The estimates of the area under the curve using rectangles is given as follows:
Two rectangles: 729 units squared.Four rectangles: 911.25 units squared.How to approximate the area?The area under a curve is approximated using the definite integral of the function that defines the curve within it's bounds.
As it is specified that the area should be approximated using rectangles, a Left Riemann Sum will be used to approximate the area.
With two rectangles, the Delta value is obtained as follows:
[tex]\Delta_x = \frac{9 - (-9)}{2}[/tex]
[tex]\Delta_x = 9[/tex]
The values of x are obtained with the rule presented as follows:
[tex]x_i = a + \Delta_x(i - 1)[/tex]
With two rectangles, the values are given as follows:
-9 and -9 + 9 = 0.
The numeric values are given as follows:
x = -9: 81 - (-9)² = 0.x = 0: 81 - 0² = 81.The definite integral is given as follows:
[tex]\sum_{i = 1}^n = \Delta_xf(x_i)[/tex]
Hence the result is of:
9 x 81 = 729 units squared.
With four rectangles, the Delta value is given as follows:
[tex]\Delta_x = \frac{9 - (-9)}{4} = 4.5[/tex]
Hence the values of x are:
x = -9, x = -4.5, x = 0, x = 4.5.
The numeric values are:
x = -9: 81 - (-9)² = 0.x = -4.5: 81 - (-4.5)² = 60.75.x = 0: 81 - 0² = 81.x = 4: 81 - (-4.5)² = 60.75.Hence the result of the integral is given as follows:
4.5(60.75 + 81 + 60.75) = 911.25 units squared.
More can be learned about Riemann sum approximation at brainly.com/question/7229305
#SPJ1
لعمل
2. According to Jacqeline's mother, what is the right way to speak? (Look at "the right way to speak" on
pes. 68-69.)
Therefore , as a result, after answering the question, we may state that the coordinates are -(68,-69); the answer is = x - y - 137 = 0.
What do coordinates mean?When locating points or other geometric objects precisely on a continuum, such as Euclidean space, a coordinate system is a technique that uses one maybe more integers or coordinates. Locating a point or item on an a double plane requires the use of coordinates, which are pairs of integers. Two numbers called the y and x coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations.
Here,
Given :
we provided with the coordinates as -
(68,-69)
so, the equation is = y -y1 = m(x-x1)
= y + 69 = x - 68
x - y - 137 = 0
Therefore , as a result, after answering the question, we may state that the coordinates are -(68,-69); the answer is = x - y - 137 = 0.
To know more about coordinates visit:
brainly.com/question/27749090
#SPJ1
The cost revenue functions for a company are given by C=1000+3.75q and R=6.25q the fixed costs of the company are
The periodic fixed costs of the company, based on the cost function, are $1,000.
What are the fixed costs?The fixed costs refer to the period costs that do not change in total concerning the production or activity level and they relate to a financial period.
The fixed cost per unit decreases as more units are produced and vice versa. However, within the relevant range, the fixed cost for the period remains the same.
What is a cost function?A cost function is a model or formula that shows the total costs based on different cost behaviors (fixed and variable) and the relationship of costs to the production quantity.
Cost functions can be used to predict the total costs to be incurred under different production levels.
In this situation, the cost function, C = 1000 + 3.75q, shows that the fixed cost per period is $1,000 and $3.75 per unit (variable).
Thus, based on the cost function, the fixed costs are $1,000.
Learn more about cost and revenue functions at https://brainly.com/question/29371627
#SPJ1
Washington, DC is on Eastern standard time, Minneapolis is on Central standard time (1 hr earlier than Eastern standard time), and Las Vegas is on Pacific standard time (3 hrs earlier than Eastern standard time).
A flight leaves Washington, DC at 9:45 A.M. Eastern standard time, stops for 2 hours and 20 minutes in Minneapolis, then arrives in Las Vegas at 4:30 P.M. Pacific standard time.
How long is the plane actually flying?
Answer:
Step-by-step explanation:
When the plane landed in Las Vegas it was 4:30PM Pacific time - this converts to 730 PM Eastern time.
The entire trip lasted from 9:45 am to 7:30 pm. This is a total of 9 hours and 45 minutes.
Subtract 2 hours and 20 minutes for the layover and the plane was flying
for 7 hours and 25 minutes.
9 - 2 = 7 hours and 45 minutes - 20 = 25 minutes
Evaluate and simplify the
expression when a=2 and b=4.
4a - 2(a + b) + 1 = [?]
Answer:
Step-by-step explanation:
Your first step should be to use the Distributive property to simplify the part where it says: -2(a+b). Then you need to put in the numbers given to you for a=2 and b=4
please answer a b and c! I really need help tysm
Step-by-step explanation: angle on a straight line equals=180
(a) x+2x+3x =180
(b) 6x=180 (divide both sides by the coefficient of x i.e 6)x
x=180divide by 60
x =30
(c) now we know the value of x substitute it to get the largest value
x+2x+3x =180
30+2(30)+3(30)=180
30+60+90=180
therefore the largest angle is 90 degrees
Assume that you earned $27,000 last year and paid $1,809 in social security taxes. What percent of your
earnings are paid in social security taxes?
Include the "%" sign in your answer.
He paid 6.7% in taxes of his annual income.
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: Income = $27000 and paid $1,809 in social security taxes.
Thus percentage of earnings paid as taxes is
1809/27000 × 100 =6.7%
Hence, He paid 6.7% in taxes of his annual income.
Learn more about percentages here:
https://brainly.com/question/29306119
#SPJ1
The cost of laser eye surgery in Country A is $2000 for each eye. The same surgery in Country B is
of this amount. What is the cost of this procedure in Country B?
The cost of laser eye surgery in Country B is for each eye.
(Simplify your answer.)
The cost of laser eye surgery in Country B is $1500 for each eye.
What is the proportion?
Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.
A proportion is two ratios that have been set equal to each other,
a proportion is an equation that can be solved.
When we say that a proportion is two ratios that are equal to each other, it means this in the sense of two fractions being equal to each other.
For instance, 5/10 equals 1/2.
We have given,
The cost of laser eye surgery in Country A is $2000 for each eye.
The same surgery in Country B is 3/4 of this amount.
Based on the given conditions, formulate: 2000 * 3/4
Reduce the expression to the lowest term: 500 * 3
Calculate the product or quotient: 1500
Hence, The cost of laser eye surgery in Country B is $1500 for each eye.
To learn more about the proportion visit,
https://brainly.com/question/1496357
#SPJ1
The cost of laser eye surgery in Country B is $1500 for each eye.
What is the proportion?Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.
A proportion is two ratios that have been set equal to each other,
a proportion is an equation that can be solved.
When we say that a proportion is two ratios that are equal to each other, it means this in the sense of two fractions being equal to each other.
For instance, 5/10 equals 1/2.
We have given,
The cost of laser eye surgery in Country A is $2000 for each eye.
The same surgery in Country B is 3/4 of this amount.
Based on the given conditions, formulate: 2000 * 3/4
Reduce the expression to the lowest term: 500 * 3
Calculate the product or quotient: 1500
Hence, The cost of laser eye surgery in Country B is $1500 for each eye.
To learn more about proportion refer to:
https://brainly.com/question/30247915
#SPJ1
If 692 = 4,761, then 4,761 / 69 =
Answer: 69
Step-by-step explanation:
In the equation 692 = 4,761, we can see that 692 is being multiplied by some number to get 4,761. To find that number, we can divide 4,761 by 692:
4,761 / 692 = 69.
So, 4,761 / 69 = 69
In this case, 692 is being multiplied by 69 to get 4,761, so 69 is the value we get when we divide 4,761 by 69.
which equation is represented by the table? y=-|x+1|-4 y
An equation is represented by the table is y= -4x+3. Therefore, option B is the correct answer.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
From the given table, we have coordinates (0, 3) and (1, -1)
Here, m=(-1-3)/(1-0)
m=-4
Substitute m=-4 and (x, y)=(0,3) in y=mx+c, we get
3=-4(0)+c
c=3
Substitute m=-4 and c=3 in y=mx+c, we get
y= -4x+3
Therefore, option B is the correct answer.
To learn more about the the equation of a line visit:
https://brainly.com/question/2564656.
#SPJ1
"Your question is incomplete, probably the complete question/missing part is:"
Which equation is represented by the table?
y=-3x+1
y=-4x+3
y=3x-4
y=-2x+1
Which function represents the data in the table?
Answer:
First choice
y = 3ˣ
Step-by-step explanation:
It is easier if you examine the obviously wrong choices
Choice 2, y = 9x is incorrect because at x = 0, y = 9x should be 0, instead it is 1
Choice 3 , y = 3x is incorrect for the same reason
Choice 4 y = x³ is incorrect because at x = 0, x³ should be 0, instead it is 1
Correct choice is the first one: y = 3ˣ
Let's check:
x = 0, y = 3⁰ = 1 because any number raised to the power 0 is 1
x = 1, y = 3¹ = 3; because any number raised to the power 1 is 1itself
x = 2; y = 3² = 9 ; so fts
You can test out the rest of the entries yourself
Using logarithmic properties, what is the solution to log3(y + 5) + log36 = log366? Show steps. all have log of base 3
log3 (y + 5)+ log3 6 = log3 66
[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{3}(y+5)+\log_3(6)~~ = ~~\log_3(66) \\\\[-0.35em] ~\dotfill\\\\ \log_3[(y+5)\cdot 6]=\log_3(66)\implies (y+5)6=66 \\\\\\ y+5=\cfrac{66}{6}\implies y+5=11\implies \boxed{y=6}[/tex]
NO LINKS!!!
For questions 1-3, decide whether each transformation will result in congruent or similar figures.
1. Quadrilateral ABCD is translated 5 units and 4 units down, then reflected in the y-axis.
2. ΔJKL is dilated by a scale factor of 2 and then rotated 180° about the origin.
3. Line segment XY is rotated 90° about the origin , dilated by a scale factor of -1/2, and then reflected in the line x = 5.
Answer:
1) Quadrilateral ABCD is translated 5 units and 4 units down, then reflected in the y-axis. This will result in congruent figures. Translation only moves the figure without changing the size or shape, and reflection in the y-axis will mirror the figure across the y-axis without altering its size or shape. Since both operations preserve the size and shape of the figure, the resulting figure will be congruent to the original.
2) ΔJKL is dilated by a scale factor of 2 and then rotated 180° about the origin. This will result in congruent figures. Dilation by a scale factor of 2 will double the size of the triangle while maintaining its shape, and rotation by 180° about the origin will flip the triangle over the origin while maintaining its shape. Since both operations preserve the size and shape of the figure, the resulting figure will be congruent to the original.
3) Line segment XY is rotated 90° about the origin, dilated by a scale factor of -1/2, and then reflected in the line x = 5. This will result in similar figures. Rotation by 90° about the origin will rotate the line segment by 90 degrees, dilated by a scale factor of -1/2 will shrink the size by half but with a change in direction and reflection in the line x = 5 will mirror the figure across the x=5 line without altering its size or shape. Since all the operations maintain the shape of the figure but the size changes, the resulting figure will be similar to the original one.
Translation and reflection doesn't change the shape or size of the figure, therefore the resulting figure is congruent to the initial one.
Question 2Rotation doesn't change the shape of the figure, but dilation changes the size, therefore the resulting figure is similar to the initial one.
Question 3Rotation and reflection don't change, but dilation changes the size, therefore the resulting segment is similar to the initial one.
Simplify the expression in exact terms (no decimals): 6√x+7√(54) - 12√(6)
Answer:
Step-by-step explanation:
First, we will use the property of radicals that states that (a √b) * (c √d) = (ac) √(bd). Since the expression has both multiplication and addition, we will break the expression down into its components and simplify each component separately.
6√x+7√(54) = 6√x + 7√(27*2) = 6√x + 7√27 * 7√2 = 6√x + 7√27 * (2*√2) = 6√x + 14√27 * √2 .
Next, we will simplify the second component of the expression: 12√(6) = 12√(2*3) = 12√2 * 6√3 = (4*3)√2 * 6√3 = 12√2 * 6√3.
Finally, we can combine the two separate parts of the expression to get the simplified version: 6√x + 14√27 * √2 - 12√2 * 6√3 = 6√x + 14√27 * √2 - 12√6.
The simplified version of the expression is 6√x + 14√27 * √2 - 12√6, in exact terms (no decimals).
Juan's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 70 coffees in all, 70% of which were regular. How many regular coffees did the cafe serve?
The cafe served 49 regular coffees.
How to calculate thisYou can use the proportion of regular coffees to the total number of coffees to find out how many regular coffees were served.
If 70% of the coffees served were regular, that means that 100-70 = 30% of the coffees served were decaffeinated.
To find out how many regular coffees were served, you can use the following proportion:
(Number of regular coffees) / (Total number of coffees) = 70% / 100%
You can then cross-multiply and solve for the number of regular coffees:
Number of regular coffees = (70/100) * (Total number of coffees)
Given the Total number of coffees = 70, you can substitute that and get:
Number of regular coffees = (70/100) * 70 = 49
Therefore, the number of regular coffees which the cafe served was 49.
Read more about percentages here:
https://brainly.com/question/24877689
#SPJ1
8 = 1/3(a + 5) pls answer fast
Answer:
19
Step-by-step explanation:
8 = 1/3 (a+5)
24 = a + 5
=> a = 19
Answer:
[tex]a=19[/tex]
Step-by-step explanation:
[tex]8=\frac{1}{3} (a+5)[/tex]
To find the answer we have to find the value of the variable. In order to find the value of the variable we need to isolate it from the equation.
[tex]8=\frac{1}{3} (a+5)[/tex]
[tex]\frac{1}{3} (a+5)=8[/tex]
Multiply 3 on both sides:
[tex]8\times3=24[/tex]
[tex](a+5)=24[/tex]
Subtract both sides by 5:
[tex]24-5=19[/tex]
[tex]a=19[/tex]
Therefore your answer is "a = 19."
Hope this helps.
Which graph represents the inequality -2x + 3y > 12?
Answer:
y>\frac{2}{3} x+4
Step-by-step explanation:
Graph the inequality by finding the boundary line, then shading the appropriate area.
Hope this helps :)
A hiker walks at a speed of 3 2 5 kilometers per hour. How many kilometers will the hiker walk in 5 hours
Answer:
17 km----------------------------------------
The distance is the product of the speed and time.
Given:
Speed = 3 2/5 km/h,Time = 5 hours.Find the distance:
3 2/5 × 5 = 3 × 5 + 2/5 × 5 =15 + 2 = 17 kmanswer asap for reward
If z = 2 [ cos ( - π 4 ) + i sin ( - π 4 ) ] = a + b i in rectangular form, then a = and b = .
The complex number in rectangular form is z = √2 - i√2
What is rectangular form of complex numbers?The rectangular form of of a complex number is given by z = a + ib where
a = rcosФ and b = rsinФwhere
r = magnitude of complex number and Ф = argument of complex numberHow to find the given complex number in rectangular form?Given the complex number
z = 2[cos(- π/4) + isin(- π/4)] , we desire to find the rectangular form of the complex number. We proceed as follows.
z = 2[cos(- π/4) + isin(- π/4)]
z = 2cos(- π/4) + i2sin(- π/4)]
z = 2cos(π/4) - i2sin(-π/4)]
Since cos(π/4) = sin(π/4) = 1/√2, we have that
z = 2cos(π/4) - i2sin(-π/4)]
z = 2 × 1/√2 - i2 × 1/√2
z = 2/√2 - i2/√2
Rationalizing the denominators, we have that
z = 2/√2 × √2/√2 - i2/√2 × √2/√2
z = 2√2/2 - i2√2/√2
z = √2 - i√2
So, we have the number in rectangular form as z = √2 - i√2
Learn more about complex number in rectangular form here:
https://brainly.com/question/4710805
#SPJ1
is x-1 a factor of x^4-3x^3+6x^2-12x+8
Answer:
32842
Step-by-step explanation:
837428942
10. 24 is 3/4% of what number?
well, the number is really "x", which oddly enough is the 100%.
we also know that 3/4% of "x" is 24, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\[1em] 24&\frac{3}{4} \end{array}\implies \cfrac{x}{24}~~ = ~~\cfrac{100}{~~ \frac{3 }{4 } ~~}\implies \cfrac{x}{24}=\cfrac{400}{3} \\\\\\ 3x=9600\implies x=\cfrac{9600}{3}\implies x=3200[/tex]
Please help!!! Will give brainlest easy 6th grade math.
A ball is dropped from different heights. The table shows the height of the first bounce after the ball is dropped.
Bouncing Ball Experiment.
Height of Drop (in inches)
10
20
30
Height of Bounce (in inches)
5
10
15
Part A
Using the data from the table, which equation can be used to find y, the height of the first bounce, in inches, when the
ball is dropped from a height of x inches?
A. y=2x
B. y=x/2
C. y=5x
D. y=x/5
Answer:
The equation that can be used to find y, the height of the first bounce, in inches, when the ball is dropped from a height of x inches is y=x/2. This can be determined by analyzing the data in the table:
-When the ball is dropped from a height of 10 inches, the height of the first bounce is 5 inches (y=5).
-When the ball is dropped from a height of 20 inches, the height of the first bounce is 10 inches (y=10).
-When the ball is dropped from a height of 30 inches, the height of the first bounce is 15 inches (y=15).
In all these cases, the height of the first bounce is half the height of the drop, meaning that the equation y=x/2 is the correct one
Answer:
B) y = x/2
Step-by-step explanation:
When the ball is dropped 10 inches, the ball bounces 5 inches
5 = 10/2
When the ball is dropped 20 inches, the ball bounces 10 inches.
10 = 20/2
When the ball is dropped 30 inches, the ball bounces 15 inches.
15 = 30/2
R=1(149×109meter)2−(298×109meter)2
Value of R = 1.72×10¹¹ meter
The correct option is B.
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.
For example, x + y is an expression, where x and y are terms having an addition operator in between.
Given, expression
R = √[1/{1/(149×10⁹)² - 1/(298×10⁹)²}]
R = √[1/{1/(149×10⁹)² - 1/(298×10⁹)²}]
R = √[1/{(6.71×10⁻¹²)² - (3.36×10⁻¹²)²}]
R = √[1/{4.50×10⁻²³ - 1.13 × 10⁻²³}]
R = √[1/3.37×10⁻²³]
R = √2.97×10²²
R = 1.72×10¹¹ meter
Hence, 1.72×10¹¹ meter is value of R.
Learn more about expression here:
brainly.com/question/14083225
#SPJ1
Complete question is here;
A region’s average movie theater ticket price in 2007 was $6.96. For 2017, it was estimated to be $8.53. Find the percent of increase in average movie theater ticket price for this 10-year period.
Answer: To find the percent increase in average movie theater ticket price, you can use the formula:
percent increase = (new value - old value) / old value * 100
Plugging in the values, we get:
percent increase = ($8.53 - $6.96) / $6.96 * 100 = 22.9%
So, the percent of increase in average movie theater ticket price for the 10-year period from 2007 to 2017 is 22.9%.
Step-by-step explanation:
Find and ordered pair (x , y) that is a solution to the equation.
4x + y = 3
(x, y) = (_, _)
Answer:
(0,3)
Step-by-step explanation
4x+y=3
anything multiplied by x would make it greater than 3 so x is 0 then y has to be equal to 3 so (0,3)
ANSWER FAST HELPP!! GIVING BRANLIEST!
Answer:
152
Step-by-step explanation:
8*10+12*6 =80+72 =152
The equation of a circle in general form is x2+y2−4x+5y−3=0.
What are the coordinates of the center of the circle and the radius of the circle?
center: (−2,52); radius = 53√2
center: (2,−52); radius = 53√2
center: (2,−52); radius = 3
center: (−2,52); radius = 3
The equation of a circle in general form is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius.
To put the equation of circle in standard form x2+y2−4x+5y−3=0 you need to complete the square and
bring the equation to the form (x-a)^2 + (y-b)^2 = r^2
so the center of the circle is (-2,2) and the radius is 3
Part A If x is the number of miles Gavin bikes on the first day, write an expression for the distance he should bike on each of the following three days
Let x be the first day's ride.The second ride will then be equal to 1.5 times.The third day's journey will cost 1.5 (1.5x)The ride on the fourth day will cost 1.5*1.5. (1.5x)
Write an expression for the distance ?The length of the line that connects two places serves as the unit of measurement for distance.
By subtracting the different coordinates from the pair if the two points are on the same horizontal or vertical line, the distance can be calculated.
Let x be the first day's ride.
The second ride will then be equal to 1.5 times.
The third day's journey will cost 1.5 (1.5x)
The ride on the fourth day will cost 1.5*1.5. (1.5x)
Consequently, the distance traveled over the four days is
65=x+1.5x+1.5*1.5x+1.5*1.5*1.5x
65=x+1.5x+2.25x+3.375x
65=8.125x
by multiplying both sides by 8.125, we get
x=65/8.125
x=8mile
the initial ride be x miles long.
The second day's ride will be 12 miles long (=1.5 x =1.5*8).
The third day's ride will be 18 miles (1.5 x 1.5).
The fourth day's ride will be 27 miles, or 1.5*1.5(1.5x).
To learn more about distance refer
https://brainly.com/question/11913405
#SPJ1
In the University belt, the traffic lights at three different road crossings
change after every 36 seconds, 64 seconds and 110 seconds, respectively. If
they change simultaneously at 11 a.m., at what time will they change
simultaneously again?
Answer:
7:48 p.m.
Step-by-step explanation:
You want to know when lights with periods 36 s, 64 s, and 110 s will change simultaneously again if they do so at 11 a.m..
LCMThe lights will change simultaneously after a time that is the least common multiple (LCM) of the periods of the lights.
The least common multiple is the product of the unique factors in each of the numbers:
36 = 2² · 3²
64 = 2⁶
110 = 2 · 5 · 11
The unique factors are 2⁶, 3², 5, and 11. Their product is 31680. The lights will change simultaneously again after 31680 seconds.
Time conversionWe can convert this to hours, minutes, and seconds by repeated division by 60:
31680 / 60 = 528 r 0
528 / 60 = 8 r 48
31680 seconds is 8 hours, 48 minutes, and no seconds.
Clock timeAdding that time to 11 a.m. gives a clock time of ...
11:00 +8:48 = 19:48 = 7:48 p.m.
The lights will change simultaneously again at 7:48 p.m..
__
Additional comment
The lights will change simultaneously at 11 a.m. again after 11 days.
graph f (x) = x and h (x) = x - 4 describe the transformation from the graph of f to the graph of h
The transformation of graph f (x) = x and h (x) = x - 4 is a translation 4 units to the left
What is translation in math?The term transformation is used in mathematics to refer to the movements made by objects.
Translation refers to a type of transformation that involve a linear movement.
Movements as seen in translation includes
up
down
left
right
The y coordinate governs movements in the vertical direction that are up and down.
While the x coordinate controls the horizontal movement in the left and right directions.
The movement as described in the graphs f(x) and h(x) is translation 4 units to the left
Learn more on translation:
https://brainly.com/question/29321966
#SPJ1
Suppose that the following exponential function gives the dollar value of a certain house that is years old.
A decaying exponential function is modeled as follows:
y = a(1 - r)^t.
In which the parameters are given as follows:
a represents the initial value.r represents the decay rate, as a decimal.For this problem, the function is defined as follows:
y = 476000(0.81)^t.
Hence the values of the parameters are given as follows:
a = 476000, r = 0.19, meaning that the percent decay is of 19%.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
