How do you find the area of the pre image and the image?
Coordinates for the pre-image are X(3,18) Y(18,18) and Z(18,9) and the image coordinates are X’(1,6) Y’(6,6) Z’ (6,3)
and what is the relationship between the two areas?
Answers
Answer: To find the area of the pre-image and the image, you can use the coordinates of the vertices of the shapes to calculate the lengths of the sides and use the formula for the area of a triangle:
Area = (base * height)/2
For the pre-image, the coordinates are X(3,18) Y(18,18) and Z(18,9). The base of the triangle is the distance between X and Z, which is 18 - 3 = 15. The height of the triangle is the distance between Y and Z, which is 18 - 9 = 9. The area of the pre-image is therefore:
Area = (15 * 9)/2 = 67.5
For the image, the coordinates are X’(1,6) Y’(6,6) Z’ (6,3). The base of the triangle is the distance between X’ and Z’, which is 6 - 1 = 5. The height of the triangle is the distance between Y’ and Z’, which is 6 - 3 = 3. The area of the image is therefore:
Area = (5 * 3)/2 = 7.5
The relationship between the two areas is that the area of the image is smaller than the area of the pre-image. This is because the image has been scaled down in size relative to the pre-image. The amount by which the image has been scaled down can be calculated by dividing the area of the image by the area of the pre-image:
Scale factor = area of image / area of pre-image = 7.5 / 67.5 = 0.11
This means that the image has been scaled down by a factor of 0.11 relative to the pre-image.
Step-by-step explanation:
Answer:
preimage area: 67.5 square unitsimage area: 7.5 square unitsimage area is 1/9 of preimage area, the square of the scale factorStep-by-step explanation:
You want to know the areas and their relationship of the preimage with coordinates X(3,18), Y(18,18), and Z(18,9), and the image with coordinates X’(1,6), Y’(6,6), Z’ (6,3).
TrianglesWhen you plot the points on a graph, you see they define right triangles. Each has sides aligned with the x- and y-axes, so it is easy to find their dimensions by counting grid squares or subtracting coordinates.
The preimage triangle is 18-3 = 15 units in the x-direction, and 18-9 = 9 units in the y-direction.
The image triangle is 6-1 = 5 units in the x-direction, and 6-3 = 3 units in the y-direction.
We notice that both the coordinates and the dimensions of the image triangle are 1/3 those of the preimage triangle.
AreasThe area of each triangle is given by the formula ...
A = 1/2bh
Using the dimensions we found above, the areas are ...
preimage area: 1/2(15)(9) = 135/2 = 67.5 . . . . square units
image area: 1/2(5)(3) = 15/2 = 7.5 . . . . square units
Relationship
We have observed that the image dimensions are 1/3 those of the preimage. The image area is 7.5/67.5 = 1/9 of that of the preimage. This value is the square of the scale factor of the dimensions,
Related Questions
The side of a square is 2.5 find its perimeter and area
Answers
6.25 is the area 2.5^2=6.25
Answer:
perimeter = 10
area = 6.25
Step-by-step explanation:
Every square has four equal sides. If we know one side is 2.5, then all sides are 2.5.
2.5*4 = 10
To find the area of a square you multiply the height and length. Since all sides of a square are the same, you just multiply 2.5 with itself.
2.5*2.5=6.25
What is the general formula for Logarithms?
Answers
The general formula for logarithms is [tex]log_b(x) = y[/tex].
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x) = log_b(x),[/tex] where b is the base of the logarithm.
The general formula for logarithms is:
[tex]log_b(x) = y[/tex]
This means that b raised to the power of y is equal to x.
Where b is the base of the logarithm, x is the number that we are taking the logarithm of, and y is the result or the logarithm of x to the base b.
Hence, the general formula for logarithms is [tex]log_b(x) = y[/tex].
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The general formula for logarithms is [tex]log_b(x)=y[/tex].
What is a logarithmic function?
A logarithmic function is a type of mathematical function that expresses the power to which a given number (the base) must be raised in order to produce a certain value. It is typically written in the form: [tex]f(x)=log_b(x)[/tex] where b is the base of the logarithm.
The general formula for logarithms is:
[tex]log_b(x)=y[/tex]
This means that b raised to the power of y is equal to x.
Where b is the base of the logarithm, x is the number that we are taking the logarithm of, and y is the result or the logarithm of x to the base b.
Hence, the general formula for logarithms is [tex]log_b(x)=y[/tex].
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Can you make a triangle with 3 different length sides?
Answers
Yes, you can make a triangle with three different length sides.
1. Draw three lines of different lengths on a piece of paper.
2. Connect the ends of the lines to form a triangle.
3. The triangle will have three different length sides. The lengths of the sides depend on the lengths of the three lines you drew.
4. To make sure the triangle is valid, use the triangle inequality theorem. This theorem states that the sum of any two sides of a triangle must be greater than the third side.
5. Measure each side of the triangle with a ruler and add them together.
6. Compare the sum of the two sides to the third side. If they are not equal or greater, adjust the lines to create a valid triangle.
7. Once the triangle is valid, it will be a triangle with three different length sides.
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pls help with his i dont get it at all
Answers
Answer:
D.
Step-by-step explanation:
They are parallel would be the best explanation. AB and PQ are in a sense the same segment but PQ is AB translated.
Example 2: An object is thrown upward from the top of a building, where h is the height of the object in metres and t is the time in seconds. The graph below represents the relationship between height and time.
a) What is the maximum height of the object above
the ground?
b) After how many seconds does the object reach this
maximum height?
c) From the moment the object was thrown, how much
time would it take for it to reach he ground?
d) How tall is the building?
Answers
The answers are given as 1) 165 m 2)3 seconds 3) 9 seconds 4)120 m
What is a curve in a graph?A curve is defined as a smoothly- flowing continuous line that has bent. It does not have any sharp turns. The way to identify the curve is that the line bends and changes its direction at least once. Curve of the graph is a pictorial representation of a particular function.
Given : A object is thrown from the top of the building thus by observing the graph we derive the following information
1) Maximum height = 165 m
2) The object reaches maximum height at t=3 seconds
3) The time it took to reach the ground is 9 seconds
4) The building is 120 m tall
Hence, the answers are 1) 165 m 2)3 seconds 3) 9 seconds 4)120 m
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For any of the vehicles listed in the table,
how many days can you rent the vehicle
before it would be less expensive to rent
for the week?
Answers
A person can rent any of the vehicles shown in the table for a minimum of two to three days before it becomes more expensive for a week.
Algebra state that it is the study of the laws and symbols of mathematics as well as the manipulation of these symbols.
The rent of the small car for a week is $250 and for a day is $100. Then,
The maximum number of days that a car could be rented is,
= 250÷100
= 2.5 days
≅ 3 days
Then, for the medium car is,
= 290÷110
= 2.7 days
≅ 3 days
For the luxury car is,
= 325÷120
= 2.7 days
≅ 3 days
For Small van is,
= 350÷150
= 2.3 days
≅ 2 days
For Large van is,
= 390÷170
= 2.2 days
≅ 2 days
We can conclude from the above calculations that a person can rent a car for 2-3 days before it becomes more expensive for a week.
The complete question is -
For any of the vehicles listed in the table, how many days can you rent the vehicle before it would be less expensive to rent for the week?
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A(3,-1); y= 1/3x +10
write an equation of the line passing through the given point that is parallel to the given line
Answers
the equation of the desired line is x = 3y + 6.
To find the equation of a line that is parallel to the given line
y = 1\3x + 10
and passes through the point (3,-1), since parallel lines have the same slope.
Therefore, the slope of the desired line is also 1\3.
Since the desired line passes through the point (3,-1), we can use the point-slope formula to write its equation:
y - (-1) = 1\{3}(x - 3)
Simplifying, we get
y + 1 = 1\ 3x - 1
Multiplying both sides by 3, we get
3y + 3 = x - 3
Adding 3 to both sides, we get
3y + 6 = x
Therefore, the equation of the desired line is x = 3y + 6.
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Hello- some help please!! I will give you brainlist :]
Answers
Answer:
standard form
= x⁶ + 53x⁵ + 2x⁴ -2
Step-by-step explanation:
the degree is 6.
leading coefficient is 1
this is called a polynomial.
it has 4 terms
Gcf of -28, 60, and 72
Answers
Answer:
4
Step-by-step explanation:
-28 = ±2^2 x ±7
60 = ±2^2 x ±3 x±5
72 = ±2^3 x ±3^2
=> Gcf of -28, 60, 72: 2^2 = 4
Answer: 12
Step-by-step explanation:
Therefore, the highest common factor of 60 and 72 is 12.
:) I know somebody already answered but like..im answering some stuff today, hope this helped by the way!
Can u please help?.........................
Answers
The coordinates of the point P on the directed line segment that partitions the segment into a ratio of 2 to 3 is the ordered pair (3, 0).
How to determine the coordinates of point P?In this scenario, we would use line ratio to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 3 to 2.
In Mathematics, line ratio can be used to determine the coordinates of the point P and this is modeled by this mathematical expression:
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have;
P(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
P(x, y) = [(2(9) + 3(-1))/(2 + 3)], [(2(6) + 3(-4))/(2 + 3)]
P(x, y) = [(18 - 3)/(5)], [(12 - 12)/5]
P(x, y) = [15/5], [0/5]
P(x, y) = [3, 0]
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Complete Question:
Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-1, -4), B(9, 6); to 3. The coordinates of P are?
how to solve inequations
Answers
Answer:
When solving an inequality: you can add the same quantity to each side •you can subtract the same quantity from each side you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.
you can add subtract multiply and divide the quantity to each side
But if you’re doing any of those with a negative quantity, the inequality symbol must be reversed
3 x -8> 29
3 x -8 < 29
Simplify the expression below:
20-10y-7y + 9
A) Зу — 29
B) 3y + 11
C) 3y + 29
D) -17y + 11
E) -17y + 29
Answers
To simplify the expression 20-10y-7y + 9, we can combine like terms.
Like terms are terms that have the same variables raised to the same exponents. For example, 10y and -7y are like terms because they both have the variable y raised to the exponent 1.
We can start by combining the like terms:
20 - 10y - 7y + 9
= 20 + (-10y - 7y) + 9
= 20 + (-17y) + 9
Next, we can combine the constants:
20 + (-17y) + 9
= (20 + 9) + (-17y)
= 29 + (-17y)
The simplified expression is: 29 + (-17y)
[tex]20-10y-7y + 9[/tex]
Combine Like Terms:
[tex](-10y+-7y)+(20+9)[/tex]
[tex]-17y+29[/tex]
[tex]\fbox{Option E}[/tex]
•18 POINTS• (don’t answer icebrain)
a.)
b.)
c.)
Answers
Answer: C
Step-by-step explanation:
The HL Theorem states that if the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
In this case, 16 is the hypotenuse (the longest side of a right triangle) and 13 is the leg.
Find the commission on a 1,250 sale with a commission rate of 5%.
Please help only if you know it and please explain the answer
Answers
The commission on the sale would be $62.5
To find the commission on a sale, you can use the following formula:
Commission = Sale Amount x Commission Rate
Sale Amount: the total value of the sale
Commission Rate: the percentage or decimal value of the commission rate (e.g. 5% = 0.05)
The commission on a sale can be calculated by multiplying the total sale amount by the commission rate.
In this case, the commission on a 1,250 sale with a commission rate of 5% would be:
= 1,250 x 0.05
= 62.5
So the commission on the sale would be $62.5
It's also worth noting that commission rate is given as a decimal and not a percentage. 5% is 0.05 as decimal.
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In the figure, a∥e, m∥n, and m∠2 = 112°.
What is m∠6?
Enter your answer in the box
Answers
The measure of the angle ∠6 = 112°
What are parallel lines?
Parallel lines are two or more lines that are always the same distance apart and never meet, no matter how far they are extended. They are coplanar lines that do not intersect or cross each other, and they have the same direction.
As given
a∥e, m∥n, and m∠2 = 112°.
As m∥n
a is the transversal (A line that cuts across two or more (usually parallel) lines is called transverasl.)
Thus
∠ 2 = ∠3 ( Corresponding angle property )
∠3 = 112°
Also
a∥e and m are transversal.
∠ 3 = ∠6 = 112 ° ( Corresponding angle property )
Hence, the measure of the angle ∠6 = 112°
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The measure of the angle ∠6 = 112°
What are parallel lines?
Parallel lines are two or more lines that are always the same distance apart and never meet, no matter how far they are extended. They are coplanar lines that do not intersect or cross each other, and they have the same direction.
As given
a∥e, m∥n, and m∠2 = 112°.
As m∥n
a is the transversal (A line that cuts across two or more (usually parallel) lines is called a transversal.)
Thus
∠ 2 = ∠3 ( Corresponding angle property )
∠3 = 112°
Also
a∥e and m are transversal.
∠ 3 = ∠6 = 112 ° ( Corresponding angle property )
Hence, the measure of the angle ∠6 = 112°
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I really need help on this question
Answers
Step-by-step explanation:
2×4=8
8×2/3
8×2=16
16×3=48
ans = 48
Find the product using any method. (Need some help!!)
Answers
Answer:
2n^2-8n-24
Step-by-step explanation:
Uhm i just did this one with one of my classmates like 2-3 months ago so it just came to mind.
Hope this helped tho! :)
EX 2
QUAD ABCD is a rectangle with
diagonals that intersect at point P.
AC = 4x-13 and DP = x + 7. Find the
value of 'x'.
Answers
QUAD ABCD is a rectangular shape whose diagonals meet at point P. AC is 4x-13 and DP is x + 7.
Can you show that the quadrilateral ABCD is a parallelogram given the provided information?When one set of opposing sides in a quadrilateral are congruent and parallel, the quadrilateral is a parallelogram. ABCD is a parallelogram if — BC — AD and — BC — AD. A quadrilateral becomes a parallelogram if its diagonals are bisected by one another.
In QUAD ABCD, DP equals x + 7 and AC is 4x-13.
4x - 13 is x + 7 + x + 7
4x - 13 = 2x+14
2x-13 = 14.
hence,
The value of x is 13.5.
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what is 2.38 correct to 2 significant figures
Answers
Answer: 2.4
Step-by-step explanation:
we start from the right most digit, that is 8. Since 8 is greater than 5, we add 1 in the number before 8, that is 3. When we add 3 and 1 we get 4. This way, we get our answer 2.4 , which is correct to 2 significant figures.
hope that helps...
1/3x-2 × 9x²-4/3x²-13x-10 - 7/x-1
Answers
Answer:
Step-by-step explanation:
Combine multiplied terms into a single fraction
one-third x minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
1 x over 3 end fraction minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
Multiply by 1
1 x over 3 end fraction minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
x over 3 end fraction minus 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
Multiply the numbers
x over 3 end fraction negative 2 ⋅ 9 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
x over 3 end fraction negative 18 x squared plus negative 4 over 3 end fraction x squared minus 13 x minus 10 plus negative 7 over x end fraction minus 1
Part A: Maci made $170 grooming dogs one day with her mobile dog grooming business. She charges $60 per appointment and earned $50 in tips. Write an equation to represent this situation. (4 points)
Part B: Logan made a profit of $210. 00 as a mobile groomer. He charged $75. 00 per appointment and received $35. 00 in tips, but also had to pay a rental fee for the truck at $10. 00 per appointment. Write an equation to represent this situation. (4 points)
Part C: Explain how the equations from Part A and Part B differ. (2 points)
Answers
The equations for parts A and B are 170 = 60x + 50 and 210 = 75x + 35 - 10x, respectively.
What is an equation ?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
The statement is not an equation if there is no "equal to" sign in it.
According to our question-
A) It is stated that Maci once earned $170 by grooming dogs.
For each appointment, she charges $60, and she received $50 in tips. Consequently, the equation to illustrate this is;
170 = 60x + 50
the number of appointments is x.
B) Logan earned $210.00 in profit. He charged $75.00 for each session and got $35.00 in gratuities. In addition, he had a $10.00 truck rental fee per appointment. In order to represent this, the equation is;
210 = 75x + 35 - 10x
the number of appointments is x.
C) The quantity of tips they will receive even without an appointment varies between the formulae.
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How do you know if you add or subtract in elimination?
Answers
Find the length of the third side. If necessary round to the nearest tenth
Answers
The side lengths of a right-angle triangle can be calculated using the Pythagorean Theorem. Which states that the square of the hypotenuse is equal to the sum of squares of the other sides in the triangle.
[tex]a^2+b^2=c^2[/tex]
the hypotenuse is always the longest side of a triangle and is always the opposite side length to the right anglerearranging the equation can help calculate the third side:
[tex]c^2-a^2=b^2[/tex]
[tex](5)^2-(4)^2=b^2[/tex]
[tex]25-16=b^2[/tex]
[tex]9=b^2[/tex]
[tex]\sqrt{9}=\sqrt{b^2}[/tex]
[tex]{ {{b_1=+3} \atop {b_2=-3}} \right.[/tex]
note: a length can never be negative so never take into account a negative answer
b = 3
Highschool Algebra: Indicated Operation.
(-ab2)(-6ab2)(3ab)
Answers
Answer:
-18a^3b^5
Step-by-step explanation:
First do -ab^2*-6ab^2=-6a^2b^4
Then multiply that by 3ab=-18a^3b^5
For the rhombus below, find the measures
Answers
Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.
what is rhombus ?A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal. A rhombus also has equal-length sides and diagonals that are at right angles to one another. The term "rhombus" can also refer to a diamond or rhombus. A rhombus has equal opposite angles. At a 90° angle, the diagonals split in half. 180 degrees is the sum of adjacent angles.
given
There is a line that passes through the parallel line; the alternate interior angles are 3 and 39.
The alternative interior angles are similar, hence Angle 3 = 39.
Since the upper left triangle is a triangle, angles 3, 4, and the center angle all add up to 180 degrees. The angle in the middle is 90 degrees. hence, we may locate angle 4.
angle 4=51.
Since Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.
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does multiplying 2 numbers together always give the first common multiple of the numbers? explain using examples
Answers
2 x 8 = 16
But the first common multiple is 8
2, 4, 6, 8, 10, 12, 14, 16…
8, 16, 24…
Write an equation of the line that passes through (3,-4) and is perpendicular to y=1/2x+7.
Answers
y = 2x + b
-4,7
Substitute:
7 = (2)(-4) + b
7 = -8 + b
b = 15
y = 2x + 15 I can do all ur work for u (813) 819-5978
A quadrilateral
is a polygon with four sides. Consider
the quadrilateral and the dashed segment. What is the sum
of the measures of the four interior angles of this quadrilateral?
Draw a different quadrilateral. Can you guess the sum
of the measures of its angles? Is it possible to generalize about
the angles of a quadrilateral?
Answers
The sum of the measures of the four interior angles of a quadrilateral is always 360°
What is a quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles.
Given is, A quadrilateral is a polygon with four sides. Consider the quadrilateral and the dashed segment
If we draw one diagonal to quadrilateral we will get two triangles i.e. △ABC and △ACD and we know that sum of the angles of a triangle is 180°
Sum of angles of quadrilateral ABCD = sum of angles of △ABC + sum of the angles △ACD
= 180° + 180°
= 360°
If we take examples of a square or a rectangle, we know that they are also a quadrilateral and also their each angle is right angle, i.e. 90°
Therefore, the sum of their interior angles will = 90×4 = 360°
Hence, we can say that the sum of the measures of the four interior angles of a quadrilateral is always 360°
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Which expression is modeled by this set of arrows on the number line?
Answers
On solving the provided question, we can say that - here in number line we jump fron 2 to 7 as we have added +5
what is number line?A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.
here,
we have +5
so 2+(+5) = 7
we will jump to 7 from 2
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11. Manuel has two different recipes for chocolate chip
muffins. The table shows the amount of chocolate chips
needed per batch for each recipe. He has 10 cups of
chocolate chips. The equation 2b = 10 can be used to
find b, the number of batches of muffins he can make if
he uses Recipe 1. Can Manuel make 3, 4, or 5 batches if
he uses Recipe 1?
n
JID
Recipe Chocolate Chips (cups)
1
2
2
1
Answers
Answer:
Manuel can make 5 batches of muffins using Recipe 1
Step-by-step explanation:
You want to know the value of b in the equation 2b = 10, where b is the number of batches of muffins Manuel can make using recipe 1.
SolutionDivide both sides of the given equation by 2 so solve for the value of b.
(2b)/2 = (10)/2
b = 5
Manuel can make 5 batches of muffins using Recipe 1.
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