Let's assume that Mr. Paquette has x pencils.
From the problem, we know that for each pencil he has, he also has 3 pens. So the total number of pens he has is 3 times the number of pencils:
Number of pencils = x
Number of pens = 3x
The total number of pencils and pens combined is given as 8, so we can write:
x + 3x = 8
Simplifying, we get:
4x = 8
x = 2
Therefore, Mr. Paquette has 2 pencils and 3x2=6 pens.
Ted and his friends went out to dinner after soccer practice last night. They decided to split the bill evenly among the 5 of them. Including the tip, Ted figured that each person will pay no more than $15.
Answer:
The inequality that describes the problem is given as follows:
x ≤ 75.
How to obtain the inequality?
To describe the inequality in this problem, we need to obtain the upper bound of the total amount that Ted and his friends are expected to spend.
To obtain the upper bound of the total amount, the relevant information is given as follows:
Ted and his friends decided to split the bill evenly among the 5 of them.
Ted figured that each person will pay no more than $15.
Hence the upper bound of the total amount is calculated as follows:
5 x $15 = $75.
The upper bound of $75 means that in total, they are expected to pay at most $75, hence the inequality that describes this problem is given as follows:
x ≤ 75.
Instructions: Use the model to fing the area of the shaded region.
Answer: [tex]\frac{1}{3}[/tex] yds²
Step-by-step explanation:
To find the area, we will multiply 2/3 by 2/4. When multiplying fractions, you multiply straight across.
[tex]\displaystyle \frac{2}{4} *\frac{2}{3} =\frac{2*2}{4*3} =\frac{4}{12} =\frac{1}{3}[/tex]
We can also use the model, see attached.
warren braxton purchased a home valued at $495,000. he purchased homeowner insurance for 70% of the value of the home. if the annual premium on the policy was $0.78 per hundred-dollar unit, how much did he pay?
Warren Braxton paid $2,700.30 for his homeowner insurance policy.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Formula for percentages: (Value/Total value) * 100
Given that, Warren Braxton purchased homeowner insurance for 70%.
Thus,
0.7 x $495,000 = $346,500.
Now, the premium is:
Premium = ($346,500 / 100) x $0.78 = $2,700.30
Hence, Warren Braxton paid $2,700.30 for his homeowner insurance policy.
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Find the discriminant.
6y² - 9y + 1 = 0
Submit
Hello and greetings ririleyyyii
The discriminant of 6y² - 9y + 1 = 0 equals 57.
Step-by-step explanation:6y² - 9y + 1 = 0
We identify the coefficients a, b and c of the quadratic equation.
The coefficients of a quadratic equation are the numbers that multiply the variables together with the independent term.
ax² + bx + c = 0
The coefficient a is usually called the leading or main coefficient and multiplies the term x.The coefficient b is usually called the linear coefficient and multiplies the term x.The coefficient c is the independent or constant coefficient.So the coefficients are: a = 6, b = -9, c = 1.
We evaluate the discriminant by substituting a, b and c inside the expression b² - 4ac.
The exercise remains: (-9)² - 4 × 6 × 1
(-9)² - 4 × 6
81 - 4 × 6 = 24, so 81 - 24 = 57
The discriminant of 6y² - 9y + 1 = 0 equals 57.
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HELP ME PLEASE
is y=4x^2-6x+10 a linear function
Answer:
NO
Step-by-step explanation:
It is a parabola, you can tell cuz of the x^2
:)
Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar. If the triangles are similar, write a valid similarity statement. Problems 3 & 4
Answer: Problem 3:
The triangles are not similar. They have different angles.
Problem 4:
The triangles are similar by SSS~. A valid similarity statement is:
Triangle ABC ~ Triangle DEF.
Step-by-step explanation:
A decagon has angles that measure 120°, 140°, 160°, 130°, 125°, 140°, 165°, 160°, 140°,
and v. What is v?
bearing in mind that the sum of all interior angles in a polygon is
180(n - 2) n = number of sides in the polygon
a DECAgon, DECA=10, has 10 sides, and thus the sum of all its interior angles is 180(10 - 8) = 1440.
[tex]\bold{120+140+160+130+125+140+165+160+140+v=1440}[/tex]
[tex]\bold{1275+v=1440 \implies v=1440-1275 \implies v=165}[/tex]
Solve 4^-2x•4^x = 64
1) Rewrite the equation using the same base. 2) Solve for x. Remember to show all work
PLEASE SHOW ALL WORK FOR BRAINLIEST
Answer:
When the bases are the same, we can combine the exponents. Therefore, we can rewrite the equation as:
4^-2x * 4^x = 4^(-2x+x) = 4^(-x) = 64
To solve for x, we need to isolate x on one side of the equation. We can rewrite 64 as a power of 4:
4^3 = 4^(-x)
Now we can equate the exponents:
3 = -x
Therefore, x = -3.
To check the solution, we can substitute x = -3 back into the original equation:
4^-2(-3) * 4^(-3) = 4^6 * 4^(-3) = 4^3 = 64
So x = -3 is indeed a solution to the equation.
find the area of this semi-circle with radius, r=68cm. give your answer rounded to 1dp
.........................
Suppose in a quadratic-linear system of equations the vertex of the parabola intersects the line. Which of the following would represent the solution to the system of equations? A. the x-value of the vertex B. the y-value of the vertex C. the x- and y-values of the vertex D. cannot be determined
Answer:
C.
Step-by-step explanation:
The vertex and the point of intersection is just one point identifiied by its x and y vlaues
the size of obtuse angle of rhombous is twice the size of acute angle of the rhombous if the side length of rhombous is 13cm and length of shorter diagonal is 10cm ,find the size of angle of rhombous,find length of longer diagonal of rhombous? please help me
So the acute angle of the rhombus is 90 degrees, and the obtuse angle is twice as large, or 180 degrees.
The Pythagorean theorem is a fundamental concept in geometry that describes the relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's start by finding the length of one half of the longer diagonal. We can use the shorter diagonal (which we know is 10 cm) and the side length (which we know is 13 cm) to form a right triangle. The hypotenuse of this triangle is half of the longer diagonal, so we can solve for it using the Pythagorean theorem:
[tex]a^2+b^2 = c^2 \\(13/2)^2 + 10^2 = c^2\\169/4+100 =c^2 \\ 269/4= c^2 \\c = \sqrt{(269)}/2\\[/tex]
Therefore, the length of one half of the longer diagonal is sqrt(269)/2 cm. To find the full length of the longer diagonal, we just need to double this value:
longer diagonal = [tex]2 \times \sqrt{(269)}/2 = \sqrt{(269)}cm[/tex]
Now, we can use the fact that the sum of the angles in a rhombus is 360 degrees to solve for x:
2x + 2x = 360
4x = 360
x = 90
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Sarah and Gavyn win some money and share it in the ratio 5:3. Sarah gets £14 more than Gavyn. How much did Gavyn get?
When Sarah and Gavyn win money, they divide it in a 5:3 ratio.If Sarah gets £14 more than Gavyn, Gavyn gets £21.
Let's call the amount of money that Sarah and Gavyn win "x".
According to the problem, they share the money in the ratio 5:3, which means that Sarah gets 5 parts and Gavyn gets 3 parts.
Let's call the amount of money that Gavyn gets "y". Then, we know that:
Sarah gets £14 more than Gavyn, which means that Sarah's share is y + £14.
We can set up an equation to represent the fact that the ratio of their shares is 5:3:
5/3 = (y + £14)/y
To solve for y, we can cross-multiply:
5y = 3(y + £14)
5y = 3y + £42
2y = £42
y = £21
Therefore, Gavyn gets £21.
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The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Answer:
A histogram would be the most appropriate graphical representation for the given data because it shows the distribution of the data and helps identify patterns or trends.
Answer: I think the answer is bar chart, but it could also be Box plot
Step-by-step explanation:
All I know is that it is either one of those 2 options, it is NOT the others.
An empty container is a cylinder of radius 3.5 cm and height 40 cm
A tennis ball is a sphere of radius 3.5 cm
Will six of the tennis balls fit in the container?
Tick a box.
Yes
No
Show working to support your answer.
Pls help, thankyou
By addressing the posed question, we can get the following conclusion: Volume equation of six tennis balls = 6 179.59 1077.54 cm
Equation: What does it mean?In mathematics, an equations is a promise that two expressions are equivalent. Two sides that are divided by the algebraic symbol (=) make up an equation. As an illustration, the claim "2x + 3 = 9" makes the statement "2x plus 3 equals the quantity "9." Finding the value or values of the variable(s) necessary for the equation to be true is indeed the goal of equation solving. Equations can include one or more parts and be simple or complex, regular or nonlinear. The formula "x2 + 2x - 3 = 0" raises the variable x to the second power. A line is utilized in many different areas of mathematics, such as algebra, calculus, and geometry. We can calculate the volume of the container and the volume of one tennis ball, and then check if the volume of six tennis balls is less than or equal to the volume of the container.
Volume of container = πr2h
Volume of container = π[tex](3.5)^2[/tex](40) ≈ 1540.48 cm
Volume of one tennis ball = 4/3 π[tex]r^3[/tex]
Volume of one tennis ball = 4/3 π[tex](3.5)^3[/tex] ≈ 179.59 cm
Volume of six tennis balls = 6 × volume of one tennis ball
Volume of six tennis balls = 6 × 179.59 ≈ 1077.54 cm
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What is the average rate of change of the function from x = 1 to x = 3?
Answer: 10
Step-by-step explanation: you look at x=1 and go over to x=3 and do rise over run
Which of the following are characteristics of a normal distribution?
Select all that apply.
A. Symmetric
B. Unimodal
C. Bimodal
D. Bell-Shaped
E. Mean and Median are equal
F. The Peak is on the left
G. 64% of the data falls within 1 standard deviation of the mean
Answer:
The mean, median and mode are exactly the same.
Step-by-step explanation:
I ( g o o g l e d ) ur answer and gave u it
The characteristics of a normal distribution are Symmetric, Unimodal, Bell-Shaped, Mean and Median are equal.
A. Symmetric: True. A normal distribution is symmetric, meaning the left and right halves of the distribution are mirror images of each other.
B. Unimodal: True. A normal distribution is unimodal, meaning it has a single peak.
C. Bimodal: False. A normal distribution is not bimodal; it has only one mode (peak).
D. Bell-Shaped: True. A normal distribution is bell-shaped, meaning it forms a symmetric, bell-like curve.
E. Mean and Median are equal: True. In a normal distribution, the mean and median are equal, and they both coincide with the highest point of the curve.
F. The Peak is on the left: False. The peak of a normal distribution is at the center; it is not necessarily on the left.
G. 64% of the data falls within 1 standard deviation of the mean: False. In a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, not 64%.
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select all of the shapes below which are rotations of shape X
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Enter your answer in the box.
Value of angle C in the cyclic quadrilateral is 62°
Define cyclic quadrilateralA cyclic quadrilateral is a quadrilateral that can be circumscribed by a circle such that all four vertices of the quadrilateral lie on the circle.
Some properties of cyclic quadrilaterals include:
The opposite angles are supplementary.The two opposite angles that are inside the circle are equal in measure.The two opposite angles that are outside the circle are also equal in measure.The sum of the measures of the two adjacent angles inside the circle is equal to the sum of the measures of the two adjacent angles outside the circle.In the given diagram
∠B=3x°
∠D=x+20°
For cyclic quadrilateral opposite angle sum is 180°
∠B+∠D=180°
3x°+x°+20°=180°
4x+20=180°
x=160/4
x=40°
∠A+∠C=180°
C=180-2x+38
C=180-2*40-38
C=62°
Hence, Value of angle C in the cyclic quadrilateral is 62°
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PLEASE HELP DUE TONIGHT
Answer: y=1/6x
Step-by-step explanation:
1. Identify the type of graph (linear)
2. the linear line equation is y=mx+b
3. find the slope, in this case, 1/6
a. to find the slope follow the equation (y1-y2)/(x1-x2)
b. plug in the x and y of two different points ex: (0,0) and (18,3)
4. plug into the equation the slope and a set of points - 3=18(1/6) +b
5. solve for b (0)
6. plug b and the slope into the original equation
7. y=1/6x
8. Done :)
please help me with this work
Answer:
b
Step-by-step explanation:
In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values collected by the manager.
{15, 0, 26, 15, 20, 15, 34, 11, 20, 39, 31, 20, 23, 20, 39, 5}
Which of the following stem-and-leaf plots correctly graphs the data set?
2021 Riverside Red Dragon Football Season Points
0 0 5
1 1 5
2 0 3 6
3 1 4 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 5
2 0 3 6
3 1 4 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 5 5 5
2 0 0 0 0 3 6
3 0 1 4 9 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
0 0 5
1 1 5 5 5
2 0 0 0 0 3 6
3 1 4 9 9
Key 1|1 = 11
The stem-and-leaf plot that correctly graphs the data set {15, 0, 26, 15, 20, 15, 34, 11, 20, 39, 31, 20, 23, 20, 39, 5} is given as follows:
0| 0 5
1| 1 5 5 5
2| 0 0 0 0 3 6
3| 1 4 9 9
Key 1|1 = 11
What is shown by a stem-and-leaf plot?A stem and leaf plot is a type of data visualization that displays numerical data in a way that shows the distribution of the data while also preserving the individual data points. It is particularly useful for small to medium-sized data sets.
In a stem and leaf plot, the digits in each data point are split into two parts: the stem and the leaf. The stem is usually the leftmost digits of the number, while the leaf is the rightmost digit. The stems are listed in a column from top to bottom, and each leaf is listed next to its corresponding stem. The resulting plot looks like a table with two columns, where the first column shows the stems and the second column shows the leaves.
For example, as the team scored 20 points four times, we have the following observation:
2| 0 0 0 0
(one leaf of zero for each time, with the stem of 2).
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The roof will be constructed so that the ridgeline runs parallel to the longest
side of the shed. The bottom chord of each roof truss will be 22 feet long.
The pitch of a roof is the slope of the slanted portion. It is given as a ratio.
Your classmate Lauren used the Roof Truss Diagram on the left side of your
screen to determine the pitch of the roof.
Here are her calculations:
tan (40°) = 0.8391
The pitch of both sides of the roof is close to .
Lauren is correct.
What logical assumption did Lauren make about the Roof Truss Diagram?
Lauren assumed that the Roof Truss Diagram is an accurate representation of the actual roof design that will be used on the shed. She used the given measurements, such as the length of the bottom chord, and the angles in the diagram to calculate the pitch of the roof. If the diagram was not accurate, her calculations would not have been useful in determining the pitch of the actual roof. Therefore, Lauren had to make the assumption that the diagram was a reliable representation of the shed's roof design.
The logical assumption that Darin make about the Roof Truss Diagram is that the rise is 4.6 ft and the run is 9 feet.
What is logical assumption?A logical assumption is simply an idea that can be inferred, or identified, in a text without the writer stating it in an obvious way. One simple example may be the logical assumption that if you do not turn in your homework, your teacher will be disappointed in you.
Here, we have,
Based on the information provided, it appears that Darin assumed that the Roof Truss Diagram is symmetrical, meaning that both sides of the roof have the same dimensions and angles. This assumption is supported by his calculation that the pitch of both sides of the roof is close to 1/2.
Rise will be:
= 9 × tan 27°
= 9 × 0.5095
= 4.6 feet.
Run will be 9ft
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help pls!!!!!!!!!!!!!!
Answer:
g(x) = -5tan(x) - 3
Step-by-step explanation:
the parent tangent function would be g(x) = tan(x)
- reflection over the x-axis is going to make it negative
- horizontal stretch by a factor of 5 is going to multiply it by 5
- vertical shift down 3 units will subtract 3
so together, this would be the equation g(x) = -5tan(x) - 3.
6. What triangle congruence theorem could you use to
prove triangle ADE is congruent to triangle CBE?
2.
ExPlain how you know
Step-by-step explanation:
The three angles of the triangles are equal ...use A-A-A theorem
Mrs.Carter took her family and friends to the movies. There were a total of 16 people. Children tickets cost $6 and adult tickets cost $9. She spent a total of $129. How many children went to the movies
Answer:
11 adults
Step-by-step explanation:
First, set up a system of equations:
Let x = number of children and y = number of adults
There is a total of 16 people, so x+y = 16. This is your first equation.
Each child ticket costs $6, so 6x = cost of children's tickets based on the number of children present (x)
Each adult ticket costs $9, so 9y = cost of adult's tickets based on the number of adults present (y)
The total cost of tickets is $129, so 6x+9y = 129. This is your second equation.
Your system of equations is now this:
x + y = 16
6x + 9y = 129
You can solve this system using the method of elimination, where we will eliminate the variable x (number of children), since we are focused on y (number of adults).
Multiply the top equation by -6. This will give the following equation:
-6x - 6y = -96
You can now solve the system of equations by placing the new equation under the second equation like this:
6x + 9y = 129
-6x - 6y = -96
Now, add the two equations together.
6x + (-6x) = 0
9y + (-6y) = 3y
129 + (-96) = 33
After doing this, you get the following equation:
3y = 33
As you can see, the variable x has been eliminated, and you are left with y.
Solve the equation for y:
3y = 33
y = 33/3 = 11
y = 11 adults
help me with this please hurry
Answer:
x = -11
Step-by-step explanation:
[tex]3x + 4(3 - \frac{1}{2} x) = 1[/tex]
[tex]3x + 12 - 2x = 1[/tex]
[tex]12 + x = 1[/tex]
[tex]x = - 11[/tex]
Fill in the blanks and find the x.
For the right-angled triangle, the value for x is obtained as √2/4.
What is a right-angled triangle?
Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.
A right angle triangle is given.
It has angles 90°, 45° and 45°.
The hypotenuse measures 4√2.
The perpendicular measures x.
In a 45°-45°-90° right triangle, the legs are congruent and the hypotenuse is √2 times the length of a leg.
Therefore, in this triangle, each of the legs has length -
(4√2)/√2 = 4
So x is equal to one of the legs, which is 4.
To fill in the blanks -
x : 4√2 = 1 : 4
4x = 4√2
x = (√2)/4
Therefore, the value for x is obtained as √2/4.
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Please help me TT I have a test tomorrow… I do not understand how to solve this problem.
Answer:
Step-by-step explanation:
The quadratic function in vertex form is f(x) = -(x + 5)^2 - 23
What is the quadratic function?To find the quadratic function in standard form, we first need to determine the factors of the quadratic equation that corresponds to the given x-intercepts. Since the x-intercepts are at x = -12 and x = 2, we can write the quadratic equation in factored form as:
f(x) = a(x + 12)(x - 2)
where a is a constant that we need to determine.
To find the value of a, we can use the given minimum y-value of -49. Since the vertex of a quadratic function occurs at the axis of symmetry, which is the midpoint of the x-intercepts, we can find the x-coordinate of the vertex by taking the average of the x-intercepts:
x-coordinate of vertex = (-12 + 2)/2 = -5
Substituting this value of x into the factored form of the quadratic function, we get:
f(-5) = a(-5 + 12)(-5 - 2) = 49a
Since the minimum y-value is -49, we have:
f(-5) = 49a = -49
Solving for a, we get:
a = -1
Substituting this value of a into the factored form of the quadratic equation, we get:
f(x) = -(x + 12)(x - 2)
Expanding this equation, we get the quadratic function in standard form:
f(x) = -x^2 - 10x - 24
To find the quadratic function in vertex form, we can complete the square on the standard form of the equation:
f(x) = -x^2 - 10x - 24
f(x) = -(x^2 + 10x) - 24
f(x) = -(x^2 + 10x + 25) + 1 - 24
f(x) = -(x + 5)^2 - 23
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Sam has a deck that is shaped like a triangle with a base of 15 feet and a height of 6 feet. He plans to build a 4:5 scaled version of the deck next to his horse's water trough.
Part A: What are the dimensions of the new deck, in feet? Show every step of your work. (4 points)
Part B: What is the area of the original deck and the new deck, in square feet? Show every step of your work. (4 points)
Part C: Compare the ratio of the areas to the scale factor. Show every step of your work. (4 points)
The area of the original deck is 45 square feet and the area of the new deck is 28.8 square feet.
The area of the new deck is 64% of the area of the original deck.
What is a triangle?
A triangle is a three-sided polygon that is formed by connecting three non-collinear points in a plane. It is one of the basic shapes in geometry and is characterized by its three sides, three angles, and three vertices.
Part A:
The original deck has a base of 15 feet and a height of 6 feet. To create a 4:5 scaled version of the deck, we can multiply the base and height by the scale factor of 4/5:
New base = 15 * 4/5 = 12 feet
New height = 6 * 4/5 = 4.8 feet
Therefore, the dimensions of the new deck are 12 feet for the base and 4.8 feet for the height.
Part B:
The area of the original deck can be calculated using the formula for the area of a triangle:
Area of original deck = 1/2 * base * height = 1/2 * 15 * 6 = 45 square feet
The area of the new deck can be calculated in the same way, using the new dimensions:
Area of new deck = 1/2 * new base * new height = 1/2 * 12 * 4.8 = 28.8 square feet
Therefore, the area of the original deck is 45 square feet and the area of the new deck is 28.8 square feet.
Part C:
The ratio of the areas can be calculated by dividing the area of the new deck by the area of the original deck:
Area ratio = Area of new deck / Area of original deck = 28.8 / 45 = 0.64
The scale factor is 4/5, which is equal to 0.8. Therefore, we can compare the ratio of the areas to the scale factor to see if they are equivalent:
Area ratio / Scale factor = 0.64 / 0.8 = 0.8
Since the result is equal to the scale factor, we can conclude that the ratio of the areas and the scale factor are equivalent. This means that the area of the new deck is 64% of the area of the original deck.
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Figure 1 and figure 2 below are congruent. Which points corresponds to point r
The point on the image of figure 2 corresponds to point I from Figure 1 is Q, as figure 2 is the image of the figure one after reflection about its origin.
Explain about the reflection about origin:When a figure is constructed around a single point known as the figure's centre, or point of reflection, the result is a point reflection.
Each point in the diagram has an exact opposite point on the other side of the centre, making the point of reflection the middle of the segment connecting the point to its image. Figures do not resize or reshape in the presence of a point reflection.Although any point with in coordinate plane is able to serve as a point of reflection, the origin is the one that is most frequently employed.The x- and y-coordinates are negated when we reflect a point in the origin (their signs are changed).From the two given figures: the figure 2 is the image of the figure one after reflection about its origin.
Thus, the point on the image of figure 2 corresponds to point I from Figure 1 is Q.
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Complete question :
Figure 1 and figure 2 below are congruent. Which points corresponds to point I.
The figure is attached.