Answers
Answer:
a. Goron 224
b. Smith 96
Fishman 256
Step-by-step explanation:
a. For Goron: 640 x 0.35 = 224
b. For Smith: 640 x 0.15 = 96
For Fishman: 640 x 0.40 = 256
Related Questions
WILL GIVE BRAINLIEST 15 POINTS PLEASEE Fill in the blanks pleaseee
Answers
Therefore, we have the values of:
a = -g(x) for -10 < x < -8
b = lower limit of the range where g(x) = -6
c = -C for -1 < x < 1
d = upper limit of the range where g(x) = 4
e = we cannot determine the value of e based on the given information.
What is function?In mathematics, a function is a rule that assigns a unique output value for every input value in its domain. It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are often represented by a formula or an equation, but they can also be defined in other ways, such as through graphs, tables, or verbal descriptions. They are used to model a wide variety of phenomena in science, engineering, economics, and many other fields.
Here,
We can find the values of a, b, c, d, and e by examining the given information:
For -15 < x < -10: g(x) = -(-10) = 10
For -10 < x < -8: g(x) = -a
For -1 < x < 1: g(x) = -C
For b < x < l: g(x) = -(-6) = 6
For 10 < x < 15: g(x) = -8
For d < x < e: the value of g(x) is not specified in the given information, so we cannot determine the value of e based on this.
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(I NEED HELP, QUICK)
[50 PTS]
Answers
Answer:
In the picture.
34 ft.
Please please please help me!!!!!
Answers
The volume of the sphere which is equivalent to the lung capacity is approximately =2,571 cm³
How to calculate the volume of the sphere?To calculate the volume of a sphere the formula used = V = 4/3 πr³
Radius = 8.5 cm
First cube the radius = 8.5³ = 614.125
The, multiply r³ by π = r³×π = 614.125× 3.14= 1928.3525
Take this answer and multiply it by 4 = 4×1928.3525= 7713.41
Last, divide this answer by 3 = 7713.41/3 = 2571.136666
Therefore the volume of the balloon = 2,571 cm³(approximately)
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Find the definite integral of f(x)=
fraction numerator 1 over denominator x squared plus 10 invisible times x plus 25 end fraction for x∈[
5,7]
Answers
Over the range [5, 7], the definite integral of f(x) = 1 / (x² + 10x + 25) is around -1/60.
To find the definite integral of f(x) = 1 / (x² + 10x + 25) over the interval [5, 7], we can use the following formula:
∫[a,b] f(x) dx = F(b) - F(a)
where F(x) is the antiderivative of f(x).
First, we need to find the antiderivative of f(x):
∫ f(x) dx = ∫ 1 / (x² + 10x + 25) dx
To do this, we can use a technique called partial fraction decomposition:
1 / (x² + 10x + 25)
= A / (x + 5) + B / (x + 5)²
Multiplying both sides by the denominator (x² + 10x + 25), we get:
1 = A(x + 5) + B
Setting x = -5, we get:
1 = B
Setting x = 0, we get:
A + B = 1
A + 1 = 1
A = 0
Therefore, the partial fraction decomposition of f(x) is:
1 / (x² + 10x + 25) = 1 / (x + 5)²
Now we can find the antiderivative:
∫ f(x) dx = ∫ 1 / (x² + 10x + 25) dx = ∫ 1 / (x + 5)² dx
Using the substitution u = x + 5, du = dx, we get:
∫ 1 / (x + 5)² dx = -1 / (x + 5) + C
where C is the constant of integration.
Now we can evaluate the definite integral over the interval [5, 7]:
∫[5,7] f(x) dx = F(7) - F(5)
∫[5,7] f(x) dx = [-1 / (7 + 5) + C] - [-1 / (5 + 5) + C]
∫[5,7] f(x) dx = [-1 / 12 + C] - [-1 / 10 + C]
∫[5,7] f(x) dx = -1 / 12 + C + 1 / 10 - C
∫[5,7] f(x) dx = -1 / 60
Therefore, the definite integral of f(x) = 1 / (x² + 10x + 25) over the interval [5, 7] is approximately -1/60.
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Given ΔABC with measure of angle B equals 78 degrees, measure of angle C equals 52 degrees, and a = 16 inches, what is the length of b?
Answers
To find the length of side b in triangle ABC, we can use the Law of Sines. The length of side b is approximately 20.058 inches.
To find the length of side b in triangle ABC, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.
Using the Law of Sines, we have:
sin(A)/a = sin(B)/b
We are given the measure of angle B as 78 degrees and side a as 16 inches. We can substitute these values into the equation:
sin(A)/16 = sin(78)/b
To find sin(A), we can use the fact that the sum of the angles in a triangle is 180 degrees:
A + B + C = 180
A + 78 + 52 = 180
A = 180 - 78 - 52
A = 50 degrees
Now we can substitute the values into the equation again:
sin(50)/16 = sin(78)/b
To solve for b, we can cross-multiply and isolate b:
b = (16 * sin(78))/sin(50)
We can calculate the length of side b by evaluating this expression using a calculator. The measurement will be roughly 20.058 inches.
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h(x)= -x + 5, solve for x when h(x) = 3
Answers
According to the given information, the solution to H(x) = 3 is x = 2.
What is equation?
In mathematics, an equation is a statement that asserts the equality of two expressions. An equation typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS). The LHS and RHS are separated by an equals sign (=), indicating that they have the same value. The general form of an equation is: LHS = RHS
To solve for x when H(x) = 3, we substitute 3 for H(x) in the equation and solve for x:
H(x) = -x + 5
3 = -x + 5
Subtracting 5 from both sides, we get:
-2 = -x
Multiplying both sides by -1, we get:
2 = x
Therefore, the solution to H(x) = 3 is x = 2.
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[tex]\huge\text{Hey there!}[/tex]
[tex]\mathtt{h(x) = -x + 5}\\\\\mathtt{3 = -x + 5}\\\\\mathtt{-x + 5 = 3}\\\\\textsf{SUBTRACT 5 to BOTH SIDES}\\\\\mathtt{-x + 5 - 5 = 3 - 5}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{-x = 3 - 5}\\\\\mathtt{-x = -2}\\\\\mathtt{-1x = -2}\\\\\textsf{DIVIDE }\mathsf{-1}\textsf{ to BOTH SIDES}\\\\\mathtt{\dfrac{-1x}{-1} = \dfrac{-2}{-1}}\\\\\textsf{SIMPLIFY it}\\\\\mathtt{x = \dfrac{-2}{-1}}\\\\\mathtt{x = 2}[/tex]
[tex]\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{x = 2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
67777+776567.55555=?
Answers
Answer: 844344.55555
243➗ _ =81
Multiplying and dividing integers
Answers
Given:
81x = 243x
= 243 / 81x
= 3
Answer:x = 3
What is the Area and Volume of this prism?
Answers
The area of the prism is given by the sum of the areas of all the parts that compose the prism.
The parts that compose the prism are given as follows:
Rectangular base of dimensions 3m and 5m.Rectangle of dimensions 5m and 10 m.Two right triangles of sides 3m and 10 m.Hence the area of the prism is given as follows:
A = 3 x 5 + 5 x 10 + 2 x 1/2 x 3 x 10
A = 95 m².
The volume is given by the multiplication of the base area by the height, hence:
Base area = 5 x 3 = 15 m².Height of 10 m.Thus:
V = 15 x 10 = 150 m³.
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For both f(x)= √x and f(x)=1/x, sketch the graph of the parent function, apply the transformations indicated, and state the domain and range. Note: You can sketch the graphs by hand or in digital form.
a) y= f(x+2)-1
b) y= -2f(x)+4
c) y= -2f(-(x-3))+1
Answers
Answer: a) Parent function:
f(x) = √x
Domain: x ≥ 0
Range: y ≥ 0
Applying transformations:
shift 2 units left: f(x+2)
shift 1 unit down: f(x+2)-1
Final equation and graph:
y = √(x+2) - 1
Domain: x ≥ -2
Range: y ≥ -1
b) Parent function:
f(x) = 1/x
Domain: x ≠ 0
Range: y ≠ 0
Applying transformations:
multiply by -2: -2f(x)
shift 4 units up: -2f(x)+4
Final equation and graph:
y = -2/x + 4
Domain: x ≠ 0
Range: y ≠ 4
c) Parent function:
f(x) = 1/x
Domain: x ≠ 0
Range: y ≠ 0
Applying transformations:
shift 3 units right: f(-(x-3))
multiply by -2: -2f(-(x-3))
shift 1 unit up: -2f(-(x-3))+1
Final equation and graph:
y = -2/(3-x) + 1
Domain: x ≠ 3
Range: y ≠ 1
Step-by-step explanation:
cathy's heart beats 12 times in 1/6 minute.how many times does her heart beats in 60 minutes.
Answers
Answer:
4,320 times
Step-by-step explanation:
12 x 6 = 72 beats per minute
72 x 60 = 4320 beats in 60 minutes
Answer: 840 in 30 minuets
Step-by-step explanation:
the quadratic sequence: 44; 52; 64; 80; Write down the next two terms of the sequence. Determine the nth term of the quadratic sequence. Calculate the 30th term of the sequence. Prove that the quadratic sequence will always have even terms.
Answers
To find the next two terms of the sequence, we need to first find the common difference between consecutive terms:
52 - 44 = 8
64 - 52 = 12
80 - 64 = 16
We notice that the common difference is increasing by 4 for each term. Therefore, the next two terms of the sequence are:
80 + 20 = 100
100 + 24 = 124
To determine the nth term of the quadratic sequence, we can use the formula:
an = a1 + (n-1)d + bn^2
where a1 is the first term, d is the common difference, b is the coefficient of n^2, and n is the term number.
Using the first four terms of the sequence, we can form a system of equations:
44 = a1 + b
52 = a1 + d + b
64 = a1 + 2d + b
80 = a1 + 3d + b
Solving for a1 and b, we get:
a1 = 20
b = 24
Substituting these values into the formula for an, we get:
an = 20 + (n-1)4 + 24n^2
an = 24n^2 + 4n - 4
To find the 30th term of the sequence, we simply substitute n = 30 into the formula we just derived:
a30 = 24(30)^2 + 4(30) - 4
a30 = 21,596
To prove that the quadratic sequence will always have even terms, we notice that the first term is even (44 = 2 x 22), and the common difference is even (8 = 2 x 4). Therefore, every term of the sequence can be expressed as an even number plus an even multiple of n^2, which is always even. Hence, the quadratic sequence will always have even terms.
Step-by-step explanation:
Sequence is 44;52;64;80;.....44;52;64;80;.....
General formula is Tn=2n2+2n+40
What are all of the solutions to the equation (cos θ)(cos θ) + 1 = (sin θ)(sin θ)?
Answers
Answer: Starting with the given equation:
(cos θ)(cos θ) + 1 = (sin θ)(sin θ)
We can use the identity cos² θ + sin² θ = 1 to rewrite the right-hand side:
(cos θ)(cos θ) + 1 = 1 - (cos θ)(cos θ)
Combining like terms, we get:
2(cos θ)(cos θ) = 0
Dividing both sides by 2, we get:
(cos θ)(cos θ) = 0
Taking the square root of both sides, we get:
cos θ = 0
This equation is true for θ = π/2 + kπ, where k is any integer. So the solutions to the equation are:
θ = π/2 + kπ, where k is any integer.
Enjoy!
Step-by-step explanation:
We can use the trigonometric identity cos²θ + sin²θ = 1 to manipulate the given equation:
cos²θ + 1 = sin²θ
Subtracting cos²θ from both sides, we get:
1 = sin²θ - cos²θ
Using the identity sin²θ - cos²θ = sin(θ + π/2)sin(θ - π/2), we can simplify the right-hand side:
1 = sin(θ + π/2)sin(θ - π/2)
Now we can use the product-to-sum identity sin(θ + π/2)sin(θ - π/2) = (1/2)[cos(θ - (-π/2)) - cos(θ + π/2)] to further simplify the equation:
1 = (1/2)[cos(θ + π) - cos(θ)]
Since cos(θ + π) = -cos(θ), we can substitute into the equation:
1 = (1/2)[-cos(θ) - cos(θ + π/2)]
Using the identity cos(θ + π/2) = -sin(θ), we get:
1 = (1/2)[-cos(θ) + sin(θ)]
Multiplying both sides by 2, we get:
2 = -cos(θ) + sin(θ)
Rearranging, we get:
cos(θ) + sin(θ) = 2
Now we can use the identity cos(θ - α) = cos(θ)cos(α) + sin(θ)sin(α) to find the solutions:
cos(θ - π/4) = cos(θ)cos(π/4) + sin(θ)sin(π/4) = (1/√2)cos(θ) + (1/√2)sin(θ)
Therefore, we have:
(1/√2)cos(θ) + (1/√2)sin(θ) = 2
Multiplying both sides by √2, we get:
cos(θ) + sin(θ)√2 = 2√2
Now we can use the identity cos(α) + sin(α) = √2 sin(α + π/4) to find the solutions:
cos(θ + π/4) = cos(θ)cos(π/4) - sin(θ)sin(π/4) = (1/√2)cos(θ) - (1/√2)sin(θ)
Therefore, we have:
(1/√2)cos(θ) - (1/√2)sin(θ) = 2√2
Multiplying both sides by √2, we get:
cos(θ) - sin(θ)√2 = 2
We now have two equations with two unknowns (cos(θ) and sin(θ)), which can be solved using algebraic methods. Adding the two equations together, we get:
2cos(θ) = 4√2
Dividing both sides by 2, we get:
cos(θ) = 2√2
Since the range of the cosine function is [-1,1], there are no real solutions to this equation. Therefore, there are no solutions to the original equation (cos θ)(cos θ) + 1 = (sin θ)(sin θ).
I believe this is helpful
Find the missing side of each triangle round your answers to the nearest 10th
Answers
Now,
Base= root of h2-p2
Determine whether the following subsets are subspaces of the given vector spaces or not.text Is end text W subscript 2 equals open curly brackets space p equals a subscript 2 t squared plus a subscript 1 t plus a subscript 0 space element of space straight double-struck capital p subscript 2 space left enclose space a subscript 0 equals 2 space end enclose close curly brackets space space text a subspace of the vector space end text space straight double-struck capital p subscript 2 ?(Note: space straight double-struck capital p subscript 2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.)Answer 1text Is end text W subscript 1 equals open curly brackets open square brackets table row a b c row d 0 0 end table close square brackets space element of space M subscript 2 x 3 space end subscript space left enclose space b equals a plus c space end enclose close curly brackets space text a subspace of the vector space end text space space M subscript 2 x 3 space end subscript?(Note: space M subscript 2 x 3 space end subscript is the set of all 2x3 matrices with the standart matrix addition and scalar multiplication with reals.)
Answers
Yes, W_2 = {p_2 = a_2t_2 + a_1t + a_0 ∈ ℙ_2 | a_0 = 2} is a subspace of the vector space ℙ_2.
Yes, W_1 = {[a b c; d 0 0] ∈ M_{2x3} | b = a + c} is a subspace of the vector space M_{2x3}.
Vector spaces are closed under vector addition and scalar multiplication, and in this case, ℙ_2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.
Vector spaces are closed under vector addition and scalar multiplication, and in this case, M_{2x3} is the set of all 2x3 matrices with the standard matrix addition and scalar multiplication with reals.
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Find the radius of the sphere with the given volume
V=4500 mm^3
Answers
Answer:
10.24
Step-by-step explanation:
i used an online calculator
Find the center of mass of a thin plate of constant density delta covering the given region. The region bounded by the parabola y = 3x - x^2 and the line y = -3x The center of mass is. (Type an ordered pair.)
Answers
The center of mass of a thin plate of constant density covering the given region is (1.8, 3.6).
To find the center of mass, we must calculate the weighted average of all the points in the region. The region is bounded by the parabola y = 3x - x² and the line y = -3x.
We must calculate the integral of the region and divide by the total mass. The mass is equal to the area times the density, .
The integral of the region is calculated using the limits of the two curves, yielding a final integral of 32/15. Dividing this integral by the density gives the total mass, and multiplying by the density gives us the center of mass, (1.8, 3.6).
We can also find the center of mass by calculating the moments of the plate about the x-axis and y-axis.
The moment about the x-axis is calculated by finding the integral of the parabola and line using the x-coordinate, and the moment about the y-axis is calculated by finding the integral of the parabola and line using the y-coordinate. Once the moments are found, we can divide each moment by the total mass to get the center of mass.
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Y=5x+17 Y=-2x+4 solve with elimination
Answers
Answer:
x = -13/7
y = 54/7
Step-by-step explanation:
Y = 5x + 17 Y = -2x + 4
5x + 17 = -2x + 4
7x + 17 = 4
7x = -13
x = -13/7
Not put -13/7 in for x and solve for y
y = 5(-13/7) + 17
y = 54/7
So, the answer is x = -13/7 and y = 54/7
Answer: x = -13 / 7, y = 54/7
Step-by-step explanation:
To eliminate a variable, we can substitute y for 5x + 17
We get 5x + 17 = -2x + 4
7x = -13
x = -13 / 7
Substituting x into the 2nd equation y = 5 * -13 / 7 + 17
y = 119/7 - 65/7
y = 54/7
Transversals of Parallel lines:
corresponding angles
Answers
In solving the given question, we can say that ∠ZEFI and ∠ZJIK are equal parallel lines by co-exterior angles property.
what is parallel lines?Geometry parallel lines are coplanar infinite lines that do not intersect anywhere. In a given three-dimensional space, parallel faces are faces that never intersect. Curves with a constant minimum distance between them and no tangents or intersections are said to be parallel. Two lines that lie in the same plane, are equally spaced, and never intersect are called parallel lines in geometry. Can be applied horizontally or vertically. Parallel lines are found in everyday objects such as railroad tracks, rows of books, and crosswalks.
∠ZHIK and ∠ZEFI are equal by alternative angles property.
∠ZGFD and ∠ZEFD are equal by co-interior angles property.
∠ZGFD and ∠ZEFI are equal by interior alt. angles property.
∠ZEFI and ∠ZJIK are equal by co-exterior angles property.
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andrew is buying a cell phone that has a regular price of $485. the cell phone is on sale for 35% off the regular price. what will be the sale price?
Answers
the sale price of the cell phone after the 35% discount is $315.25.
How to solve and what is sale?
To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:
Sale price = Regular price - Discount amount
Sale price = $485 - (0.35 x $485)
Sale price = $485 - $169.75
Sale price = $315.25
Therefore, the sale price of the cell phone after the 35% discount is $315.25.
A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.
In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.
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A box with a square base and open top must have a volume of 62500 cm3. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible. A(x) = Next, find the derivative, A'(x). A'(x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by x² .] A'(x) = 0 when x =
Answers
The area of the square base = x².
we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ...
The dimension of the box that minimizes the amount of material used is x = (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x = (2V)1/3
The given volume of the box is 62500 cm³. We wish to find the dimensions of the box that minimize the amount of material used.
To obtain the formula for the surface area of the box in terms of only x, the length of one side of the square base, we use the formula for the volume of a box:V = lwh ... (1) ... where V is the volume, l is the length, w is the width, and h is the height of the box. Here, the base of the box is a square with side length x.
Hence, the area of the square base = x². Therefore, we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ... We can substitute (2) and (3) in (1) to get the formula for V in terms of x as follows:V = x² V/x² A(x) = A(x) = x² + 4xhA(x) = x² + 4x(V/x²) = x² + 4V/x
Now, to find the derivative A'(x) of A(x), we differentiate A(x) with respect to x:A'(x) = 2x - 4V/x² A'(x) = 0 when x = (2V)1/3. Therefore, the dimension of the box that minimizes the amount of material used is x = (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x = (2V)1/3
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on saturday a local hamburger shop sold a combined total of 416 hamburgers and cheeseburgers.the number of cheeseburgers sold was three times the number of hamburgers sold. how many hamburgers were sold?
Answers
Answer: Let x be the number of hamburgers sold.
Then, the number of cheeseburgers sold is 3x.
The total number of burgers sold is x + 3x = 4x.
Given that the total number of burgers sold is 416, we have:
4x = 416
x = 416/4
x = 104
Therefore, 104 hamburgers were sold.
Step-by-step explanation:
Find the area under the curve y = 2 x^-3 from x = 6 to x = t and evaluate it for t = 10 , t = 100 . Then find the total area under this curve for x ≥ 6 .
(a) t = 10
(b) t = 100
(c) Total area
Answers
The total area under the curve for x ≥ 6 is 449/4500.
The area under the curve y = 2x-3 from x = 6 to x = t and its evaluation at t = 10 and t = 100The area under the curve y = 2x-3 from x = 6 to x = t can be calculated as follows:
We know that the area of the region under the curve f(x) between x = a and x = b is given by [tex]A = ∫abf(x)dx[/tex]
Since the given function is y = 2x-3, we can write it as y = 2x^(-3) by applying the power rule.
Hence,A = [tex]∫62x^(-3)dx = [-2x^(-2)]6t = -2/t^2 + 2/36[/tex]We need to evaluate this area for t = 10 and t = 100, so we get[tex]A = -2/10^2 + 2/36 = -1/25 + 1/18 = 7/450andA = -2/100^2 + 2/36 = -1/5000 + 1/18 = 449/4500[/tex]Total area under this curve for x ≥ 6
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what type of data is a questionnaire
Answers
Answer:
A questionnaire can collect quantitative, qualitive or both types of data.
Step-by-step explanation:
Answer:
Categorical data
Step-by-step explanation:
Data that relates to certain categories e.g males, females or any types of car
Mei Mei wraps a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift box.
Answers
Mei Mei utilized wrapping paper that was 337.212 square inches in size.
What is the triangular pyramid formula?The formula V = 1/3AH, where H is the height of the pyramid or the distance from its base to its apex, may be used to calculate the volume of a triangular pyramid.
To find the amount of wrapping paper Mei Mei used
we need to find the surface area of the triangular pyramid.
The formula for an equilateral triangle's area is as follows:
[tex]A = (\sqrt{(3)/4}) \times s^2[/tex]
where s is a side of the triangle's length.
The base of the triangular base is 13 inches, so the sides of the triangles are also 13 inches.
The slant height of the pyramid is given as 11.26 inches.
Using the formula, we find that the area of each triangular face is:
[tex]A = (\sqrt{(3)/4)} \times s^2 = (\sqrt{(3)/4)} \times 13^2 = 84.303[/tex]
To find the total surface area of the pyramid, we add up the areas of all four triangular faces. There are four triangles, so:
total surface area =[tex]4 \times A = 4 \times 84.303 = 337.212[/tex]
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Complete question -
Mei Mei wraps a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift box.
NEED THIS ANSWERED ASAP!!
The line of site to the horizon would be tangent to the Earth’s surface. What kind of angle is formed between the radius of the Earth and the line of site?
Answers
Answer:
right angle
Step-by-step explanation:
You want to know the kind of angle formed between a radius and a tangent.
TangentA tangent to a circle is always perpendicular to the radius at the point of tangency.
The angle is a right angle.
use the unique factorization theorem to write the following integers in standard factored form. (a) 504 (b) 819 (c) 5,445
Answers
Using the Unique factorization theorem for the following integers the standard factored form of 504 is 2³ x 3²x 7 , for 819 is 3² ×7×13 and for 5,445 is 3²×5×7².
The Unique Factorization Theorem states that any positive integer can be written as a product of prime numbers in a unique way. To write each of the integers in standard factored form.
Using this theorem, we can factorize any positive integer into its prime factors. Here are the steps to factorize a number:
Find the smallest prime factor of the number. Divide the number by this prime factor, and repeat step 1 with the result. Continue this process until the result is 1.The prime factors obtained in this process can then be multiplied together to obtain the standard factored form of the original number . Therefore,
)504 = 2³ x 3² x 7)819 = 3² ×7×13)5,445 =3²×5×7²To learn more about 'Unique Factorization Theorem':
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mai has a jar of quarters and dimes. she takes at least 10 coins out of the jar and has less than $2.00. write a system of inequalities that represents the number of quarters, `x`, and the number of dimes, `y`, that mai could have.
Answers
The system of inequalities that represents the number of quarters, x, and the number of dimes, y, that Mai could have is given by:
x + y ≥ 10 and 0.25x + 0.1y < 2
These are the two systems of inequalities that represent the number of quarters, x, and the number of dimes, y, that Mai could have.
Let x be the number of quarters and y be the number of dimes that Mai has. Then, the system of inequalities can be represented as:
Thus, the first inequality is x + y ≥ 10.
Also, Mai has less than $2.00, therefore, the second inequality is 0.25x + 0.1y < 2. The value of x and y are assumed to be non-negative integers.+
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I need help on 10 and 11
Answers
Answer:
x = +8
x = -8
That's the thing that I only know. Im a seventh grader(turned 13) so I wouldn't know this fully. Ask someone else to get it fully.
Step-by-step explanation:
5x + 6x - 10 + 12 = 90
11x = -88
x = -8
or
x = 8
In 915. 23, the digit 3 is in the
place.
Answers
Answer:
hundreth
Step-by-step explanation:
the 2 is in the tenth and the 3 is in the hundreth
