Which system of linear inequalities is represented by thegraph?+ 3 and 3x-y> 22...4-5 -4 -3 -2 -1.O ye**+O yz}x+3 and 3x –y> 2O yz}x+3 aO yax+3 and 2x -y> 22-+ 3 and 3x + y > 2
Answers
Inequalities
We are given a graph where a shaded area is shown. It's bounded by a solid line.
We first need to find the equation of that line by selecting any pair of clear points on the line.
For example, I can see the points (-4,1) and (0,3).
To find the equation of the line passing through them we use the following equation.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
\(\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)Substituting the given points:
\(\displaystyle y-1=\frac{3-1}{0+4}(x+4)\)Simplifying:
\(\begin{gathered} \displaystyle y-1=\frac{2}{4}(x+4) \\ \displaystyle y-1=\frac{1}{2}(x+4) \\ 2y-2=x+4 \\ 2y=x+6 \\ y=\frac{1}{2}x+3 \end{gathered}\)Since the shaded area is below the line, the inequality is:
\(y\leq\frac{1}{2}x+3\)Note the symbol is 'less or equal' and not 'less' because the line is solid, which includes equality, or the points in the line.
Related Questions
make e the subject
e-5=2f
Answers
Answer:
e-5=2f
take '-5' to the other side where '2f' is
e=2f+5
A
-2+
Which graph represents the
function y = tan x?
B
2T
2T
D
-2+1
21
4+
ㅠ
2T
2πT
Answers
The graph that represents the function y= tanx is Option A.
What is the description of the above function?The graph of y =tan (x) is a periodic function that has vertical asymptotes at x = (n + 1/2)π, where n is an integer.
It oscillates between positive and negative infinity, creating a wave- like pattern.
It has a repeating pattern of sharp peaks and valleys, exhibiting both positive and negative slopes.
Thus, option A is the correct answer.
Learn more about graph:
https://brainly.com/question/25184007
#SPJ1
Each triangle in the net has a base length that measures 6 inches and a height that measures 4 inches. What is the surface area of the pyramid that can be formed from this net? 12 inches squared 24 inches squared 36 inches squared 48 inches square
Answers
Answer:
Surface area of triangular pyramid = 48 inch²
Step-by-step explanation:
Given:
Base length of triangle = 6 inches
Height of triangle = 4 inches
Find:
Surface area of triangular pyramid
Computation:
Surface area of triangular pyramid = 4 x [Surface area of triangle]
Surface area of triangular pyramid = 4 x [(1/2)(b)(h)
Surface area of triangular pyramid = 4 x [(1/2)(6)(4)
Surface area of triangular pyramid = 4 x [(1/2)(24)]
Surface area of triangular pyramid = 4 x 12
Surface area of triangular pyramid = 48 inch²
The temperature in a hotel is 21 °C.
The temperature in the hotel is 26,7°C warmer than at the top of the mountain.
The temperature at the top of the mountain is 3.2°C colder than at the bottom of the mountain.
Work out the temperature at the bottom of the mountain.
Answers
The temperature at the bottom of the mountain is 50.9 °C.
Let's work through the given information step by step to find the temperature at the bottom of the mountain.
The temperature in the hotel is 21 °C.
The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.
Let's denote the temperature at the top of the mountain as T_top.
So, the temperature in the hotel can be expressed as T_top + 26.7 °C.
The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.
Let's denote the temperature at the bottom of the mountain as T_bottom.
So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.
Now, let's combine the information we have:
T_top + 26.7 °C = T_bottom - 3.2 °C
To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:
T_bottom = T_top + 26.7 °C + 3.2 °C
T_bottom = T_top + 29.9 °C
Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:
T_bottom = 21 °C + 29.9 °C
T_bottom = 50.9 °C
Therefore, the temperature at the bottom of the mountain is 50.9 °C.
for such more question on temperature
https://brainly.com/question/14820864
#SPJ8
How would you solve
"if f(x) / (x - 2) = x ^ 3 + 2x - 4 + 13/(x - 2) what is f(2)"
and
"if f(x) / (x + 3) = 3x ^ 2 - 4x + 2 what is f(-3)"
Answers
The denominator is zero (0/0 is undefined), we cannot determine the exact value of f(-3) using this equation.
To solve the given equations, we need to find the value of the function f(x) for specific values of x.
"If f(x) / (x - 2) = x³ + 2x - 4 + 13/(x - 2), what is f(2)?"
To find f(2), we can substitute x = 2 into the equation and solve for f(2).
Plugging in x = 2, we get:
f(2) / (2 - 2) = 2³ + 2(2) - 4 + 13/(2 - 2)
Since the denominator is zero (2 - 2 = 0), the equation is undefined. Therefore, there is no solution for f(2) in this case.
"If f(x) / (x + 3) = 3x² - 4x + 2, what is f(-3)?"
To find f(-3), we can substitute x = -3 into the equation and solve for f(-3).
Plugging in x = -3, we get:
f(-3) / (-3 + 3) = 3(-3)² - 4(-3) + 2
Simplifying, we have:
f(-3) / 0 = 3(9) + 12 + 2
f(-3) / 0 = 27 + 12 + 2
f(-3) / 0 = 41
Additional information or context is needed to solve for f(-3).
For similar questions on denominator
https://brainly.com/question/20712359
#SPJ8
helpppp...........................
Answers
Answer:
see explanation
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
a hexagon has 6 sides , then
sum = 180° × (6 - 2) = 180° × 4 = 720°
12
the polygon has 5 sides , so
sum = 180° × (5 - 2) = 180° × 3 = 540°
sum the interior angles and equate to 540
y + 90 + 120 + 90 + 110 = 540
y + 410 = 540 ( subtract 410 from both sides )
y = 130
13
the polygon has 7 sides , so
sum = 180° × (7 - 2) = 180° × 5 = 900°
sum the interior angles and equate to 900
p + 90 + 141 + 130 + 136 + 123 + 140 = 900
p + 760 = 900 ( subtract 760 from both sides )
p = 140
- left his house and drove to the store. He stopped and went inside. From he drove in the same direction until he got to the bank. He stopped and went the bank. Then he drove home. The graph below shows the number of blocks com home Connor is a minutes after he left his house, until he got back home.Connor left his house and drove to the store. He stopped and went inside. From there, he drove in the same direction until he got to the bank. He stopped and went inside the bank. Then he drove home. The graph below shows the number of blocks away from home Connor is a minutes after he left his house, until he got back home.
Answers
The graph shows that Connor traveled a total of seven blocks from his house to the store and then from the store to the bank.
What is graph?Graph is a data structure used to represent data in a visual way. It is composed of a set of nodes and edges, where each node represents an object and each edge represents a connection between two objects. Graphs can be used to represent a variety of data structures, such as a network of roads, a family tree, or a list of friends. Graphs are powerful tools for understanding complex relationships in data.
It also shows that he stayed at the store and the bank for five and seven minutes respectively. After leaving the bank, he drove the remaining four blocks back home.
The graph also reveals that Connor was driving at a steady pace between the store and the bank and that the total journey time was twenty-two minutes. This time could have been reduced if he had driven faster. However, it is possible that he was being cautious due to the traffic or other conditions.
Overall, the graph provides a visual representation of Connor's journey and his decisions along the way. It also provides insight into his driving habits, as well as his ability to manage his time. Based on this data, it is clear that Connor was able to complete his errands in an efficient manner.
To know more about graph click-
https://brainly.com/question/19040584
#SPJ1
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
The statements that are always true regarding the given diagram of the triangle are m∠2 + m∠3 = m∠6, m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°. Therefore, options (4) and (5) are not always true.
What is an exterior angle?An exterior angle of a polygon is an angle that forms a linear pair with an interior angle of the polygon. In other words, it is an angle formed by extending one of the sides of the polygon. For any given vertex of the polygon, the exterior angle is the angle between a line containing the side of the polygon next to the vertex and a line that is an extension of the adjacent side. The measure of an exterior angle is equal to the sum of the measures of its corresponding remote interior angles (interior angles that are not adjacent to the exterior angle). The sum of the exterior angles of any polygon, including a triangle, is always equal to 360 degrees. Exterior angles are used in a variety of geometric proofs and constructions.
We know that the sum of all the interior angles of any triangle is 180 degrees. Therefore, we can use this fact to determine which statements are always true regarding the given diagram.
Now, we can use the following relationships between the interior and exterior angles of a triangle:
Exterior angle = Sum of interior angles adjacent to it
Interior angle = 180 - Exterior angle
Using these relationships, we can determine which statements are always true:
m∠5 + m∠3 = m∠4: This is true because the exterior angle at angle 3 is equal to the sum of angles 3 and 4, and the exterior angle at angle 5 is equal to the sum of angles 5 and 6. Therefore, m∠5 + m∠3 + m∠6 = m∠4 + m∠3, which simplifies to m∠5 + m∠3 = m∠4.
Given m∠3 + m∠4 + m∠5 = 180°: This is true because the sum of all the interior angles of a triangle is 180 degrees.
m∠5 + m∠6 = 180°: This is not always true because sum of all the angles should be 180. It is true in this specific case because angle 1 is a straight angle, which means that m∠5 + m∠6 = 180°. However, in general, this statement is not always true.
m∠2 + m∠3 = m∠6: This is true because the exterior angle at angle 2 is equal to the sum of angles 2 and 6. Therefore, m∠2 + m∠3 = m∠6.
Given m∠2 + m∠3 + m∠5 = 180°: This is may not always true. It is true in this specific case because angle 1 is a straight angle, which means that m∠2 + m∠3 + m∠5 = 180°. However, in general, this statement is not always true.
Therefore, the three statements that are always true from the diagram are:
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠2 + m∠3 = m∠6
To know more about exterior angles visit:
brainly.com/question/28835566
#SPJ1
Which number has the least value?
A 7.078
B 7.708
C 7.807
D 7.007
Answers
Answer: D
Step-by-step explanation: It has the least value in the hundredths and thousandths place, so it is D.
Help pls and thank you!
Answers
Answer:
120 such cubes could fit in the prism.
Step-by-step explanation:
Volume of prism = length × breadth × height
\( = \frac{5}{3} \times \frac{4}{3 } \times 2\)
\( = \frac{40}{9} cm {}^{3} \)
___________________________________
Volume of cube = a³
\( = ( \frac{1} {3}) {}^{3} \)
\( = \frac{ {1}^{3} }{ {3}^{3} } \)
\( = \frac{1}{27} cm {}^{ 3} \)
____________________________________
\( \frac{40}{9} \div \frac{1}{27} \)
\( \frac{40}{9} \times 27\)
\(40 \times 3\)
120
N is an integer.
Write the values of n such that -15<3n≤6
Answers
Answer:
n = - 4, - 3, - 2, - 1, 0, 1, 2
Step-by-step explanation:
Given
- 15 < 3n ≤ 6 ( divide the 3 intervals by 3 )
- 5 < n ≤ 2
Thus n ≠ - 5 but n can equal the upper limit of 2
Hence
n = - 4, - 3, - 2, - 1, 0 , 1, 2
what is the length of rs
Answers
Answer: 24 units.
Step-by-step explanation: Because you go down 12 and then across the x -axis which is over 12 and when you add both positive numbers you get 24 units.
An airplane is flying with a constant altitude at a speed of 450 mph in a direction 10° north of west directly towards its final destination. The airplane then encounters wind blowing at a steady 34 mph in a direction 85° north of east. If the pilot does not correct his course after encountering the wind, at what speed and in what direction (counterclockwise from east) will the plane be traveling? Speed: _____mph Direction:______ °
Answers
Answer:
your answer is gonna be 579 miles that would be your answer
The ground speed will be 454.2 mph in north east.
What is a vector?The quantity which has magnitude, direction and follows the law of vector addition is called a vector.
Given that airplane is flying with a constant altitude at a speed of 450 mph in a direction 10° north of west directly towards its final destination.
The airplane then encounters wind blowing at a steady 34 mph in a direction 85° north of east.
The component of an airplane will be
x =450 sin 10
x = -244.8
y = 450 cos 10
x = -377.5
The component of wind will be
x =34sin 85
x = -5.98
y = 34 cos 85
x = -33.4
Then the ground speed will be 454.2 mph in north east.
More about the vector link is given below.
brainly.com/question/13188123
#SPJ2
a number p is not positive
Answers
please find the value of a
Answers
Answer:
I cant lp because
i'm on the school computer so sorry. <:(
so I cant see your Step-by-step explanation:
Reduce 2a/5a. Thanks!!!!
Answers
Hey there!
ANSWER: \(\frac{2}{5}\)EXPLANATION.\(2a/5a\)
Simplfy and remove a to solve.
\(\frac{2a}{5a} =\frac{2}{5}(ANSWER)\)
Hope this helps!
\(\text {-TestedHyperr}\)
The reduction of 2a/5a will be 0.4.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
Given the expression,
2a/5a
Now by the law of multiplication
(2a/5a) = (2/5)(a/a)
(2a/5a) = 0.4
Hence "The reduction of 2a/5a will be 0.4".
To learn more about expression,
https://brainly.com/question/14083225
#SPJ2
Help i'll give you brainlyest
Answers
Answer:
Its not A and B and I know that, but can you show the rest so I can see if its C because the rest of the picture isn't there
If the triangle's sides are a base that is 4 inches, a height that is 3 inches, and the other side that is 5 inches, what is the area of that triangle?
Answers
Answer:
6 in ^2
Step-by-step explanation:
divide side lengths by two and add those numbers
Can 7/30 be reduced?
Answers
Answer:
no
Step-by-step explanation:
as 7 is a prime numbers and prime numbers cannot be reduced .
4
A gasoline pump delivers 4 gallons of
gas per minute. How many minutes will
it take to fill a gas tank that holds
16 gallons?
2
min
14
Answers
If a gasoline pump delivers 4 gallons of gas per minute, proportionately, it will take it 4 minutes to fill a gas tank that holds 16 gallons.
What is proportion?Proportion refers to the ratio of one unit or quantity compared to another unit or quantity.
Proportions are represented as fractional values using decimals, fractions, and percentages.
The time it takes the gasoline pump to deliver 4 gallons = 1 minute
Proportionately, to deliver 16 gallons, the time = 4 minutes (16 ÷ 4)
Thus, using proportional relationships, to deliver 16 gallons, the gasoline pump will take 4 minutes.
Learn more about proportions at https://brainly.com/question/1496357.
#SPJ1
Match each set of vertices with the type of triangle they form.
A(2, 0), B(3, 2), C(5, 1)
obtuse scalene triangle
A(4, 2), B(6, 2), C(5, 3.73)
isosceles right triangle
A(-5, 2), B(-4, 4), C(-2, 2)
right triangle
A(-3, 1), B(-3, 4), C(-1, 1)
acute scalene triangle
A(-4, 2), B(-2, 4), C(-1, 4)
Answers
9514 1404 393
Answer:
rightacuteobtuserightobtuseStep-by-step explanation:
When the same problem is repeated, I like to solve it using a spreadsheet. That way, the formulas only need to be entered once, and the arithmetic is (almost) guaranteed to be done correctly.
A "form factor" computed from side lengths can be used to determine the type of triangle. Where 'c' is the long side, that factor can be computed as ...
f = a² +b² -c²
and interpreted as follows:
f = 0, right trianglef > 0, acute trianglef < 0, obtuse triangle(The sign of f matches the sign of the cosine of the largest angle computed using the law of cosines.)
Of course, a right triangle can also be identified by looking at the slopes of the sides of the triangle. If any pair of slopes has a product that is -1, or if any pair is 0 and "undefined", then the triangle will be a right triangle.
__
The attached spreadsheet is designed to accommodate a number of different problem requirements. It shows both side lengths and slopes, and it shows the "form factor" as described above. The final classification is shown at far right.
P = 3t² + 7t
Work out the value of P when t = -4
Answers
Answer:
P = 20
Step-by-step explanation:
Hello!
We can solve this by substituting -4 for t.
EvaluateP = 3t² + 7tP = 3(-4²) + 7(-4)Remember that any negative number squared is the absolute value of that number squared.
P = 3(|-16|) - 28P = 3(16) - 28P = 48 - 28P = 20The final evaluation is 20.
at what value of x does the graph of the following function f(x) have a vertical asymptote? f(x)=1/x-6
Answers
Answer:
x = 6
Step-by-step explanation:
A vertical asymptote is a vertical line going through the x-axis at an x-value that x is not actually allowed to have.
In this case, we have a 'rational' function, meaning there is a 'ratio' or fraction involving the variable x.
With these 'rational' or fractional expressions, we always have to watch out to make sure we never have a denominator equal to zero, because division by zero is not defined. It is meaningless.
The denominator x-6 will equal zero if x is 6, so x cannot actually ever be 6.
That is where the vertical asymptoe goes: a vertical line with the equation x = 6.
The value of x is 6.
The following information should be considered:
A vertical asymptote is a vertical line that gone via the x-axis at an x-value where x is not actually allowed to have. In the given case, it have a rational function, that means there is a ratio or fraction involving the variable x. The denominator x-6 will equal zero in the case when x is 6, so x cannot actually ever be 6. So, where the vertical asymptoe goes: a vertical line with the equation x = 6.Learn more: brainly.com/question/17429689
Which of the following is an example of a producer?
1. tree
2. hawk
3.rabbit
4. mushroom
Answers
Answer:
1. treeStep-by-step explanation:
Tree as an autotroph can prepare its own food and which animals and humans feed upon, so the tree is a producer
Complete the statement describing the key features of function h. Function h has an x-intercept of -3, an x-intercept of 0, an x-intercept of 1, no x-intercept and a y-intercept of -3, 0, 1. The function is positive for x>-3, x>0, x>1, all x and increasing, decreasing on all intervals of x. The average rate of change for the function on the interval [0,2] is 4.5, 7.5, 9, 15. Saved the answer
Answers
The answer for blanks in statements are, an x-intercept of 1 , -3, x>1 , increasing , 7.5.
Describe Function?Many mathematical and real-world phenomena are described by functions. Modeling real-world occurrences like population increase, interest rates, or physical motion is frequently done using them. There are many distinct features that functions can have, including continuity, differentiability, and periodicity. Functions can also be linear or nonlinear.
The domain and range of functions are crucial components. The set of all potential input values makes up the domain of a function, whereas the set of all possible output values makes up the range. The behaviour of a function, such as whether it is increasing, decreasing, or constant, can also be used to categorize it. A function's graph shows the relationship between its input and output values graphically.
Function h has an x-intercept of 1 and a y-intercept of -3. The function is positive for x>1 and increasing on all intervals of x. The average rate of change for the function on the interval [0, 2] is 7.5
To know more about intercept visit:
https://brainly.com/question/11872755
#SPJ1
78% of x is 3.822, y% of 8 is 0.248
What is the answer?
Answers
Answer:
x = 4.9
y = 3.1%
Step-by-step explanation:
When dealing with percents, we can use the formula
Pa=b, where P is the percentage (either as a decimal or as a fraction over 100).
We can think of the formula saying P% of a is b.
In this first example, the percentage can be converted to a decimal.
Depending on which what numbers, we have and trying to find, we plug it in to the formula accordingly:
\(0.78x=3.822\\x=4.9\)
In this second example, we should make the percentage a fraction over 100 since it's unknown:
\(8(\frac{y}{100})=0.248\\ \frac{y}{100}=0.031\\ y=3.1\)
please help me with this thank you
Answers
(9) The slope of a line perpendicular to the line, f(x) = 0.75x + 6 is - 4/3.
(10) The slope of a line parallel to this line, y = 10 -8x is -8.
What is the slope of a line perpendicular to the line?The slope of a line perpendicular to the line is the negative reciprocal of the slope of the line equation.
Question 9.
f(x) = 0.75x + 6
where;
0.75 is the slope of the line6 is the interceptThe slope of a line perpendicular to this line = -1/0.75 = -100/75 = -4/3
Question 10.
For the equation of another line, y = 10 - 8x
The slope of a line parallel to this line is equal to the slope of this line and it is calculated as follows;
y = 10 - 8x
where;
-8 is the slope10 is the y interceptslope of a line parallel to the line = -8
Learn more about slope of lines here: https://brainly.com/question/3493733
#SPJ1
PLEASE HELP
I need this done is 13 minutes.
Polygon ABCD with vertices at A(1,-1) B(3,-1), C(3,-2) and D(1-2) is dilated to create polygon ABCD with vertices at A’(2,-2), B(6,-2), C’(6,-4) and D’(2,-4). Determine the scale factor used to create the image
A. 3
B. 2
C. 1/2
D. 1/3
Answers
The correct answer is B. 2, as the scale factor used to create the dilated polygon is 2.
To determine the scale factor used to create the image, we can compare the corresponding side lengths of the original polygon ABCD and the dilated polygon A'B'C'D'.
Let's calculate the lengths of the corresponding sides:
Side AB: The length of side AB is 3 - 1 = 2 units in the original polygon. In the dilated polygon, the length of side A'B' is 6 - 2 = 4 units.
Side BC: The length of side BC is -2 - (-1) = -1 units in the original polygon. In the dilated polygon, the length of side B'C' is -4 - (-2) = -2 units.
Side CD: The length of side CD is 1 - 3 = -2 units in the original polygon. In the dilated polygon, the length of side C'D' is 2 - 6 = -4 units.
Side DA: The length of side DA is -1 - (-2) = 1 unit in the original polygon. In the dilated polygon, the length of side D'A' is -2 - (-4) = 2 units.
Now, let's compare the corresponding side lengths:
AB: A'B' = 4 units / 2 units = 2
BC: B'C' = -2 units / -1 units = 2
CD: C'D' = -4 units / -2 units = 2
DA: D'A' = 2 units / 1 unit = 2
The scale factor used to create the image is the ratio of the corresponding side lengths.
In this case, all the corresponding side lengths have a ratio of 2.
For similar question on scale factor.
https://brainly.com/question/30581940
#SPJ8
PLEASE HELP ME ON QUESTION ASAP!!
IF YOU HAVE A TOPIC LIST IN YOUR EXAMS AND IT SAYS AVERAGES AND THE RANGE ARE YOU GOING TO BE HAVING MEAN AND RANGE IN YOUR TEST OR MEAN, RANGE MODE, MIDPOINT BASICALLY ALL OF IT ? IF ANSWERS CORRECT ILL RATE YOU FIVE STARS, GIVE YOU A THANKS AND MAYBE EVEN BRAINLIEST (sorry for caps)
Answers
Answer:
Step-by-step explanation:
Typically yes you need to know
Mean
Median
Mode
and Range
Mean = average, add all numbers then divide by how many
Median = midpoint, middle number. Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers
Mode = numbers that occurs the most in the list of numbers
Range = This is the largest number minus the smallest number.
The coordinates of point A on a coordinate grid are (−2, −3). Point A is reflected across the y-axis to obtain point B and point A is reflected across the x-axis to obtain point C. What are the coordinates of points B and C?
B(2, 3) and, C(−2, −3)
B(−2, −3) and C(2, 3)
B(2, −3) and C(−2, 3)
B(−2, 3) and C(2, −3)
Answers
Answer: B(2, -3) and C(-2, 3) which is choice 3
Further Explanation:
The rule for a y-axis reflection is \((\text{x}, \text{y}) \to (-\text{x}, \text{y})\) meaning the x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same.
Therefore, point A(-2,-3) moves to B(2, -3) when reflecting over the y-axis.
A similar rule is \((\text{x}, \text{y}) \to (\text{x}, -\text{y})\) to describe an x-axis reflection. This time the y coordinate flips in sign, and the x coordinate stays the same.
In this case, we move from A(-2,-3) to C(-2, 3)
The graph of all three points is shown below. I used GeoGebra to make the graph, but Desmos is another option. I also recommend graphing by hand on graph paper to get practice that way if possible.
