4. A local video store has seen good linear growth in rentals since 2005. In 2009, the store had
23,500 rentals. In 2015, the store had 28,540 rentals.
a. Find the average rate of change of the store's rentals in rentals per year.
b. Using the average rate of change, determine the number of rentals in 2005.
The average rate of change of the store's rentals in rentals per year is 840 rentals per year and the number of rentals in 2005 is 20,140.
According to the question,
We have the following information:
A local video store has seen good linear growth in rentals since 2005. In 2009, the store had 23,500 rentals. In 2015, the store had 28,540 rentals.
a) Average rate of change of store's rentals =(Rentals in 2015-rentals in 2009)/Number of years
Now, the number of years passed between 2009 and 2015 is 6 years.
So, we have:
Average rate of change = (28540-23500)/6
Average rate of change = 5040/6
Average rate of change = 840 rentals per year
b) Now, the number of rentals in 2005:
(Number of rentals in 2009-number of rentals in 2005)/4 = 840
Let's take the number of rentals in 2005 to be x.
(23500-x)/4 = 840
23500-x = 3360
-x = 3360-23500
-x = -20140
x = 20,140
Hence, the average rate of change of the store's rentals in rentals per year is 840 rentals per year and the number of rentals in 2005 is 20,140.
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Critique Reasoning An office manager has $10,000 to spend on new equipment. He planned to purchase 300 lamps for $72 each. He completed the calculations at the right and concluded that there would be plenty of money left to buy additional equipment. 4. What does the office manager do to support his thinking?
The probability that the sum of the two die rolls is 9 is 4 / 11.
What is the probability?Probability determines the chances that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability that the sum of the two die roll is 9 = number of sides that roll a sum of 9 / total number of sides that at least one of them is a 5
number of sides that roll a sum of 9 =(4,5) (6 , 3), (3 , 6), ( ,4) = 4
total number of sides that at least one of them is a 5 = (1, 5), (2, 5), (3, 5), (4, 5) , (5, 5), (6, 5), (5, 1), (5, 2) , (5, 3), (5, 4), (5, 6) = 11
Probability that the sum of the two die roll is 9 = 4/11
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The office manager will either put up a clearer calculation and model the equation to ascertain money remaining at each quaintly bought or a graph to present his calculations
What is a graph ?A graph is a representation of data, it helps to analyze data clearly with lesser time
The calculation the office manager will do is to multiply the number of lamps with the unit price then subtract from the amount set aside to spend on new equipment
The calculation
let the money left be z
10000 = 300 * 72 + z
10000 = 21600 + z
subtraction
z = 10 000 - 21600
z = - 16000
The calculation shows that the money will not be enough
The equation is modeled as
y = 10000 - 300x
where x is the number of bulbs
y is amount left
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The distance from -8 to 0 is the same as the distance from 8 to 0 on the number line
The distance from -8 to 0 is the same as the distance from 8 to 0 on the number line which is 8 units.
According to the question,
We have the following information:
The distance from -8 to 0 is the same as the distance from 8 to 0 on the number line.
We know that the distance can not be negative in any case even when the points given are negative.
So, when we find the distance from -8 to 0, then we have the distance as 8 units.
Now, when we find the distance from 8 to 0, then we have the distance as 8 units.
Hence, the distance from -8 to 0 is the same as the distance from 8 to 0 on the number line which is 8 units.
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Which integer makes the following sentence true? -10 < ? < -1
Answer:
Below
Step-by-step explanation:
Any of the following
-9 -8 -7 -6 -5 -4 -3 -2
kaitlin deposited $4000 into an account with 5.2% interest,compounded annually. assuming that no withdrawals are made,how much will she have in the account after 3 years?
Kaitlin will have $4657 as the total amount in her account after 3 years which was found using the compound interest formula.
What exactly is Compound Interest?
The interest earned on savings that is computed using both the original principle and the interest accrued over time is known as compound interest. The compound interest formula is calculated as: A = P (1+r)^tGiven: Kaitlin put $4000 into an account earning 5.2% annual compound interest.
We need to find how much will she have in the account after 3 years.
Let,
P = initial sum of money
r = interest rate,
t = number of years in decimal form
A = total amount in her account
Using the compound interest formula we obtain,
A = P (1+r)^t
A = 4000(1 + 0.052)³
A = 4000(1.052)³
A = 4000(1.164)
A = $4657
Therefore, Kaitlin will have $4657 as the total amount in her account after 3 years.
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n is an odd number.
Which statements are true?
You must get them all correct to get any marks.
A: n²+2 is odd
B: n(n + 1) is odd
D: n² + 1 is odd
E: n(n + 2) is odd F: (n + 2)² is odd
C: (n+1)² is odd
The following statements are marked true or false accordingly
A: n²+2 is odd true
B: n(n + 1) is odd false
C: (n+1)² is odd false
D: n² + 1 is odd false
E: n(n + 2) is odd true
F: (n + 2)² is odd true
How to show the statementsExamples are used to support or counter the statements
A: n²+2 is odd
3^2 + 2
= 9 + 2
= 11 (true)
B: n(n + 1) is odd
= 5(5+1)
= 5 * 6
= 30 (false)
C: (n+1)² is odd
= (7 + 1)^2
= 64 (false)
D: n² + 1 is odd
= 9^2 + 1
= 81 + 1
= 82 (false)
E: n(n + 2) is odd
= 3 ( 3 + 2)
= 3 (5)
= 15 (true)
F: (n + 2)² is odd
= (13 + 2)²
= 225 (true)
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Kathleen’s grandfather has a very old pet tortoise. He told Kathleen that the tortoise was 61 years old when she was born 10 years ago. Kathleen is amazed and wants to know how old the tortoise is now. Write an equation Kathleen can use to find the tortoise’s age t and solve.
Answer:
t - 10 = 61
Step-by-step explanation:
We are given that the tortoise was 61 years old 10 years ago. Let's suppose that t is the tortoise's current age. We can then write the equation t - 10 = 61
so t = 71.
The distance covered by a car traveling at a constant speed is directly proportional to the
time spent traveling. If the car goes 75 miles in 2.5 hours, how far will it go in 7 hours?
Answer:75/5 = x/7
Step-by-step explanation:
Complete this equation and you will end up with the answer 105
Amanda is on a swim team. Each day she swims 800 meters. How much is this in kilometers if 1 kilometers be is equal to 1000 meters
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each set of prices with the correct percent of increase or decrease.
11% decrease
11% increase
8.7% decrease
7.4% increase
8% decrease
12.4% decrease
9.9% increase
8% increase
original price: $63.00
new price: $56.07
arrowRight
original price: $98.00
new price: $108.78
arrowRight
original price: $37.50
new price: $34.50
arrowRight
original price: $12.25
new price: $13.23
arrowRight
Each set of prices should be matched with the correct percentage of increase or decrease as follows:
12.4% decrease = original price: $63.00 and new price: $56.07.11% increase = original price: $98.00 and new price: $108.78.8.7% decrease = original price: $37.50 and new price: $34.50.8% increase = original price: $12.25 and new price: $13.23.How to calculate percentage change?Mathematically, percentage increase can be calculated by using this formula:
Percentage increase = [original price - new price]/new price × 100
At original price: $63.00 and new price: $56.07, we have:
Percentage decrease = [63.00 - 56.07]/56.07 × 100
Percentage decrease = 6.93/56.07 × 100
Percentage decrease = 0.124 × 100
Percentage decrease = 12.4%.
At original price: $98.00 and new price: $108.78, we have:
Percentage increase = [108.78 - 98.00]/98.00 × 100
Percentage increase = 10.78/98.00 × 100
Percentage increase = 0.11 × 100
Percentage increase = 11%.
At original price: $37.50 and new price: $34.50, we have:
Percentage decrease = [37.50 - 34.50]/34.50 × 100
Percentage decrease = 3/34.50 × 100
Percentage decrease = 0.087 × 100
Percentage decrease = 8.7%.
At original price: $12.25 and new price: $13.23, we have:
Percentage increase = [13.23 - 12.25]/12.25 × 100
Percentage increase = 0.98/12.25 × 100
Percentage increase = 0.08 × 100
Percentage increase = 8%.
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Write an equation and solve:
Sandy has $60 and saves $10 a month. Randy has
$45 and saves $20 per month. After how many
months will they have the same amount of
money?
Answer:
3/2 month
Step-by-step explanation:
Write an equation and solve: Sandy has $60 and saves $10 a month. Randy has $45 and saves $20 per month. After how many months will they have the same amount of money?
When x = months:
Sandy: 10x + 60
Randy: 20x + 45
You are looking for x when:
Sandy = Randy
10x + 60 = 20x + 45
subtract 45 from both sides:
10x + 60 - 45 = 20x + 45 - 45
10x + 15 = 20x
subtract 10x from both sides:
10x + 15 - 10x = 20x - 10x
15 = 10x
divide both sides by 10:
15/10 = 10x/10
x = 15/10
reduce:
x = 3/2
It will take 3/2 months of Sandy and Randy to have the same amount of money.
[3/2 month also equals 1.5 months, depending on the format of the answer you need]
Consider the graph of a function that is negative over its entire domain. Can the graph have an X-intercept? Explain
A function that is negative over its entire domain can be having its values of x and y negative i.e. it can be (-3,-4). Yes, the graph has an X-intercept.
A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.
X-intercept illustration:
Where a line on a graph crosses the x-axis is known as the x-intercept. At that time, the y coordinate's value is zero. For instance, the x-intercept would be where the equation y = x + 5 crosses the x-axis at the location (-5, 0).
Calculate the x-intercept:
We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.
An illustration of y-intercept:
This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).
If we can locate the x-intercept of a linear function, finding the zero should be simple. The x-coordinate of the x-intercept is zero.
The x-intercept can be positive or negative.
Summary:
The location on the graph where our line crosses the x-axis is known as the x-intercept.
Positive numbers are to the right of the origin and negative numbers are to the left of the origin on the x-axis.
The location on the graph where our line crosses the y-axis is known as the y-intercept.
The side of a graph is negative:
Consider the numbers as being on the x-axis to help us remember this. The positive values are located to the right of the origin, and the negative values are located to the left of the origin.
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Complete the number sentence:
-show your work-
-7 -6=?
?-(-6)=1
32-33=?
12-?=21
In hypothesis testing,the assumption(s) for the Z test for a Mean when the σ is known The sample is a random sample Either n > or = 25 or the population is normally distributed if n < 25 both a) and b) none of the above
In hypothesis testing, the assumption for the Ztest for a mean when the σ is known then n > 30. Hence the answer is : None of the above
What is hypothesis?Using sample data, hypothesis testing is used to assess the plausibility of a hypothesis. Given the data, the test provides evidence for the hypothesis's plausibility.
Statistical analysts put a hypothesis to the test by measuring and examining a random sample of the population under consideration. Because the distributions of small samples are not normal, a t-test is required. If the sample size is large (n> 30), statistical theory predicts that the sample mean is normally distributed and that a z test for a single mean can be used.
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(18x³ - x² + 9x - 3) and (5x³ + 6x² - 14x +11) Add the polynomials (Provide only the coefficients. If a coefficient is negative, include the negative sign on the left side of the number. Do not type 'plus' sign)
Answer: put it in a caculator
Step-by-step explanation:
Combine 18x^3 and 5x^3.
23x³ - x² + 9x-3 + 6x² - 14x+11Combine x^2 and 6x^2.
23x³ + 5x² + 9x -3 - 14x + 11Combine 9x and −14x.
23x³ + 5x² + -5x -3 + 11Add −3 and 11.
23x³ + 5x² -5x + 8If 20 g of pure drug are added to a container of sterile water, and the total volume of this solution is 50 mL, what would be the strength of this solution expressed as a ratio and as a percent?
The strength of the solution is 2:5 g/ml expressed as a ratio and the strength expressed as percent is 20%
Total amount of drug = 20 gm
Total volume of solution = 50ml
Strength (as ratio)
= 20/50 g/mL
= 0.4 g /mL
Amount of drug = M = 20 g
Volume of solution = V = 50 mL
Concentration or strength (ratio) = M/V = 0.4 g/mL
Concentration or strength (percent)
= M/V × 100
=20/50 × 100%
= 40%
The concentration is 40% expressed as a percentage.
Solution concentration is the perfect measurement of how much of the solute has been dissolved in a particular amount of solvent or solution.
A solution that contains a large amount of the dissolved solute is said to be highly concentrated. A solution that contains only a small quantity of dissolved solute is said to be diluted.
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a sponsor of one person walking in a charity walkathon will donate 7 plus an additional .25 for each mile a person walks. which of the following functions , d, models the total amount , in dollars that the sponsor will donate to teh charity when the person walks m miles?
The function that models the total amount, in dollars, that the sponsor will donate to the charity when the person walks m miles is F(d) = 7 + 0.25m.
What is a function?Mathematically, a function is an expression involving two or more variables (independent and dependent) showing that a mathematical relationship exists between the expressions.
Functions use the equation symbol to show that the expressions are equal when the variables are substituted with integers.
Every function has a domain (input variable) and a range (output variable) or codomain.
Constant donation = $7
Variable donation per mile = $0.25
Function, F(d) = 7 + 0.25m
where d = the total amount donated
m = the total miles the person walks
Thus, the total donation made by the sponsor is represented by the function, F(d) = 7 + 0.25m.
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help please, the question in the picture
The probability of either A or B is 0.48 and the probability neither A nor B would be 0.52
What is Probability?Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event
probability A will occur pr(A) = 0.39, probability A will not occur pr(A') = 1 - 0.39 = 0.61,
Probability B will occur pr(B) = 0.42, probability B will not occur, pr(B') = 1 - 0.42 = 0.58
For mutually exclusive events if A will occur it means that B will not occur
So, probability either A or B is
= pr(A) x pr(B') + pr(B) x Pr(A')
= 0.39 x 0.58 + 0.42 x 0.61
= 0.4824 and to 2 decimal places the answer becomes 0.48
The probability neither A nor B is equal to 1 - 0.48 = 0.52
In conclusion the probability Either A or B will occur is 0.48 and the probability neither A nor B is 0.52
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NO LINKS! Please help me with this problem #3
Answer:
b) f(x) = -16x² + 8x + 30
Step-by-step explanation:
When a ball is thrown, its path of motion can be modelled as a parabola that opens downwards.
The graph of a quadratic equation f(x) = ax² + bx + c is a parabola.
If a > 0, the parabola opens upwards.If a < 0, the parabola opens downwards.Therefore, f(x) = -16x² + 8x + 30 could potentially model the time (in seconds) it takes a ball tossed from a window to touch the ground, as its graph is a parabola that opens downwards.
If this function was used to model the scenario, the height of the window above the ground would be the y-intercept (30 feet), and the time when the ball touched the ground would be the positive x-intercept (approx 1.64 s).
The temperature in the United States last night was -9℃. It is now -3℃. What was the change in temperature?
The change in temperature in United States since last night is -6 degree centigrade.
Given the temperature in United States last night is = -9 degree C
Now the temperature is = -3 degree C
So the change in temperature is given by,
= Final Temperature - Initial Temperature
= -9 - (-3)
= -9 + 3
= -6 degree C
Hence the change in temperature in United States since last night is -6 degree centigrade.
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6. You built a driveway ½ mile long to your new
house. You have an 8-foot-wide road ditch on
both sides of the road.
a. What is the total length of the road ditch?
(in ft)
b. What is the measurement in square feet of
the road ditch?
The total length of the road ditch is 1/2 mile and the measurement in square feet of the road ditch is 42,240 square feet.
According to the question,
We have the following information:
You built a driveway ½ mile long to your new house. You have an 8-foot-wide road ditch on both sides of the road.
a) Now, the length of the ditch will be equal to the length of the driveway.
Length of ditch = 1/2 mile
b) Measurement of the road ditch in square feet:
Area of rectangle = length*width
Converting length into feet:
1 mile = 5280 feet
1/2 mile= 2640 feet
Area of ditch =(2640)*8
Area of ditch =21,120 square feet
Now, ditch is on both sides:
So, total area of ditch = 2*21,120
Total area of ditch = 42,240 square feet
Hence, the total length of the road ditch is 1/2 mile and the measurement in square feet of the road ditch is 42,240 square feet.
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Figure ABCD is reflected across the x-axis.
What are the coordinates of
of A'B'C', and D'₂
Enter your answer by filling in the boxes.
A'Go
B'GD
C'OD
D'OD
Answer: The required vertices after reflection are A'(2, -3), B'(5, -5), C'(7, -3) and D'(5, -2).
Step-by-step explanation: Given that the figure ABCD is reflected across the X-axis.
We are to find the co-ordinates of A, B, C and D after reflection.
From the figure, we note that the co-ordinates of the vertices of ABCD are
A(2, 3), B(5, 5), C(7, 3) and D(5, 2).
After reflection from X-axis, the y co-ordinate of each vertex will change its sign (y → -y).
Therefore, the vertices of ABCD after reflection are
A(2, 3) ⇒ A'(2, -3),
B(5, 5) ⇒ B'(5, -5),
C(7, 3) ⇒ C'(7, -3),
D(5, 2) ⇒ D'(5, -2).
Thus, the required vertices after reflection are A'(2, -3), B'(5, -5), C'(7, -3) and D'(5, -2).
Monica’s dose from the fluoroscopy tower, at a distance of 9 feet, is 100 mR/hr. What is the radiation intensity, in Roentgens, at 1 foot from the fluoroscopy tower?
The radiation intensity, in Roentgens at a distance of 1 foot is 8.1 R/hr
How to the radiation intensity, in Roentgens?
Radiation intensity is defined as the radiation energy that strikes in one second upon a surface of 1 square unit perpendicular to the direction of the ray
The equation below relates the radiation intensity and distance:
I₁/I₂ = D₂²/D₁²
where: I₁ = intensity at distance 1, I₂ = intensity at distance 2, D₁ = distance 1 from source and D₂ = distance 2 from source
Given: D₁ = 9 feet, I₁ = 100 mR/hr and D₂ = 1 foot
Using the formula:
100/I₂ = 1²/9²
100/I₂ = 1/81
I₂ = 100 × 81
I₂ = 8100 mR/hr
I₂ = 8100×10⁻³ R/hr (1 mR/hr = 1×10⁻³ R/hr)
I₂ = 8.1 R/hr
Therefore, the radiation intensity in Roentgens is 8.1 R/hr
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Kristen's Blossoms sells roses in groups of 8. Across town, Hector's Blooms sells roses in groups of 12. If a customer wants to buy the same number of roses from both vendors, what is the smallest number of roses the customer will have to buy from each vendor?
The smallest number of roses the customer will have to buy from each vendor is 24.
What is a multiple?It should be noted that the multiple simply means the product of a number.
In this case, Kristen's Blossoms sells roses in groups of 8 and across town, Hector's Blooms sells roses in groups of 12.
The multiples of 8 = 8, 16, 24, 32 ....
The multiples of 12 = 12, 24, 36...
Therefore, the least number of roses is 24.
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For the following, based on the information given which would you use to find the missing variable?
The missing variables are b, x, x and y are 3.73m, 7.88 units, 41.06 units and 8.94 units respectively
How to find the missing variables?We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent or tan = sin/cos
The opposite is the side the angle of consideration is facing
The hypotenuse is the side the right angle is facing
The adjacent is the side left after determining the opposite and hypotenuse
1st triangle
tan 25° = b/8 (tan = opp/adj)
b = 8 tan 25° = 3.73m
2nd triangle
sin 21° = x/22 (sin = opp/hyp)
x = 22 sin 21° = 7.88 units
3rd triangle
cos 47° = 28/x (cos = adj/hyp)
x = 28/cos 47° = 41.06 units
4th triangle
Use Pythagoras' theorem:
12² = 8² + y²
y² = 12² - 8²
y² = 144 - 64
y² = 80
y = √80 = 8.94 units
Therefore, the missing variables are b = 3.73m, x = 7.88 units, x = 41.06 units and y = 8.94 units
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Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question.
Listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. What do the results tell us?
70 54 46 85 61 81 45 6 35 39 3
The mean is 47.73.
The median is 46.
The dataset has no mode.
The midrange is 44.
What is the mean, mode, median and midrange?
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number
Mean = sum of the numbers / total number
Mean = (70 + 54 + 46 + 85 + 61 + 81 + 45 + 6 + 35+ 39 + 3) / 11
= 525 /11 = 47.73
Median is a measure of central tendency that is used to determine the number that is at the center of a set of values when the numbers are arranged in either ascending or descending order.
3, 6, 35, 39, 45, 46, 54, 61, 70, 81, 85
The median is 46.
Mode is the most frequent number in a dataset. The jersey numbers only occur once. Thus, there is no mode.
Midrange is the average of the maximum and minimum values of the dataset.
Midrange = (maximum value + minimum value) / 2
Midrange = (3 + 85) / 2
Midrange = 88 / 2
Midrange = 44
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Help i need it fast!
Benjamin went shopping for a new phone because of a sale. The price on the tag was $28, but Benjamin paid $15.40 before tax. Find the percent discount.
if price on the tag was $28, but Benjamin paid $15.40 before tax then the percent of discount is 45%.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Benjamin went shopping for a new phone because of a sale. The price on the tag was $28, but Benjamin paid $15.40 before tax
We need to find the percent discount that Benjamin received
Compare the difference between the original price and the discounted price to the original price, and then express that difference as a percentage of the original price.
We can use the following formula:
Percent Discount = (Original Price - Discounted Price) / Original Price × 100%
=28-15.4/28 × 100
=0.45×100
=45%
Hence, Benjamin received a discount of 45%
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Complete the table representing a linear function.
hint:Use the rate of change to find the missing values.
hint:Find the rate of change using change in y divided by change in x.
After finding the rate of change, this table representing a linear function can be completed as follows:
x y
1 0
2 10
5 40
10 90
What is the rate of change?Mathematically, the rate of change can be calculated by using this formula;
Rate of change, k = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, k = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the value of y with respect to the value of x as follows:
Rate of change, k = (40 - 0)/(5 - 1)
Rate of change, k = 40/4
Rate of change, k = 10.
For the first blank, we have:
10 = (40 - y)/(5 - 2)
10 = (40 - y)/3
30 = 40 - y
y = 40 - 30
y = 10.
For the second blank, we have:
10 = (90 - 40)/(x - 5)
10 = (50)/(x - 5)
10x - 50 = 50
10x = 50 + 50
10x = 100
x = 10.
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Find the discriminant of -18p=p^2+81
Step-by-step explanation:
[tex] \sf - 18p = p^2+81 [/tex]
Moving all the expression to the Left side of the equation,
[tex] \sf -18p + p^2 - 81 = 0 [/tex]
To find the discriminant of the above equation we can simply use the Quadratic formula.
The discriminant formula of a quadratic equation[tex] \sf ax^2 + bx + c = 0 \: is \: (d = b^2 - 4ac )[/tex]
Where d represents the discriminant
a, b and c are the coefficient of the above equation,
p^2, here coefficient of p² is a = 1
-18p, here coefficient of p is b = -18
81, here the number is constant so coefficient is c = 81.
So simply by substituting the value of a, b and c in the above discriminant formula we get,
[tex] \sf d = b^2 - 4ac [/tex]
[tex] \sf d = (-18)^2 - (4 \times 1 \times 81) [/tex]
[tex] \sf d = 324 - 324[/tex]
[tex] \sf d = 0 [/tex]
Therefore, The discriminant of 18p = p² + 81 is 0.
Answer:
0 (zero)
Step-by-step explanation:
To find the discriminant of the quadratic equation -18p = p² + 81, we first need to rewrite the equation in standard form, which is of the form ax² + bx + c = 0.
[tex]\begin{aligned}-18p&=p^2+81\\p^2+81&=-18p\\p^2+81+18p&=-18p+18p\\p^2 + 18p + 81 &= 0\end{aligned}[/tex]
Compare the coefficients of the rewritten quadratic equation with the standard form:
a = 1b = 18c = 81The discriminant of a quadratic equation in the form ax² + bx + c = 0 is given by the formula:
[tex]\boxed{\textsf{Discriminant} = b^2 - 4ac}[/tex]
Substitute the values of a, b, and c into the formula:
[tex]\begin{aligned}\textsf{Discriminant} &= (18)^2 - 4(1)(81)\\&=324-4(81)\\&=324-324\\&=0\end{aligned}[/tex]
Therefore, the discriminant of the given quadratic equation is zero.