Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. f(x) = 2x + 3, [0, 2], 4 rectangles
Two approximations of the area of the region between the graph are
(9, 11)
Given;
To calculate two approximations of the area of the region between the graph of the function and the x-axis across the given interval, use the left and right endpoints and the specified number of rectangles. rectangles f(x) = 2x + 3, [0, 2], 4
The graph is positive and the width of each subinterval will be,
a = 0, b = 2, n = 4
Δx = b-a/n = 2-0/4
= 0.5
Now for different values;
x → f(x) = 2x+3
x₀ = 0 → f(x₀ ) = 2x+3 = 2(0)+3 = 3
x₁ = 0.5 → f(x₁) = 2x+3 = 2(0.5)+3 = 4
x₂ = 1.0 → f(x₂) = 2x2+3 = 2(1) +3 = 5
x₃ =1.5 → f(x₃) = 2x+3 = 2(1.5)+3 = 6
x₄ = 2 → f(x₄) = 2x+3 = 2(2)+3 = 7
The area by using the approximation using 4 approximating rectangles and right endpoints is given by,
A ≈ R₄ = ∑f(x) Δx = ( ƒ(x1)Δx + ƒ (x2)Δx+ ƒ (x3)Δx + ƒ (x4)Δx)
= 0.5 (4 + 5 + 6 + 7)
= 0.5 × 22
= 11
The area by using the approximation using 8 approximating rectangles and left endpoints is given by.
A ≈ L₄ = ∑f(x) Δx = ( ƒ(x0)Δx + ƒ (x1)Δx+ ƒ (x2)Δx + ƒ (x3)Δx)
= 0.5 (3 + 4 + 5 + 6)
= 0.5 × 18
=9
Thus, 9 < Area < 11.
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a rectangle has a area of 50
the length is x+10
the width is x
solve for x.
The value of x in the rectangle is -5 + 5√3.
How to find the area of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other. Opposite sides are parallel to each other.
Therefore, the area of a rectangle can be found as follows:
area of a rectangle = lw
where
l = lengthw = widthTherefore,
length = x + 10
width = x
Hence,
50 = x(x + 10)
50 = x² + 10x
x² + 10x - 50 = 0
using quadratic formula,
[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
a = 1
b = 10
c = -50
Therefore,
x = [tex]\frac{-10+\sqrt{10^{2}-4(1)(-50) } }{2(1)}[/tex] and x = [tex]\frac{-10-\sqrt{10^{2}-4(1)(-50) } }{2(1)}[/tex]
Hence,
x = -5 + 5√3 and x = -5 - 5√3
Therefore, we can't use negative values
The value of x = -5 + 5√3
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10 - 2(4 + 12x)
pls give me an equation answer, not the solution!!!
Answer:
-2 ( 12x - 1 )
Step-by-step explanation:
1) Simplify the equation
To simplify the equation, we have to get rid of any brackets. To do this multiply the term to left of it with everything inside the bracket
-2 x 4 = -8-2 x 12x = -24xNow we can plug these numbers into our equation
2) Collect like terms
The equation we are left with from the previous step would be 10-8-24x
The terms that are similar are 10 and -8.
To collect like terms simplify the terms down to one term
10 - 8 = 23) Find common factor and simplify
What we are left with from the previous step is -24x+2
To find the common factor you have to find a number that goes it both numbers which for 2 and 24 would be 12.
-24x ÷ 2 = -12x2 ÷ 2 = 1We are left with -2 ( 12x - 1 )Hope this helps, have a great day!
determine lf (t) for the functions f (t), with t > 0, defined below. make sure to specify the frequency domain for s as well, namely, the domain of convergence of the laplace transform.
An Integral transform that converts a function of a real variable to a function of a complex variable is a Laplace Transformation.
F =L (f)
We are interested in signal defined for t≥ 0.
The Laplace transformation of a signal function (f) if the function
F = L(f)
F(s) = ∫∞ ₀ f(t) e⁻ᵃᵇ dt
for those a ∈ C for which the integral makes sense.
F is a complex valued function is a complex numbers.s is called the complex frequency variable with units sec⁻¹, t is called the time variable in sec.Lets find Laplace transformation of f(t) =eᵃ
F(s) = ∫₀∞ eᵃ e⁻ᵃᵇ da
= [ 1/1-a e⁽¹ ⁻ ᵃ⁾ ] = 1 / a-1
the integral defined F makes sense for all a ∈ C with a >1 but the resulting formula for F makes sense for all a ∈ C except a = 1Learn more about Laplace Transformation:
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What’s the unit rate for three dollars for 2 1/2 hours of work
The unit rate for three dollars for 2 1/2 hours of work will be $1.2 using the concept of unitary method.
What is unitary method?The unitary method is a technique that involves determining the value of a single unit and then calculating the value of the requisite number of units based on that value. The term unitary refers to a single or unique entity. As a result, the goal of this approach is to determine values in reference to a single unit. The unitary technique is a method for determining the value of any necessary quantity by first obtaining the value of the unit (one) quantity.
Here,
$3 for 2.5 hours of work,
1 hour will cost $x,
3/2.5=x/1
2.5x=3
x=$1.2
Using the unitary technique, the unit rate for three dollars for two and a half hours of labour will be $1.2.
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fill in the blank, somebody help please. will mark brainliest + 20pt
Answer:
c) divide both sides by 8
hope this helps!
Answer:
Its the 3 option
the anser answer are A(250 feet)-(b)150 feet)-c)100 feet)-d(200 feet)
Answer:
(b) 150 feet
Step-by-step explanation:
You want to know the height of a kite at the end of 225 feet of string, flying at an angle of elevation of 45°.
Right triangleThe 45° angle in the given right triangle tells you this is one of the "special" right triangles. Its side lengths have the ratios ...
1 : 1 : √2
where √2 is the hypotenuse.
That means the other two legs of this right triangle are ...
(225 ft)/√2 ≈ 159.099 ft
Rounded to the nearest 50 feet, this is about 150 feet.
__
Additional comment
The sine function relates the angle value to the opposite side:
Sin = Opposite/Hypotenuse
Opposite = Hypotenuse · Sin
height = (225 ft)·sin(45°) = 225 ft/√2 ≈ 159.099 ft
Find both unit rates.
: An object traveled 691.12 feet in 21.2 seconds.
Question 1 options:
A: 32.6 s/ft and approximately 0.03 s/ft
B: 32.6 ft/s and approximately 0.03 s/ft
C: 32.6 ft/s and approximately 0.03 ft/s
D: 32.6 s/ft and approximately 0.03 ft/s Warning: Whoever Answers this wrong will be reported. :l
The unit rate is 32.6 ft/s and approximately 0.03 s/ft.
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:
An object traveled 691.12 feet in 21.2 seconds.
So, the unit rate as feet per second.
= 691.12/ 21.2
= 32.6 ft/s
and, the unit rate as second per feet
= 21.2/ 691.12
= 0.03 s/ ft
Hence, the unit rate is 32.6 ft/s and approximately 0.03 s/ft
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Prove: <1= <3
Complete the proof (reasons A and B).
A. Definition of supplementary angles
And Substitution property
B. Angle addition postulate
And Subtraction property of equality
C. Subtraction property of equality
And Definition of linear pair
D. Addition property of equality
And Angle addition postulate
The reason that proves the above conditions is option A. Definition of supplementary angles And Substitution property.
Supplementary angles:
The pair of angles that gives 180° on adding is known as Supplementary angles. In other words, the sum of two supplementary angles is 180°. Two pairs of Supplementary angles will always form a linear pair.
Here we have
∠1, ∠2, ∠3, and ∠4 are formed by 2 intersecting lines
As we know
∠1, ∠2 is a linear pair and form supplementary angles
=> Sum of the ∠1, ∠2 will equal 180°
∠2, ∠3 is a linear pair and form supplementary angles
=> Sum of the ∠2, ∠3 will equal 180°
Therefore,
By the Definition of supplementary angles ∠1+∠2= 180° and ∠2+∠3= 180°
From the above observations,
=> ∠1+∠2= 180° and ∠2+∠3= 180°
=> ∠1 + ∠2 = ∠2 + ∠3
Therefore,
By the Substitution property ∠1 + ∠2 = ∠2 + ∠3
Hence,
The reason that proves the above conditions is option A. Definition of supplementary angles And Substitution property
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Eric owns shares of a certain stock. If he sells off 8 shares each month for a year, find the change in the number of shares of stock he owns.
After solving the word problem, the change in the number of shares of stock he owns, is x-96.
In the given question we have to find the change in the number of shares of stock he owns.
As given that Eric owns shares of a certain stock. If he sells off 8 shares each month for a year.
Let Eric owns x shares of a certain stock.
If he sells off 8 shares each months for a year.
So as we know that in a year have 12 months.
In 1 month = 8 shares sells
12 months = 12×8 shares sells
12 months = 96 shares sells
So in a year Eric sells 96 shares and he have total x shares.
So the remaining shares are x-96.
Hence, the change in the number of shares of stock he owns, is x-96.
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a box is given a sudden push up a ramp. friction between the box and the ramp is not negligible. which of the following diagrams best represents the directions of the actual forces acting on the box as it moves upward after the push?
For a box given a sudden push up a ramp and the friction between the box and the ramp is not negligible, the diagrams which best represent the directions of the actual forces acting on the box as it moves upward after the push is Option A.
Friction refers to the force of resistance in the relative motion of solid surfaces in contact and sliding or rolling against each other. Frictional forces are affected by the surface texture and the amount of force impelling them together and the angle and position of the object. The actual forces acting on the box will be the normal force (always perpendicular to the surface), weight force (acting downward) and frictional force (acting opposite to the direction of push).
Note: The question is missing options which are provided in the figure.
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There is a line whose y-intercept is -2 and whose slope is 1. What is its equation in
slope-intercept form?
Write the equation of the line that goes through point (-4, 1) and is perpendicular to the line 2y - 4x = -10. Write the equation in slope intercept form.
Answer:
y = 1/2x + 3
Step-by-step explanation:
first we change the first equation to slope-intercept form to find the reciprocal slope
2y - 4x = -10
add 4x to both sides
2y = 4x - 10
divide both sides by 2
y = 2x - 5
since perpendicular lines have reciprocal slopes the slope of our new line is 1/2
y = 1/2x + b
to find b we plug in the point
1 = 1/2(-4) + b
1 = -2 + b
add 2 to both sides
3 = b
___
our new line is
y = 1/2x + 3
Answer:
-83+8=19
Step-by-step explanation: how i figured this out is by guessing so i can get more points sorry guys.
a 12oz box of cereal costs $3.50. An 18oz box of cereal costs $5.40. Set up equations to determine which is the better buy.
Answer:
12oz box of cereal for $3.50 is the better buy
Step-by-step explanation:
12oz=$3.50
36oz = $10.50
----------------------------
18oz=$5.40
36oz=$10.80
A z-test with a z observed of 2.56 (two-tailed) would have a p-value of ______, which would lead a research to _______ the null hypothesis if alpha is .05.
A z-test with a z observed of 2.56 (two-tailed) would have a p-value of 0.010467 , which would lead a research to reject the null hypothesis if alpha is .05.
Given:
z - score = 2.56
p value at z = 2.56 is:
p = 0.010467
The result is statistically significant: you can reject the null hypothesis and accept the alternative.
This decision is made at significance level α = 0.05.
Therefore a z-test with a z observed of 2.56 (two-tailed) would have a p-value of 0.010467 , which would lead a research to reject the null hypothesis if alpha is .05.
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Slope = -1/5, y-Intercept = -1/4
Answer:
[tex]\sf y =\dfrac{-1}{5}x-\dfrac{1}{4}[/tex]
Step-by-step explanation:
Slope y-intercept form of equation: y =mx +bHere, m is the slope and b is the y-intercept.
Substitute the values of m and b in the above equation.
[tex]\sf m = \dfrac{-1}{5} \\\\b = \dfrac{-1}{4}[/tex]
Slope y-intercept form:
[tex]\sf \boxed{y=\dfrac{-1}{5}x - \dfrac{1}{4}}[/tex]
i need to know how to find the slope!!
Answer:
Step-by-step explanation:
Slope of a straight line is the gradient of that line.
Formula for gradient is rise over run. Meaning: m = (y2 - y1) / (x2 - x1)
To use this formula, you need 2 points of the straight line. They have already given you one: (8, -3). For the second one, we consider the equation of the line. The y-intercept is given too: -4.
Now, keep in mind, the y intercept is the point of the line that passes from x = 0. Meaning, the point where the line touches the y axis, and at y axis, x = 0. So our second point is (0, -4).
Now as we have 2 points, (8, -3) and (0, -4), we put the values in the formula: m = (y2 - y1) / (x2 - x1) = (-4 - (-3)) / (0 - 8) = -1 / -8 = 1 / 8
tickets for a baseball game are $69 for main level seats and $39 for terrace level seats. a group of fifteen friends went to the game and spent a total of $735 for the tickets. how many of main level and how many terrace level tickets did they buy?
Tickets for a ball game are $69 for Primary Level seats and $39 for Porch Level seats. A total of $804 was spent on the tickets by a group of 16 friends who attended the game.
How many tickets were purchased for the Main Level and the Terrace Level?
No. of tickets for the Main Level = X
No. total price = 804 = 39(16 - X) + 69X = 624 - 39X + 69X = 624 + 30X 30X = 804 - 624 = 180 X = 180/30 = 6
No. of Terrace Level Tickets = 16 - X
Main Level Tickets Prace = 69X
Terrace Level Tickets Prace = 39X
Total Price = 804 = 39(16 - X) + 69X = 624 - 39X + 69X =of tickets for the Main Level, X = 6
No. of tickets for the Terrace Level: 16 - X = 16 - 6 = 10 Check:39x10 + 69x6 = 390 + 414 = 804
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please help me fast!!
Answer:
4(y+3)(y+5)
Step-by-step explanation:
4y^2+32y+60 = 4(y^2+8y+15) = 4(y+3)(y+5)
y^2+8y+15 = (y+3)(y+5)
LCD = 4(y+3)(y+5)
The function h(x)=x² +5 maps the domain given by the set {-2, -1, 0, 1, 2}. Which of the following sets
represents the range of h(x)?
(1) {0, 6, 10, 12)
(2) {5,6,7}
(3) {5, 6,9}
(4) {1, 4, 5, 6,9}
For the given function h(x) = x² +5 ,the domain of the function h(x) maps by the set { -2, -1, 0, 1, 2 } then the range of the function h(x) is given by the set { 5, 6, 9 } .
As given in the question,
Given function is equal to :
h(x) = x² +5
Domain of the function h(x) = x² +5 maps by the set { -2, -1, 0, 1, 2 }
Range of the function h(x) = x² +5 is represented by the set as follow :
Substitute the value x = -2, -1, 0, 1, 2 in the function h(x) = x² +5 we get,
h(-2) = (-2)² + 5
= 9
h(-1) = (-1)² + 5
= 6
h(0) = (0)² + 5
= 5
h(1) = (1)² + 5
= 6
h(2) = (2)² + 5
= 9
Range of the function is represented by the set : { 5, 6, 9 }
Therefore, for the given function h(x) = x² +5 ,the domain of the function h(x) maps by the set { -2, -1, 0, 1, 2 } then the range of the function h(x) is given by the set { 5, 6, 9 }.
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A certain insect can beat its wings 10 times per second. Write an equation in slope-intercept form that shows the relationship between flying time in seconds and the number of times the insect beats its wings.
The equation in slope-intercept form that shows the relationship is y = 10x
How to determine the equation?From the question, we have the following parameters that can be used in our computation:
Rate of beating wings = 10 times per second
The equation in slope-intercept form of the relationship is then represented as
y = Rate of beating wings * x
Where
y is the number of times
x is the wings
So, we have
y = 10 * x
Evaluate
y = 10x
Hence, the equation is y = 10x
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Determine the equation of the axis of symmetry for the parabola that passes through
points (-4,0) and (6,0).
(A) x = -2
(B) x=2 (C) x=-1
10
D
с
a
b
n
d
(D) x = 1
Answer:
D
Step-by-step explanation:
the axis of symmetry is a vertical line with equation x = c
where c is the value of the x- coordinates the line passes through.
the line crosses the x- axis at the midpoint of the zeros
given (- 4, 0 ) and (6, 0 ) , that is
zeros are x = - 4 and x = 6
then equation of axis of symmetry is
x = (- 4 + 6) ÷ 2 = 2 ÷ 2 = 1 , that is
x = 1 ← axis of symmetry
Are these 4 problems SSS SAS ASA AAS HL
1. The first figure posses the SSS property.
2. The second figure posses the ASA property.
3. The third figure posses the hypotenuse length property.
4. The fourth figure posses the SAS property.
Given:
1. The first figure shows the SSS property.
Side-Side-Side criterion is referred to as the SSS criterion. According to this standard, two triangles are congruent if their respective triangles' three sides are equal to one another.
hence the two triangles are congruent.
2. The second figure posses the ASA property.
Angle-Side-Angle criterion is also known as ASA criterion. According to the ASA criterion, two triangles are congruent if any two of their included sides and related angles are equivalent in size to those of the other triangle.
hence the two triangles are congruent.
3. The third figure posses the hypotenuse length properety.
RHS criterion stands for right angle-hypotenuse-side congruence criterion. Under this criterion, two triangles are congruent, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle.
hence the two triangles are congruent.
4. The fourth figure posses the SAS property.
Side-Angle-Side criterion is referred to as the SAS criterion. According to this standard, two triangles are said to be congruent if their matching sides and included angles are the same on each side of each other.
hence the two triangles are congruent.
Hence we get the required answer.
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an article in a medical journal suggested that approximately 18% of such operations result in complications. using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.06?
The needed Sample size is 32.2 so that the confidence interval will have a margin of error of 0.06.
We have provided that , An article in a medical journal approx. 18% of operation results complications.
Using the estimate formula, for standard margin of error
Margin of error (E) = Z x √p(1-p)/n
where , E---> margin of error
Z---> estimate value
p----> sample proportion
n -----> Sample size
we have the value of E = 0.06 , p = 18% = 0.18
put all the values in above formula we get,
0.06 = Z × √0.18× 0.82/n
critical value or Z-value for sample proportion 0.18 is 0.91
Now, 0.06 = 0.91 × √0.18×0.82/n
=> √0.14/n= 0.065 => 0.14/n = 0.0043
=> n= 32.2
So, sample size is 32.2
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Based on the following calculator output, determine the mean of the dataset, rounding to nearest 100th if necesssrt.
The mean is 63.12 using the data given.
Given that,
Calculate the dataset's mean using the output from the following calculator, rounding to the nearest 100th if necessary.
1-Var-Stats
[tex]\bar x[/tex] = 63.1428571429
∑x = 442
∑x² = 28266
Sₓ = 7.71208081364
σₓ = 7.13999942834
n = 7
minX = 48
Q₁ = 58
Med = 66
Q₃ = 69
maxX = 69
Mean value is defined as sum of all data values divided by the total number of data values
Using the given data output
We get,
Mean = 63.14 (rounded to 2 decimals)
Therefore, The mean is 63.12 using the data given.
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what is the value of the expression below ?
Answer: -10.
Step-by-step explanation:
30/3 = 10.
However, there is a negative number in the expression.
A rule you need to remember is when you divide 2 numbers with different signs, the answer is negative. If you divide 2 numbers with the same sign, the answer is positive.
30/-3 = -10.
What value of a makes lines m and n parallel?
Answer:
20
Step-by-step explanation:
3x + 5 should be equal to 65
3x + 5 = 65
3x = 65 - 5
3x = 60
x = 60/3
x = 20
please help me
what ∞ times x = what
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Infinity is denoted by ∞.
∞ = 1/0
∞ times x is ∞
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Infinity is denoted by ∞.
∞ = 1/0
Now,
∞ times x = ∞
Whatever we multiply with infinity will always give us infinity.
Thus,
∞ times x is ∞
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y + 2.1 > 0.8 Solve the inequality for y.
Simplify your answer as much as possible.
Answer:
y>-1.3
Step-by-step explanation:
y+2.1>0.8
-2.1. -2.1
y>-1.3
Hopes this helps please mark brainliest
Answer:
Hi! Okay so the Inequality form would be: Y>-1.3
and the Interval Notation would be: (-1.3, ∞)
Sorry if it doesn't work btw
Step-by-step explanation:
what 27 over 54 in lowest terms
Answer: 1/2
Step-by-step explanation: Divide both the numerator and denominator by the GCD (Greatest Common Denominator)
27 ÷ 27
54 ÷ 27 (its 27/54 divided by 27/27
Reduced fraction:
1/2
Therefore, 27/54 simplified to lowest terms is 1/2.