The slant height of the cone c² = 5² + (1)² or c ≅ 5.1.
Option (A) is correct option.
What is cone?A cone is a three-dimensional geometric structure with a smooth transition from a flat, usually circular base to the apex or vertex, a point that creates an axis to the base's center.
Given that,
The radius of the cone = 1 inch,
And the height of the cone = 5 inch.
Let the slant height of the cone is c,
To find the slant height of the cone, use Pythagorean theorem,
c² = 5² + (1)²
c² = 25 + 1
c² = 26
c= 5.09
c ≅ 5.1
The slant height of the cone is 5.1 inch.
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Find the angle of “z”. A triangle has 180 degrees.
Answer:
z=26
Step-by-step explanation:
85+69
154
180-154
26
i hope this helps!
Find the measure of angle x. Round your answer to the nearest hundredth.
Answer:
28.07°
Step-by-step explanation:
use SohCahToa
in this case we use tan^-1 to get the angle x°
tan^-1(8/15)=28.07248694
to the nearest hundredth
=28.07°
The question is in the picture.
Easy way to do this, divide 24 with 3, you will get 8. That means 8 is 1/3 of 24. To get 2/3 you just add 8+8 which equals to 16
An article is bought and sold with a profit of 25 of selling price. find the profit percent.
Answer:
33 percent
Step-by-step explanation:
Let's see what we have here.
A shopkeeper sold Item X for a his selling price (SP).
Let SP = x
Since the question says that
Profit is 25% of the selling price,
we have: Profit = 25% SP = 0.25x
Now, we already know that:
Profit = SP - Cost
This part is the catch.
To find out how much Item X originally cost,
Cost = SP - Profit = x - 0.25x = 0.75x
Now that we know the original cost of Item X,
we can easily calculate the
Real profit % using this formula:=
(Profit/Cost)*100=
(0.25x/0.75x)*100= 33%
A 747 airplane weighs about 600,000 pounds. It can also be expressed as approximately 3 times 10 Superscript n tons. If there are 2,000 pounds in 1 ton, which is the most reasonable value of n? –2 –1 2 4
Answer:
n=2
Step-by-step explanation:
2000 pounds = 1 ton 600000 pounds = X tons Hence X tons = (600000 x 1) ÷ 2000 = 300 tons 3 x 10ⁿ = 300 Hence 3 x 10ⁿ = 3 x 10² Hence n= 2
Answer:N = 2
Step-by-step explanation:
I took the quiz and got 100%
Match each expression with A, B, C or D.
A=a^3
B=6a
C=12a
D=3a^2
i)3a x 4
ii)a^2xa
iii) 6 1/2 a^2
The matching expressions are:
\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)
i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.
ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.
iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.
To understand the matching expressions, let's break down each one:
i) 3a x 4:
This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).
ii) a^2 x a:
This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).
iii) 6 × 1/2 a^2:
This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).
Therefore, the matching expressions are:
i) 3a x 4 = C (12a)
ii) a^2 x a = A (a^3)
iii) 6 × 1/2 a^2 = D (3a^2)
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Two sides of a triangle have lengths 43 and 67. The angle included between these sides measures 27degrees°. To the nearest hundreth, what is the length of the third side?
The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.
1. We have a triangle with two known side lengths: 43 and 67 units.
2. The angle included between these sides measures 27 degrees.
3. To find the length of the third side, we can use the Law of Cosines, which states that \(c^2 = a^2 + b^2\) - 2ab * cos(C), where c is the third side and C is the included angle.
4. Plugging in the known values, we get \(c^2 = 43^2 + 67^2\) - 2 * 43 * 67 * cos(27).
5. Evaluating the expression on the right side, we get \(c^2\) ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.
6. Simplifying further, we have \(c^2\) ≈ 6338 - 5156.898.
7. Calculating \(c^2\), we find \(c^2\) ≈ 1181.102.
8. Finally, taking the square root of \(c^2\), we get c ≈ √1181.102 ≈ 34.32.
9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.
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The function f(x)=x(200-x) models the area of a pasture, in square yards, as a function of its length. Which are possible lengths of the pasture? 125 yards 200 yards 170 yards 225 yards 210 yards
Answer:
(a): x = 125 yards.
(c): x = 170 yards.
Step-by-step explanation:
Given
\(f(x) = x(200 - x)\)
\(x = length\\\\\)
\(f(x) = area\)
Required
Determine the possible length
For a length to be possible or usable, the calculated area must be greater than 0.
(a): x = 125 yards.
\(f(x) = x(200 - x)\)
Substitute 125 for x
\(f(125) = 125 * (200 - 125)\)
\(f(125) = 125 * 75\)
\(f(125) = 9375\)
(b): x = 200 yards.
\(f(x) = x(200 - x)\)
Substitute 200 for x
\(f(200) = 200 * (200 - 200)\)
\(f(200) = 200 * 0\)
\(f(200) = 0\)
(c): x = 170 yards.
\(f(x) = x(200 - x)\)
Substitute 170 for x
\(f(170) = 200 * (200 - 170)\)
\(f(170) = 200 * 30\)
\(f(170) = 6000\)
(d): x = 225 yards.
\(f(x) = x(200 - x)\)
Substitute 225 for x
\(f(225) = 200 * (200 - 225)\)
\(f(225) = 200 * (- 25)\)
\(f(225) = -5000\)
(e): x = 210 yards.
\(f(x) = x(200 - x)\)
Substitute 210 for x
\(f(220) = 200 * (200 - 210)\)
\(f(220) = 200 * (- 10)\)
\(f(220) = -2000\)
From the above calculations, only values of x that are 125 and 170 makes the function true
50 Points! Multiple choice algebra question. Photo attached. Thank you!
The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is, 3 / 5
We have to given that;
the terminal side of theta in standard position contains the point (6,-8)
Hence, For given condition we get;
The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,
Here, x = 6, y = - 8
Hence, We get;
r = √x² + y²
r = √6² + 8²
r = √36 + 64
r = √100
r = 10
So, The exact value of cos theta if the terminal side of theta in standard position contains the point (6,-8) is,
cos θ = x / r
cos θ = 6 / 10
cos θ = 3 / 5
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Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 feet per day. Write an equation for the water level, L after d days.
In how many days will the water level be 26 feet
The linear function that represents the water level is L = -0.5d + 34 while the number of days will the water take to level 26 feet is 16 days.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given,
Initial water level = 34 feet
Rate of receding = 0.5 feet per day = -0.5
New level L = -0.5d + 34
For the level to be 26 feet,
26 = -0.5d + 34
0.5d = 34 - 26
d = 16 days
Hence "The equation L = -0.5d + 34, which represents the water level, states that it will take 16 days for the water to reach a level of 26 feet".
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solve the PDE using separation of variables method Uxx = 1/2 Ut 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
The general solution of the partial differential equation is:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
How to solve Partial Differential Equations?The partial differential equation (PDE) is given as:
Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
Assume that the solution can be written as a product of two functions:
U(x, t) = X(x)T(t)
Substituting this into the PDE, we have:
X''(x)T(t) = (1/2)X(x)T'(t)
Dividing both sides by X(x)T(t), we get:
(X''(x))/X(x) = (1/2)(T'(t))/T(t)
Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:
(X''(x))/X(x) = -λ²
(1/2)(T'(t))/T(t) = -λ²
Simplifying the second equation, we have:
T'(t)/T(t) = -2λ²
Solving the second equation, we find:
T(t) = Ce^(-2λ²t)
Applying the boundary condition U(0, t) = 0, we have:
U(0, t) = X(0)T(t) = 0
Since T(t) ≠ 0, we must have X(0) = 0.
Applying the boundary condition U(3, t) = 0, we have:
U(3, t) = X(3)T(t) = 0
Again, since T(t) ≠ 0, we must have X(3) = 0.
Therefore, we can conclude that X(x) must satisfy the following boundary value problem:
X''(x)/X(x) = -λ²
X(0) = 0
X(3) = 0
The general solution to this ordinary differential equation is given by:
X(x) = Asin(λx) + Bcos(λx)
Applying the initial condition U(x, 0) = 5*sin(4πx), we have:
U(x, 0) = X(x)T(0) = X(x)C
Comparing this with the given initial condition, we can conclude that T(0) = C = 5.
Therefore, the complete solution for U(x, t) is given by:
U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)
where:
Σ represents the summation over all values of n
λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).
To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):
X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0
X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0
From the first equation, we have Bₙ = 0.
From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.
This implies that 3λₙ = nπ, where n is an integer.
Therefore, λₙ = (nπ)/3.
Substituting the eigenvalues into the general solution, we have:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
where Aₙ are the coefficients that can be determined from the initial condition.
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a histogram showing u.s. household income is highly skewed right. which of following statistics would best describe the center of the distribution? question 10 options: 1) median 2) variance 3) mean 4) mode
......,,........,.....-.......
The median would best describe the centre of the distribution for a highly skewed right histogram of US household income. The correct option is A.
What is the median?The median is the value that separates the distribution into two equal parts and is less influenced by extreme values than the mean.
Since a highly skewed right distribution has a long tail on the right side, the mean is likely to be pulled towards that tail, making it an unreliable measure of the centre.
The mode, or most frequently occurring value, may not be useful for describing the centre of a skewed distribution. The variance is a measure of the spread or dispersion of the data, not its centre.
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which number has a greater magnitude 2 or -3
Answer:
2
Step-by-step explanation:
I think but I may be wrong
What is the perimeter of the triangle?
Answer:
this triangle is a acute angel so it 3
whats the equation of a line that passes through point (-1,3) with slope of 1
The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.
To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.
Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:
y - 3 = 1(x - (-1))
Simplifying:
y - 3 = x + 1
Now, we can rewrite the equation in the standard form:
y = x + 4
Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.
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Ximena pays a flat cost of $44.50 per month and $4 per gigabyte. She wants to keep her bill at $50.10 per month. How many gigabytes of data can she use while staying within her budget?
Answer:
Ximena can use 1 gigabytes of data
Step-by-step explanation:
The first thing you want to do is subtract
51.10 - 44.50 = 5.6
5.6 is the amount of money she will have to spend on data
With each gigabyte costing 4 dollars and only 5 dollars to spend
she can only use one gigabyte
Theo solved n + 5 = 11 for the unknown. The steps he took are shown.
He started with 5 tiles.
5 tiles.
Then he added tiles as he counted up to 11.
6 tiles.
He realized he added 6 more tiles to his original 5 to make 11. So he found the unknown to be 6.
How could Theo check his work? Check all that apply.
He could substitute 5 for n in the original equation and add.
He could substitute 6 for n in the original equation and add.
He could subtract 5 from 11 and check that the answer is 6.
He could subtract 11 from 5 and check that the answer is 6.
He could put all the tiles in 1 pile to count them to see if there are 11 in all.
Answer:
the second one, the fourth one, and the fifth one
Step-by-step explanation:
Determine If AB is tangent to the circle.
Answer:
no its not
Step-by-step explanation:
radius doesn't make 90 degree with AB. use Pythagoras theorem
What is the constant of proportionality in the equation y=5/4x
The constant of proportionality in the equation is 5/4
What is constant of proportionality?The constant connecting two given numbers in what is known in a proportional relationship is the constant of proportionality.
The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
In the problem, y = 5/4x
The constant term 5/4 as used in the equation is used t multiply the input x values to get the out put y values
The term helps in relating x to y
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s with Mean, Median, and Mode: Mastery Test
The company's allocation for expense
accounts on the average is $150 per
month. Pat has just received his
quarterly statement for his expense
account and the amount for the quarter
is $576. A quarter is three months.
The difference between Pat's monthly average income and the Company's allocation is $41
Company's average allocation per month = $150
Pat's total expenses as per the quarterly account statement = $576
Average: The core value of a set of data is expressed as the average of a list of variables. It is defined mathematically as the ratio of the total number of data points to the number of units in the list.
Now, Average = Sum of observation/Total no. of observations
It is given that a quarter is of 3 months
Average = 576/3
Average = $191
The difference between Pat's monthly average income and the company's allocation is = Pat's average income - Company average allocation
= 191 - 150
=$41
Hence, the difference is $41
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You are asked to create a graphic that would make it easy to quickly tell which locations require that ear protection be worn after 12 hours of exposure with the understanding that the sound level limit is 87. Would the proposed new graphic accomplish this purpose?
Answer:
Step-by-step explanation:
The answer would be "Yes, because ordering from lowest sound level to highest sound level makes it easy to use the exposure graph to see what time is permitted."
Hopes this helps.
Determine how long it takes for the leaf to fall to the ground.
Answer:
1.5
Step-by-step explanation:
Solve for x
ax+bx=10
Answer:
\(ax + bx = 10 \\ \\ x(a + b) = 10 \\ \\ x = \frac{10}{a + b} \)
I hope I helped you^_^
How many 7/8-teaspoon servings are in 1/4 of a teaspoon of sugar? Yor anwer needs to be in farction in simplest form.
What is the measurement of D? Enter number only for your answer. (hint: two secants)
The answer of the given question based on the measurement of angle ∠D the answer is the measurement of angle ∠D is 40°degrees.
What is Circumference?In mathematics, circumference is distance around edge of a circle. It is the total length of boundary of a circle, and is also referred to as perimeter of a circle. The circumference of circle is proportional to its diameter, which is distance across the circle passing through its center.
The formula for calculating circumference of circle are:
C =πd or C =2πr
where C is circumference, d is diameter of circle, r is radius of circle, and π (pi) is mathematical constant approximately equal to the 3.14159.
The circumference is important measurement in geometry and is used to solve various problems related to circles, like finding area, volume, and surface area of circles, as well as calculating length of arcs and measure of angles formed by intersecting chords, secants, and tangents.
Using the Two Secants Theorem, we can say that:
m∠D = 1/2 (mAB - mAC)
From the given diagram, we can see that mAB = 130° degrees and mAC = 50° degrees.
Therefore,
m∠D = 1/2 (130 - 50) = 1/2 (80) = 40° degrees.
So the measurement of angle D is 40° degrees.
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Which ordered pair solves this linear system?
Y= -x
Y= 2x
The ordered pair that solves the system of equation is (0, 0).
To solve this system, we can substitute the first equation into the second equation to eliminate y:
x = 2x
Solving for x, we get x = 0.
Substituting x = 0 into the first equation, we get y = 0.
Therefore, the ordered pair that solves the system is (0, 0).
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help! offering 15 points
The formula for the centripetal force, as a function of the radius, is given as follows:
F = 896/r.
What is a proportional relationship?The equation that defines a direct proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality.
For an inverse proportional relationship, the equation is given as follows:
y = k/x.
The centripetal force varies inversely with the radius, hence the equation is given as follows:
F = k/r.
When F = 56, r = 16, hence the constant k is obtained as follows:
56 = k/16
k = 56 x 16
k = 896.
Hence the equation is given as follows:
F = 896/r.
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A roofing company charged 14 different families 697$ to replace their roofs how much money did the roofing company charge in all
Answer:
9758
Step-by-step explanation:
697 x 14 = 9758
suppose you borrow $1000 for 3 years and you owe $200 interest. what is the interest rate?
Answer:
6.67%
Step-by-step explanation:
By question I borrow $1000 for 3 years and I owe $200 interest . We can use the formula of Simple Interest as ,
\(\implies SI =\dfrac{ P*R*T}{100}\)
Plug in the values .\(\implies \$200 =\dfrac{3*\$1000*R }{100}\\\\\implies R = \dfrac{ \$ 200 * 100}{3*\$ 1000} \\\\\implies\underline{\underline{ R = 6.67 \%}} \)
What type of function is shown below?
y=6/19x
Answer:
That is a linear function
Step-by-step explanation:
A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.
If you try to graph that function on a graphing calculator, you will get a straight line.
Therefore, it is a linear function.
mark brainliest please!
Answer:
I think it's a linear one(function)
y=6x÷19