The dimensions of the cylinder are -
{r} = √500/πh
{h} = (500/r²)
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the volume of the cylinder as -
V = 500 cm³
We can write -
V = 500
So, we can write -
πr²h = 500
So, we can write -
{r} = √500/πh
{h} = (500/r²)
Therefore, the dimensions of the cylinder are -
{r} = √500/πh
{h} = (500/r²)
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{Question in english -
What are the measurements of a cylinder (height, radius) if its volume is 500 cm3}
A garden table and a bench cost $621 combined. The garden table costs $79 less than the bench. What is the cost of the bench?
Answer:
$389.5
Step-by-step explanation:
621/2 = 310.5 assuming they're equal therefore, it is stated that the table cost cost 79 less than the bench so we substract.
310.5 - 79 = 231.5
This is the cost of garden table, lets find the bench now.
621(both table and bench)-231.5(garden table)= 389.5 is the cost of the bench.
solve the system if equations using the substitution method.
2x+y=5
6x+2y=17
A triangle with angles of 50°, 60°, and 70° is inscribed in a circle of radius 8 inches. Find the lengths of all three sides of the triangle.
The lengths of all three sides of the triangle are;
43.6 inches
52.3 inches
61.1 inches
What are the lengths of the triangle?The arcs are seen to be two times the angles and as such, the arc made by the 50° angle is 100° and then we see that the one made by the 60 degree angle given as 120°.
Formula for the circumference of a circle is;
C = 2πr
C = 50π inches
C = 157 inches
The arc made by the 50° angle is;
Arc length = 157*100/360
= 43.6 inches
The arc length made by the 60° angle = 157(120/360)
= 52.3 inches
The arc length made by the remaining 70° angle is;
Arc length = 157(140/360)
Arc length = 61.1 inches
Total arc length = 43.6 + 52.3 + 61.1
= 157 inches.
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2. Finds
Geometry - Clark
Midpoint and Distance Formulas
© 2011 Kuta Software LLC. All rights reserved.
Find the midpoint of the line segment with the
1) (-4,-2), (3, 3)
The midpoint of the line segments with
1) (-4,-2), (3, 3) is ( -1/2 , 1/2).
2) (−1, −6), (−6, 5) is ( -7/2 , -1/2 ).
3) (2, 4), (1, −3) is ( 3/2 , -1/2).
In geometry, the midpoint is defined as the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment. To determine the midpoint, just add the two X-values, then divide by 2 and add the two Y-values, then divide by 2. Mathematically, let (xm , ym) be coordinates of mid point of line segment ents with end points ( x₁, y₁) , (x₂, y₂). Then, xₘ =( x₁ + x₂)/2 and yₘ = ( y₁ + y₂)/2
We have , the line segments with coordinates
1) (-4,-2), (3, 3)
Midpoint = ( (-4 + 3)/2 , (-2 + 3/2) )
= ( -1/2 , 1/2)
2) (−1, −6), (−6, 5)
Midpoint = ( ( -6 +(-1))/2 , ( -6 + 5)/2)
= ( -7/2 , -1/2 )
3) (2, 4), (1, −3)
Midpoint = ((2 + 1)/2 , (4+(-3))/2)
= ( 3/2 , -1/2)
Hence, we got all midpoints for line segments.
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Complete question:
Geometry - Clark Midpoint and Distance Formulas
© 2011 Kuta Software LLC. All rights reserved.
Find the midpoint of the line segment with the given endpoints.
1) (-4,-2), (3, 3)
2) (−1, −6), (−6, 5)
3(2, 4), (1, −3)
What are the 3 defining characteristics of parallel lines?.
The characteristics of parallel lines:
1) Parallel lines lie in the same plane
2) The parallel lines never intersect each other.
3) The slopes of parallel lines are equal.
We know that two lines are parallel to each other if they lie in the same plane and never intersect each other.
Parallel lines are always equidistant from each other.
Also, the parallel lines are coplanar.
Mathematically, the parallel lines are represented by the symbol, ‘||‘.
If two lines l₁ and l₂ are parallel to each other then they are represented as l₁ || l₂.
Also, the slopes of parallel lines are equal.
Let m₁ be the slope of line l₁ and m₂ be the slope of line l₂.
If line l₁ and l₂ are parallel to each other then m₁ = m₂
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What is the 2nd step when solving for systems of equations using the elimination method?.
The 2nd step when solving for systems of equations using the elimination method is explained below.
Equations in math is defined as a mathematical statement that shows that two mathematical expressions are equal.
Here we need to find the steps to the 2nd step when solving for systems of equations using the elimination method.
Here first we need to find Enter the equations.
And then multiply each equation by a number to get the lowest common multiple for one of the variables.
And then add or subtract the two equations to eliminate that variable .
Now we have to substitute that variable into one of the equations and solve for the other variable.
Finally we have to check by substituting your answer into one of the equations,
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What is the answer for this problem
Answer:
Step-by-step explanation:
I think №2Without knowing its side lengths, can you determine the ratio of the perimeter of a square to the length of one of its sides? Explain.
A square's side to perimeter ratio is one to four.
How do you calculate a perimeter's ratio?The quantity of two-dimensional space a shape occupies is referred to as its area. Simply dividing the perimeter by the area yields the ratio of a shape's perimeter to area. It is simple to calculate this. The perimeter ratio and scale factor are the same. In reality, the scaling factor for every ratio between any two similar shapes is the same (diagonals, medians, midsegments, altitudes, etc.).The Perimeter is equal to a constant multiplied by the Side length, or the Perimeter is equal to four when divided by the Side length. There is so no doubt that the link between Side length and Perimeter is proportionate.To learn more about ratio, refer to:
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The value of a motorcycle is depreciating by 2.8% each year. If the bike was purchased for $12,000, how much will it be worth in 12 years?
Type your answer as a decimal rounded to the nearest cent.
Answer:8534.46
Step-by-step explanation:
The depreciated value of the bike after 12 years is $8534.46
What is depreciated value?Depreciated value is the minimum amount that an asset is worth after depreciation.
Given that, the value of a motorcycle is depreciating by 2.8% each year, the bike was purchased for $12,000,
We know that, the depreciation value is given by,
A = P(1-r)ⁿ
A = final amount
P = initial amount
r = rate
n = years or time
Therefore,
A = 12000(1-0.028)¹²
A = 12000(0.972)¹²
A = 8534.46
Hence, the depreciated value of the bike after 12 years is $8534.46
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Help pleaseee Double points
Answer: y=17.3
refer to the image for the steps
The amount of revenue for a business can be modeled by the function
L(t) = 7300(1.012) 4t. Write an equivalent function of the form L(t) = abt.
Round your final values to 4 decimal places.
Answer:
a=7300, b=1.0108.
L(t) = 7300(1.0108)^t
Step-by-step explanation:
First, we can see that L(t) = 7300(1.012)^(4t) can be rewritten as L(t) = 7300e^(4tln(1.012))
Using the properties of logarithms, we can simplify this to L(t) = 7300e^(4t(ln(1.012))
Now, we can see that the function L(t) is in the form L(t) = ab^t, where a = 7300 and b = e^(ln(1.012))
Therefore, we can write the equivalent function as L(t) = 7300e^(0.048t)
The final values rounded to 4 decimal places are a=7300, b=1.0108.
L(t) = 7300(1.0108)^t
Answer
L(t)=
7300
1.0489
7300(1.0489)
Step-by-step explanation:
What is the graph of the solution set?.
The set of all possible solutions to a linear equation with two variables is called the solution set. Specifically, the collection of all ordered pairs that are equivalent to the equation.
What is the graph of the inequality's solution set?A region always appears on the graph of the solution to a linear inequality. However, that set might not always include the boundary. The "or equal to" part of the inclusive inequality made the line a part of the solution set in the previous example.
What is the solution set?Any value of a variable that makes the equation true is a solution. The set of all variables that makes the equation true is called a solution set. Because 2(4) + 6 = 14, the solution set for 2y + 6 = 14 is 4.
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Complete the statement with the correct value. When z = -4. -2z + 1 = A. 6. B. 7. C. 9
The statement with the correct value is C. 9
What are simple substitutions?Simple substitution is a topic which are mathematical expressions with variables whose value/s has been given. Thus it is just required to solve the question by simple substitution of the given value in the expression. Example, given that a = 2, determine the value if a + 6.
This can be solved by substituting 2 for a in the question, so that;
a + 6 = 2 + 6
= 8
Therefore, it can be deduced from the given question that;
-2z + 1, but z = -4
Thus,
-2z + 1 = -2(-4) + 1
= 8 + 1
= 9
To complete the statement, the correct value is 9. Option C.
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Marcus buys 7 3/4 feet of wrapping paper. He lets his sister use 2 1/3 feet if the wrapping paper to wrap a gift. How much wrapping paper does Marcus have left?
The wrapping paper Marcus have left is 5 5 / 12 feet.
How to find the wrapping paper Marcus have left?Marcus buys 7 3/4 feet of wrapping paper. He lets his sister use 2 1/3 feet of the wrapping paper to wrap a gift.
The amount of wrapping paper Marcus have left can be calculated as follows:
The amount of wrapping paper Marcus have left is the subtraction of the paper used by the sister by the wrapping paper he had initially.
Hence,
wrapping paper Marcus have left = 7 3 / 4 - 2 1 / 3
wrapping paper Marcus have left = 31 / 4 - 7 / 3
wrapping paper Marcus have left = 93 - 28 / 12
wrapping paper Marcus have left = 65 / 12
Therefore,
wrapping paper Marcus have left = 5 5 / 12 feet
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If there are 50 dogs and 30 cats at a pet daycare, fill out all of the possible ratios of dogs to cats that could be made.
Answer:
50/30, 25/15, 10/6, 5/3
Step-by-step explanation:
To answer the question, you need to decompose the numerator and denominator into simple factors and see what combinations are possible.
50:2 = 25
25:5 = 5
5:5 = 1
Multipliers for 50: 2, 5, 5
30:2 = 15
15:3 = 5
5:5 = 1
Multipliers for 30: 2, 3, 5
Common multipliers for dogs and cats: 2 and 5
So we can divide the our ratio by 2, by 5 and by their product 2 x 5 = by 10.
We get the following series:
50/30, 25/15, 10/6, 5/3
Show the fractions in order from least to greatest
well the bottom number the bigger the number means it's small The small the number the bigger it is
so 5/8 and 3/8 They're the smallest again the bigger the number means it's small now we will look at the top 5 is bigger than 3 so 3/8 is first and 5/8 is next. The rest I let you solve.
A diagonal of a rectangle splits the rectangle into two 300-60 •-90° triangles. If the diagonal of the rectangle is 21 in, what is the length and width of the rectangle. Find the area
When the diagonal of a rectangle splits the rectangle into two producing angles 30 - 60 - 90 the sides of the rectangle is
Area of a rectangle is solved to get 191 square in
How to find the lengths of the rectangleThe problem is solved using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The shape describes a right triangle of
opposite = width
adjacent = length
hypotenuse = diagonal
The dimensions are calculated using SOH and CAH
sin 30 = opposite / hypotenuse
sin 30 = width / 21
width = 21 * sin 30
width = 10.5
For the length
cos 30 = adjacent / hypotenuse
cos 30 = length / 21
length = 21 * sin 30
length = 18.19
Area of a rectangle = length * width
Area of a rectangle = 18.19 * 10.5
Area of a rectangle = 190. 995
Area of a rectangle = 191 square in
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What are the domain and range of g of x equals the square root of the quantity x minus 3?
D: [3, ∞) and R: [0, ∞)
D: [–3, ∞) and R: [0, ∞)
D: (–3, ∞) and R: (–∞, 0)
D: (3, ∞) and R: (–∞, 0)
Answer:
90-99=86x45[80[
Step-by-step explanation:
Answer:
The function g(x) = √(x - 3) is defined for all real numbers x such that x - 3 ≥ 0, since the square root of a non-negative number is a real number.
Solving for x, we have:
x - 3 ≥ 0
x ≥ 3
Therefore, the domain of the function is D: [3, ∞).
Since the square root of a non-negative number is always non-negative, the range of the function is R: [0, ∞).
Therefore, the correct answer is: A. D: [3, ∞) and R: [0, ∞).
A bakery ell pie and cake. In November, they old 400 pie and 250 cake totaling $8,550. In December, they old 300 pie and 500 cake totaling $11,100. What i the price of the pie?
The price of the Pie will be $12 and the price of the cake will be $15.
We will solve this problem with the help of equations.
Let the price of Pie be $X and the price of Cake be $Y.
According to a given question in November, they sold 400 Pie and 250 Cake and the total amount is $8550.
So our first equation will be,
400X + 250Y = 8550.
And in December they sold 300 pies and 500 cakes respectively totaling $11100.
So our second equation will be:
300X + 500Y = 11100.
Taking the value of X from our first equation we get:
X = (8550-250Y)/400
Putting it in our second equation we get:
300(8550-250Y)/400 + 500Y = 11100
On solving this:
3/4(8550-250Y)+500Y = 11100
25650/4 - 750/4 Y + 500Y = 11100
1250/4 Y = 18750/4
Y = 15
So the price of the Cake is $15.
Similarly, we can find the price of Pie as (8550-250*15)/400 = 12
So the price of the pie is $12.
Therefore the price of the pie is $12 and the cake price is $15.
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A man got a 10% increase in his salary. If his new salary is rupee 1,54,000, find his original salary
1,40,000 Rs. is his original Salary.
Let the original Salary of the man be = X
His New Salary = 1,54,000 Rs. (given)
X + (10/100 × X ) = 154000
X + (X/10) = 154000
11X / 10 =154000
X = 154000 × (10/11)
x = 140000
Hence we can say that his original Salary was 1,40,000 Rs.
Uing the following table, what term bet decribe the entry of 62%?
Which location would you mot like to viit?
Apen, Colorado New York,
New York Row total
Male tudent 22% 28% 50%
Female tudent 16% 34% 50%
Column total 38% 62% 100%
Group of anwer choice
Joint frequency
Joint relative frequency
Marginal frequency
Marginal relative frequency
Answer:
50%
Step-b50%y-step explanation:
Joint relative frequency
write 2 equations that relate distance and time
HELP ASAP PLSSSSS
Part A: Given the function g(x) = |x − 7|, describe the graph of the function, including the vertex, domain, and range. (5 points)
Part B: If the parent function f(x) = |x| is transformed to h(x) = |x| + 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
Part A:
The graph of the function g(x) = |x - 7| is a V-shaped graph that opens upwards and has a vertex at x = 7. The vertex is the midpoint of the graph and occurs at the value of x where the absolute value changes from positive to negative. The domain of the function is all real numbers and the range is all non-negative numbers.
Part B:
The transformation from f(x) to h(x) occurs by shifting the graph of the parent function up by 2 units along the y-axis. In other words, every y-coordinate in the graph of f(x) is increased by 2 in the graph of h(x). The vertex of the parent function is (0,0) and is shifted to (0,2) in the transformed function. The range of h(x) is all non-negative numbers greater than or equal to 2.
Bob has a credit limit of $3500 on his credit card . He has a balance of $2200 on the card . How much can he charge before he goes over his limit ?
The ideal utilization would be $150but he can choose to borrow $1050
What is a credit card in simple words?A credit card is a type of credit facility, provided by banks that allow customers to borrow funds within a pre-approved credit limit. It enables customers to make purchase transactions on goods and services.
Given here: Bob's credit limit is $3500 and he has a balance of $2200
Therefore available credit is equal to $3500-$2200=$1300
Thus if he spends more than $1300 then he goes over his limit.
But ideal utilization ratio is 30% and therefore 30%×3500=$1050
Thus ideal credit usage would be = 3500-1050
=2450
Then $2450-$2200=150
Hence, The ideal utilization would be $150but he can choose to borrow $1050
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Rewrite the entence, adding a nonretrictive element uing parenthee hi book mut be intereting becaue he han’t put it down once
The revised form of the sentence would be as follows: Mark Twain, who was born in Florida, is one of America's most famous authors.
Nonrestrictive elements are sets of words that can be deleted from a statement without affecting its meaning.
A nonrestrictive element is nonessential because we don't need the information it provides. These elements are always separated with commas from the rest of the sentence to specify that they are not essential. If they were dropped, the meaning of the sentence would be left unchanged.
Mark Twain, is one of America's most famous authors. - In the above sentence the nonrestrictive element is a nonessential relative clause.
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DRIVING While on a bike ride, Tyra’s distance from home can be modeled by f(x) = −15∣∣x−40∣∣+8
, where x is the time since Tyra left home in minutes and f(x) her distance from home in miles. Graph the function on a separate piece of paper. Find and interpret the key features of the graph in the context of the situation.
The graph of the function f(x) = −15|x−40|+8 will be a piecewise linear function.
Graph explain: What is it?
A graph is defined as a mathematical structure that connects a collection of points to express a specific function. A pairwise relationship between the objects is established using it. The edges that connect the graph's vertices (also known as nodes) are its vertices (lines).
It will be a V-shape, with the vertex at x = 40 and y = 8.
On the left side of the vertex, the function will be decreasing, representing Tyra moving away from home.
On the right side of the vertex, the function will be increasing, representing Tyra moving towards home.
The vertex at x = 40 and y = 8 represents the point in time where Tyra reaches her furthest distance from home (8 miles) and then begins to head back towards home.
Key features of the graph in the context of the situation:
The vertex at x = 40 and y = 8 represents the point in time where Tyra reaches her furthest distance from home (8 miles) and then begins to head back towards home.
The left side of the vertex represents the time period when Tyra is moving away from home, and the right side represents the time period when Tyra is moving towards home.
The slope of the graph on the left side of the vertex is negative, indicating that Tyra is moving away from home at a decreasing rate, while the slope of the graph on the right side of the vertex is positive, indicating that Tyra is moving towards home at an increasing rate.
The y-intercept is at 8, which means Tyra starts 8 miles away from home.
The graph is symmetric about the y-axis because for every time x on the left side of the vertex, there is a corresponding time on the right side of the vertex.
The graph is not a function because for every x value, there are two y values, one for when Tyra is moving away from home and one for when Tyra is moving towards home.
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how to solve −9x + 5 < 17
Answer:
x > -1 1/3
Step-by-step explanation:
-9x + 5 < 17
Subtract 5 on each side
-9x < 17
divide by -9 on each side, which causes for the greater than sign to flip because we are dividing by a negative
x > -1 1/3
Help fast please! (Find the value of y.)!!!
Answer:
y = 10 and x = 5
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{5\sqrt{3} }{y}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
y × [tex]\sqrt{3}[/tex] = 10[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
y = 10
-----------------------------------
using Pythagoras' identity in the right triangle
x² + (5[tex]\sqrt{3}[/tex] )² = y² = 10²
x² + 75 = 100 ( subtract 75 from both sides )
x² = 25 ( take square root of both sides )
x = [tex]\sqrt{25}[/tex] = 5
NEED TO FINISH BY 5!!! WILL MARK BRAINLIEST
Answer:
10 1/8
Step-by-step explanation:
good luck to you :)
Answer:
10 1/8
Step-by-step explanation:
hope this helps good luck!
How should you graph the equation y =- 3 4x 2?.
The final graph is given below in the image.
The equation is [tex]y = -\frac{3}{4}x - 2[/tex]
The graph of a linear equation in two variables is a line (that's why they call it linear).
If you know an equation is linear, you can graph it by finding any two solutions
(x1,y1) and (x2,y2)
plotting these two points, and drawing the line connecting them.
You can find two solutions, corresponding to the x-intercepts and y-intercepts of the graph, by setting first x=0 and then y=0.
To graph the line [tex]y = -\frac{3}{4}x - 2[/tex] we are going to take advantage of the fact that its y-intercept is -2 when x = 0, so our first point is (0,-2). To find our second point, we are going to find the x-intercept; to do it, we are going to set y = 0 and solve for x:
[tex]y = -\frac{3}{4}x - 2\\0 = -\frac{3}{4}x - 2\\2 = -\frac{3}{4}x \\x = -\frac{8}{3}[/tex]
Now, we have our second point (0, -8/3), we just need to join the 2 points with a straight line.
The final graph is given below in the image.
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