The slopes of the two lines that form them must be equal (m1 = m2). This implies that the two lines are parallel.
1) Biconditional statement: If two lines are parallel, then the alternate interior angles formed by a transversal are equal.
Formula: m∠1 = m∠3 and m∠2 = m∠4
Calculation: If two lines are parallel with a transversal intersecting them, the slopes of the two lines must be equal (m1 = m2) and the alternate interior angles formed by the transversal must have the same measure (m∠1 = m∠3 and m∠2 = m∠4).
2) Biconditional statement: If two lines are parallel, then the corresponding angles formed by a transversal are equal.
Formula: m∠1 = m∠4 and m∠2 = m∠3
Calculation: If two lines are parallel with a transversal intersecting them, the slopes of the two lines must be equal (m1 = m2) and the corresponding angles formed by the transversal must have the same measure (m∠1 = m∠4 and m∠2 = m∠3).
3) Biconditional statement: If two angles are equal, then the lines that form them are parallel.
Formula: m1 = m2
Calculation: If two angles have the same measure, then the slopes of the two lines that form them must be equal (m1 = m2). This implies that the two lines are parallel.
Learn more about parallel here:
https://brainly.com/question/16701300
#SPJ4
find the domain and range of the function. Use a graphing utility to verify your results. (Enter your answer using interval notation.)
f(x) = ?x2 ? 6x + 7
The domain is [0,100].[0,100]. The range is [0,1500] [0,1500]
(a) To find the cost of making 25 items substitute
x=25 in the equation
=10+500(25)
=10(25)+500(25)=750
c(x)=10x+500
c(25)=10(25)+500
c(25)=750
the cost of making 25 items is
$750
(b)
Since the maximum cost allowed is
$1500
10+500≤1500
10x+500≤1500
To solve this inequality
First, subtract 500 from both sides
10≤1000
10x≤1000
Divide both sides by 10
≤100x≤100
This means you can make at most 100 items.
The domain is
[0,100].[0,100].
The range is
[0,1500] [0,1500].
Know more about the domain
https://brainly.com/question/2264373
#SPJ4
Question 23 of 41
Which of the following is equivalent to the product below?
√9.√5√2
OA. 18√5
OB. 10√3
OC. 3√10
OD. 5√18
Which graph shows the new image of the rectangle after a translation of two units to the left?
The new image of the rectangle after a translation of two units to the left is of option D
How to draw a shifted figure if the shifts are provided?Suppose the graph is drawn on the coordinate plane.
Let the shifting be (x,y) → (x+a, y+b)
Then, add 'a' to all x coordinates of the graph's points. Add 'b' to all y coordinates of the graph's points.
The resultant set of new points will be plotted.
Given;
A rectangle area on graph with coordinates (1,0), (6,0),(6,2), (1,2)
Now after the shift of 2 unit left, the x coordinates will be affected;
=(1-2,0), (6-2,0),(6-2,2), (1-2,2)
=(-1,0), (4,0),(4,2), (-1,2)
Therefore, the coordinates of shifted graph will be (-1,0), (4,0),(4,2), (-1,2)
Learn more about finding the graphed function here:
https://brainly.com/question/27330212
#SPJ1
If a plane can travel 490 miles per hour with the wind and 430 miles per hour against the wind, find the speed of the plane in still air.
Answer:
460
Step-by-step explanation:
Let b = base speed and w = wind power.
Here's what we know:
b + w = 490
b - w = 430
From here, we can use the elimination method. If we treat each variable and constant as columns, we do the following:
b + b = 2b
w - w = 0
490 + 430 = 920
Leaving us with:
2b = 920
Divide by 2:
2b / 2 = b
920 / 2 = 460
So b = 460 mph
Consider the slope field shown: (a) For the solution that satisfies y(0) 0,sketch the solution curve and estimate the following: y(I) ~ 0.75 and y(-1) 0.5 (b) For the solution that satisfies Y(O) = 4, sketch the solution curve and estimate the following: Y(0.5) -0.5 and Y(-1) 0.75 (c) For the solution that satisfies Y(O) = -1, sketch the solution curve and estimate the following: Y(I) ~ and y(-1) ~
For the solution that satisfies, sketch the solution curve and estimate the following y(0)=0: y(1)≈0.75, y(-1)≈0.5; Y(0)=4: Y(0.5)≈-0.5, Y(-1)≈0.75; Y(0)=-1: Y(1)≈-1.5, Y(-1)≈-1.5.
(a) To sketch the solution curve for the given slope field, beginning at the point (0, 0) and following the arrows, draw a curved line that gradually moves from left to right, gradually increasing in value and then slowly decreasing. The estimated value of y(1) is 0.75 and y(-1) is 0.5.
(b) To sketch the For the solution that satisfies, sketch the solution curve and estimate the following y(0)=0: y(1)≈0.75, y(-1)≈0.5; Y(0)=4: Y(0.5)≈-0.5, Y(-1)≈0.75; Y(0)=-1: Y(1)≈-1.5, Y(-1)≈-1.5. curve for the given slope field, beginning at the point (0, 4) and following the arrows, draw a curved line that gradually moves from right to left, gradually decreasing in value and then slowly increasing. The estimated value of Y(0.5) is -0.5 and Y(-1) is 0.75.
(c) To sketch the solution curve for the given slope field, beginning at the point (0, -1) and following the arrows, draw a curved line that gradually moves from left to right, gradually increasing in value and then slowly decreasing. The estimated value of Y(1) is and y(-1) is -1.5.
Learn more about curve here
https://brainly.com/question/28793630
#SPJ4
College Algebra! Worth 20 points. Can anyone help?
The solution set to inequality - 5 ≤ (1 / 2) · (2 · m + 2) ≤ 14 is equal to - 6 ≤ m ≤ 13. (Correct choice: A)
How to solve a simultaneous inequality
Herein we find a simultaneous inequality, that is, the combination of two inequalities. We find the following case below by algebra properties:
- 5 ≤ (1 / 2) · (2 · m + 2) ≤ 14
(1 / 2) · (2 · m + 2) ≥ - 5 and (1 / 2) · (2 · m + 2) ≤ 14
Now we proceed to determine the solution set to this inequality by algebra properties:
2 · m + 2 ≥ - 10 and 2 · m + 2 ≤ 28
2 · m ≥ - 12 and 2 · m ≤ 26
m ≥ - 6 and m ≤ 13
- 6 ≤ m ≤ 13
To learn more on inequalities: https://brainly.com/question/30231190
#SPJ1
On the coordinate plane, the segment from D(-6, 3) to E(2, 3) forms one side of ADEF. The
triangle has an area of 28 square units. Select all of the points where F could be.
(5,-4)
(1, 10)
(7,4)
(-6, 10)
On the coordinate plane, the segment from D(-6, 3) to E(2, 3) forms one side of ADEF. The possible point F are (5,-4), (1, 10), (7,4), (-6, 10).
How many points does a F earn?Since we are aware that the triangle's area is 28 square units and that the base is the segment DE, which has a length of 8 units, we can construct the equation:
Area equals (1/2) × base × height = (1/2) × 8 × height=28
We can calculate the height and discover that it is 7 units.
Point F must be situated 7 units above or below the line DE since the triangle's height is perpendicular to the base DE. Therefore, any position that is 7 units above or below the line DE, which is determined by the equation y = 3, is considered to be at point F.
So the possible point F are (5,-4), (1, 10), (7,4), (-6, 10)
To learn more about coordinate plane refer to:
brainly.com/question/3903921
#SPJ1
Complete question -
On the coordinate plane, the segment from D(-6, 3) to E(2, 3) forms one side of ADEF. The
triangle has an area of 28 square units. Select all of the points where F could be. (5,-4), (1, 10), (7,4),(-6, 10)
43)A tree13feet high grows at the rate of3feet each year. How many years will it take for the tree to grow to a height of 28 feet?
the answer is 5 please show me how to get that answer?
in exercises 11 and 12, determine if b is a linear combination of subscript[a, 1], subscript[a, 2], and subscript[a, 3].
Yes b can be written as linear combination of 3 vectors
What is linear combination of vector?A linear combination of vectors is a sum of scaled vectors, where the scaling factors are scalars. In other words, it's a linear combination of the form a_1v_1 + a_2v_2 + ... + a_n*v_n, where v_1, v_2, ..., v_n are vectors and a_1, a_2, ..., a_n are scalars. This is a fundamental concept in linear algebra and vector spaces and is used in many areas of mathematics and physics.
if b is linear combination of [tex]a_1,a_2,a_3[/tex]
then [tex]xa_1+ya_2+za_3=b[/tex]
from here we got :
x+5z = 2
-2x+y-6z = -1
2y + 8z = 6
after solving the above equation we get the solution as
{x,y,x} = {2,3,0} is a solution to the above equation so b is a linear combination of [tex]a_1,a_2,a_3[/tex]
To know more about linear combination click on below link:
https://brainly.com/question/29770393#
#SPJ4
Complete question:
determine if b is a linear combination of [tex]a_1,a_2,a_3[/tex]
[tex]a_1[/tex] = [tex]\left[\begin{array}{ccc}1\\-2\\0\end{array}\right][/tex] , [tex]a_2 = \left[\begin{array}{ccc}0\\1\\2\end{array}\right][/tex] , [tex]a_3 = \left[\begin{array}{ccc}5\\-6\\8\end{array}\right][/tex] , b= [tex]\left[\begin{array}{ccc}2\\-1\\6\end{array}\right][/tex]
someone please answer and explain how to do this in steps i will give you a cookie
17. The equation can be rewritten as 2x²-8x+1=0.
18. The axis of symmetry is x = 5. The parabola opens up and has a maximum at the vertex (5, 6). The quadratic equation has two solutions, x = 4 and x = 6.
How many solutions does the graph have?17.
The equation can be rewritten as 2x²-8x+1=0.
Vertex:
The vertex is (4, -1). A minimum.
Axis of symmetry:
The axis of symmetry is x = 4.
The parabola opens up.
The graph has 1 solution.
18. How many solutions does the quadratic
have?
Answer: The axis of symmetry is x = 5, which is calculated by taking the coefficient of x (which is -10) and dividing it by 2. This is because the axis of symmetry is always in the middle of the two x-intercepts. The parabola opens up, which means it has a maximum at the vertex. The vertex is (5, 6), which is calculated by substituting x = 5 into the equation and solving for y.The quadratic equation has two solutions, x = 4 and x = 6. To find the solutions, one must set the equation equal to 0 and solve for x. This can be done by either factoring or using the quadratic formula. After finding the x-intercepts, the solutions can be determined by plugging in the x-intercepts into the equation and solving for y.To learn more about Solutions in the graph refer :
brainly.com/question/30374139
#SPJ1
17. The equation can be rewritten as 2x²-8x+1=0. 18. The axis of symmetry is x = 5. The parabola opens up and has a maximum at the vertex (5, 6). The quadratic equation has two solutions, x = 4 and x = 6.
17. The equation can be rewritten as 2x²-8x+1=0.
Vertex:
The vertex is (4, -1). A minimum.
Axis of symmetry:
The axis of symmetry is x = 4.
The parabola opens up.
The graph has 1 solution.
18. The coefficient of x, which is -10, is multiplied by two to determine the axis of symmetry, which is x = 5.
This is due to the fact that the axis of symmetry is always located halfway between the two x-intercepts.
The parabola widens, indicating that the vertex is where its maximum is located. The vertex is (5, 6), which is determined by solving for y while changing x = 5 in the equation.
There are two answers to the quadratic equation: x = 4 and x = 6. The equation must be made equal to 0 in order to get the solutions.
Either factoring or applying the quadratic formula can be used to accomplish this.
To learn more about parabola refer :
https://brainly.com/question/29211188
#SPJ1
Rework problem 27 from section 1.2 of your textbook, about the three subsets X1, X2, and X3 that partition a set X, except assume that the number of elements in X, is 4 times the number of elements in X2, the number of elements in X3 is 6 times the number of elements in X2, and n(X) = 99. (1) n(X1) = (2) n(X2) = (3) n(X3) =
The value of three subsets is [tex]n(x_{1})=36, n(x_{2})=9, & n\left(x_3\right)=54[/tex].
A set is a collection of objects or elements, grouped in the curly braces, such as {a, b, c, d}. If a set A is a collection of even number and set B consists of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B.
The elements of sets could be anything such as a group of real numbers, variables, constants, whole numbers, etc. It consists of a null set as well.
If set A has {X, Y} and set B has {X, Y, Z}, then A is the subset of B because elements of A are also present in set B.
Let the number of elements in [tex]$x_2$[/tex] be [tex]$x$[/tex], then
[tex]$$\begin{aligned}& n\left(x_1\right)=4 x \\& n\left(x_2\right)=x \\& n\left(x_3\right)=6 x\end{aligned}$$[/tex]
Given that number of elements in [tex]$x=99$[/tex]
[tex]$$\begin{aligned}\Rightarrow & n\left(x_1\right)+n\left(x_2\right)+n\left(x_3\right)=99 \\\Rightarrow & 4 x+x+6 x=99 \\\Rightarrow & 11 x=99 \\\Rightarrow & x=9 \\\therefore & n\left(x_1\right)=4 x=4 \times 9=36 \\& n\left(x_2\right)=x=9 \\& n\left(x_3\right)=6 x=6 \times 9=54\end{aligned}$$[/tex]
Therefore, the value of [tex]& n\left(x_3\right)[/tex][tex]=54[/tex].
For more such questions on Subsets:
https://brainly.com/question/23454979
#SPJ4
Which equation has a solution of x= 3/4
The equation has a solution of x= 3/4 will be B. 8x = 6
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this case, the value of x in 3x = 6 will be:
x = 6 / 3
x = 2
The value of x in 8x = 6 will be:
x = 6 / 8
x = 3 / 4
The value of x in 4x = 2 will be:
x = 2/4
x = 1/2
The value of x in 3x = 15 will be:
x = 15 / 3
x = 5
The correct option is B.
Learn more about equations on:
brainly.com/question/17025518
#SPJ1
Complete question
Which equation has a solution of x= 3/4?
A. 3x = 6
B. 8x = 6
C. 4x = 2
D. 3x = 15
Please help me find each measure!! Thank you
THIS IS URGENT, What is the GCF of 36x^2 and 18xy^2
The greatest common factor (GCF) of two or more expressions is the largest monomial that divides each expression exactly.
To find the GCF of 36x^2 and 18xy^2, we can factor out the greatest common factor from each expression.
The prime factorization of 36 is 2^2 * 3^2 and of 18 is 2*3^2
The GCF of 36x^2 and 18xy^2 is 18x^2y^2 = 2*3^2 * x^2 * y^2
So, the GCF of 36x^2 and 18xy^2 is 18x^2y^2
Answer:
18xy
Step-by-step explanation:
Read the following prompt and type your response in the space provided.
Give an example of a problem involving multiplication of fractions that can be made easier using the associative property. Explain how it makes the problem easier.
An example of a question that can be solved using the associative method is : (2/5) * (3/4) * (5/6)
How to use the associative propertyOne example of a problem involving multiplication of fractions that can be made easier using the associative property is:
(2/5) * (3/4) * (5/6)
Using the associative property of multiplication, we can change the grouping of the fractions to make the problem easier. The associative property states that the way we group the numbers being multiplied does not change the product. For example,
(2/5) * (3/4) * (5/6) = (2/5 * 3/4) * (5/6) = (6/20) * (5/6) = 30/120
This simplification makes it easier to see that the final answer is 1/4.
By using the associative property, we can first multiply (2/5) * (3/4) = (6/20) which is easier to cancel out the common factor and then multiply it with (5/6) = (5/6) * (6/20) = (30/120) = 1/4 which is the final answer
Read more on associative property here:. https://brainly.com/question/13181
#SPJ1
Is this sequence arithmetic or geometric?
List at least 5 terms of the sequence
Write a recursive definition for the sequence
This formula states that each term in the sequence is equal to the previous term plus 3.
Is this sequence arithmetic or geometric?This sequence is arithmetic, because the difference between consecutive terms is consistent.The first five terms of the sequence are 1, 3, 5, 7, and 9.The recursive definition of the sequence is a(n) = a(n-1) + 2, where a(1) = 1.This sequence appears to be arithmetic, as the difference between consecutive terms is constant.This can be seen by looking at the graph, where the y-values of each point are regularly spaced apart.The first five terms of the sequence are 2, 5, 8, 11, and 14.A recursive definition of the sequence is a formula that can be used to generate subsequent terms of the sequence.In this case, the recursive definition of the sequence is a(n) = a(n-1) + 3, with a(1) = 2.For example, the fourth term in the sequence (11) is equal to the third term (8) plus 3, and the fifth term (14) is equal to the fourth term (11) plus 3.This sequence appears to be arithmetic, as each consecutive term increases by the same amount. The difference between each term is constant, so this is a defining characteristic of arithmetic sequences.The first five terms of this sequence are 0, 2, 4, 6, 8.\A recursive definition of this sequence is a formula that describes the relationship between each term and the preceding term. The recursive definition of this sequence is an_n = a_(n-1) + 2, where a_n is the nth term of the sequence and a_1 = 0. This definition states that each term is two more than the previous term.To learn more about the sequence refer to:
https://brainly.com/question/6561461
#SPJ1
In the figure the boundary of the shaded region consists of four semicircular arcs, the smallest two being equal. If the diameter of the largest is 14 cm and of the smallest is 3.5 cm, find1 . The length of the boundary2 . The area of the shaded region
The area of the shaded region and the length of the boundary is 86.59 cm^2 and 44cm respectively.
A semicircle is a shape that is half of a circle. It is defined by a center point and a radius, and it is made up of an arc that is 180 degrees of the full circle.
The circumference of a semicircle is given by the formula: C = π * d, where C is the circumference and d is the diameter of the semicircle.
Diameter of the biggest semi-circle = 14cm.
Diameter to two small semi-circles = 3.5cm.
Diameter of other semi-circle = 14 - 2(Diameter to two small semi-circles)
=14 - 7 cm
= 7cm
Length of boundary = Circumference of bigger semi-circle + Circumference of small semi-circle + 2 ×circumference of the smaller semi-circles
∴Length of boundary= [tex]\pi R+\pi r_{1}+2\pi r_{2}[/tex]
=> Length of boundary=[tex]\pi (R+r_{1})+2\pi r_{2}[/tex]
=> [tex]\frac{22}{7}(7+3.5)+2X\frac{22}{7}X1.75[/tex]
=> 44cm
Area of the biggest semi-circle = [tex]\frac{1}{2}\pi (7)^{2} cm^{2}[/tex]
Area of two small semi-circles = [tex]\pi (1.75)^{2}cm^{2}[/tex]
Area of other semi-circle= [tex]\frac{1}{2}\pi (3.5)^{2}cm^{2}[/tex]
Area of shaded region= π×(24.5−3.0625+12.25)
=π×27.5625 cm^2 =86.59 cm^2
Therefore, the area of the shaded region and the length of the boundary is 86.59 cm^2 and 44cm respectively.
To know more about semi-circles refer to:
brainly.com/question/16688824
#SPJ4
Marissa bought 7 ounces of yogurt for $3.50.
What is the unit price?
$0.35 per ounce
$0.50 per ounce
$3.50 per ounce
$5.00 per ounce
Answer:
$0.50
50 cents per ounce.
Step-by-step explanation:
To get the unit price, you take the cost of the package divided by the parts it has. Since Marissa has a package of yogurt that costs $3.50 and there are seven ounces in the package we have this equation:
($3.50)/(7 ounces)= $0.50 = 50 cents = the second answer available.
Summarize what these bond funds have in common.
Vanguard and Fidelity
There are many similarities between Vanguard and Fidelity, but there are also some significant distinctions. Vanguard focuses primarily on long-term, buy-and-hold investing.
What are bond funds?Fidelity, on the other hand, caters to investors who prefer a more hands-on approach.
There are more than 8,300 domestic investment-grade bonds held by the Vanguard Total Bond Market ETF.
Therefore, You'll need to study two (or more) sets of statements, keep track of several phone numbers, access a number of websites, and comprehend and keep track of hundreds of different funds.
Learn more about bond funds, here:
https://brainly.com/question/30050727
#SPJ1
There are many similarities between Vanguard and Fidelity, but there are also some significant distinctions. Vanguard focuses primarily on long-term, buy-and-hold investing. Fidelity, on the other hand, caters to investors who prefer a more hands-on approach.
What do you mean by Bond?Bonds are issued by borrowers to attract capital from investors ready to extend a loan to them for a specific period of time. When you purchase a bond, you are making a loan to the issuer, which could be a corporate, government, or municipality.
By purchasing a bond, you are effectively lending the issuer money. In exchange, they commit to repay you the face amount of the loan on a particular date and to make periodic interest payments—typically twice a year—along the way. Unlike stocks, which grant you ownership rights, bonds issued by corporations do not.
Therefore, Vanguard's primary investment strategy is long-term buy-and-hold investing. On the other hand, Fidelity caters to investors who favor a more active strategy.
Learn more about Bond, here;
https://brainly.com/question/10777799
#SPJ1
Calculate the percent by mass of a solution where 13.687 grams is dissolved in 46.833 grams of water. answer without the percent sign
The percent by mass of a solution is 29.21.
To calculate the percent by mass of a solution, divide the mass of the solute (13.687 grams) by the total mass of the solution (46.833 grams). Then, multiply this value by 100 to get the percent.
% by mass = (mass of solute/total mass of solution) x 100
% by mass = (13.687/46.833) x 100 = 29.21.This calculation can be used to determine the amount of a solute in a given solution. It is important to know the percent by mass of a solution in order to make sure the solution is composed of the desired amount of solute. Knowing the percent by mass can also be used to compare the solutions of different concentrations.
Learn more about amount here:
https://brainly.com/question/29066172
#SPJ4
Si el costo de 1 Kg de azucar es $8?cual es el precio de 3 3/4 kg?
Answer:
$30
Step-by-step explanation:
1kg= $8
3kg *$8= $24
3/4= 0.75
$8 *0.75= $6
$24+$6= $30
3.75 kg * $8= 30
* = multiply
There exist two complex numbers c, say c1 and c2, so that 2+2i, 5+i, and c form the vertices of an equilateral triangle. Find the product c1c2 .enter image description here
So far, I have used the distance formula to get (a−2)2+(b−2)2=(a−5)2+(b−1)2 for c1(a,b). I expanded and simolified this to get b=3a−9. What do I do next?
The product of the two complex number c₁c₂ is thus 10 + 9i.
Let c₁ = a + ib and c₂ = c + id. Also z₁ represent 2 + 2i and z₂ represent 5 + i. The length of side of the equilateral triangle formed can be obtained by
|z₁ - z₂| = r = √((5 - 2)² + (1 - 2)² = √10
a² + b² - 4a - 4b + 8 = 10
a² + b² - 10a - 2b + 26 = 10
So 6a - 2b = 18 that is 3a - b = 9
Thus b = 3a - 9
Similarly c² + d² - 4c - 4d + 8 = 10
c² + d² - 10c - 2d + 26 = 10
So 3c - d = 9, that is d = 3c - 9
Midpoint of line joining c₁ and c₂ is same as that of z₁ and z₂, so
(c + a)/2 = ( 5 + 2)/ 2 and (d + b)/2 = (1 + 2)/2
So midpoint is 3.5 + 1.5i
Altitude of equilateral triangle of side a is √3a/2
That is √(a - 3.5)² + (b - 1.5)² = √3×√10/2
√(a - 3.5)² + (3a - 9 - 1.5)² = √30 /2
a² - 7a + 12.25 + 9a² - 63a + 110.25 = 30/4
On solving a = (7 ± √3)/ 2
So a = (7 - √3)/ 2, c = (7 + √3)/ 2
b = 3a - 9 = (3 - 3√3)/ 2, d = (3 + 3√3)/2
So c
c₁ = (7 - √3)/2 + i (3 - 3√3)/ 2
c₂ = (7 + √3)/2 + i (3 + 3√3)/ 2
So the product c₁c₂ is
= ((7 - √3)/ 2) * ((7 + √3)/ 2) - ((3 - √3)/ 2) * ((3 + √3)/ 2) + i (((7 - √3)/ 2) * ((3 + √3)/ 2) + ((7 + √3)/ 2) * ((3 - √3)/ 2))
= 10 + 9i
To know more on complex plane
https://brainly.com/question/24296629
#SPJ4
g the space complexities of bfs and dfs are o(b^d) and o(bd) respectivaly, why is one exponential with respect to d and the other not
BFS has an exponential space complexity with respect to d because it stores all the nodes at the same depth level before moving on to the next level
DFS doesn't have an exponential space complexity with respect to d because it only stores the nodes that need to be visited next.
The space complexity of breadth-first search (BFS) is O([tex]b^d[/tex]) and the space complexity of depth-first search (DFS) is O(bd), where b is the maximum branching factor of the search tree and d is the maximum depth of the tree.
The reason for the difference in the space complexities is that BFS uses a queue to store the nodes to be visited, while DFS uses a stack.
To learn more about breadth-first search:
https://brainly.com/question/15142337
#SPJ4
The land area of Statesville, NC, is 20.7 square miles. If the entire US population (currently about 322.9 million) were put inside the city limits of Statesville, determine the number of square feet that each person would have. Round your answer to two decimal places. [Hint: Remember that a mile is 5,280 feet, so a square mile is (5,280 x 5,280) square feet.]
In the land area of Statesville, NC there would be 133.54 persons per square foot.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, One mile is 5280 feet so a square mile is
(5280 × 5280) = 27878400 square feet.
Therefore, The number of persons in each square foot should be,
= 322900000/27878400 persons per square foot.
= 3229000/278784 persons per square foot.
= 133.54 persons per square foot.
learn more about the unitary method here :
https://brainly.com/question/28276953
#SPJ1
Can someone please help me
The cost of each shirt is $6 and the cost of each pant for the given condition is $9.
What is elimination method?The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.
Let us suppose the cost of shirt = x.
Let us suppose the cost of pant = y.
Given that 3 shirts and 3 pants cost $45, this is represented as:
3x + 3y = 45 (equation 1)
1 shirt and 2 pants cost $24, this is represented as:
x + 2y = 24 (equation 2)
Using the elimination method to solve:
Multiply the second equation with 3 and change the signs of all the variables.
(x + 2y = 24) (3)
-3x - 6y = -72 (equation 3)
3x + 3y = 45
Comparing equation 1 and equation 3, the x term is cancelled, and the remaining equation after subtracting both equations is:
- 3y = -27
y = 9
Substitute the value of y in equation 2.
x + 2y = 24
x + 2(9) = 24
x + 18 = 24
x = 24 -18
x = 6
Hence, the cost of each shirt is $6 and the cost of each pant is $9.
Learn more about elimination method here:
https://brainly.com/question/30287548
#SPJ1
If there are 24 apples and 12 bananas for a fruit basket, fill out all of the possible ratios of apples to bananas that could be made
Answer:
Step-by-step explanation:
for every 24 apples there is 12 bananas
so if you dived it by 2 it will be 12 apples 6 bananas
so it will always be half amount of bananas
Show that the two-variable function f given by f(x, y) = 2x^2 − xy is
differentiable at any point (a, b). What is the derivative of f at (a, b)?
Step-by-step explanation:
To show that the function f(x,y) = 2x^2 − xy is differentiable at any point (a,b), we need to show that the partial derivatives of f with respect to x and y exist and are continuous at that point.
The partial derivative of f with respect to x is:
∂f/∂x = 4x - y
The partial derivative of f with respect to y is:
∂f/∂y = -x
We can see that both of these partial derivatives are continuous functions of x and y and are defined for all (x,y) in the domain of f. Therefore, f is differentiable at any point (a,b).
The derivative of f at (a,b) is the gradient vector of f evaluated at (a,b), which is given by:
Gradient vector of f(a,b) = ∇f(a,b) = ( ∂f/∂x, ∂f/∂y ) = (4a-b, -a)
So the derivative of f at (a, b) is (4a-b, -a).
Draw the graph of y=f(x) and y= 1/f(x) on the same axes.
f) f(x) = -(x+4)²+1
are there any specific steps to get the answers here?
Answer: To graph y = f(x) = -(x+4)²+1 and y = 1/f(x) on the same axes, you can follow these steps:
Plot the y-intercept of y = f(x) which is (0,-1)
For y = f(x), the parabola opens downward since the coefficient of x² is -1, thus the vertex is at (-4,1)
Plot the x-intercepts of y = f(x) which are x = 4 and x = -8
The parabola of y = f(x) is symmetric about the y-axis, so the graph will be reflected about the y-axis.
For y = 1/f(x), the x-intercepts will be the same as y = f(x) and the y-intercept is (0,1)
To graph y = 1/f(x), we can start by plotting the x-intercepts and the y-intercept, and then connecting the points.
Label the x-intercepts, y-intercepts, and vertex for both graphs
Shade the regions above the parabola of y = f(x) and below the graph of y = 1/f(x)
Note: It is important to remember that the graph of y = 1/f(x) is a reflection of the graph of y = f(x) across the x-axis, so the y-intercept of y = 1/f(x) is (0,1)
Step-by-step explanation:
6 1/2 divided by 1 2/3 as a mixed number in simplest form
The value of 6 1/2 divided by 1 2/3 is 3 9/10
How to determine the quotient of the numbersFrom the question, we have the following parameters that can be used in our computation:
6 1/2 divided by 1 2/3
When represented as an expression, we have
6 1/2 / 1 2/3
Convert to improper fractions
13/2 / 5/3
Express as products
13/2 * 3/5
So, we have
39/10
Express as mixed number
3 9/10
Hence, the solution is 3 9/10
Read more about fractions at
https://brainly.com/question/1622425
#SPJ1
A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue. Find a mixture that will make the different shade of green but has a smaller amount.
Use 1.75 cups of blue and 1 cup of yellow
What is a mixture?
Mixture can be defined as a substance made by combining two or more different materials in such a way that no chemical reaction occurs. A mixture can usually be separated back into its original components.
The given problem can be placed in the category of ratios and proportions.
There is a ratio of color mixing which contains the proportion of two colors i.e blue and yellow. When we use 2 cups of yellow with 3.5 cups of yellow then we get green color so if we mix half of their amounts then we can get less or simply half amount of color too.
Therefore adding 1 cup of yellow and 1.75 cup of blue will give us small amount in result.
Learn more about mixture here: brainly.com/question/2331419
#SPJ1