Answer:
To solve this problem, we can use the Pythagorean Theorem to solve for a.
For part (a), we know that P(2, 3) and Q(a, -1) are 4 units apart, so we can use the Pythagorean Theorem to calculate a:
(a - 2)² + (-1 - 3)² = 4²
Solving for a, we get:
a = 7
For part (b), we know that P(-1, 1) and Q(a, -2) are 5 units apart, so we can use the Pythagorean Theorem to calculate a:
(a + 1)² + (-2 - 1)² = 5²
Solving for a, we get:
a = 4
For part (c), we know that X(a, a) is √√8 units from the origin, so we can use the Pythagorean Theorem to calculate a:
a² + a² = 8
Solving for a, we get:
a = 2√2
For part (d), we know that A(0, a) is equidistant from P(3, -3) and Q(-2, 2), so we can use the Pythagorean Theorem to calculate a:
(3 - 0)² + (-3 - a)² = (-2 - 0)² + (2 - a)²
Solving for a, we get:
a = -1
Therefore, the value of a that satisfies all conditions is a = -1.
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Please help
Which equations represent linear functions?
Select all that apply.
y=x(2x+4)
x=2y+4
y=x2−19
y=3x2 squared 2
x=y
Answer:
x = 2y+4
y = 3x2 squared 2
x = y
Step-by-step explanation:
Kevin invests money in an account paying simple interest. He invests $40 and no money is added or removed from the investment. After one year, he has $42.80. What is the simple percent interest per year?
The simple interest is 7% per year.
What is the simple interest?Simple interest is the borrowing amount added only to the principal amount.
The formula to calculate the simple interest is;
S.I. = P x T x R / 100,
Where S.I. is simple interest, P is principal amount, T is time period and R is interest rate in a year.
Given:
Kevin invests money in an account paying simple interest.
He invests $40 and no money is added or removed from the investment. After one year, he has $42.80.
That means,
A = $42.80, P = $40, T = 1 year.
So,
R =(1/T) (A/P - 1)
R = (1/1)((42.8/40) - 1) = 0.07
R = 0.07
Therefore, interest rate is 7% per year.
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what is 100000 times 1/100000 as multiplying 10 to a power by 10 to a power
Answer:
The correct answer would be 10^0.
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
[tex]\frac{10^{5} }{10^{5} }[/tex] When the bases are the same and you are dividing, you subtract the exponents.
[tex]10^{5-5}[/tex]
[tex]10^{0}[/tex]
A number with an exponent of 0 equals 1
For $x > 0$, the area of the triangle with vertices $(0, 0), (x, 2x)$, and $(x, 0)$ is 64 square units. What is the value of $x$
The value of x, here x is non-negative integer (i.e x> 0) is equals to the eight.
We have, the vertices of a triangle are (0, 0), (x, 2x), and (x, 0), where x > 0 .
Area of triangle formed by those vertices = 64 square units . The area of the triangle whose vertices are (x₁ , y₁) ,( x₂ , y₂) and (x₃ , y₃) is 1/2 ∣x₁(y₂ - y₃) + x₂( y₃ - y₁) + x₃ (y₁ - y₂)|.
Comparing the vertices (0, 0), (x, 2x), and (x, 0) with standard vertices (x₁ , y₁) ,( x₂ , y₂) and (x₃, y₃). We get, x₁ = 0 , y₁ = 0 , x₂
= x , y₂ = 2x , x₃ = x and y₃ = 0.
Now, the area of the triangle is equals to
1/2 ∣0(2x - 0) + x( 0 - 0) + x (0 - 2x)| = 64
=> 1/2| 0 + 0 + (-2x)x| = 64
=> 1/2 | - 2x²| = 64
=> 1/2(2x²) = 64
=> x² = 64
=> x = ±√64
=> either x= - 8 or x = 8 , but x > 0
So, value of x is 8.
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in a well-insulated calorimeter, 1.0 kg of water at 20∘c is mixed with 1.0 g of ice at 0∘c.
The final temperature of the mixture is approximately 4.2°C.
1. Calculate the total heat capacity of the calorimeter:
Heat capacity = Mass x Specific heat capacity of water = 1.0 kg x 4.18 J/g°C = 4180 J/°C
2. Calculate the heat lost by the water:
Heat lost = Mass of water x Specific heat capacity of water x (T_final - T_initial)
= 1.0 kg x 4.18 J/g° C x (4.2°C - 20°C)
= -41360 J
3. Calculate the heat gained by the ice:
Heat gained = Mass of ice x Specific heat capacity of ice x (T_final - T_initial)
= 1.0 g x 2.09 J/g° C x (4.2°C - 0°C)
= 8.36 J
4. Calculate the final temperature of the mixture:
Final temperature = (Heat lost + Heat gained) / Heat capacity
= (-41360 J + 8.36 J) / 4180 J/°C
= 4.2°C
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Factor this expression completely, then place the factors in the proper location on the grid. X 3 - 1.
The expression will be (x - 1) (x² + x + 1).
How to find the expression ?
As per given x³ - 1, The first things you have to do is rewrite the the expression as :
a³ ± b³ : x³ - 1³
then factorize both expression
a³ ± b³ : x³ - 1³ = (a ± b) (a² ± ab + b²) : (x - 1) (x² + x + 1²)
last, calculate the power of (x - 1) (x² + x + 1²)
(x - 1) (x² + x + 1²) = (x - 1) (x² + x + 1)
Hence, the answer of that question will be (x - 1) (x² + x + 1)
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phillip has twice as many tropical fish as jody. if phillip gave jody 10 of his tropical fish, he would have half as many as jody. how many tropi
Jody has 20 tropical fish and Phillip has 2x = 2*20 = 40 tropical fish.
Together, Phillip and Jody have 20 + 40 = 60 tropical fish.
Let x be the number of tropical fish Jody has.
We know that Phillip has twice as many tropical fish as Jody, so Phillip has 2x tropical fish.
We also know that after giving Jody 10 tropical fish, Phillip would have half as many as Jody, so 2x - 10 = x/2.
Solving for x, we get:
x = 20
So Jody has 20 tropical fish and Phillip has 2x = 2*20 = 40 tropical fish.
Together, Phillip and Jody have 20 + 40 = 60 tropical fish.
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Which action is most helpful in preventing sexual involvement?
1. bringing condoms “just in case”
2. voicing personal boundaries
3. indicating that parents will be upset
4. suggesting that it is not the right time for a dating relationship
The correct answer for preventing sexual involvement would be option 2: voicing personal boundaries.
Voicing personal boundaries: This action is crucial in preventing sexual involvement.
By clearly communicating one's personal boundaries, desires, and limits, individuals establish their autonomy and expectations within a relationship. Open and honest communication allows both parties to understand and respect each other's boundaries, leading to a healthier dynamic.
Voicing personal boundaries is essential because it allows individuals to communicate their limits and expectations regarding sexual involvement, promoting consent and healthy relationships.
It empowers individuals to take ownership of their bodies and decisions, fostering an environment where all parties involved can make informed choices and respect each other's boundaries.
Hence the correct option is 2.
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Adaptive Cruise Control with Cloud Connectivity Objective Use MATLA to develop and implement an adaptive cruise control system for vehicles that automatically adjusts the speed to maintain a safe distance from vehicles ahead. The speed information has to be uploaded on the cloud to support connected vehicles and intelligent transport. Hardware Arduino uno x 1, button x 5, distance sensor x 1, 4 digit 7-segment anode display x 1 Description Implement an adaptive cruise control system using the Arduino UNO board. The system is controlled by five buttons of (1) Set_speed, (2) Adaptive_speed, (3) Cancel, (4) Increase_speed, and (5) Decrease_speed. After power on, the display has to show the initial speed of 0. 1. When the increase_speed button is pressed, the speed increases, and when the Decrease_speed button is pressed the speed decreases however without pressing the Set_speed button the speed will not remain constant and it changes slowly over time. 2. When the Set_speed button is pressed the system enters the cruise control mode where the speed is held constant. In this mode, the Increase_speed button and the Decrease_speed button are still functional and can be used to change the Set_speed. If the Cancel button is pressed, the system quits the cruise control mode where the speed decreases slowly. 3. If the Adaptive_speed button is pressed, the speed is set and held constant until a vehicle shows up at the front or an object is detected where the speed automatically decreases. When the road becomes clear, the speed increases to reach the set speed again. In the adaptive cruise control mode, the display has to blink to differentiate this mode from the cruise mode. In this mode, the Increase_speed button and the Decrease_speed button do not function but the Cancel button can still be used to quit the adaptive cruise mode. If the Cancel button is pressed, the display stops blinking and the vehicle speed begins to slow down. 4. The implemented system has to be able to communicate with the ThingSpeak platform to store the speed data on the cloud. ThingSpeak is an Internet of Things (IoT) application that supports MATLAB to analyze and visualize data
The objective is to develop and implement an adaptive cruise control system for vehicles using MATLAB, Arduino UNO, and ThingSpeak that automatically adjusts the speed to maintain a safe distance from vehicles ahead and uploads speed information to the cloud for connected vehicles and intelligent transport.
The system uses an Arduino UNO board, five buttons, a distance sensor, and a 4-digit 7-segment anode display. The buttons include Set_speed, Adaptive_speed, Cancel, Increase_speed, and Decrease_speed. The system has two modes, cruise control, and adaptive cruise control.
In cruise control, the speed is held constant and can be adjusted with the Increase_speed and Decrease_speed buttons. In adaptive cruise control, the speed automatically adjusts to maintain a safe distance from vehicles or objects in front and the display blinks to indicate this mode.
The system also communicates with the ThingSpeak platform to store speed data on the cloud for analysis and visualization in MATLAB.
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What are the 4 parts of a scatter plot?
The steps of scatter plots are mapped as follows :
Step 1: Decide the Two Variables - First of all, we shall have to select the variables between which there exists a material relationship.
Step 2: Collect Data - After selecting the variables, we shall have to collect relevant data to draw meaningful conclusions.
Step 3: Map the Data - After completion of data collection, we shall have to map it on the X and Y axes of the Cartesian Co-ordinate system.
Step 4: The Line of Best Fit - In the next step, we shall have to statistically compute the line of best fit for the scattered data points.
Step 5: Come Up With an Exact Number - In the next step, we shall have to come up with a correlation coefficient. This number is the best metric to understand correlation and lies between -1 and +1.
Step 6: Interpret the Number - In the last step, we shall have to interpret the number. Any data above + or - 0.5 suggests a strong correlation.
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The correct question is:
What are the steps of a scatter plot?
Which of the following statements best describes that two triangles are similar?
A. Two triangles are similar if two angles of one triangle are congruent to the two corresponding angles of another triangle.
B. Two triangles are similar if two sides of one triangle are congruent to two sides of another triangle.
C. Two triangles are similar if one angle of one triangle is congruent to corresponding angle of another triangle.
D. Two triangles are similar if one side of one triangle is congruent to one side of another triangle.
Select the correct answer.
Which number best represents the slope of the graphed line? -3, -1/3, 1/3 or 3?
The slope of a graphed line that spans grid points (0, 2) and best represents the slope as -5 (1, -3)
what is slope ?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).
given
If the line rises to the right, the slope has a positive sign. The slope of this line is negative since it descends to the right. (Removes options C and D)
The ratio of the vertical to horizontal distance between two sites determines the slope's magnitude. This line has a slope of rise/run = -5/1 = -5 because it descends five vertical squares for every square to the right.
-5 is the best way to describe the slope.
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the eighth grade class at lincoln middle school has 93 students. each student takes a math class or a foreign language class/or both. there are 70 eighth graders taking a math class, and there are 54 eighth graders taking a foreign language class. how many eighth graders take only a math class and not a foreign language class?
31 students eighth graders take only a math class and not a foreign language class
The computation of eighth graders take only a current events class and not a foreign language class is shown below:-
We will assume the x that shows the number of students which we will take both languages
So, the equation will be
70 + 54 - x = 93
-x = 93 - 124
x = 31 students
So the number of eighth graders only take a current event class is
= 70 - 39
= 31 students
31 students eighth graders take only a math class and not a foreign language class
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Solve for X, Leave in simplest radical form. (Help, and the degree shown is 30)
The simplest radical form of X of the triangle is [tex]\sqrt{}[/tex]30.
How can the value of x be determined in its simplest radical form?AI Recommended Response Division by the radical sign yields the value of x in its simplest radical form.
Due to the absence of any perfect square factors for the number beneath the square root,[tex]\sqrt{}[/tex] 30 is in its simplest radical form.
Due to the fact that the number under the square root,
[tex]\sqrt{}[/tex]30 = [tex]\sqrt{2} * \sqrt{3} *\sqrt{5}[/tex]
may be factored to equal, and that [tex]\sqrt{}[/tex]30 is a perfect square since
is not in its simplest radical form.
so we can add [tex]\sqrt{30}[/tex]
The simplest radical form of X of the triangle is [tex]\sqrt{}[/tex]30
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m
6
at is in
n
24
m = [?]✓
Give your answer in simplest form.
please help
The value of m is 12. The metric system as well as the International Systems with Units both employ the meter as a unit of length (m).
What does the letter m denote in measurements?The meter (m), also known as the word "meter," is a unit of length that is used by both the International Systems with Units and the metric systems (SI). It is converted to a measurement of approximately 39.37 inches by both the British Imperial and The us Customary systems.
M is measured at 12.
The metric system as well as the International Standards of Units both employ the metre as a unit of length (m).
According to the given information:In line with the altitude theorem;
24/n = n/6
Cross multiply
24 * 6 = n²
144 = n²
Swap
n² = 144
n = √144
n = 12
As a result, n has a value of 12.
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What is the part of line having 1 endpoint and extending in one direction?
A part of a line that has 1 endpoint and extends indefinitely in only one direction is called a ray.
A ray is named using its endpoint first, and then any other point on the ray
Properties of ray:
A line is a series of points placed together that continue infinitely.When this line is restricted from one direction and is extended in the other direction indefinitely, it forms a ray.It has just one starting point and does not have an opposite end and goes through and cuts many points and lines and is often used to draw angles, and we cannot measure the length of a ray.To know more about ray:
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Rate constant help? Greatly appreciated!
Consider the reaction A-->B
-2 The rate of the reaction is 1.6 × 10 M/s when the concentration of A is 0.11 M.
Calculate the rate constant if the reaction is first order in A. (Give units.)
A. s
B. s -1
C. M
D. M -1
E. M/s
-1 -1 F. M • S
Calculate the rate constant if the reaction is second order in A. (Give units.)
A. s
B. s -1
C. M
D. M-1
E. M/s
F. M -1 • S
F. M⁻¹ s⁻¹
The rate constant if reaction is second order in A is:D. M⁻¹
RATE CONSTANT REACTIONIf the reaction is first order in A, the rate law is rate = k[A], where k is the rate constant. Since the rate of the reaction is 1.6 x 10⁻³ M/s and the concentration of A is 0.11 M, we can find the value of the rate constant by plugging in the given values:
1.6 x 10⁻³ M/s = k(0.11 M)
Solving for k:
k = (1.6 x 10⁻³ M/s) / (0.11 M) = 14.55 x 10⁻⁴ s⁻¹
So the rate constant for a first order reaction in A is 14.55 x 10⁻⁴ s⁻¹.
If the reaction is second order in A, the rate law is rate = k[A]², where k is the rate constant. Since the rate of the reaction is 1.6 x 10⁻³ M/s and the concentration of A is 0.11 M, we can find the value of the rate constant by plugging in the given values:
1.6 x 10⁻³ M/s = k(0.11 M)²
Solving for k:
k = (1.6 x 10⁻³ M/s) / (0.11 M)² = 0.1395 x 10⁻³ M⁻¹ s⁻¹
So the rate constant for a second order reaction in A is 0.1395 x 10⁻³M⁻¹ s⁻¹.
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Calculate the double integral.∫∫R 8x/1+xydA ; R = [0,8]×[0,1]
The double integral ∫∫R 8x/1+xydA ; R = [0,8]×[0,1] is evaluated using the iterated integral formula, and the value of the integral is found to be 5.99146454710798.
The double integral can be calculated using the iterated integral formula:
∫∫R 8x/1+xydA = ∫0,1 ∫0,8 8x/1+xydxdy
= ∫0,1 [8x/1+xydx]|0,8dy
= ∫0,1 [8ln(1+8y) - 8ln(1+0)]dy
= 8ln(1+8) - 8ln(1)
= 8ln(9) - 8ln(1)
= 8ln(9)
= 5.99146454710798
The double integral is calculated by transforming it into an iterated integral. This is done by evaluating the inner integral first and then the outer integral. The inner integral is evaluated by using the fundamental theorem of calculus and the outer integral is evaluated by substituting the upper and lower limits of the integral. Finally, the value of the double integral is calculated by subtracting the expression for the lower limit from the expression for the upper limit.
The double integral ∫∫R 8x/1+xydA ; R = [0,8]×[0,1] is evaluated using the iterated integral formula, and the value of the integral is found to be 5.99146454710798.
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How do you add all the numbers from 1 to 500?
Answer:
125250
Step-by-step explanation:
a(1)=1a(n)=500n=(500-1)+1S(n)=( (a(1) + a(n)) ×500 ) ÷ 2
S(500) = (501 ×500) ÷ 2 = 125250
ABOVE 6-3 Practice Square Root Functions and Inequalities Graph each function. State the domain and range. State the vertex. 1. y = 5x 2. y=-x-1 3. y=2 /x +2 1Y o O 4. y -V3x - 4 6. y - 1 - 2x +3 5, y= (x +7-4 ty HY O O lo 0
The graph of the square root function is attached.
What are Domain and Range?A relation's domain and range are established, and they consist of all ordered pairs' x- and y-coordinate sets, respectively.
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function.
Given functions, we can find the domain and range from the curve,
y = √(5x)
graph in Red line,
from curve domain (0, ∞)
range (0, ∞)
y = -[tex]\sqrt{x - 1}[/tex]
graph in blue line,
domain(1, ∞)
range (-∞, 0)
vertex (1, 0)
y = 2[tex]\sqrt{x + 2}[/tex]
graph in green line,
domain (-2, ∞)
range (0, ∞)
vertex (-2, 0)
y = [tex]\sqrt{3x - 4}[/tex]
graph in purple line,
domain (4/3, ∞)
range (0, ∞)
vertex(4/3, 0)
y = [tex]\sqrt{x+ 7}[/tex] - 4
graph in black line,
Domain (-7, ∞)
range (-4, ∞)
vertex (-7, -4)
y = 1 - [tex]\sqrt{2x + 3}[/tex]
graph in orange line,
Domain(-3/2, ∞)
range (-∞, 1)
vertex (-3/2, 1)
Hence the domain and range of functions are as follows.
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A sphere and a right cylinder have the same radius and volume. The cylinder has a height of 9 inches. Find the radius.
4)Kelly and her friends ordered fries and milkshakes at a diner. They ordered 3 plates of
fries and 5 milkshakes. Each plate of fries cost $4, and each milkshake cost $7. How much
did they spend in all?
Answer:
$47
Step-by-step explanation:
(3 plates)($4/plate) + (5 shakes)($7/shake) = $47
4. An artice marked at Rs.800 sold at a
Discount of 10%.Find its cost
price, if the dealer makes a profit of. 20% , also find its profit
The profit is Rs. 200.
What is discount?The pricing system in which a commodity's (goods or services') price is lower than its listed price is referred to as a "discount." Simply put, "discount" refers to a percentage of the advertised price. A discount is a type of price reduction on products that is seen in consumer transactions. In these transactions, buyers propose a percentage of rebates on various products to increase sales. A discount is the seller's offer of a discount to the buyer.
Given marked price = Rs. 800
discount % = 10%
discount = 10% of 800
discount = 800 x 0.1 = 80
selling price = marked price - discount
selling price = 800 - 80 = Rs. 720
The dealer makes a profit of 20% means is selling the article at 120%.
120%=720
1%=6
Hence, 100%=600
Thus, the cost price of article= 600
profit = SP - CP = 800 - 600
profit = Rs. 200
Hence profit is Rs. 200.
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Type the correct answer in each box.
Consider this expression.
3x/x+2 + 4x/x-2
Find the values for a, b, and c that make this expression equivalent to the given expression.
Ax^2+bx/x^2+c
A= , b= , and c =
The required values are a = 7, b = -2, and c = -4 to make the given expression equivalent to the given expression.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Consider expression.
3x/(x+2) + 4x/(x-2)
To begin, we factor out an x from both numerators:
3x/(x+2) + 4x/(x-2) = x(3/(x+2) + 4/(x-2))
Then, factor out a common denominator from the two terms in the parentheses:
x(3/(x+2) + 4/(x-2)) = x((x-2)(3/(x+2)) + (x+2)(4/(x-2)))
Then, we can expand and simplify:
x((x-2)(3/(x+2)) + (x+2)(4/(x-2))) = (7x² - 2x)/(x² - 4)
Therefore, we can set a = 7, b = -2, and c = -4 to make the given expression equivalent to the given expression.
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Mrs. Bowlin organized the glue sticks into 7 bins. How many glue
sticks were in each bin? ANSWER QUICKLY PLEASE ANYONE
Answer:
35
Step-by-step explanation:
245 divided by 7 = 35
Answer:
Yeah if she has 245 glue sticks and put the glue sticks in 7 bins ofc we are going to be dividing.
Step-by-step explanation:
245 divided by 7 = 35
Describe an algorithm that takes as input a list of n integers and produces as output the largest difference obtained by subtracting an integer in the list from the one following it.
The conductance of a conductor is inversely related to the cross-sectional area of the conductor.
Conductance is directly related to the ease offered by any material to the passage of electric current. Conductance is the opposite of resistance. The higher the conductance, the lower the resistance, and vice versa, the greater the resistance, the less conductance, so both are inversely proportional
Refer to this complete questionWhich of the following describes the relationship of conductance to a conductor?
The conductance of a conductor is directly proportional to the length of the conductor.
The conductance of a conductor is directly proportional to the cross-sectional area of the conductor.
The conductance of a conductor is inversely proportional to the square of the length of the conductor.
The conductance of a conductor is inversely proportional to the cross-sectional area of the conductor.
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Todd and his friends are painting 5 equal sections of a wall. The wall is 10 feet tall, but its length is unknown.
Each section will be a different color, so they need to know the area of each section.
1. Write an expression for the total area of the wall. Explain how you came up with your expression. (3 points)
2. To find the area of each section, what do you need to do to the total area? (3 points)
3. Write an expression for the area of each section of the wall. (4 points)
5(10x) is the expression for the total area of the wall, the total area you just need to divide by five to find the area of each section and 10x is an expression for the area of each section
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that Todd and his friends are painting 5 equal sections of a wall.
The wall is 10 feet tall, but its length is unknown.
Let the unknown length is x
Expression for the total area of the wall is 5(10x)
To get area you do like the times width so it’s 10 times X and theres five sections
If you have the total area you just need to divide by five to find the area of each section
10x is an expression for the area of each section of the wall because it’s just the length times the width of the wall segment
Hence, 5(10x) is the expression for the total area of the wall, the total area you just need to divide by five to find the area of each section and 10x is an expression for the area of each section
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When renting a limo for prom, the number of people is inversely proportional to the cost per person. Originally there were 3 people and the cost per person was $72. If the number of people changed to 12, what would be the new cost per person?
If the number of people changed to 12, the new cost per person is equal to $18.
What is an inverse variation?In Mathematics, an inverse variation can be modeled or represented by this mathematical expression:
p ∝ 1/c
p = k/c
Where:
p represents the number of people.c represents the cost per person.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) by substituting the value of the given variable as follows:
k = pc
k = 3(72)
k = 216
Now, we can determine the value of c:
c = k/p
c = 216/12
c = $18.
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What is the slope of the line?
-1/4 is the slope of the line draw in the graph.
What is the slope?An indication as to how sharp a line is its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).
The ratio of the increase in elevation between two places to the run in elevation between those same two points is referred to as the slope.
Slope-related equations The "change in y" over the "change in x" of a line is referred to as the slope. By dividing (y₂ - y₁) over (x₂ - x₁) and choosing two locations on the line (x₁, y₁) and (x₂, y₂), you can get the slope.
Slope = (y₂ - y₁) / (x₂ - x₁)
Here, (x₁, y₁) = (4,0)
(x₂, y₂) = (0,1)
Thus, slope = (1 - 0) / (0 - 4)
slope = - 1/4
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Mandy bought p notebooks for the first day of school. She gave her brother 4 of the notebooks. Mandy had more than 3 notebooks left. Which inequality represents p, the number of notebooks Mandy bought?
Answer: 8 or more, There is no exact number.
Step-by-step explanation:
4 - p = -4
then to get to greater than 3, you have to do -4 + 8 = 4
So Mandy bought 8 or more notebooks
