the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 7x^2-6 \qquad \begin{cases} x_1=4\\ x_2=b \end{cases}\implies \cfrac{f(b)-f(4)}{b - 4} \\\\\\ \cfrac{(7b^2-6)~~ - ~~(7(4)^2-6)}{b-4}\implies \cfrac{7b^2-6~~ - ~~(112-6)}{b-4} \implies \cfrac{7b^2-112}{b-4}[/tex]
[tex]\cfrac{7(b^2-16)}{b-4}\implies \cfrac{7(b^2-4^2)}{b-4}\implies \cfrac{7~~\begin{matrix} (b-4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(b+4)}{~~\begin{matrix} b-4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \boxed{7(b+4)}[/tex]
This expression gives the average rate of change of the function over the interval [4, b].
How is rate of change determined?The average rate of change of a function on an interval is equal to the rise (change in the y-value) divided by the run (change in the x-value) over that interval.
For f(x) = 7x² - 6 on the interval [4, b], the average rate of change can be found by calculating the slope of the secant line connecting the points (4, f(4)) and (b, f(b)).
Therefore, the average rate of change of f(x) = 7x² - 6 on the interval [4, b] is:
(7b² - 6 - (7(4)² - 6)) / (b - 4) = (7b² - 28) / (b - 4)
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calculate the measure of x
The measure of x use Pythagorean Theorem
1. x= 15
x= 26x= 7.6About Pythagorean TheoremTh Pythagorean theorem only applies to right triangles. This is the same as explained in the Pythagorean Theorem Module which states that for each right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other side or the sides of the right angle.
Meanwhile, there is the opposite of the Pythagorean theorem which functions to determine the type of triangle if the lengths of the sides are known. The types of triangles include:
A right triangle is a triangle in which one of the angles is a right angle or equal to 90 degrees. An acute triangle is a triangle in which all three angles are acute or less than 90 degrees. An obtuse triangle is a triangle in which one of the angles is obtuse or measures more than 90 degrees.Learn more about Pythagorean theorem at
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Which of the following shows independent events?
Select the correct answer below:
drawing a jack and then drawing a 7 without replacement from a standard deck of cards
drawing a 10 and then drawing a 9 without replacement from a standard deck of cards
rolling two 4's from two rolls of a standard die
rolling a sum less than 3 from two rolls of a standard die and rolling a 1 for the second throw
Answer:
Step-by-step explanation:
evaluate, correct to four significant figure,(573.06× 184.25)
Answer:
103,847
103,847.0
Step-by-step explanation:
Step 1: Multiply the two numbers: 573.06 x 184.25 = 106,157.45
Step 2: Round the answer to four significant figures: 106,200
Ramona and Malika are walking along linear routes in their county. On a map of their county, Ramona’s route passes through the coordinates (2,1)
and (0,−2)
. Malika’s route passes through the coordinates (0,3)
and (−2,0)
. Do the friends pass through a common coordinate, walk along the same route, or never cross routes?
Explain your answer
The path's of the two persons don't cross as their lines don't intersect and thus they never cross routes.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here: Ramon's path passes through the co-ordinates (2,1)
and (0,−2) while Malika's passes through (0,3)
and (−2,0)
Thus using the two point of a line to construct the linear equations we get
Ramona's path is y=1.5x−2
Malika's path is y=1.5x+3
Now solving for the two equations we get
1.5x-2=1.5x+3
-2=3 which is not possible
Hence, The path's of the two persons don't cross as their lines don't intersect and thus they never cross routes.
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hello teacher can u help me with this
The scale on a 1:50 000 ordnance survey map indicates that 2cm on the map = 1km on the ground. How many centimetres would 1km be represented by on a 1:25 000 scale map
1km would be represented by 4cm on a 1 : 25000 scale map.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, The scale on a 1 : 50000 ordnance survey map indicates that 2cm on the map = 1km on the ground.
We know 1 km = 1×100000 = 100000 cm.
So, If 2 cm represents 100000 cm it has a scale factor of 100000/2 = 50000.
Now, Again 1 km = 100000 cm,
So, 1km will be represented by 100000/25000 = 4 cm.
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x=√40-3x can someone help solve
The solution of the given equation is x= 5 and x = -8.
What is quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. First, there must be a term other than zero in the coefficient of x^2 for an equation to be a quadratic equation. The x^2 term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term.
The given equation is x = √40 - 3x.
Square on both sides of the equation:
x^2 = (√40 - 3x)²
x² = 40 - 3x
Regroup to one side of the equation:
x² + 3x - 40 = 0
x² + 8x - 5x - 40 = 0
x(x + 8) - 5 (x+8) = 0
(x - 5)(x + 8) = 0
Equate each term to 0:
x - 5 = 0
x= 5
x+ 8 = 0
x = -8
Hence, the solution of the given equation is x= 5 and x = -8.
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The graph of a parent function is shown. Which function belongs to the same function family as the graphed function?
Answer:
I doubt I'm wrong but it's D
11 Answer:
Consecutive integers are integers that follow each other in order (for
example 5, 6, and 7). The sum of three consecutive integers is 417.
Let n be the first one. Write an equation that will determine
the three integers.
12 Answer:
Solve the equation in question #11 for the value of n.
Step-by-step explanation:
n + (n+1) + (n+2) = 417
3n + 3 = 417
3n = 414
n = 138
so, the 3 integers are
138, 139, 140
Answer:
138
Step-by-step explanation:
n,n+1,n+2
so 3n+3=417
3n=414
n=138
Sam is moving bags of soil from a loading dock into a storeroom. The topsoil
weighs 40 pounds per bag, and the mulch weighs 20 pounds per bag. The
cart Sam uses to move the bags can only carry up to 480 pounds.
Which graph represents the number of topsoil bags and mulch bags that Sam
can move in a single trip? Graphed
The inequality that can be used to represent the number of topsoil and mulch Sam can carry is, 40x + 20y ≤ 480
And, The graph which represents the number of topsoil bags and mulch bags that Sam can move in a single trip is shown in figure.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that:
Weight of top soil = 40 pounds
Weight of mulch = 20 pounds
Total weight Sam can carry = 480 pounds
Now, Let number of bags of top but soil = x
And, The number of weight of mulch = y
Hence, The inequality is,
⇒ 40x + 20y ≤ 480
Therefore, the inequality that can be used to represent the number of topsoil and mulch Sam can carry is 40x + 20y ≤ 480
And, The graph which represents the number of topsoil bags and mulch bags that Sam can move in a single trip is shown in figure.
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After a 75% reduction, you purchase a new dvd player on sale for $150. What was the original price of the dvd player ?
Step-by-step explanation:
The original price was 150 / (1 - 0.75) = $600.
Find the Profit value
if the supply cost of each electric bicycle is £950, and the company decides to set the price less than £1300, then we can repeat the above process to find the optimal price and profit.
It can be seen that the sale volume has changed according to its price in different periods. The values have been reported in the following table. This company is going to launch a new product and the price needs to be decided based on the market analysis. Determine the appropriate price for the newly developed electric bicycle with the aim of maximizing the company’s profit. The demand for new products has a direct relationship with its price.
Table 1- Demands of an electric bicycle based on a price level according to previous experiences
Price (£) Demand
1150 415
1185 405
1210 390
1235 380
1260 345
1285 302
1310 270
1335 255
1360 246
1385 240
1410 230
1435 222
1460 216
1485 214
1510 210
1540 200
The main objective of the company is to maximize profit regarding to the new product. It is assumed that the unit production and supply cost of each electric bicycle is £740, so the profit of each unit will be (the sale price – unit production cost).
Determine the optimal demand
Compute the optimal profit.
Interpret the results.
If the supply cost of each electric Bicycle is £250 and then £950 determine the optimal price and interpret the results appropriately.
Suppose that the supply cost is £950 and the company has decided to set the price less than £1300, then what will be the optimal price? Interpret the results
To find the optimal price, we need to find the price that maximizes the company's profit. Profit is calculated as (sale price - unit production cost), and we have been given the unit production cost as £740. So, the profit function can be written as:
Profit = (sale price - £740) * demand
Using the data in the table, we can plot the demand as a function of price and then calculate the profit for each price level:
Price (£) Demand Profit (£)
1150 415 121,750
1185 405 133,650
1210 390 141,600
1235 380 146,200
1260 345 140,100
1285 302 113,640
1310 270 75,600
1335 255 67,170
1360 246 66,480
1385 240 66,600
1410 230 63,700
1435 222 62,820
1460 216 62,160
1485 214 62,370
1510 210 61,500
1540 200 59,200
From the table, we can see that the maximum profit is obtained at a price of £1210, which gives a profit of £141,600. The optimal demand at this price is 390 units.
Interpretation: The company can maximize its profit by setting the price of the electric bicycle at £1210, and the optimal demand at this price is 390 units. The company can earn a profit of £141,600 if it sells 390 electric bicycles at this price.
If the supply cost of each electric bicycle is £250, then the profit function becomes:
Profit = (sale price - £250 - £740) * demand
Profit = (sale price - £990) * demand
Using the same method as before, we can calculate the profit for each price level:
Price (£) Demand Profit (£)
1150 415 157,450
1185 405 169,950
1210 390 177,300
1235 380 181,300
1260 345 174,150
1285 302 146,890
1310 270 110,250
1335 255 96,525
1360 246 95,040
1385 240 95,400
1410 230 92,400
1435 222 91,512
1460 216 90,720
1485 214 91,422
1510 210 89,100
1540 200 85,600
The maximum profit is obtained at a price of £1210, which gives a profit of £177,300. The optimal demand at this price is 390 units.
Interpretation: If the supply cost of each electric bicycle is reduced to £250, then the optimal price remains the same as before at £1210. However, the maximum profit increases to £177,300, which is an increase of £35,700 compared to the previous scenario.
If the supply cost of each electric bicycle is £950, and the company decides to set the price less than £1300, then we can repeat the above process to find the optimal price and profit.
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Last year at a certain high school, there were 95 boys on the honor roll and 64 girls on the honor roll. This year, the number of boys on the honor roll increased by 20% and the number of girls on the honor roll increased by 25%. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
Answer:
1.9 percent
Step-by-step explanation:
95 boys + 64 girls = 159 total honor roll students
To quickly find percentages of numbers, think of the current number as 100%, or 1.00. Then, go from there to find the number to multiply to get the percentage you need.
For example, a 25% decrease in the number of girls means the new number will be 75% of the old number, so we multiply the number of girls by 0.75 to get the new number of girls. 64*0.75 = 48.
Same with the boys, 95 boys is 100%, but this year the number increased by 20%, so we need to find 120% of the number, so we multiply it by 1.20. 95*1.20 = 114
To answer this question, we need to know by what percent the total number of honor students increased by, so we need to know the new total number. 48+114 = 162
To find out what percent 162 is out of 159, we divide them. 162 / 159 = 1.0188, or 101.9 percent if you round to the nearest tenth. So, the number of students increased by 1.9%.
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Assume an exponential function has a starting value of 14 and a decay rate of 42%. Write an equation to model the situation.
The equation is y=
The equation to model the situation will be written as y = 14 × (0.58)ˣ.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
y = a (1 ± r)ˣ
Assume an exponential function has a starting value of 14 and a decay rate of 42%. Then the equation is given as,
y = 14 × (1 - 0.42)ˣ
y = 14 × (0.58)ˣ
The equation to model the situation will be written as y = 14 × (0.58)ˣ.
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In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 23% of your total grade, each major test is worth 21.5%, and the final exam is worth 34%. Compute the weighted average for the following scores: 94 on the lab, 89 on the first major test, 63 on the second major test, and 73 on the final exam. Enter your answer as a whole number.
Answer: 79
Step-by-step explanation: The weighted average for the scores can be calculated as follows:
Lab score: 94 x 0.23 = 21.62
First major test: 89 x 0.215 = 19.135
Second major test: 63 x 0.215 = 13.495
Final exam: 73 x 0.34 = 24.82
Total weighted average: 21.62 + 19.135 + 13.495 + 24.82 = 78.976
Rounding to the nearest whole number, the weighted average is 79.
will give brainliest to correct answer
The sequence that represents the arithmetic sequence will be {-6, 1, 8, 15, 22,...}. Then the correct option is A.
What is an arithmetic sequence?Arithmetic succession or arithmetic sequential is a numerical series in which the difference between subsequent terms is uniform.
Let's check all the options, then we have
A. {-6, 1, 8, 15, 22,...}, then the common difference is given as,
d = 1 - (-6) = 8 - 1 =
d = 7 = 7
B. {64, 32, 16, 8, 4,...}, then the common difference is given as,
d = 32 - 64 = 16 - 32
d = -32 ≠ - 16
C. {1, 2, 4, 8, 16,...}, then the common difference is given as,
d = 1 - 2 = 2 - 4
d = - 1 ≠ - 2
D. {1, 3, 6, 10, 15,...}, then the common difference is given as,
d = 1 - 3 = 3 - 6
d = - 2 ≠ - 3
The sequence that represents the arithmetic sequence will be {-6, 1, 8, 15, 22,...}. Then the correct option is A.
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Anyone know how to do math work like this?? I'm
Answer: IT IS EZ IT JS 67 AND 194
Step-by-step explanation
Please help me thank you so much!
Answer:
It's the second one because -3x3-5 equals -14
what's 5 plus 5 guys I'm so tired
Answer: it think 10
Step-by-step explanation:
and Get some sleep bro
Answer: 10
Step-by-step explanation:
5+5=10
The area of the circular base of a cone is 16π cm², and the slant height of the cone is 4 times the radius of the cone.
What is the approximate lateral area of the cone?
The approximate lateral area of the cone is equal to 200.96 cm².
How to calculate the lateral area of the cone?Mathematically, the lateral area of a cone can be calculated by using this mathematical expression:
Lateral surface area of a cone, LSA = πrl or πr√(r^2 + h^2)
Where
l represents the slant height of the cone.r represents the radius of the cone.h represents the height of the cone.How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this formula:
Area of a circular base = πr²
16π = πr²
Radius, r = √16
Radius, r = 4 cm.
Substituting the given parameters into the lateral area of a cone formula, we have the following;
Lateral surface area of a cone, LSA = πrl = πr4(r)
Lateral surface area of a cone, LSA = 3.14 × 4 × 16
Lateral surface area of a cone, LSA = 200.96 cm².
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Answer:
201 beause you are rounding to the nearest whole number
Step-by-step explanation:
Peter recorded the snowfall each winter in New York for the last 4 years. He predicts that the snowfall change from year 4 to year 5 will be twice as much as the change was from year 3 to year 4. Plot ONE point on the graph that could represent Peter’s prediction for the snowfall in New York in year 5.
Plot the point on the coordinate grid below. You must graph the specified number of points; any other graphed points will cause all points to be scored as incorrect.
The snowfall change is plotted on the graph attached with the answer below.
What is coordinate geometry?A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that Peter recorded the snowfall each winter in New York for the last 4 years. He predicts that the snowfall change from year 4 to year 5 will be twice as much as the change was from year 3 to year 4.
Let the snowfall in years 3 to 4 is (2,0) so it will be in year 4 to 5 will be (4,0). Plot the two points on the graph. The graph is attached with the answer below for better understanding.
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Ms. Pesko pulled 5 candy bars out of a bag. She pulled the following candies: Twix, Kit-Kat, Milky Way, Twix, Twix. What is the experimental probablity of getting a Twix?
Answer:
Step-by-step explanation:
The experimental probability of getting a Twix is 3/5 or 60%.
If a fair die is rolled 5 times what is the probability of rolling 3 sixes to the nearest thousandth
The probability of rolling 3 sixes to the nearest thousandth is 0.556.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Using binomial distribution.
[tex]^nC_r P^cQ^{n - r}[/tex]
Now,
Probability of getting a six = 1/6
P = 1/6
Probability of not getting a six = 5/6
Q = 5/6
Now,
n = 5 and r = 3
So,
[tex]^nC_r P^rQ^{n - r}[/tex]
= [tex]^5C_3(1/2)^3(5/6)^2[/tex]
= (5 x 4)/2 x (1/2) x (1/2) x (1/2) x (5/6) x (5/6)
= 10 x 1/8 x 25/36
= 5/9
= 0.556
Thus,
The probability of rolling 3 sixes is 0.556.
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Mei Mei signed up for a streaming music service that costs $6 per month. The service allows Mei Mei to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $0.50 per song. How much total money would Mei Mei have to pay in a month in which she downloaded 35 songs? How much would she have to pay if she downloaded
�
s songs?
Answer:
She would have to pay $17.50 for 35 songs.
Step-by-step explanation:
We have the amount it costs per song (0.50), and we have the amount of songs that she wants to buy (35). If we multiply 35 the amount of songs by 0.50 the price per song, we will have a grand total of $17.50.
35 * 0.50 = 17.50
-Hope this helped
How many degrees is the peripheral angle above the circular arc that represents 4/9 of the circle
The peripheral angle above the arc would be:
160 / 2 = 80 degrees.
Solution
The peripheral angle above a circular arc is equal to the central angle subtended by the arc divided by 2.
The central angle of a circle is 360 degrees, so if the arc represents 4/9 of the circle, the central angle subtended by the arc would be:
360 * (4/9) = 160 degrees
The peripheral angle above the arc would be:
160 / 2 = 80 degrees.
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Which number line represents the solution set of the inequality -2x + 0.25 > 6.25
Answer:
Step-by-step explanation:
-2x+0.25>6.25
-2x>6
Swap the sign when you divide or multiply by a negative in an inequality.
x<-3
Option #1
HELP
______________________
Inverse of function f(x) is f⁻¹(x) = x³/125 - 7
What is inverse function?An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f⁻¹ or F⁻¹.
Given function,
f(x) = 5∛(x + 7)
f⁻¹(x) = 5∛(f(x) + 7)
Cubing both sides
x³ = 5³(f(x) + 7)
x³ = 125 (f(x) + 7)
f(x) + 7 = x³/125
f(x) = x³/125 - 7
Hence, f⁻¹(x) = x³/125 - 7 is inverse of function f(x).
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Five times the sum of a number and six is equal to eight times the number, minus six. Find the number.
Answer: x=12
Step-by-step explanation:
[tex]5(x+6)=8x-6[/tex]
On the left side of the equation, open the parentheses:
[tex]5x+30=8x-6\\\\5x+30-5x=8x-6-5x\\\\30=3x-6\\\\30+6=3x-6+6\\\\36=3x[/tex]
Divide both parts of the equation by 3:
[tex]12=x[/tex]
[tex]Thus,\ x=12[/tex]
A catapult launches a pumpkin from the base of a hill.
The height of the pumpkin is 5.7 m.
What is the height of the pumpkin?
The height of the pumpkin is calculated by applying the following formula.
y = -0.1x² + 4.9x
where;
y = 0.9x
Now, our new equation becomes;
0.9x = -0.1x² + 4.9x
re-arrange the equation, and solve for x
0.1x² = 4.9x - 0.9x
0.1x² = 4
x² = 4 / 0.1
x² = 40
x = √ ( 40 )
x = 6.32
The height of the pumpkin = 0.9x = 0.9 x 6.32 = 5.7 m
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Which of the following numbers is probably an irrational number? 0 1.6490221... 3/4 -5
The number that probably is an irrational number is 1.6490221...
How to determine the irrational numberAn irrational number is a number that cannot be expressed as a finite decimal or a fraction.
The number 0 is not irrational.
The number 1.6490221... is an example of a decimal that goes on forever, which is the characteristic of an irrational number.
The number 3/4 can be expressed as a fraction and is therefore not irrational.
The number -5 is not irrational.
Therefore, the answer is 1.6490221..., which is probably an irrational number.
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