By splitting the range into three equal pieces and approximating the area under the graph using rectangles with right endpoints, the area under the graph of f(x) from x=-2 to x=4 is calculated.
Area = (55 - (-2)^2) + (55 - (1)^2) + (55 - (4)^2) = 55 + 9 + 1 = 65
By splitting the interval into three equal pieces and approximating the area under the graph using rectangles with right endpoints, the area under the graph of
f(x)=55x2 from x=2 to x=4
is calculated. We begin by calculating the area of the rectangle whose right endpoint is at
x = -2. F(-2)
provides the height of this rectangle, which is equal to
55 - (-2)2 = 55 + 4 = 59.
The rectangle's width is
(4 - (-2))/3 = 6/3 = 2.
The area of this rectangle is therefore 59 x 2 = 118. The area of the rectangle with x = 1 as its right terminus can also be determined in a similar manner. This rectangle has a height of f(1), which equals
55 - (1)2 = 55 - 1 = 54.
The rectangle's width is
(4 - (-2))/3 = 6/3 = 2
The area of this rectangle is therefore 54 x 2 = 108. f(4), which equals 55 - (4)2 = 55 - 16 = 39, gives the area of the rectangle with x = 4 as the right endpoint. The rectangle's width is
(4 - (-2))/3 = 6/3 = 2.
The area of this rectangle is therefore 39 x 2 = 78. The sum of the areas of the three rectangles, which equals 118 + 108 + 78 = 304, represents the total area under the graph.
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Una compañía de autobuses quiere saber si el número de quejas que recibe está en función del número de autobuses que tiene. La compañía realizó un estudio en el que comparó el número promedio de autobuses por hora en días distintos y el número de quejas que recibieron en esos días. Se ajustó una recta a los datos para modelar la relación.
The line that represent the graph have the equation of y = 4x + 42 .
What is a equation ?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Equations with graphs as the unknowns are known as graph equations. The concept of isomorphism is one of the key issues in graph theory. When are two graphs identical, we inquire Different graph equations may be used to express the aforementioned graphs.
We must determine the slope and the y-intercept in order to graph this line. Y=mx+b, where m is the slope and b is the y-intercept, is the equation's slope-intercept form.
From the graph we can 2 points on the graph are
(0, 42) and (6, 18)
The equation of the graph will be
y - 42 = 18 - 42 /(6 - 0) *(x - 0)
⇒ (y -42)*6 = 24x
⇒y-42 = 4x
⇒y = 4x + 42.
The line that represent the graph have the equation of y = 4x + 42 .
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gallium-67 has a half-life of 78 hours. if you began with 10.0 g of ga-67, how many grams remain after 6.5 days?
The amount of gallium-67 remain after 6.5 days = 2.5 grams
We know that the half-life of the radioactive isotope is nothing but the time needed for the isotope to be half of its initial value of mass.
This means, with each half-life, the isotope will be halved of its initial value.
The formula for the numbers of half-lives:
numbers of half-lives = total time passed / the half-life of the isotope
Here, total time passed = 6.5 days
= 156 hours
the half-life of the isotope = 98 hours
Let n represents the number of half lives.
Using above formula,
numbers of half-lives n = 156 / 98
numbers of half-lives n = 1.59
numbers of half-lives n ≈ 2
So, the remaining mass would be,
remainig mass m = initial mass / [tex]2^n[/tex]
m = 10 / 2²
m = 2.5 g
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What is the length of a side of rhombus jklm? 4 units 8 units 12 units 16 units
The length of the sides of the rhombus JKLM is 12 units.
A rhombus is one of parallelograms. The opposite sides of a rhombus are parallel, and the opposite angles are equal. Furthermore, all of the sides of a rhombus are the same length, and the diagonals intersect at right angles.
In the problem, the sides of rhombus JKLM are:
JK = 2x + 4
JM = 3x
Since the length all of the sides of a rhombus are the same, then:
JM = JK
3x = 2x + 4
Substract both sides by 2x:
3x - 2x = 2x + 4 - 2x
x = 4
To find the length of a side, substitute x = 4 into:
JM = 3x
JM = 3(4) = 12
Hence, the length of the sides of the given rhombus is 12.
The picture in your question is missing. Most likely it was like on the attached picture.
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Answer:
12
Step-by-step explanation:
JK = JM
2x + 4 = 3x
x = 4
JK = JM = 3 x 4 = 12
i cant do this! help
Answer:
r= 45 s=5
5(r-s)= 45-5= 40
Step-by-step explanation:
5(9-1) <--- You substitute the values
(5*9-5*1)<--- Multiply
45-5<--- Subtract
40 <-- Answer
r= 45
s=5
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{5(r - s)}\\\mathsf{= 5(9 - 1)}\\\mathsf{= 5(9) + 5(-1)}\\\mathsf{= 45 - 5}\\\mathsf{= 40}\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{40}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
I need help on scale factors and dilations
Mira's scale factor of 7 in would not be reasonable because it would make the dimensions of A' too small.
Why the scale factor Mira found would not be reasonable and give the correct scale factor?For example, if A had a width of 8 inches and a length of 5 inches, then using a scale factor of 7 in would result in A' having a width of 56 inches and a length of 35 inches. This would be much smaller than what the client wants. The correct scale factor would be 1.5 in, which would make A' a rectangle with a width of 12 feet and a length of 7.5 feet, which meets the client's request.Jess could use any of the following scale factors: 1.33, 1.5, 1.67, 1.75, 2, 2.25, 2.5, 2.75, 3, and 3.5. All of these scale factors would result in a rug with a width of 12 feet while still increasing the size. This process of finding the scale factor to meet a certain criteria is known as scaling.Mira's scale factor of 7 in would not be reasonable because the dimensions of A and A' are not proportional. A' is larger than A, but its sides are not 7 times larger than A. The correct scale factor would be the ratio of the lengths of A' and A. In this case, A is 8 cm and A' is 15 cm, so the correct scale factor is 15/8, or 1.875.Jess can use any scale factor between 1 (no change) and 1.5 to dilate the rug and meet the customer's request. A scale factor between 1 and 1.5 would increase the length of the rug without making the width exceed 12 feet. This process is called enlargement or scaling up.To learn more about scale factor refer to:
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Given the curve y2 = x in the xy-plane, for what value of y, if any, does the derivative of y with respect to x not exist?a. y=0b. y=-1c. y= - (1/ ln 2)d. for no value of y
The derivative of y with respect to x exist for all values of y, that is it does not exist for no value of y.
Therefore the answer is d. for no values of y
The curve y^2 = x is a parabolic function and its derivative is continuous for all x in its domain, which is x >= 0. The derivative of this function, which is y' = (dy/dx) = 1/2 * √x, is well-defined for all x >= 0 and therefore, the derivative exists for all values of y, including y = 0 and y = -1.
In general, a function is said to be differentiable at a point if its derivative exists at that point, and the derivative provides information about the rate of change of the function at that point.
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Bob is an artist and creates 3 sketches in 45 minutes. Write and solve a proportion to find how many sketches the artist can create in 8 hours.
The sketches after 8 hours is 32
How to determine the sketches after 8 hoursFrom the question, we have the following parameters that can be used in our computation:
Bob is an artist and creates 3 sketches in 45 minutes
This means that
3 sketches = 45 minutes
Convert minutes to hour
3 sketches = 3/4 hour
Multipy both sides by 8
So, we have
8 * 3 sketches = 3/4 * 8 hours
Multipy both sides by 4/4
So, we have
32 sketches = 8 hours
Hence, the sketches is 32
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if the probability that one of these circuit boards is defective is 0.75, what is the probability of simple event {ddnn}?
Answer:
Step-by-step explanation:
=0.25
Comment on any relationship that may exist between ACT scores and gender of t
- The largest percentages of both genders' ACT scores are above 25. More ma students have scores under 20 than female students. - The largest percentages of both genders' ACT scores are in the 20 to 25 rang more female students have scores under 20 than male students.
- The largest percentages of both genders' ACT scores are under 20. More male students have scores above 25 than male students.
- The largest percentages of both genders' ACT scores are above 25. More fema students have scores under 20 than male students.
-The largest percentages of both genders' ACT scores are in the 20 to 25 range. more male students have scores under 20 than female students.
The relationship between ACT scores and gender varies depending on the data and analysis performed.
ACT scores are an important aspect in the college admissions process. They measure a student's knowledge and skills in English, mathematics, reading, and science.
In the first scenario, it states that the largest percentage of both genders' ACT scores are above 25. It also mentions that more male students have scores under 20 than female students.
In the second scenario, it mentions that the largest percentage of both genders' ACT scores are in the 20 to 25 range and that more female students have scores under 20 than male students.
In the third scenario, it states that the largest percentage of both genders' ACT scores are under 20 and that more male students have scores above 25 than female students.
In the fourth scenario, it mentions that the largest percentage of both genders' ACT scores are in the 20 to 25 range and that more male students have scores under 20 than female students.
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x-intercept of the line 3x+20y=–12.
Answer:x=-4
Step-by-step explanation
1. Set y as 0. Doing so will help you solve for x
3x +20(0)=-12 aka 3x=-12
2. Divide each sides by 3
3x(divided by three) = -12 (divided by three)
x=-4
(your answer would be negative because a negative divided by a postitive is negative.)
can someone help with this inequality question with explanation.Thanks!
Haven't answered an inequality question in a while so this
might be complete bullhonkey.
Answer:
154 minutes of talktime.
Step-by-step explanation:
To find out how many minutes of talktime John can have per month, we need to set up an equation using the information given.
Let x be the number of minutes of talktime John can have per month.
The equation for John's monthly phone bill is:
26.50 + 0.35x = 80
To find the value of x, we can solve for x by subtracting 26.50 from both sides:
0.35x = 53.50
To find the number of minutes, we can divide both sides by 0.35:
x = 153.57
To the nearest whole number, John can have 154 minutes of talktime per month.
the Indianapolis 500 race takes 200 laps to complete. if 1 lap is 4km, how many kilometers must a competitor drive to complete the race
The competitor drive 804.672 or 800 Km to complete the race.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The Indianapolis 500 race takes 200 laps to complete.
and, 1 lap = 4 Km
Then, for 200 laps the competitor need to drive
= 200 x 4
= 800 Km
also, Indianapolis 500 race is to cover 500 miles in 200 laps then we can write it as
1 miles = 1.60934 Km
and 500 miles= 804.672 Km
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Assume that you graph lines f and g on the same coordinate plane and they intersect at point (4, 5). Which of the following statements is NOT true.
The statement that is not true is the fourth one.
"Other points that are on line f are also solutions of the system".
Which one of the given statements is not true?We know that the graphs of lines f and g intercept at the point (4, 5). So trivially, the point (4, 5) belongs to both graphs.
That also means that (4, 5) is the solution of the system of equations:
y = f(x)
y = g(x).
And because these two are lines, these will intercept only once, then (4, 5) is the only solution of the system.
That means that the correct option (the false statement) is the fourth one.
"Other points that are on line f are also solutions of the system".
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Please help me with this geometry question
Are the two triangles similar?
Answer:
Similar by SAS
Step-by-step explanation:
:)
The um of two number i 50. The larger number i 4 le than 5 time the lower number. Find the number
After solving, the lower number is 9 and the larger number is 41.
The sum of two number is 50.
The larger number is 4 less than 5 times the lower number.
Let the lower number is x.
Five times the lower number = 5x
Larger number 4 less than five times the lower number = 5x - 4
Sum of number = 50
Lower Number + Larger number = 50
x + 5x - 4 = 50
Simplify
6x - 4 = 50
Add 4 on both side, we get
6x = 54
Divide by 6 on both side, we get
x = 9
Now finding the number.
Lower Number = x = 9
Larger Number = 5x - 4
Larger Number = 5(9) - 4
Larger Number = 45 - 4
Larger Number = 41
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The complete question is:
The sum of two number is 50. The larger number is 4 less than 5 times the lower number. Find the number.
Write a function that models the data.
x y
0 250
1 150
2 90
3 54
4 32.4
Answer:250(0.6)
Step-by-step explanation:
The value of the function is f ( x ) = 250 ( 0.6 )ˣ
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The values of x are in set x = { 0 , 1 , 2 , 3 , 4 , }
The values of y are in set y = { 250 , 150 , 90 , 54 , 32.4 }
Now , the equation will be y = 250 ( 0.6 )ˣ
when x = 0
y = 250 ( 0.6 )⁰
y = 250 ( 1 )
y = 250
when x = 1
y = 250 ( 0.6 )¹
y = 250 ( 0.6 )
y = 150
when x = 2
y = 250 ( 0.6 )²
y = 250 ( 0.36 )
y = 90
when x = 3
y = 250 ( 0.6 )³
y = 250 ( 0.216 )
y = 54
when x = 4
y = 250 ( 0.6 )⁴
y = 250 ( 0.1296 )
y = 32.4
Hence , the function is y = 250 ( 0.6 )ˣ
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Drag each part of the expression to categorize it as a term or a coefficient in the expression.
Parts that are neither a term nor a coefficient belong in the "Neither One" category.
3x2+6x+7
Terms = 3x² , 6x , 7
Coefficients = 3,6
Neither One = x²
How to find the calculation?A quantity or number that is combined with a variable is known as a coefficient.
Adding a variable to a number produces a coefficient.
The variable next to it is often multiplied by an integer.
Three terms make up the trinomial: 3x² + 6x + 7
3x²
6x
7
Enter the first column as a result.
The coefficients at and are respectively 3 and 6.
The second column should have these two integers.
x² is not a term (because 3x² is a term) and is not a coefficient, because coefficients are numbers.
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PLEASE ANSWER THIS IS DUE MONDAY!!! The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller one. When x is the bigger number, find the numbers.
The numbers are 19 and 71 respectively
How to determine the numbersLet's call the smaller number "y".
The larger number would be 3 times y plus 14,
Which we can write as 3y + 14.
From the problem, we know that the sum of the two numbers is 90, so we can write an equation:
y + (3y + 14) = 90
Remove the brackets
y + 3y + 14 = 90
So, we have
4y + 14 = 90
4y = 76
Divide both sides by 4
y = 19
So the smaller number is 19 and the larger number is 3 times that plus 14, which is 3 * 19 + 14 = 71.
So the two numbers are 19 and 71.
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math ia on how airlines decide to sell tickets
Tickets are sold by airlines based on availability and demand. To increase their amount of earnings, they consider things like flight capacity, the time of year that people travel, the number of tickets available, and pricing.
Tickets are sold by airlines based on availability and demand. To choose the best course of action for their firm, they carefully analyse variables including aeroplane capacity, travel season, seat availability, and cost. Airlines assess the current market and forecast future trends using sophisticated mathematical models. This aids them in figuring out the ideal quantity of tickets to market and the finest selling price. To make sure that their tickets are reasonably priced, airlines also take into account the demand for their flights and the competition from other airlines. In order to make their tickets appealing to customers, airlines may consider promotional activities and unique offers. Airlines may increase their revenue by selling tickets at the proper price by studying the data and making wise judgements.
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Please help me answer this question on equations of lines. 10 points and brainliest available.
Answer:
a) (0,1)
b) k = 6.5
Step-by-step explanation:
When a line crosses the y-axis at a point, the point's x-coordinate must be 0. Let's substitute the value of x into the equation of the line to find its y-coordinate.
y - 4x = 1
Rearrange terms to isolate y.
y = 4x + 1
Substitute x = 0 into the equation.
When x = 0, y = 4(0) + 1
y = 0 + 1
y = 1
Thus, the coordinates of the point is (0, 1).
---
The second question uses the general equation of a straight line which is y = mx + c where m is the gradient of the line and c is the y-intercept of the line. As you can see from the graph drawn, the line cuts the y-intercept at (0, -3) so c = -3. You are given the y-coordinate of the point (which is 10) so you can find the x-coordinate (k) by substituting the value of y into the equation of the line once again.
y = 2x + c
You know the value of c from the y-intercept. c = -3
y = 2x - 3
Substitute y = 10 into the equation.
When y = 10, 10 = 2x - 3
10 + 3 = 2x
2x = 13
x = 6.5 when y = 10
Thus, the value of k is 6.5.
Dan, Juan, and Thuy are sharing 4 oranges equally. How
many oranges does each person have?
Answer: 1 1/3
Step-by-step explanation: To find this answer, we simply divide the people by the oranges. So, 4 / 3 is 1.3333333333333...... We round this to about 1.3. So, that as a fraction is 1 1/3. So, each person gets 1 1/3. To check, we multiply 1 1/3 by 3 (people) and we get 4. I hope this helped!
a food scientist collected data on a sample of organic snacks. they summarized the amount of sugar (in mg) in each snack in the histogram below. which statement best describes the meaning of one of the bars in the histogram?
The sample size is: n=39
Class frequency
120-125 1
125-130 3
130-135 7
135-140 13
140-145 10
145-150 3
150-155 2
Total 39
∵Therefore, The sample size is: n=39
A histogram is a graphical representation of a frequency distribution with continuous classes that has been grouped. It is an area diagram with bases and intervals between class boundaries, and areas proportional to frequencies in the corresponding classes. Because the base spans the intervals between class boundaries, all rectangles in such representations are adjacent.
How Do You Plot a Histogram?
Practice proving that a quadrilateral is a parallelogram.
Quadrilateral W X Y Z is shown. Diagonals are drawn from point W to point Y and from point Z to point X and intersect at point C. Line segments Z C and C X are congruent. The length of W C is 2 x + 5 and the length of C Y is 3 x + 2.
In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?
x =
Answer:
x = 3
Step-by-step explanation:
2x + 5 = 3x + 2
-5 -5
2x = 3x + 2 - 5
-3x -3x
2x - 3x = 2 - 5
-x = -3
x = 3
the positive variables p and c change with respect to time t. the relationship between p and c is given by the equation p2= (20−c)3. at the instant when dpdt=41 and c = 15 what is the value of dc/dt
At the instant when dp/dt=41 and c = 15, the value of dc/dt is -0.273333.
The derivative of p with respect to time t is given by:
dp/dt = 2p dp/dc * dc/dt
Since dp/dt = 41, we have:
41 = 2p dp/dc * dc/dt
To find dp/dc, we can use the relationship between p and c:
p^2 = (20-c)^3
Taking the derivative of both sides with respect to c, we get:
2p dp/dc = -3(20-c)^2
Substituting this expression into the equation for dp/dt, we get:
41 = 2p * (-3(20-c)^2) * dc/dt
Plugging in the value of c = 15, we find:
41 = 2 * p * (-3(5)^2) * dc/dt
Using the relationship p^2 = (20-c)^3, we can find p:
p = sqrt((20-c)^3) = sqrt((20-15)^3) = sqrt(5^3) = 5
Substituting the value of p into the equation for dp/dt, we get:
41 = 2 * 5 * (-3(5)^2) * dc/dt
Solving for dc/dt, we find:
dc/dt = 41 / (2 * 5 * (-3(5)^2)) = 41 / (2 * 5 * (-3 * 5^2)) = 41 / (-150) = -41/150 = -0.273333...
So the value of dc/dt at the instant when dp/dt = 41 and c = 15 is approximately -0.273333.
Correct Question :
the positive variables p and c change with respect to time t. the relationship between p and c is given by the equation p2= (20−c)3. at the instant when dp/dt=41 and c = 15 what is the value of dc/dt?
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Answer:
[tex]-\frac{82\sqrt{5} }{15}[/tex]
Step-by-step explanation:
[tex]p^{2} =(20-c)^{3}[/tex]
[tex]2p(\frac{dp}{dt}) =3(20-c)^{2}(-\frac{dc}{dt} )[/tex]
Took the derivative of both sides ^
It gives you [tex]\frac{dp}{dt} =41[/tex] and [tex]c=15[/tex], so you just need [tex]p[/tex]
[tex]p=\sqrt{(20-15)^{3} } =5\sqrt{5}[/tex]
Now plug in
[tex]2(5\sqrt{5} )(41)=3(20-15)^{2} (-\frac{dc}{dt} )[/tex]
[tex]-\frac{410\sqrt{5} }{75} =\frac{dc}{dt}[/tex]
[tex]-\frac{82\sqrt{5} }{15} =\frac{dc}{dt}[/tex]
(c) sin² A(1 + cot² A) = 1
The sine of an angle's complementary angle is equal to the cosine of that angle, and the reverse is true for the other direction.
What is sine and cosine?The cosine of an angle is equal to the sine of its complementary angle, and the opposite is true for the other way around. The functions sine and cosine, sometimes known as sin() and cos(), show the shape of a right triangle. Sin() is the ratio of the opposite side to the hypotenuse when viewed from a vertex with angle, while cos() is the ratio of the adjacent side to the hypotenuse.Sin 180 has exactly zero value. In order to determine the angle or sides of a right-angled triangle, one of the basic trigonometric functions is sine. Trigonometric ratio is another name for it.Identity :
[tex]{cosec}^2 \mathrm{~A}-\cot ^2 \mathrm{~A}=1$[/tex]
LHS [tex]$=\left(1+\cot ^2 \mathrm{~A}\right) \sin ^2 \mathrm{~A}$[/tex]
[tex]{cosec}^2 \mathrm{~A} \times \sin ^2 \mathrm{~A}$[/tex]
[tex]$=\frac{1}{\sin ^2 A} \times \sin ^2 A$[/tex]
= 1
= RHS
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(1 point) is the conditional statement "if a human being has 7 heads, then they have 11 arms" true or false? explain
As per the concept of reasoning, the conditional statement is false.
The term reasoning in math is called as students who genuinely make sense of mathematical ideas can apply them in problem solving and unfamiliar situations and can use them as a foundation for future learning.
Here we have the conditional statement "if a human being has 7 heads, then they have 11 arms".
And here we need to find out whether this statement is true or false.
While we looking into the given statement we have identified that this is false because this statement is missing the necessary or sufficient words.
Simply said that it is not possible situation.
Therefore the statement is false.
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given the quadratic function y=x^2+ax+b, the minimum value is -3, and the graph passes through point (1,1). find the values of the consists a and b.
What is the area of the parallelogram?
(2,3)
(2-5)
(6, 1)
(6.-7)
Answer:
32
Step-by-step explanation:
The area of a parallelogram is bh where b = base, h = height
This is one of the questions where plotting the points and seeing the parallelogram is vital
See the attached figure
height h = |difference between x-coordinates of A and C| =
= |6 - 2| = 4.
This will be the same as |difference between x-coordinates of B and D
base b = |difference between y-coordinates of A and B| = |1-(-7)| = 8.
This will be same as |difference between y-coordinates of C and D|
Area = bh = 8 x 4 = 32
the area of a rectangular wall of a barn is square feet. its length is feet longer than the width. find the length and width of the wall of the barn.
The length and width of the wall of the barn are 12 feet and 6 feet respectively.
The formula for area of rectangle is -
Area of rectangle = length × width
Let the width of rectangle be x. So, the length of rectangle = x + 6. Keep the values in formula to find the length and width of the barn.
x × (x + 6) = 72
Performing multiplication
x²+ 6x - 72 = 0
x² + 12x - 6x - 72 = 0
x (x + 12) -6(x + 12) = 0
x = 6 and - 12
Thus, width of rectangle = 6 feet
Length of rectangle = x+ 6
Length of rectangle = 6 + 6
Length of rectangle = 12 feet
Thus, length and width are 12 and 6 feet.
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The complete question is -
The area of a rectangular wall of a barn is 72 square feet. Its length is 6 feet longer than the width. Find the length and width of the wall of the barn.
