The construction steps for bisecting an angle are similar to those for bisecting a line segment as both involve using a compass and straightedge, but the former creates an angle with a specific degree measure while the latter divides a line segment into two equal parts.
The construction steps for constructing and bisecting an angle are similar to the steps for constructing and bisecting a line segment in that they both involve using a compass and straightedge to create geometric constructions.
However, the steps are different in that constructing and bisecting an angle involves creating an angle with a specific degree measure, whereas constructing and bisecting a line segment involves dividing a line segment into two equal parts.
To construct and bisect an angle, the compass is used to create congruent arcs on either side of the angle, and the straightedge is used to connect the intersections of those arcs to create the angle. To bisect a line segment, the compass is used to create arcs of equal length from the endpoints of the segment, and the straightedge is used to connect the intersection of those arcs to the midpoint of the segment.
So while both constructions involve the use of similar tools and techniques, the specific steps required for each are unique.
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5+sin(3x)=4
solve for x on the unit circle where x is between 0 and 2pi
The solutions for x between 0 and 2π are: x = π/2, (5π)/6, and (11π)/6.
To solve the equation 5 + sin(3x) = 4 for x on the unit circle, where x is between 0 and 2π, follow these steps:
1. Subtract 5 from both sides: sin(3x) = -1
2. Determine the angle for which sin is -1: sin(3x) = sin(3π/2)
3. Since the sine function has a period of 2π, the general solution is: 3x = 3π/2 + 2πk, where k is an integer.
4. Divide both sides by 3: x = π/2 + (2πk)/3
Now, find the values of x between 0 and 2π by trying different integer values of k:
- If k = 0, x = π/2
- If k = 1, x = π/2 + 2π/3 = (5π)/6
- If k = 2, x = π/2 + 4π/3 = (11π)/6
Thus, the solutions for x between 0 and 2π are: x = π/2, (5π)/6, and (11π)/6.
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On Saturday mornings, Roger volunteers at the hospital. One Saturday, he answers phone calls at the information desk while the receptionist is away. Then he spends 40 minutes delivering flowers to patients' rooms. In all, Roger volunteers at the hospital for 90 minutes that day. Which equation can you use to find the amount of time t that Roger answers phone calls?
We know that by solving for t, you can find the amount of time Roger spent answering phone calls
You can use the equation t + 40 = 90, where t represents the amount of time Roger answers phone calls at the information desk.
This equation takes into account that Roger spends 40 minutes delivering flowers and the total time he volunteers at the hospital is 90 minutes.
By solving for t, you can find the amount of time Roger spent answering phone calls.
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A man buys a car at a cost of r60 000 from cape town and transported it to durban at a cost price of by r4 500. at what price must he sell the car to make an overall profit of 25%
He must sell the car at R80,625 to make an overall profit of 25%
To find the selling price of the car that gives a 25% profit, we need to use the following steps:
Calculate the total cost of buying and transporting the car to Durban:
Total cost = Cost of car + Cost of transportation
Total cost = R60,000 + R4,500
Total cost = R64,500
Calculate the desired profit:
Profit = 25% of total cost
Profit = 0.25 x R64,500
Profit = R16,125
Calculate the total amount that the car needs to be sold for:
Total amount = Total cost + Profit
Total amount = R64,500 + R16,125
Total amount = R80,625
Therefore, the man needs to sell the car for R80,625 to make an overall profit of 25%.
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Does the budgeted amount cover the actual amount for expenses, savings, and emergencies? A) No, it's short $207. 0. Eliminate B) No, it's short $227. 0. C) Yes, there's a surplus of $207. 0. D) Yes, there's a surplus of $227. 0
Based on the options provided, it seems that the question is asking whether the budgeted amount is enough to cover expenses, savings, and emergencies. The answer would be either A, B, C, or D.
A) No, it's short $207.0.
B) No, it's short $227.0.
C) Yes, there's a surplus of $207.0.
D) Yes, there's a surplus of $227.0.
Unfortunately, without more information about the specific budgeted amount and the actual expenses, savings, and emergencies, it is impossible to determine the correct answer. It is important to regularly track expenses and compare them to the budgeted amount to ensure that there is enough money to cover all necessary expenses and unexpected events. If there is a shortfall, it may be necessary to adjust the budget or find ways to increase income or decrease expenses to ensure financial stability.
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Can you help me with part C? Please
Answer: -40
Step-by-step explanation:
Rate of change is calculated as the slope. The formula for Slope is:
S = [tex]\frac{x_{1}-x_{2} }{ y_{1}-y_{2}}[/tex]
The two points we have are when x = 3 and 6.
the points are (3, 120) and (6, 0), as we can see.
plugging into the slope formula:
S = [tex]\frac{120-0 }{ 3-6}[/tex]
S = 120/-3
S = -40
Which hopefully makes sense, because the slope is negative, (the graph is falling).
solve quadratic equation 6x²-11x-35= 0 pls needed urgently
Answer:
Step-by-step explanation:To solve the quadratic equation 6x²-11x-35= 0, we can use the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation.
In this case, we have:
a = 6
b = -11
c = -35
Substituting these values into the quadratic formula, we get:
x = (-(-11) ± sqrt((-11)² - 4(6)(-35))) / 2(6)
Simplifying this expression:
x = (11 ± sqrt(121 + 840)) / 12
x = (11 ± sqrt(961)) / 12
x = (11 ± 31) / 12
So, we have two solutions:
x = (11 + 31) / 12 = 3
and
x = (11 - 31) / 12 = -5/2
Therefore, the solutions to the equation 6x²-11x-35= 0 are x = 3 and x = -5/2.
Taylor would like to have a karaoke deejay at her graduation party. her three sisters volunteered to split the cost of hiring the deejay. they need to rent a tent for $45 and a microphone system for $60 and then pay the deejay $30 an hour for four hours. how much do each of the sisters owe?
write out all the work used to determine the answer to the question.
Each of the three sisters owes $75 to cover the cost of hiring the karaoke deejay for Taylor's graduation party.
To determine how much each sister owes, we need to first calculate the total cost of the party and then divide that cost by three, since there are three sisters splitting the cost.
1. Tent rental: $45
2. Microphone system: $60
3. Deejay cost: $30/hour × 4 hours = $120
Now, we'll add these costs together to find the total cost:
Total cost = $45 (tent) + $60 (microphone) + $120 (deejay) = $225
Finally, we'll divide the total cost by the number of sisters (3) to find out how much each sister owes:
Amount owed per sister = $225 (total cost) ÷ 3 (sisters) = $75
So, each sister owes $75 for the karaoke deejay at Taylor's graduation party.
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Jesus works at a computer outlet. He receives a bi-weekly salary of
$300 plus 5. 5% commission on his sales. In the last two weeks, he sold
$16,200 of computer equipment. He pays 8% for State Income Tax,
12. 3% for Federal Income Tax, 6. 3% for Social Security, and 1. 45%
for Medicare. What steps did I take to find Jesus' net bi-weekly
pay? (Show your work)
Jesus' net bi-weekly pay is $856.69 after paying his taxes and deductions.
To find Jesus' net bi-weekly pay, I followed these steps:
Calculate Jesus' commission: Jesus sold $16,200 of computer equipment, so his commission is 5.5% of $16,200, which is $891.
Calculate Jesus' gross bi-weekly pay: Jesus receives a bi-weekly salary of $300 plus his commission of $891, so his gross bi-weekly pay is $1,191.
Calculate Jesus' deductions: Jesus pays 8% for State Income Tax, 12.3% for Federal Income Tax, 6.3% for Social Security, and 1.45% for Medicare. To calculate the deductions, I multiplied his gross bi-weekly pay by each percentage rate:
State Income Tax: 8% of $1,191 = $95.28
Federal Income Tax: 12.3% of $1,191 = $146.67
Social Security: 6.3% of $1,191 = $75.09
Medicare: 1.45% of $1,191 = $17.27
Subtract the deductions from the gross bi-weekly pay: To find Jesus' net bi-weekly pay, I subtracted the total deductions of $334.31 from his gross bi-weekly pay of $1,191:
Net bi-weekly pay = $1,191 - $334.31 = $856.69
Therefore, Jesus' net bi-weekly pay is $856.69 after paying his taxes and deductions.
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44
In the expression 5 x y/7, what value of y would make a product greater than 5 ?
Explain your answer.
Answer: ⬇️⬇️
Step-by-step explanation:
In the expression 5 x y/7, the value of y that would make a product greater than 5 is 8.
HOW TO SOLVE ALGEBRAIC EXPRESSIONS?
According to this question, the following algebraic equation was given:
5 x y/7
This equation reveals that the result can only be equal to 5 when y is exactly 7.
This is because if y = 7, y/7 = 1.
Therefore, the value of y that would make a product greater than 5 is 8.
I Need help with a Math Problem (zoom in if you can’t see it) (if you can’t see it the problem is ( x degrees 49 degrees and 39 degrees) find the value of x
Answer:
Step-by-step explanation:
If there are 180 degrees in a triangle total and in this problem we know that one angle is 49 and the other is 39, we can assume that subtracting 39 and 49 from 180 will find x. In this case, x will be 92.
Para el periódico mural, los alumnos decidieron representar un pino por medio de un triángulo que tiene una superficie de 1. 5m si la base mide 1. 5 m ¿cuanto mide la altura? 
The height of the triangle is 2 meters.
How tall is triangle?Para encontrar la altura del triángulo, podemos utilizar la fórmula para calcular el área de un triángulo:
Área = (base x altura) / 2
Sabemos que el área es de 1.5 m² y que la base mide 1.5 m, por lo que podemos despejar la altura de la siguiente manera:
1.5 m² = (1.5 m x altura) / 2
Multiplicando ambos lados por 2:
3 m² = 1.5 m x altura
Despejando la altura:
altura = 3 m² / 1.5 m
altura = 2 m
Por lo tanto, la altura del triángulo que representa al pino en el periódico mural es de 2 metros.
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Let f(x) = x² – 6x. Round all answers to 2 decimal places. = a. Find the slope of the secant line joining (2, f(2) and (7, f(7)). Slope of secant line = b. Find the slope of the secant line joining (6, f(6)) and (6 + h, f(6 + h)). Slope of secant line = c. Find the slope of the tangent line at (6, f(6)). Slope of the tangent line d. Find the equation of the tangent line at (6, f(6)). y =
The equation of the tangent line at (6, f(6)) is y = 6x - 48.
a. The slope of the secant line joining (2, f(2)) and (7, f(7)) is:
slope = (f(7) - f(2)) / (7 - 2)
We can find f(7) and f(2) by plugging in x = 7 and x = 2 into the expression for f(x):
f(7) = 7² - 6(7) = 7
f(2) = 2² - 6(2) = -8
Substituting these values into the slope formula, we get:
slope = (7 - (-8)) / (7 - 2) = 3
Therefore, the slope of the secant line joining (2, f(2)) and (7, f(7)) is 3.
b. The slope of the secant line joining (6, f(6)) and (6 + h, f(6 + h)) is:
slope = (f(6 + h) - f(6)) / ((6 + h) - 6) = (f(6 + h) - f(6)) / h
We can find f(6) and f(6 + h) by plugging in x = 6 and x = 6 + h into the expression for f(x):
f(6) = 6² - 6(6) = -12
f(6 + h) = (6 + h)² - 6(6 + h) = h² - 6h + 36 - 36 - 6h = h² - 12h
Substituting these values into the slope formula, we get:
slope = (h² - 12h - (-12)) / h = h - 12
Therefore, the slope of the secant line joining (6, f(6)) and (6 + h, f(6 + h)) is h - 12.
c. The slope of the tangent line at (6, f(6)) is the derivative of f(x) at x = 6:
f'(x) = 2x - 6
f'(6) = 2(6) - 6 = 6
Therefore, the slope of the tangent line at (6, f(6)) is 6.
d. To find the equation of the tangent line at (6, f(6)), we use the point-slope form of a line:
y - f(6) = f'(6)(x - 6)
Substituting f(6) and f'(6) into this equation, we get:
y - (-12) = 6(x - 6)
Simplifying, we get:
y = 6x - 48
Therefore, the equation of the tangent line at (6, f(6)) is y = 6x - 48.
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a florida citrus grower estimates that if 60 orange trees are planted, the average yield per tree will be 400 oranges. The average yield will decrease by 4 oranges per tree for each additional tree planted on the same acreage. Express the grower's total yield as a function of the number of additional trees planted, draw the graph and estimate the total number of trees the grower should plant to maximize yield.
Answer: 80 trees
Step-by-step explanation:
YIELD = (NUMBER OF TREES)*(NUMBER OF ORANGES PER TREE)
Let's assume NUMBER OF TREES = 60 + x, where x is the number of additional trees above 60
The NUMBER OF ORANGES PER TREE will = (400-4x). Hence:
YIELD = (60+x)*(400-4x) = 24000-240x+400x-4x2 = -4x2 + 160x + 24,000
To find the maximum YIELD, take the derivative of YIELD wrt x, set it to zero, and solve for x:
d(YIELD)/dx = -8x + 160
0 = -8x +160
8x = 160
x = 20
The grower should grow 60 + 20 = 80 trees to maximize yield.
Answer: 80 trees
Step-by-step explanation: just bc it is
Find an equation of the plane that passes through the given point and is perpendicular to the given vector or line.
Point (0, 9, 0) Perpendicular to
n = -2i ÷ 4k
To find the equation of the plane that passes through the point (0, 9, 0) and is perpendicular to the vector n = -2i ÷ 4k, we first need to find the normal vector of the plane.
Since the plane is perpendicular to the given vector, the normal vector will be parallel to it. So, we can take the given vector and multiply it by -1 to get a vector in the opposite direction, which will be normal to the plane.
n = -2i ÷ 4k = -1/2i ÷ k
Multiplying by -1 gives us:
n = 1/2i ÷ k
Now we can use the point-normal form of the equation of a plane:
r · n = d
where r is the position vector of any point on the plane, n is the normal vector, and d is the distance of the plane from the origin (since the normal vector is normalized, d will be the signed distance of the plane from the origin).
Substituting the given point (0, 9, 0) and the normal vector n = 1/2i ÷ k into the equation, we get:
(0, 9, 0) · (1/2i ÷ k) = d
0 + 9(1/2) + 0 = d
d = 4.5
So the equation of the plane is:
x/2 + z/2 = 4.5
or, multiplying by 2 to eliminate fractions:
x + z = 9
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Clara's class is preparing for a field trip. Her teacher purchased bottled water for the trip and asked Clara to stock a cooler with 2 bottles for every student who is going. 5 of the students didn't turn in permission slips and aren't going on the trip. So, Clara stocks the cooler with 38 bottles of water.
Which equation can you use to find the total number of students, n, in Clara's class?
The equation that can be used to find the total number of students would be n = 19 + 5.
How to find the equation ?It is acknowledged that Clara provided 2 bottles per each pupil joining her on the excursion. Denote, by using ‘x’, the quantity of learners present; we can then inscribe the succeeding formula:
2x = 38
By resolving this mathematical principal, the total number of students attending the event is revealed.
x = 38 / 2
x = 19
Currently, 19 individuals are confirmed to embark upon the outing, due to five individuals failing to furnish required consent forms and will be absent. Subsequently, we may deduce the quantity of pupils (designated as ‘n’) in Clara’s class:
n = 19 (students going on the trip ) + 5 ( students not going )
n = 19 + 5
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Help give me an Explanation
Answer:
if the two angles are equal
we use sss therom to solve it
2ft/6ft=24ft/xft
x=(6*24)/2
=72
Which of the following tables represent a proportional relationship
a. y/x= 40/1 76/2 112/3 148/4
Table c represents a proportional relationship because the ratio of y to x is constant at 18.
Which table represent a proportional relationship?A proportional relationship is a relationship between two quantities where their ratios always remain the same.
In option (a), the ratio of y to x is not constant. For example, y/x = 40/1 = 40, but y/x = 148/4 = 37. Therefore, this table does not represent a proportional relationship.
In option (b), the ratio of y to x is not constant either. For example, y/x = 48/2 = 24, but y/x = 192/5 = 38.4. Therefore, this table does not represent a proportional relationship.
In option (c), the ratio of y to x is constant. For example, y/x = 18/1 = 18, but y/x = 126/7 = 18. Therefore, this table represent a proportional relationship.
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Complete questionWhich of the following tables represent a proportional relationship?
a. y/x= 40/1 76/2 112/3 148/4
b. y/x= 48/2 96/3 144/4 192/5
c. y/x= 18/1 54/3 90/5 126/7
d. 24/1 21/2 18/3 15/4
What are all the possible rectangle with the perimeter 16cm,20cm,and 14cm, find the area of each rectangle
The area of a rectangle can be found by multiplying its length and width.
For perimeter 16cm: 15 cm² and 16 cm²For perimeter 20cm: 24 cm² and 25 cm²For perimeter 14cm: 12 cm²How to find area of rectangles?To find the area of rectangles with different perimeters, we need to use the formula:
Area = length x width
Perimeter = 16 cmPossible dimensions:
Length = 5 cm, Width = 3 cm
Length = 4 cm, Width = 4 cm
Area of the first rectangle = 5 cm x 3 cm = 15 cm²
Area of the second rectangle = 4 cm x 4 cm = 16 cm²
Perimeter = 20 cmPossible dimensions:
Length = 6 cm, Width = 4 cm
Length = 5 cm, Width = 5 cm
Area of the first rectangle = 6 cm x 4 cm = 24 cm²
Area of the second rectangle = 5 cm x 5 cm = 25 cm²
Perimeter = 14 cmPossible dimensions:
Length = 4 cm, Width = 3 cm
Area of the rectangle = 4 cm x 3 cm = 12 cm²
Therefore, the areas of the possible rectangles with perimeters 16cm, 20cm, and 14cm are:
For perimeter 16cm: 15 cm² and 16 cm²
For perimeter 20cm: 24 cm² and 25 cm²
For perimeter 14cm: 12 cm²
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Step 2: Construct regular polygons inscribed in a circle.
B) The completed construction of a regular hexagon is shown below. Explain why △ACF is 30°-60°-90° triangle. (10 points)
The explanation on why △ACF is 30°-60°-90° triangle is given below.
How to explain the informationWith a regular hexagon, each of its sides and angles are equal in measure. Consider the centre of the encompassing circle, connected to two neighbouring vertices - labeled A and B here. This then creates a radius wherein the length of AB is basically equal to any other side, denoted as 's'. Furthermore, △ABF will be an isosceles triangle (with AB = BF).
From these facts, we can produce △ACF which is a right angled triangle – with AC being its hypotenuse, A F and FB both equating to s/2, finally concluding that ∠AFB is equivalent to 120°/2 = 60° while establishing that ∠ACF is also a right angle constituent making △ACF essentially a 30°-60°-90° triangle.
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An 8-inch-by-4-inch hole is cut from a
rectangular metal plate, leaving borders
of equal width x on all four sides. The
area of the metal that remains is 32 in².
The equation (8 + 2x)(4+2x) - 32 = 32
models the area of the plate. What is the
value of x, the frame width?
Answer:
2 inches
Step-by-step explanation:
The area of the metal plate can be calculated by subtracting the area of the hole from the area of the original plate. The area of the original plate is:
8 inches x 4 inches = 32 square inches
The area of the hole is:
8 inches x 4 inches = 32 square inches
So the area of the metal that remains is:
32 square inches - 32 square inches = 0 square inches
According to the equation given, we know that:
(8 + 2x)(4 + 2x) - 32 = 32
Expanding this equation we get:
32 + 16x + 8x + 4x^2 - 32 = 32
Simplifying and rearranging we get:
4x^2 + 24x - 32 = 0
Dividing both sides by 4 we get:
x^2 + 6x - 8 = 0
We can solve this quadratic equation by factoring:
(x + 4)(x - 2) = 0
So x = -4 or x = 2. Since the width of the frame cannot be negative, the only valid solution is x = 2.
Therefore, the frame width is 2 inches.
Consider the following series: (-1)^ 71n n We will test this series for convergence or divergence. (i) What test(s) is(are) applicable to test this series? Click for List (i) Determine whether this series converges or diverges. O Converges O Diverges (iii) What is the sum of the series? Note: Write the exact answer not the decimal approximation (for example write 1 / not 0.8). Answer: The sum of the series is PO
The series given is (-1)^71n*n. To test for convergence or divergence, the alternating series test as the series alternates in sign. Also, the absolute value of the terms of the series is decreasing as n increases. In conclusion, the given series (-1)^71n * n diverges, and it does not have a finite sum.
According to the alternating series test, if a series alternates in sign, and the absolute value of its terms is decreasing as n increases, then the series converges.
Thus, the series converges.
To find the sum of the series, we use the formula for the sum of an alternating series:
Sum = (-1)^71*1 - (-1)^71*2 + (-1)^71*3 - (-1)^71*4 + ...
= (-1)^71*(1 - 2 + 3 - 4 + ...)
= (-1)^71*(n(n+1)/2)
= 0
Therefore, the sum of the series is 0.
I'd be happy to help you with your question. To determine the convergence or divergence of the series (-1)^71n * n, we can follow these steps:
(i) Since the series has terms that alternate in sign, we can use the Alternating Series Test to test for convergence.
(ii) To apply the Alternating Series Test, we must first verify that the sequence of positive terms is decreasing and has a limit of zero. In this case, the sequence of positive terms is given by "n". As "n" goes to infinity, the sequence increases, not decreases, and the limit is not zero. Therefore, the series (-1)^71n * n does not pass the Alternating Series Test, and it diverges.
(iii) Since the series diverges, it does not have a finite sum.
In conclusion, the given series (-1)^71n * n diverges, and it does not have a finite sum.
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El 91 no es un número primo porque tiene más divisores que el 1 y el 91 verdadero o falso
The statement''El 91 no es un número primo porque tiene más divisores que el 1 y el 91'' is true because 91 is not a prime number.
A prime number is a positive integer that has only two divisors, 1 and itself. To check if 91 is a prime number, we need to find its divisors. We can start by dividing 91 by 2, but we find that 2 is not a divisor of 91. Next, we can try dividing it by 3, and we get 30 with a remainder of 1. This means that 3 is not a divisor of 91 either.
We continue dividing by 4, 5, 6, and so on until we reach 13, which gives us 7 as a quotient and 0 as a remainder. Therefore, the divisors of 91 are 1, 7, 13, and 91, which means that 91 is not a prime number because it has more than two divisors. Hence, the statement is true.
91 ÷ 2 = 45 r 1
91 ÷ 3 = 30 r 1
91 ÷ 4 = 22 r 3
91 ÷ 5 = 18 r 1
91 ÷ 6 = 15 r 1
91 ÷ 7 = 13 r 0
Since 91 has more than two divisors, it is not a prime number.
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
12
,
8
,
4
,
.
.
.
12,8,4,...
This is sequence and the is equal to
Answer: arithmetic. Common difference is -4
Step-by-step explanation:
constantly subtract four to get to the next
A cement walkway is in the shape of a rectangular prism. The length is 10 feet, the width is three feet and the depth is 1.5 feet. How much cubic feet of cement will they need?
The volume of cement in cubic feet that will be needed is 45 cubic feet.
What is volume?Volume is the space occuppied by an object.
To calculate the volume of cement in cubic feet that will be needed, we use the formula below
Formula:
V = lwh....................... Equation 1Where:
V = Volume of the cement that is neededl = Length of the walkwayw = width of the walkwayh = depth of the walkwayFrom the question,
Given:
l = 10 feetw = 3 feeth = 1.5 feetSubstitute these values into equation 1
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Add the polynomials. (5x3+x)+(3x3+8) enter the answer in the box, in standard form (highest exponent to lowest).
The sum of the polynomials (5x³ + x) + (3x³ + 8) is 8x³ + x + 8
(5x³ + x) + (3x³ + 8) can be simplified by adding the coefficients of the like terms. The like terms are 5x³ and 3x³, which can be combined to give 8x³. The single terms are x and 8, which can be combined to give 8 + x. Therefore, the polynomials add up to
8x³ + x + 8
In standard form (highest exponent to lowest), the answer is:
8x³ + x + 8
Therefore, the sum of the polynomials (5x³ + x) + (3x³ + 8) is 8x³ + x + 8 in standard form (highest exponent to lowest)
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Find the height of a cone with a diameter of 12m whose volume is 226m3. Use 3. 14, and round your answer to nearest meter
The height of a cone with a diameter of 12m whose volume is 226m³ is 6 meters.
The formula for the volume of a cone is
V = (1/3) * π * r^2 * h
where V is the volume, r is the radius, h is the height, and π is approximately equal to 3.14.
We know the diameter of the cone is 12m, which means the radius is 6m.
We also know that the volume of the cone is 226m^3.
Substituting these values into the formula, we get:
226 = (1/3) * π * 6^2 * h
Simplifying:
226 = (1/3) * 3.14 * 36 * h
226 = 37.68h
h = 226/37.68
h ≈ 6
Therefore, the height of the cone is approximately 6 meters.
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The fifth and tenth terms of an arithmetic sequence,
respectively, are -2 and 53. What is the seventh
term of the sequence?
If the fifth and tenth terms of an arithmetic sequence, respectively, are -2 and 53, the seventh term of the arithmetic sequence is 20.
To find the seventh term of the arithmetic sequence, we need to first find the common difference (d) of the sequence. We know that the fifth term is -2 and the tenth term is 53.
The formula for the nth term of an arithmetic sequence is: an = a1 + (n-1)d
Using this formula, we can set up two equations:
-2 = a1 + 4d (since the fifth term is a1 + 4d)
53 = a1 + 9d (since the tenth term is a1 + 9d)
We now have two equations with two variables (a1 and d). We can solve for either variable using substitution or elimination. I'll use elimination:
-2 = a1 + 4d
53 = a1 + 9d
Subtracting the first equation from the second equation, we get: 55 = 5d
Therefore, d = 11
Now that we know the common difference is 11, we can use the formula for the nth term again to find the seventh term:
a7 = a1 + (7-1)d
a7 = a1 + 6d
We still don't know a1, but we can solve for it using one of the previous equations:
-2 = a1 + 4d
-2 = a1 + 4(11)
-2 = a1 + 44
a1 = -46
Now we can substitute a1 and d into the formula for the seventh term:
a7 = -46 + 6(11)
a7 = -46 + 66
a7 = 20
Therefore, the seventh term of the arithmetic sequence is 20.
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Find the smallest number of terms of the series ∑ n = 1 (-1)^n+1/2^n you need to be certain that the partial sum Sn is within 1/100 of the sum.n=2 n=4 n=6 n=8 n=7
We need at least 7 terms of the series to be certain that the partial sum Sn is within 1/100 of the sum.
We want to find the smallest value of n such that the absolute value of the difference between the sum of the first n terms and the sum of the entire series is less than 1/100.
The sum of the first n terms of the series is given by:
Sn = ∑_(k=1[tex])^n[/tex] (-1[tex])^(k+1)[/tex]/[tex]2^k[/tex]
We can write the sum of the entire series as:
S = ∑_(k=[tex]1)^∞[/tex] (-1[tex])^(k+1)[/tex]/[tex]2^k[/tex]
The absolute value of the difference between the sum of the first n terms and the sum of the entire series is:
|S - Sn| = |∑_(k=n+1[tex])^∞[/tex] [tex](-1)^(k+1)/2^k|[/tex]
We want to find the smallest value of n such that |S - Sn| < 1/100.
Let's start by evaluating the sum of the series:
S = ∑_(k=1) (-1[tex])^(k+1)[/tex]/[tex]2^k[/tex] = 1/2 - 1/4 + 1/8 - 1/16 + ...
This is a geometric series with first term a = 1/2 and common ratio r = -1/2. The sum of the series is:
S = a/(1-r) = (1/2)/(1+1/2) = 1/3
Now we can write:
|S - Sn| = |∑_(k=n+1[tex])^∞[/tex] (-1[tex])^(k+1)[/tex]/[tex]2^k|[/tex] <= 1/[tex]2^(n+1)[/tex]
The last inequality is true because the terms of the series are decreasing in absolute value, and we are summing an infinite number of terms.
Therefore, we need to find the smallest value of n such that 1/2^(n+1) < 1/100. This gives:
n+1 > log2(100)
n > log2(100) - 1
n > 6.64
The smallest integer value of n that satisfies this inequality is n = 7.
Therefore, we need at least 7 terms of the series to be certain that the partial sum Sn is within 1/100 of the sum.
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In a given diagram below, ray AB bisects angle FAE. BF = 2x + 8 and BE = 42.
A. Set up an equation to solve for "x".
B. Show your work and solve for "x".
a. The equation to solve for x is given as follows: 2x + 8 = 42.
b. The solution for x is given as follows: x = 17.
How to obtain the value of x?The value of x is obtained applying the angle bisection theorem, which divides an angle into two angles of equal measure, hence the opposite segments also have equal length.
The segments for this problem, along with their lengths, are given as follows:
BF = 2x + 8.BE = 42.Hence the equation is given as follows:
2x + 8 = 42.
The value of x is given as follows:
2x = 34
x = 17.
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Can someone please help me ASAP? It’s due tomorrow. I will give brainliest if it’s correct.
The probability values when calculated are
P(2 numbers greater than 3) = 0.1P(2 even numbers) = 0.4P(2 cards with same numbers) = 0P(1 card is 3) = 0.3Evaluating the probability valuesFrom the question, we have the following parameters that can be used in our computation:
Cards = {1, 2, 3, 4, 5}
Selecting two cards without replacement
So, we have
P(2 numbers greater than 3) = 2/5 * 1/4
P(2 numbers greater than 3) = 0.1
P(2 even numbers) = 2/5 * 4/4
P(2 even numbers) = 0.4
P(2 cards with same numbers) = 1/5 * 0/4
P(2 cards with same numbers) = 0
P(1 card is 3) = 2 * 1/5 * 3/4
P(1 card is 3) = 0.3
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