginal cost, Marginal revenue and Marginal profit of the company.
The market research department of a Company recommends that the Company to manufacture and market a new transistor radio after suitable test. The marginal cost of the company is 7000 - 2X and marginal revenue is 10X - X/250.
What is Marginal Cost?Marginal cost is an extra cost per unit incurred when an extra unit of output produced or service rendered. Or in other words it can be said that marginal cost is an element of additional unit cost that incurred due to production of goods or services. Some time it is also considering as relevant cost or variable cost.
So in order to compute the transistor manufacturing company's marginal cost, marginal revenue and marginal profit of the company one shall equated the derivative function between them.
In micro economics technical relationship between the said marginal terms is written through derivative function:
Revenue = Price × Quantity Demanded,
Profit Maximize Point where Marginal cost is equal to marginal revenue;
MR = MC,
The marketing department also presents the following demand equation:
X = 5,000 - 500 P
P = 10 - (X ÷ 500), where P is Price and X is quantity demand.
Furthermore, the financial department provides the following cost equation:
C(X) = 7, 000 + 2x
So the revenue function by the help of substitution method:
X = 5,000 - 500 P
Revenue = Price × Quantity Demanded,
Revenue = 10 - (X ÷ 500) × X
= 10X - X^2 ÷ 500
Marginal Revenue! = 10X - !2X/500 = 10X - X/250
Marginal Cost = 7, 000 + 2 (5,000 - 500 P)
= 7000 + 10000 - 1000 P
= 17000 - 1000 ( 10 - (X ÷ 500))
= 17000 - 10000 - 2X
= 7000 - 2X
Therefore marginal revenue is revenue or additional earning made by a seller by selling an extra unit. Revenue is earned when extra unit is being sold.
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Val had 2 1/2 hours to finish a slide presentation. It takes her 1/6 hour to create each slide. Will Val have enough time to create 12 slides? Explain ur reasoning
will she have enough time for 12 slides? we dunno, but we know it takes 1/6 hour to make one hmmm for 12 slides that'd be simply their product
[tex]\stackrel{slides}{12}\cdot \stackrel{\textit{it takes one}}{\cfrac{1}{6}}\implies \cfrac{12}{6}\implies 2~hours\qquad \textit{yeap, she has enough time}[/tex]
she even has an extra 30 minutes to check out what's for dinner.
What is the domain of the function below?
A) x < 2
B) x ≤ 3
C) x ≥ 2
D) All Real Numbers
Answer:
I would say (option A)
Step-by-step explanation:
Domain is the set of x-values that can be inputted into function f(x).
We see that our x-values can be any number. Therefore, we have all real numbers as our domain:
→ A) x < 2.
Hope this helps!
Show that 20 subtracted by O is 20, using at least four daily life examples
Answer:
true
Step-by-step explanation:
20 away from nothing is 20
Answer:
Step-by-step explanation:
20-0=20
Example 1: Suppose you have 20 friends and they are given the choice of choosing a sport from cricket or basketball. All of them decide to play cricket and 0 chooses basketball. So, the total number of students who decided cricket is 20 students(20-0=20).
Example 2: Suppose you have 20 chocolates and you give 0 chocolates to your sister then you have a total of 20 chocolates(20-0=20).
Example 3: Suppose there are 20 students in a class and 0 were absent out of them. So, the total number of students that were present are 20 students(20-0=20).
Example 4: Suppose you have 20 clothes in your wardrobe and you gave 0 clothes for washing. So, the total number of clothes in the wardrobe is 20 clothes(20-0=20).
a tee junction occurs when a connection meets an existing pipe of header at what angle? A 180 degree, B 30 degree, C. 90 degree, D.45 degree
Tee welding joints are formed when two members intersect at a 90-degree angle that makes the edges come together in the center of a plate or component
Graph the linear equation q(x)=-3x+1
The linear function q(x) = -3x + 1 is graphed and attached
How to graph the linear functionThe graph of the linear function is a straight line graph and the table of values used in making the plot is calculated as follows
For x = -20, q(x) = -3 * -20 + 1 = 61
For x = -10, q(x) = -3 * -10 + 1 = 31
For x = 0, q(x) = -3 * 0 + 1 = 1
For x = 10, q(x) = -3 * 10 + 1 = -29
For x = 20, q(x) = -3 * 20 + 1 = -59
Table of values
x y
-20 61
-10 31
0 1
10 -29
20 -59
These points are plotted in the cartesian coordinate by tracing the point of intersection of the x and y and marking it. Then the marked points are joined together to form a straight line
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Katerina needs 200 balloons fillied with helium for a party. She knows that each balloon will need 0.7ft^3 of helium. the helium canisters hold 0.20m^3. 1m^3 = 35ft^3. How many Canisters will Katerina need to buy?
=======================================================
Explanation:
1 balloon = 0.7 ft^3 of helium
200 balloons = 200*0.7 = 140 ft^3 of helium
Katerina needs 140 cubic feet of helium to fill all 200 balloons.
---------------
1m^3 = 35ft^3 which is approximate
0.2 m^3 = 0.2*35 = 7 ft^3
Each canister holds approximately 7 cubic feet of helium.
----------------
To summarize so far.
Katerina needs 140 cubic feet of helium.Each canister holds approximately 7 cubic feet of helium.Let x be the number of canisters. Because of fact 2 mentioned above, 7x represents the total amount of helium from all of the x number of canisters.
Set this equal to the amount she needs (140) and solve for x.
7x = 140
x = 140/7
x = 20
Katerina needs 20 canisters.
All of the quadrilaterals in the shape below are squares. Find the area of the shaded
region.
Answer: I don't remember how to solve, but, I figured out the lengths of each side in the shaded region:
11, 11, 7, 7, 4, 4
Step-by-step explanation:
Hope this helps!! :D
Henrie plays baseball. He hits 80% of the time he bats. If he is up to bat 20 times this weekend at his baseball tournament, how many times is he expected to hit
Answer:16
Step-by-step explanation: If henry hits 80% of pitches, then the easiest way is to make 80% of 10, which is half of 20, is 8. So if it is 20 times he is up to bat, then 8*2, 2*8 is 16, so he hits the ball 16 times.
Find the midpoint of the line segment with endpoints:
(9, -5/2) to (-5, -3/2)
Answer must be as a point, using integers or reduced fractions for coordinates.
Answer:
Step-by-step explanation:
Midpoint formula is x3 = (x1+x2)/2, y3=(y1+y2)/2
so x3=(9-5)/2=2, y3=(-5/2-3/2)/2=-2.
the coordinates is (2, -2).
An office uses paper drinking cups in the shape of a cone, with dimensions as shown. To the nearest tenth of a cubic inch, what is the volume of each drinking cup?
The volume of each drinking cup is 7.9 cubic inches.
What is the volume?An office uses paper drinking cups in the shape of a cone, with dimensions as shown.
The formula provides the volume of a cone.
V = (1/3) * π * r² * h.
We can find the solution by entering the already-known data into the formula.
d = 2.75 m.
Since radius is half of d, we can say
0.5 * 2.75 = 1.375 in.
4 inches is listed as the height.
The result of plugging all of them into the original formula is:
V = (1/3) * π(1.375)² (4) = 7.9
Our final response, rounded to the closest tenth, is:
V = 7.9 cubic inches.
The volume of each drinking cup is 7.9 cubic inches.
The complete question is An office uses paper drinking cups in the shape of a cone, with dimensions as shown. To the nearest tenth of a cubic inch, what is the volume of each drinking cup?
d = 2.75 m.
h = 4
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15. The center of the circle in the figure is at O. Determine the measure of ZABC.
According to the Central Angle Theorem, the central angle occupied by two points on a circle will always be twice the inscribed angle occupied by those same two points, therefore ∠ABC = 1/2 × 56 = 28°.
What is Central Angle Theorem?Since subtended and inscribed angles are mentioned in the definition, we must first understand them in order to understand the central angle theorem. An object at a specific outer position forms an angle known as a subtended angle.
If you disagree with that definition, think about this: On Earth, you are standing and gazing up at the sun. A triangle with three sides is created. The sun's height, the sun ray that travels from the bottom of the sun to your eyes, and these three directions are the three sides of the sun.
The Central Angle Theorem states that the central angle occupied by two points on a circle is always twice the inscribed angle occupied by those same two points.
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2. A gallon of gas cost $3.50 at the
beginning of the month. At the e
of the month it cost $3.75. What
was the percent change in the
price of a gallon of gas?
Answer: 0.071%
Step-by-step explanation:
To get from $3.50 - $3.75, there was an increase of $0.25.
(Sorry if I'm getting the currency bit wrong, I'm British.)
Divide 0.25 by the original cost of 3.50, and you get:
0.07142857142857142857142857142857
Round this and you get a 0.071% increase
Answer:
The percent change in the price of a gallon of gas is 0.0714%.
Step-by-step explanation:
Given;A gallon of gas costs $3.50 at the beginning of the month.At the end of the month it costs $3.75.Here, The price increased from $3.50 to $3.75, a change of $0.25.
To find What is the percent change.Formula[tex] \frac{changed \: \: price}{original \: \: price} \times 100\% \\ [/tex]So,
$0.25 ÷ $3.50 × 100% = 0.0714%
Thus, The percent change in the price of a gallon of gas is 0.0714%.
What is the reciprocal of 1 4/13
Answer:
Step-by-step explanation:
Find the area of a regular 12-sided polygon inscribed in a circle of radius
8 cm.
area of n sided polygon inscribed in a circle is
A = (1/2)nr²sin(360/n) (r = radius of circle)
A = (1/2)12*8²*sin30
= 1/2*12*64*1/2
A = 192 square unit
help pleaseeeeeeeee
︎
︎
The correct answer in the number line is 2 and 0.888 .
In elementary math, what is a number line?A picture of numbers on a straight line is referred to as a number line in mathematics. Across the length of a number line, the numbers are arranged in a sequential manner at equal intervals. It is frequently seen horizontally and can extend indefinitely in any direction.
The addition, subtraction, division, and times table problems can all be illustrated with a number line. You can better comprehend the idea of negative numbers by using the number line.
The addition, subtraction, division, and times table problems can all be illustrated with a number line. You can better comprehend the idea of negative numbers by using the number line.
1. 9/2 in 2
2.4/9 by 2 is = 4/4.5 = 0.888 .
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Suppose you have fewer than 10 place value blocks. How many different ways could you show 1214? Explain.
There are 3,024 different ways 1,214 can be shown.
What is permutation?Basically A permutation is an arrangement of items in a specific direction or sequence. One should consider both the selection and the arrangement while dealing with permutation. In permutations, ordering is crucially important. The permutation is seen as an ordered combination, in other words.
Given 1,214
since there are 4 places in the digit,
so 4 values less than 10 can be solved by
9, 8, 7, and 6
so by permutation to find ⁹P₄ = 9!/(9 - 4)!
= (9 x 8 x 7 x 6 x5!)/5!
⁹P₄ = 3,024
Hence there are 3,024 different ways.
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is 3/16 greater than 1/16