The area of the region is between the upper and lower sums, which are 0.5625 and 0.5.
Calculate Area Using SumsTo use upper and lower sums to approximate the area of a region, we need to first divide the region into subintervals of equal width. Once we have the subintervals, we can then use the function values at the upper and lower bounds of each subinterval to calculate the upper and lower sums.
In this case, we are given that y = 3x, and we are asked to use n = 4 subintervals to approximate the area of the region.To find the width of each subinterval, we can use the formula:width = (b - a) / n, where a and b are the lower and upper bounds of the region, and n is the number of subintervals.
Let's assume the region is between x = 0 and x = 1.Therefore, the width of each subinterval is (1 - 0) / 4 = 0.25.Next, we can use the upper and lower bounds of each subinterval to calculate the upper and lower sums.The upper sum is calculated by multiplying the function value at the upper bound of each subinterval by the width of the subinterval and summing up the results:Upper sum = 0.25 × f(0.25) + 0.25 × f(0.5) + 0.25 × f(0.75) + 0.25 × f(1)The lower sum is calculated by multiplying the function value at the lower bound of each subinterval by the width of the subinterval and summing up the results:Lower sum = 0.25 × f(0) + 0.25 × f(0.25) + 0.25 × f(0.5) + 0.25 × f(0.75)Since we know y = 3x, we can use this to calculate the function value at each bound:Upper sum = 0.25 × 30.25 + 0.25 × 30.5 + 0.25 × 30.75 + 0.25 × 31 = 0.5625Lower sum = 0.25 × 30 + 0.25 × 30.25 + 0.25 × 30.5 + 0.25 × 30.75 = 0.5Therefore the area of the region is between the upper and lower sums, which are 0.5625 and 0.5 respectively.Learn more about Lower and Upper Sums here:
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The measures of the angles of a triangle are shown in the figure below. Solve for x. (3x)° 58° 80°
Answer:
x=14
Step-by-step explanation:
The angles inside a triangle add up to 180 degress all the time, therefore
58+80+3x=180
simplify
138+3x=180
subtract 138 from both sides of the equation
3x=42
divide both sides by 3
x=14
Help me outtt please I reallyyyy need it
Answer:
Step-by-step explanation:
x36 + 24
x39x² + 24x - 28
x3(x2 + 9x - 28/3)
x3(x + 28/3)(x - 3)
Write an expression in simplest form to represent the area of the shaded region 3X 2 2X 3X 4X 
Answer:
6[tex]x^{2}[/tex] + 8x
Step-by-step explanation:
4x(3x + 2) = 12[tex]x^{2}[/tex] + 8x is the area of the big rectangle
2x(3x) = 6[tex]x^{2}[/tex] is the area of the small rectangle.
Subtract the small rectangle from the large rectangle to find the area of the shaded region
12[tex]x^{2}[/tex] + 8x - 6[tex]x^{2}[/tex]
6[tex]x^{2}[/tex] + 8x
it's overlapping triangles, high school 10th grade math.
the statements need to be matched to the reasons.
In the overlapping triangles, the statements needed to be match to the reasons are explained below.
Properties of a triangle.A triangle is sometimes referred to as trigon because it is bounded by three straight sides, and has a measure of internal angles which add up to 180^o.
Considering the overlapping triangles given in the question, the statements to be matched to the reasons are given below:
STATEMENT REASON
1. ΔRTN ≅ ΔSTM Side-Angle-Side (SAS)
2. <T ≅ <T Betweenness
3. RN = SM Reflexive property
4. RM = SM, TM = TN Given
5. RT = ST Substitution
6. RM + TM = TN + SN CPCTE
7. RM + TM = SN + TM Addition property of equality
The match of statements with the reasons are required to proof that RN = SM
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The product (x+5)(x - 1)(x+2) is equal to:
OA³+61²-13x-10
OB. ³+6x² +13x+10
Ox³+6x²-3x - 10
D. x³ +6x² + 3x - 10
E. x² +6x-3x+10
The product (x+5)(x - 1)(x+2) is equal to x³ +6x² + 3x - 10 (C)
What is the product rule in math?According to the Product Rule, the derivative of a product of two functions is equal to the product of the first function times the second function's derivative plus the second function times the first function's derivative.
What are the product and sum rules?The sum rule explains how many different methods there are to choose between two distinct groups of options. The product rule explains how many different methods there are to choose from each of two sets of options. Both laws apply to bigger sets families in general.
In the given question:-
=(x+5)(x - 1)(x+2)
=(x+5)(x^2+x-2)
=x^3+6x^2+3x-10
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Find the missing value so that the line passing through the points has the given slope.
(x,9) and (1,6); m=1
Answer:
m = [F(y2) - F(y1) ] / [[F(x2) - F(x1)] slope of a line
[9 - 6] / [x - 1] = 1 that an increase in x equals the increase in y
Obviously, x must equal 4 so 3 / 3 = 1 or when x increases by 3, y must also increase by 3 for m to equal 1
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of xx that support your conclusion -x=1
Answer: The equation -x = 1 has only one solution, x = -1.
This can be shown by solving the equation for x:
-x = 1
x = -1
To show that this equation has only one solution, we can plug in -1 for x and check that the equation is true:
-(-1) = 1
1 = 1
So x = -1 is the solution.
No other values of x would work here and make the equation true.
Step-by-step explanation:
What are the 4 properties of solution?
The 4 properties of solutions are:
1) Consistency
2) Validity
3) Feasibility
4) Stability
PROPERTIES OF SOLUTIONSIn mathematics, a solution to an equation or system of equations is a set of values that can be substituted into the equation(s) to make the statement(s) true. The four properties of a solution are:
1) Consistency: A solution exists and is unique, or multiple solutions exist.
2) Validity: The solution(s) must satisfy the equation(s) and any constraints or boundary conditions.
3) Feasibility: The solution(s) must be within the domain of the equation(s) and any constraints or boundary conditions.
4) Stability: The solution(s) should be insensitive to small changes in the equation(s) or initial conditions.
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can someone help mr solve this i dont understand it
Answer: THE ANSWER IS 12
Step-by-step explanation:
HOPE IT HELPS =D
Solve 3x^2+16x-5 using quadratic equation
Using quadratic equation, the value of x is 5 and -1/3
How to calculate the value of x using quadratic equation?3x²+16x-5
3x² +16x -5= 0
Split the middle term using two factors
3x² -15x -x -5= 0
Take out the common factors
(3x-1)(x-5)= 0
3x+1= 0
3x= 0-1
3x= -1
x= -1/3
x-5= 0
x= 0+5
x= 5
Hence x = 5 and x= -1/3
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A relation is plotted as a linear function on the coordinate plane starting at point E at(0, 27)and ending at point F at (5, −8).
What is the rate of change for the linear function and what is its initial value?
Select from the drop-down menus to correctly complete the statements.
The rate of change for a linear function, also known as the slope, can be found by calculating the change in the y-coordinate (rise) divided by the change in the x-coordinate (run) between two points on the line. The slope of a line describes how steep the line is and whether it is increasing or decreasing.
In this case, the slope of the linear function can be found by using the coordinates of points E and F:
Slope = (y2 - y1) / (x2 - x1)
Slope = (-8 - 27) / (5 - 0)
Slope = -35/5
The slope of the linear function is -35/5 or -7.
The initial value of a linear function is the y-intercept, which is the point where the line crosses the y-axis. To find the y-intercept, we can use the slope and one point on the line (in this case point E (0,27)):
y = mx + b
27 = -7(0) + b
b = 27
The y-intercept of the linear function is 27.
So, the linear function starts at point E (0,27) with an initial value of 27, and has a rate of change or slope of -7.
To assist faculty and students with
research, a school librarian must be
which of the following?
Professional librarians should be accessible to pupils, according to administrators
What are the main leadership roles performed by a school librarian?Professional librarians should be accessible to pupils, according to administrators. Although librarians wear many hats, their three primary responsibilities are to promote literacy, manage resources, and specialize in research. By identifying and acquiring library items based on the curriculum and student interests, school librarians, who are information specialists, build a resource base for the school. Additionally, they keep the library collection organised and up-to-date to encourage individual reading and lifelong learning. They could teach you the fundamentals of literature or perhaps do it for you. They can offer you facts or data that they have gleaned from years of experience.
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213.5 miles in 3.5 hours. At that rate, how many miles will he travel in 7.2
hours?
Answer: 439.2 miles
Step-by-step explanation:
213.5/3.5=61
61*7.2=439.2 miles in total
What is the value of exponential 2?
The value of exponential 2 is 2^2, or 4. This means two multiplied by itself two times or squared.
Exponential notation is a way of expressing a number, usually greater than 10, as a base number, the number 2 in this case, raised to a power, which in this case is 2. Therefore, exponential 2 is written as 2^2, which means two multiplied by itself two times or squared.
For example, if we wanted to find the value of exponential 8, we could easily calculate 2^8, or 256, which is much faster than multiplying 2 by itself 8 times. Exponential notation is also helpful when calculating exponents with variables.
For example, if we wanted to find the value of 3^x, we could use exponential notation to find the answer quickly. In summary, exponential notation is a useful tool for quickly finding the value of a number raised to a power.
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What is the best way to show that the side lengths 8 feet, 16 feet, and 22 feet do NOT form a right triangle?
1. Substitute the values into the Pythagorean theorem and show that a false statement results.
2. Determine the sum of the side lengths and compare it to the Pythagorean theorem.
3.Calculate the difference between the horizontal and vertical coordinates of each pair of measurements to show the triangle is equilateral.
4.Use the coordinate plane to draw the triangle and show that it is an acute triangle.
Substitute the values into the Pythagorean theorem and show that a false statement results.
What is the best way to show that the side lengths 8 feet, 16 feet, and 22 feet do NOT form a right triangle?The best way to show that the side lengths 8 feet, 16 feet, and 22 feet do not form a right triangle is to substitute these values into the Pythagorean theorem and show that a false statement results.The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side.In this case, 8^2 + 16^2 = 64 + 256 = 320, which does not equal 22^2 = 484.This disproves the possibility of the triangle being a right triangle. As an alternative, one could also determine the sum of the side lengths and compare it to the Pythagorean theorem.In this case, the sum of the side lengths is 8 + 16 + 22 = 46, which again does not equal the square of the longest side.Both these methods show that the side lengths 8 feet, 16 feet, and 22 feet do not form a right triangle.To learn more about Pythagorean theorem refer to:
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Someone please help rn I’ll mark brainliest !!
The length of the side BD is; 8
The measure of the angle DAB is; ∠DAB = 53°
How to interpret Congruent Triangles?Two triangles are said to be congruent by any of the following postulates;
1) SSS (Side Side Side) Congruence Postulate.
2) SAS (Side Angle Side) Congruence Postulate.
3) ASA (Angle Side Angle) Congruence Postulate.
4) AAS (Angle Angle Side) Congruence Postulate.
5) HL (Hypotenuse Leg) Congruence Postulate
Now, for the given triangles that are congruent, we can say that;
∠ADC ≅ ∠ACB
∠DAB ≅ ∠CAB
BD ≅ BC
AC ≅ AD
Thus;
BD = 8
∠DAB 53°
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Is it 3 pair or 3 pairs?
It is "3 pairs" not "3 pair", because a pair is a set of two things, so if you have 3 of them it would be 3 sets of two things or 3 pairs.
find the area of shaded region
Answer:
119 cm²
Step-by-step explanation:
Area of shaded region:Area of white triangle:
base = 9 cm
height = 14 cm
[tex]\sf \boxed{Area \ of \ triangle = \dfrac{1}{2}*base *height}[/tex]
[tex]\sf =\dfrac{1}{2}*9*14\\\\ = 9*7\\\\= 63 \ cm^2\\[/tex]
Area of trapezium:
[tex]\sf \boxed{Area \ of \ trapezium =\dfrac{(a+b)*h}{2}}[/tex]
Here, a and b are the parallel sides of trapezium & h is the height.
a = 9 cm ; b = 17 cm and h =14 cm
[tex]\sf Area \ of \ trapezium = \dfrac{(9+17)*14}{2}[/tex]
[tex]= \dfrac{26*14}{2}\\\\\\=13*14\\\\= 182 \ cm^2[/tex]
Area of shaded region = area of trapezium - area of white triangle
= 182 - 63
= 119 cm²
Answer:
area of shaded region = 119 cm²
Step-by-step explanation:
the outer figure has one pair of parallel sides and is a trapezium.
the shaded area (A) is calculated as
A = area of trapezium - area of white triangle
the area of a trapezium is calculated as
area = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
here h = 14 , b₁ = 9 , b₂ = 17 , then
area = [tex]\frac{1}{2}[/tex] × 14 × (9 + 17) = 7 × 26 = 182 cm²
the area of the triangle is calculated as
area = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = 9 and h = 14 , then
area = [tex]\frac{1}{2}[/tex] × 9 × 14 = 4.5 × 14 = 63 cm²
then area of shaded region (A) is
A = 182 - 63 = 119 cm²
Suppose DE is 500 yards, AB is 200 yards, and BC is 100 yards. What is the distance across the river (BD)?
The distance across the river (BD) is 800 yards
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Types of equation are linear, quadratic, cubic and so on.
From the image shown, triangle ABC and triangle ADE are similar triangles. For similar triangles, the ratio of corresponding sides are proportional to each other. Hence:
AD/AB = DE/BC
substituting values:
AD / 200 = 500/100
AD = 1000 yards
AD = AB + BD
substituting:
1000 = BD + 200
BD = 800 yards
The value of BD is 800 yards
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Find the SP
Radio : cp =2,720, profit = 5 % sp
Cost is equal to Selling price plus Loss ( when selling price and loss is given )Therefore, the cost price (C.P.) is 350.
Find the C.P ?Cost is the same as the selling price plus the loss ( when selling price and loss is given ).
The Profit and Loss Percentage Formula
Profitability (P%) is calculated as (Profit /Cost Price) / 100.
Loss percentage (L%) Equals 100 divided by (Loss / Cost price).
S.P. = {(100 + P%)/100}
if SP > CP, then CP
If SP > CP, S.P. = (100 - L%)/100 CP
C.P. = {100/(100 + P%)}
if SP > CP, then SP
C.P. = SP (if SP > CP)/100/(100 - L%)
Loss percent = 10%
To find:
The C.P.
Solution:
Let x be the C.P.
We have,
S.P. = 315
Loss percent = 10%
S.P = C.P - 10% 0f C.P
315 = X- 0.1X
315 = 0.9 X
Divide both sides by 0.9.
315/0.9 =X
350 = x
Therefore, the cost price (C.P.) is 350.
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A rectangular box has the length of [tex]\sqrt{90}[/tex] inches, width of [tex]\sqrt{14}[/tex] inches, and height of [tex]\sqrt{70}[/tex] inches.
a. What is the volume of the box?
b. What is the area of the top of the box?
c. What is the ratio of the height of the box to the length of the box?
Don't answer in decimals.
The volume, surface area, and ratio of the height of the box to the length will be 296.98 cubic inches, 292.35 square inches, and 0.88, respectively.
What is a rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
A rectangular box has a length of √90 inches, a width of √14 inches, and a height of √70 inches.
The volume of the box is given as,
V = LBW
V = (√90) x (√14) x (√70)
V = 296.98 cubic inches
The area of the top of the box is given as,
SA = 2(LW + WB + BL)
SA = 2(√90 x √14 + √14 x √70 + √70 x √90)
SA = 292.35 square inches
The ratio of the height of the box to the length of the box is given as,
H / L = √70 / √90
H / L = 0.88
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How do you reflect a line over Y =- 2?
To reflect a line over the line y = -2, we can first graph the line and then apply a transformation. A reflection in the y = -2 line can be thought of as a reflection in the x-axis, followed by a translation 2 units upward.
The transformation for a reflection over the line y = -2 is given by (x, y) → (x, -y - 4). To reflect a point (x, y) over the line y = -2, we substitute the coordinates of the point into the transformation and solve for the reflected point.
For example, to reflect the point (3, 4) over the line y = -2, we would substitute the coordinates into the transformation to get (3, -4 - 4) = (3, -8).
To reflect a line, we can reflect each point of the line over the line y=-2 and plot the reflected points.
In conclusion reflecting a line over y=-2 is done by applying a transformation (x, y) -> (x, -y - 4) to each point of the line, this can also be thought of as reflecting the line over x-axis and then translating 2 units upward.
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Compared to lat year, the population of Boom Town ha increaed by 25%. The population i now 6,000. What wa the population lat year
The population of the Boom town increased by 25% compared to last year, present population is 6000 then last year population is equal to 4800.
As given in the question,
Given population of the present year is equal to 6000
Let us consider 'x' be the last year population.
Increased in population compared to last year = 25%
Required equation is given by :
x + (25/100)x = 6000
⇒ (125 / 100 )x = 6000
⇒ x = ( 6000 × 100 ) / 125
⇒ x = 4800
Therefore, the population of the last year as per given data of the present year is equal to 4800.
The above question is incomplete, the complete question is:
Compared to last year, the population of Boom Town has increased by 25%. The population is now 6,000. What was the population last year?
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Inusah is x years old now if his age in 11 years time will be 3 times his age 7 years ago, how old is he now
===============================================
Work Shown:
x = his age now
x+11 = his age 11 years into the future
x-7 = his age 7 years ago
The equation to set up is
x+11 = 3(x-7)
since his age 11 years into the future is triple that of his age 7 years ago.
-------
Let's solve for x.
x+11 = 3(x-7)
x+11 = 3x-21
x-3x = -21-11
-2x = -32
x = -32/(-2)
x = 16
He is currently 16 years old.
11 years from now he'll be 16+11 = 27, and 7 years ago he was 16-7 = 9.
Note that 9*3 = 27 to help confirm the answer.
Answer:
16
Step-by-step explanation:
3(x-7)=x+11
Plug into equation and find value of x
A banker loaned $5000 to one cutomer and $8000 to another. If the annual interet on the econd loan i %2 higher than the firt and the combined annual interet i $810, What i the interet rate for each loan?
The interest rate for first loan is 5% and for the second loan is 7%.
The amount of first loan = $5000
Let the rate of interest for first loan = r
The interest from first loan = ($5000 × r)/100
= 50 r
The amount of second loan = $5000
Let the rate of interest for second loan = r+2
The interest from first loan = ($8000 × (r+2))/100
= 80 r + 160
Total interest = 50 r + 80 r + 160
= 130 r + 160
As per the question statement combined annual interest = $810
810 = 130 r + 160
r = (810-160)/130
r = 5%
Rate of second loan = r+2 = 5+2
= 7%
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Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).
YOU WILL GET BRAINLIEST IF SOLVED WITH EXPLANATION!
The area of the shaded region would be 4π - 8 square units.
What is the area of a circle?
The area of a circle is given by the formula: A = πr^2, where A is the area, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. The radius is the distance from the center of the circle to its edge.
In the given figure we have to find the height of the triangle and that will be the radius of the triangle.
In the triangle LMO,
Angle opposite to 45 = 1/√2* hypotenuse
MO = 1/√2 * 4
MO =2√2
Radius of the circle= 2√2
Area of the triangle = 1/2* MO * LN
= 1/2 * 2√2*4√2
= 8
Area of semi-circle =1/2 * πr²
=1/2 * π(2√2)²
= 4π
Area of shaded region = 4π - 8
Hence, the area of the shaded region would be 4π - 8 square units.
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the length of a rectangle is 3in longer than its width. if the perimeter of the rectangle is 66in, find its length and width
Answer:
Length = 18inch
Width = 15inch
Step-by-step explanation:
(Process/Explanation Below)
⇒ 66 ÷ 2 = 33 (We divide by 2 because we need to find two measurements which are our length and width)
⇒ 33 - 3 = 30 (Since the width is 3inches smaller than the length we have to subtract by 3.)
⇒ 30 ÷ 2 = 15in width (This is our width because since a rectange has 2 sides we have to divide by 2.)
⇒ 5 + 3 = 18in length (This is our length because it says the length is 3inches longer than the width and the width is 15inches.)
you decide to buy a custom frame for painting which measures 6 by 14 inches. if the framing material cost 6$ per inch, what is the total(
The total cost of the rectangular frame is C = $240.
How to find the total cost?After a small search online, I found the original question, it is written at the end of the answer.
Remember that for a rectangle of length L and width W, the perimeter is given by:
P = 2*(L + W)
In this case, we know that the frame is 6 inches by 14 inches, then the perimeter will be:
P = 2*(6in + 14in)
P = 2*20in = 40in
And we know that the framing material costs $6 per inch, then the total cost of the frame will be:
cost = 40*$6 = $240
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After a small search online, I found that the complete question is:
"You decide to buy a custom frame for a painting which measures 4 by 6 inches. If the framing material costs $2 per inch, what is the total cost of framing material?"
What do 2 straight lines mean in math?
In mathematics, two straight lines can mean a number of things depending on the context. In general, a straight line is a geometric object that has no curvature and extends infinitely in both directions.
When two straight lines are considered together, they can either be parallel, meaning they will never intersect, or they can be intersecting, meaning they will cross at exactly one point. If the two lines are parallel, they will have the same slope, and if they are intersecting, the lines will have different slopes.
The slope-intercept equations for the two straight lines in analytical geometry are written as y = mx + b, where m is the slope, x and y are the coordinates of a point on the line, and b is the y-intercept.
In conclusion, two straight lines can have different meanings in mathematics depending on the context, such as parallel or intersecting, which can be represented by their equations in slope-intercept form.
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• A cylindrical potato chip container has a diameter of 3.5 inches and a height of 12 inches. What is the volume of thi
chip container? Use 3.14 for pi. Round your answer to the nearest hundredth. (4 points)
57.73 in3
115.40 in3
• 350.65 in3
461.81 in3
Accordingly, the cylinder's volume would be 115.45 cubic inches given its parameters.
Calculate the cylinder's volume?By multiplying the base area and height of a cylinder, one may get its volume. The radius of the circular base equals half its diameter, and the area of the base is equal to the area of a circle, which is denoted by the formula A = r2. As a result, a cylinder's volume equals:
Cylinder volume equals (r2)
h = 12 inches, where r = D/2 = 3.5 inches, 2 inches, and 1 inch.
Cylinder volume equals (1.75")2. ( 12 in )
147/4 in3 or 115.45353 in3 is the volume of the cylinder.
Accordingly, the cylinder's volume would be 115.45 cubic inches given its parameters.
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