Debemos tomar la integral definida de la diferencia entre las dos funciones en el intervalo dado.
¿Como se determina el area entre dos funciones?Supongamos que queremos encontrar el area entre dos funciones f(x) y g(x) en un intervalo (a, b).
Vamos a suponer que f(x) > g(x) en todo el intervalo (a, b), entonces el area entre la funcion f(x) y g(x) en ese intervalo se calcula como:
[tex]\int\limits^b_a {(f(x) - g(x))} \, dx[/tex]
Si por ejemplo tuvieramos que para un valor c en el intervalo (a, b) se da que:
f(x) > g(x) en (a, c)
g(x) > f(x) en (c, b)
Entonces la integral sería:
[tex]\int\limits^c_a {(f(x) - g(x))} \, dx + \int\limits^b_c {(g(x) - f(x))} \, dx[/tex]
Y similarmente si debemos separar el intervalo mas segmentos.
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19. Number Sense A company had
9 x 106 dollars in sales last year. Explain
how to find the product 9 × 106.
Answer: 954
Step-by-step explanation:
9x106 = 954
98x972-67=??????????????????????????
Answer:
95,189
Step-by-step explanation:
98x972-67
95256-67
95189
Answer:95189
Step-by-step explanation: First you ave to multiply 98 x 972 which would equal to 95256 ten subtract 67 which would give you the answer 95189
If 2 ½ teaspoons of vanilla are needed for a recipe for 18 people, how many
teaspoons of vanilla are needed for 27 people?
Answer:
3.75
Step-by-step explanation:
2.5 teaspoons for 18 people
divide by two to get
1.25 teaspoons for 9 people
9 * 3 = 27 so we multiply 1.25 by 3 to get
3.75 for 27 people
Complete the table of values for the equation 9x+2y=18
Answer:
x-intercept(s): (2,0)
y-intercept(s): (0,9)
y=−9/2x+9
x=2−2y9
Step-by-step explanation:
I don't know what else you need
Answer:
y=9
x=2
y=-9
Step-by-step explanation:
we just replace the values with whatever numbers
9(0)+2y=18
2y=18
/2. /2
y=9
9x+2(0)=18
9x=18
/9. /9
x=2
9(4)+2y=18
36+2y=18
-36. -36
2y=-18
/2. /2
y=-9
Hopes this helps please mark brainliest
Find the product, list the units. 5Ib times $6.00/Ib
Please help, 50 points & brainiest if you answer all 3!!!
9. The plane's speed would be of 340 and 350 miles per hour.
10. She runs the downhill portion of the course at a rate of 10 miles per hour.
11. The total time would be of 24 minutes.
How to obtain the velocity?
Velocity is distance divided by time, hence the equations is:
v = d/t.
For the first plane, the velocity and the distances are given by:
v = v + 10, d = 495.
Hence:
v + 10 = 495/t
t = 495/v + 10
For the second plane, the velocity and the distance are:
v = v, d = 510.
Hence:
v = 510/t
t = 510/v
The time is equal, hence the velocity of the slower plane is obtained as follows:
495/v + 10 = 510/v
Applying cross multiplication:
510v + 5100 = 495v
15v = 5100
v = 5100/15
v = 340 mph
For the runner, we have two parts, as follows:
First part: distance of 3 miles, velocity of v - 5, time of t.Second part: distance of 4 miles, velocity of v, time of 1 - t.Hence the equations are given as follows:
v - 5 = 3/t.v = 4/(1 - t).From the first equation, we have that:
v = 5 + 3/t.
Replacing in the second, we have that:
5 + 3/t = 4/(1 - t)
(5t + 3)/t = 4/(1 - t)
Applying cross multiplication, we have that:
(5t + 3)(1 - t) = 4t
-5t² + 2t + 3 = 4t
5t² + 2t - 3 = 0.
The positive solution, as time is a positive measure, of the quadratic equation is given by:
t = 0.6.
Hence the velocity of the downhill part is given by:
v = 4/(1 - t) = 4/0.4 = 10 miles per hour.
What is the together rate?The together rate is the sum of each separate rates.
The rates in this problem are given as follows:
Jason: 1/30.Kevin: 1/120.Together: 1/x.Hence:
1/x = 1/30 + 1/120
1/x = 5/120
x = 120/5
x = 24 minutes.
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Question
Write the word sentence as an equation. Then solve.
A number x divided by −9 is −16.
Equation:
Solution: x=
Answer:
Equation: x/-9 = 16
Solution: x = -144
Step-by-step explanation:
The "number x divided by -9 is 16" means x/-9 = 16, then we solve for x by multiplying both sides by "-9" to solve for x
x/-9 = 16
-9x/-9 = 16(-9)
x = -144
Kevin has a coin collection. He keeps 5 of the coins in his box, which is 25% of the collection. How many total coins are in his collection?
Answer:
20 coins
Step-by-step explanation:
[tex]\frac{5}{\frac{25}{100} }[/tex] = 20
Answer:
[tex]\huge\boxed{\sf Total\ collection = 20\ coins}[/tex]
Step-by-step explanation:
25% of the collection = 5 coins
Total collection = 100%So,
100% = 25% + 25% + 25% + 25%
100% = 5 + 5 + 5 + 5
100% = 20 coins
Total collection = 20 coins[tex]\rule[225]{225}{2}[/tex]
Last week, a florist sold 715 roses. Of the
roses sold, 7 out of every 11 roses were
red. How many red roses did she sell?
Can you please help with this question?
The flower arrangements with $200 has lower unit price than the flower arrangements with $70 unit price.
What is meant by unit price?The average price of a product is calculated by dividing the total sales income by the total number of units sold. When a same product is supplied in variants, such as bottle sizes, managers must define "similar" units. Average prices can be estimated by dividing distinct unit selling prices by the percentage of unit sales (mix) for each product variant. When we utilize a standard rather than an actual mix of sizes and product variations, the result is price per statistical unit. Statistical units are sometimes known as analogous units.
Unit price for 15 flower arrangements for $200 is,
200/15=13.33
Unit price for 5 flower arrangements for $70 is,
70/5=14
Therefore, 14>13.33
So, the flower arrangements with $200 has lower unit price than the flower arrangements with $70 unit price.
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The equation m=3b represents the times in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b) A: 3 B: 6 C:1/3 D: 1
For the given equation:
m = 3b
The constant of proportionality is 3, so the correct option is A.
How to determine the constant of proportionality?
After a small search on the internet, I've found that this question asks for the constant of proportionality.
Remember that a proportional relation is of the form:
y = k*x
Where k is the constant of proportionality, and x and y are the variables.
Here the relation is:
m = 3*b
Where m and b are the variables, then the remaining coefficient is the constant of proportionality, which is 3.
In this way, we can see that the correct option is A.
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Point C is an orthocenter. Solve for X
Look at pic thanks
In the triangle Point C is the orthocenter then the value of x will be equal to 42.
What is Orthocenter?The intersection of the cutting point of the triangle's three elevations is known as the orthocenter. The height in this instance is indeed the line to be drawn from the triangle's apex that is perpendicular to the other side.
As per the given diagram and data in the question,
The orthocenter is at Point C.
C = 3x - 36
3x - 36 = 90
3x = 90 + 36
3x = 126
x = 126/3
x = 42
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f(x) = 2x2 − 7x − 72
PLS HELP DUE TODAY!!!
The graph g has a minimum value at it's vertex, (3, -1).
What is vertex?
The point where a parabola's line of symmetry intersects with the parabola itself is known as the vertex. The vertex of a parabola whose equation is given in standard form will be the lowest point on the graph and the highest point on the graph depending on certain conditions.
The given graph g is a upward parabola.
Since the upward parabola having a minimum value at it's vertex.
And the downward parabola having a maximum value at it's vertex.
Here, the vertex of the upward parabola is, (3, -1).
Therefore, the minimum value of g is, (3, -1).
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What is an algebraic expression for 15 more than the product of 52 and a number?
52y(15)
52y + 15
52y − 15
15 − 52y
Answer:
(b) 52y +15
Step-by-step explanation:
You want an algebraic expression for 15 more than the product of 52 and a number.
ProductIf y represents "a number", then "the product of 52 and a number" can be written as ...
52 × y = 52y
MoreThe wording "15 more than ..." means the value 15 is added to the product. That makes the expression ...
(b) 52y +15
<95141404393>
Help me please its the last question before I finish.
Answer:5/2
Step-by-step explanation: Slope is rise (how far up or down) over run (how far left to right. Look for points where the line crosses a perfect grid line intersection. The graph goes up to 50 and right 20 (started at 10 and ended at 30). The rise/run is 50/20 or 5/2 reduced.
first, find two places on the line that intersects the grid boxed neatly. This occurs at (10 , 0) and (30 , 50).
slope = change in rise / change in run
slope = change in y / change in x
slope = ( 0 - 50) / (10 - 30)
slope = -50/-20
slope = 50/20
slope = 5/2
Question 12(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $136.45 and earn $35.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
35.5 + 136.45w = 455.95; w = 9
35.5w + 136.45 = 455.95; w = 9
35.5w − 136.45 = 455.95; w = 17
35.5w − 455.95 = 136.45; w = 17
The equation that represents the number of weeks that is needed to baby sit to buy gaming chair is 35.5w + 136.45 = 455.95; w = 9 , the correct option is (b) .
In the question ,
it is given that
the cost of the gaming chair = $455.95
amount of money already saved for the gaming chair = $136.45
amount of money earned by baby sitting each week = $35.50 .
let the number of weeks required to baby sit is " w " .
the equation can be represented by
cost of chair = money saved + money earned in w weeks
Substituting the values from above ,
we get
455.95 = 136.45 + 35.5w
On solving further ,
136.45 + 35.5w = 455.95
35.52w = 455.95 - 136.45
35.52w = 319.5
w = 319.5 / 35.52
w = 8.99
w ≈ 9
the number of weeks = 9
Therefore , The equation that represents the number of weeks that is needed to baby sit to buy gaming chair is 35.5w + 136.45 = 455.95; w = 9 .
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A car travels 55 miles per hour for 2 hours
How much will it travel 1/2 per hour
How much will it travel in 1 1/2 per hour?
Answer:
2 hours 110
Step-by-step explanation:
Jeffrey is selling lemonade in the park. last year when the price per serving was $0.80 he sold 200 servings of lemonade. for each $0.10 that he adds to the price,Jeffrey will lose 10 customers. What price will get him the greatest total revenue? How can you verify that your solution is correct? What assumptions did you make in creating and using this model function
Jeffry will get greatest total revenue when he charges the lemonade $1.40
Given,
The price per servings of lemonade = $0.80
Number of servings = 200
For each $0.10 that he adds to the price, Jeffrey will lose 10 customers.
We have to find the greatest total revenue he got.
Lets check.
0.80 x 200 = $160
0.90 x 190 = $171
1.00 x 180 = $180
1.10 x 170 = $187
1.20 x 160 = $192
1.30 x 150 = $195
1.40 x 140 = $196
1.50 x 130 = $195
1.60 x 120 = $192
Here this continues
From the above data we came to know that Jeffry will get greatest total revenue when he charges the lemonade $1.40
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What is the GCF of x*y2z and x1y?
Answer:
xy
Step-by-step explanation:
if you take xy out of xy^2z it will become yz
if you take you xy out of xy it becomes 1 so this is the greatest factor
(please tell me if i got any digits wrong i assumed some were exponets)
hopes this helps please mark brainliest
Answer:
1. x² 2. x
Step-by-step explanation:
For these problems, there actually pretty easy. What you do is the numbers like x2 are x times 2. So, like if x is 3, it would be equal to 6 because 3 times 2 is 6. Easy, right?
But this time, it is asking you for GCF. It's harder, but it will be easy after you understand it.
#1
So, it organizes the equation. So x2 gets simplified to x times 2. x*2 is double the amount. x + y and x - z. Take the x's that is 2 x's. So x2. Then y and z which are unknown has the value left. And 1 more thing. Since there is no operation, it turns in to times/multiply. Please don't ask why. Ask it in a new question. So you can cross them off and multiply x2 with y times z. The equation now is basically x2 y times z). y times z. Again, the numbers are unknown. So you need to count them as zero. Add 2 zero's together is 0. Add x2 to 0. Which is x2.
You can now do problem 2 by yourself after you read the explanation. Remember, your answer isn't always like this type of explanation. Some one's work, try this for all your problems related. See if it works.
Therefore, the GCF of x2(x + y) (x - z) is x2
Solve for m.
- 3/7 m = 12
Answer:
-28
Step-by-step explanation:
Isolate m in the equation first: m = 12 / (-3/7)
Simplify and solve: m = -84/3 = -28
Answer:
-28
Step-by-step explanation:
3/7=0.4285714285714
0.4285714285714 × 28 equals 11.99 which is estimated to 12.
Solve for the missing measure of X
Answer:
x = 4
Step-by-step explanation:
4x+8 = 6x
6x-4x = 8
2x = 8
2/2 x = 8/2
x = 4
Assume that a three-month CD purchased for $1900 pays simple interest at an annual rate of 7%. How much total interest does it earn? What is the balance at maturity?
Answer: Total interest: $399
Balance = $2,299
Step-by-step explanation:
Total interest=
1900 * 7/100 * 3
= 133 * 3
= 399
Balance at maturity:
1900 + 399
= 2299
What is the Domain & Range of A(t)=487-264t
Range of the given function A(t)=487-264t is (-∞, +∞)
Domain of the given function A(t)=487-264t is also (-∞, +∞)
What is domain?
it is the values which x can take in the function. so that it does not get indefined.
What is range?
It is all the values which comes after x is put in the equation.
The domain and range are defined for a given function and they are the sets of all the x-ordinates and all the y-ordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then.
Domain = it is the set of all x-coordinates = {1, 2, 3, 4}Range =it is the set of all y-coordinates = {2, 3}Given function
A(t)=487-264t
Hence, Range of the given function is (-∞, +∞)
and Domain of the given function is also (-∞, +∞)
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HELPPPP ASAPP
The number of chapters read, y, after x days. The slope of the line is 5/4 and the y-intercept is 2. The slope of 5/4 means that....
A. Every 4 days, you read 5 chapters
B. Every 5 days you read 4 chapters
C. You started on chapter 4 out of 5 chapters
someone answer these please, must have work done by tonight
A rhombus has diagonals with lengths of 24 and 20.
1. A rhombus is a parallelogram. What is a property of a parallelogram that describes the intersection of the diagonals?
2. The diagonals of a rhombus intersect in a way that does not apply other parallelograms. How do the diagonals of a rhombus intersect?
3. What is the length of a side of the rhombus? Show work to get credit.
4. What is the perimeter of the rhombus? Show work to get credit
Answer:
Step-by-step explanation:
1. The diagonals of a parallelogram are congruent.
2. The diagonals of a rhombus form congruent acute angles.
3. To get each side length of the rhombus, double each diagonal. That means 24 times 2 will be 48 and 20 times 2 will be 40.
4. The perimeter is the sum of the sides. 48+40+48+40 = 176
Solve the following system of equations for all three variables.
2x + 2y - 3z = -2
7x + 8y + 6z = 2
- x - y + 6z = 1
Answer:
x = -10
y = 9
z = 0
Step-by-step explanation:
What kind of transformation converts the graph of f(x) = 8x² - 7 into the graph of g(x) =
-8x²
+7?
The transformation g(x) = -f(x) converts the graph of
f(x) = 8x^2 - 7 into the graph of g(x) = -8x^2 + 7.
What is transformation of graph?
The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the change of algebraic equations, it is a typical kind of algebraic problem.
Given: f(x) = 8x^2 - 7.
We have to find what kind of transformation converts the graph
f(x) = 8x^2 - 7 into the graph of g(x) = -8x^2 + 7.
Let,
f(x) = 8x^2 - 7
Multiply both sides by -1.
⇒ -f(x) = -8x^2 - (-7)
- f(x) = -8x^2 + 7
Since g(x) = -8x^2 + 7
⇒ -f(x) = g(x)
⇒ g(x) = -f(x)
Therefore, the transformation g(x) = -f(x) converts the graph of
f(x) = 8x^2 - 7 into the graph of g(x) = -8x^2 + 7.
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The midpoint of AB is M(1,-4). If the coordinates of A are (-3, -6), what are
the coordinates of B?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x -3}{2}~~~ ,~~~ \cfrac{ y -6}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(1~~,~~-4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x -3}{2}=1\implies x-3=2\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -6}{2}=-4\implies y-6=-8\implies \boxed{y=-2}[/tex]
ASAP 100 Points!!!!!
The table represents the amount of money in a bank account each month.
Month Balance ($)
1 3,600.00
2 3,960.00
3 4,356.00
4 4,791.60
5 5,270.76
What type of function represents the bank account as a function of time? Justify your answer.
This is an exponential function because there is a common difference in the balance between the months.
This is an exponential function because there is a common ratio in the balance between the months.
This is a linear function because there is a common difference in the balance between the months.
This is a linear function because there is a common ratio in the balance between the months.
Answer:
the second answer
Step-by-step explanation:
Answer:
This is an exponential function because there is a common ratio in the balance between the months.
Step-by-step explanation:
If we look at the first and second month of balance, we can see that the difference is 360. If we multiply that by 5, it equalls 1800. If we subtract 5270--3600, it equals 1670, meaning that there is not a linear function, nor a common difference, meaning that the second answer would be correct.
