The values of X1 and X2 that maximize the function Z = 30X1 + 50X2 are given as follows:
X1 = 50.X2 = 50.The maximum value is given as follows:
4000.
How to maximize the function?The function for this problem is defined as follows:
Z = 30X1 + 50X2.
The constraints are given as follows:
X1 + 3X2 ≤ 200X1 + X2 ≤ 100.X2 has the higher multiplier, hence we should:
Minimize X1.Maximize X2.The maximum value of X2 is obtained when:
X2 = 100 - X1.
Replacing into the first equation, the value of X1 is given as follows:
X1 + 3(100 - X1) = 200
-2X1 = -100
2X1 = 100
X1 = 50.
Hence the value of X2 is of:
X2 = 100 - X1
X2 = 50.
The maximum value of the function is obtained as follows:
Z = 30 x 50 + 50 x 50
Z = 4000.
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can you answer this for me please
The length of LN for the triangle is 18.
What are triangles?A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is the sum of its internal angles to 180 degrees
Given triangle JKL,
and MN is parallel to JK,
taking ΔJKL and ΔLMN
∠L = ∠L (common angle)
because MN is parallel to JK, so corresponding angles are equal,
so ∠K = ∠N
and ∠J = ∠M
ΔJKL ≈ ΔLMN(triangles are similar)
since both triangles are similar the ratio of their corresponding sides is equal,
JL/LM = JK/MN = LK/LN
and JK = 55 and LK = 33
and MN = 12 + LN
JK/MN = LK/LN
substitute the values
55/(12 + LN) = 33/LN
55LN = 33(12 + LN)
55LN - 33LN = 396
22LN = 396
LN = 396/22
LN = 18
Hence the length of LN is 18.
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The small square has the length of Ycm
The large square has the length of 12cm
The area of the small square is 1/9 the area of the large square
Answer:
Y=4cm
Step-by-step explanation:
We can use the relationship between the side length and area of a square to solve for Y. Let's call the area of the small square "A" and the area of the large square "B". From the problem statement, we know:
A = 1/9 * B
Since the area of a square is equal to the side length squared, we can substitute this relationship into the equation above:
Y^2 = 1/9 * 12^2
Solving for Y:
Y^2 = 1/9 * 144
Y^2 = 16
Y = sqrt(16)
Y = 4
So, the side length of the small square is 4 cm.
2. What is the correlation between the number of hours driving and the number of gallons of gas used?
What is 55/99 rounded to the nearest half?
Answer:
1/2 i think this is it
Step-by-step explanation:
Avery was modeling the number of people standing in line to enter a park. She saw that at 8:04am. there was 35 people standing in line and at 8:09 a.m. there were 65 people standing in line. If represents the number of people standing in line and m represents the minutes since 8:00 a.m., answer the follow questions.
a). Represent the information given in the problem as two coordinate points, where the input is the minutes since 8:00 a.m. and the output is the number of people in line.
b). If the relationship between the minutes since 8:00 a.m. and the number of people in line is linear, then what is the slope of the linear function? Include units in your answer.
c). Assuming the relationship is linear, how many people were standing in line at 8:00 a.m.? Show how you found your answer.
d). Write a linear function for the number of people standing in line, n, as a function and number of minutes, m, since 8:00 a.m.
(e) If the linear function in (d) is valid until the park opens at 9:00 a.m., how many people are standing in line when the park opens?
The value of b set to 2 is the third option, which is the correct one.
Find the linear equation ?The provided equation is h(x) = -x + 5.
We obtain b=5 when comparing with the slope-intercept form y = mx+b.
Consequently, the y-intercept is at 5.
To lower the graph by three units, we must make changes.
As per the transformational laws, f(x)+c shifts c units upward, whereas f(x)-c shifts c units downward.
Therefore, we need to subtract the supplied function by 3 in order to move the graph down 3 units, and we get
y = -x+5 -3
y = -x +2.
Here, the y-intercept is 2.
The provided equation is h(x) = -x + 5.
The value of b set to 2 is the third option, which is the correct one.
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Two high speed ferries leave at the same time from a same city to go to the same island. The first ferry, the Cat, travels at 38 miles per hour. The second ferry, the bird, travels at 25 miles per hour. In how many hours will the two ferries be 13 miles apart?
f(x) = (x-1)/4
g(x) = 2x + 5
for what value of x is g(x) =f^-1(x) true?
For x=2, the functions g(x)=[tex]f^{-1}(x)[/tex] are true.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is f(x)=(x-1)/4 and g(x)=2x+5.
Here, y=(x-1)/4
Interchange x with y and y with x, we get
x=(y-1)/4
4x=y-1
y=4x+1
[tex]f^{-1}(x)[/tex]=4x+1
Now, g(x)=[tex]f^{-1}(x)[/tex]
2x+5=4x+1
2x=4
x=2
Therefore, for x=2, the functions g(x)=[tex]f^{-1}(x)[/tex] are true.
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Please help will give out brainlest !!!
During a heavy rainstorm a river became flooded. The flood waters still have 2/3 of the way to go back down until the depth of the water is at the normal level. If it continues to recede at a rate of 1/9 the flood level per hour, how many more hours will it take for the
water to reach its normal depth?.
Answer:
162/5 hours.
Step-by-step explanation:
Let's call the normal depth of the river "D". Since 2/3 of the way to go back to normal is still flooded, the current depth of the water is D + 2/3D = 5/3D.
The flood waters recede at a rate of 1/9 the flood level per hour, so the change in water level each hour is -1/9 * 5/3D = -5/27D.
To find the number of hours it takes to go from the current depth (5/3D) to the normal depth (D), we need to divide the change in depth (-5/27D) by the change in depth per hour (-5/27D): (5/3D - D) / (-5/27D) = (5/3D - D) / (-5/27D) = -(5/3D - D) / (5/27D) = (2/3D) / (5/27D).
This can be simplified to 2/3 * 27/5 = 162/5 hours. The answer is 162/5 hours.
Answer: Since the flood waters still have 2/3 of the way to go back down to reach the normal level, it means that 1/3 of the flood level has already receded.
If the flood level recedes at a rate of 1/9 the flood level per hour, then it will take 1/9 * 1 hour = 1 hour to recede 1/9 of the flood level.
Therefore, to recede 2/3 of the flood level, it will take 2/3 * 1/9 hours = 2/27 hours.
Since there are 60 minutes in 1 hour, the time it takes for the flood waters to reach the normal level in minutes is: 2/27 hours * 60 minutes/hour = 20 minutes.
Therefore, it will take 20 more minutes for the water to reach its normal depth.
Step-by-step explanation:
I need to know x and y
x = 2
y = 2 [tex]\sqrt{2}[/tex]
Step-by-step explanation:Special right triangles are triangles with specific angle measurements whose side lengths have patterns.
45-45-90 Triangle
The triangle above is a 45-45-90 triangle since it has two 45-degree angles. For this explanation, let a and b represent the legs of a right triangle and c be the hypotenuse. In this type of triangle, the legs are equal, so a=b. The hypotenuse is [tex]\sqrt{2}[/tex] times the leg length. So, c = a√2.
Finding x and y
In this problem, x is one of the legs. This means that x = 2 since 2 is the length of the leg. The y-value represents the hypotenuse, so we can multiply the leg by √2. Thus, y = 2√2.
Write an equation (In the form of g(m) = P(1+r)^m) for the exponential function from the table below.
Answer:
Equation is
[tex]\mbox {\large \boxed{g(m) = 4.411 (0.94988)^m}}[/tex]
Step-by-step explanation:
We have to translate the information in the table as an equation of the form
[tex]g(m) = P(1 + r)^m\cdots \cdots(1)[/tex]
Let's take the date from the table
For m = 1, g(m) = 4.19
Substituting these values in equation (1) we get:
[tex]g(1) = P(1 + r)^1[/tex]
[tex]4.19 = P(1 + r)^1[/tex]
[tex]P(1 + r)^1 = 4.19 \; \textrm{ (by switching sides)}[/tex]
[tex]P(1+r) = 4.19\; \cdots \cdots (2)\\\textrm{ (an expression raised to the power 1 is the expression itself)}[/tex]
For the next entry in the table, m = 2, g(m) = 3.98
Plugging into (1)
[tex]3.98 = P(1 + r)^2 \cdots\cdots(3)[/tex]
or
[tex]P(1 + r)^2 = 3.98[/tex]
Divide equation (3) by equation (2)
[tex]\dfrac{P(1+r)^2}{P(1+r} = \dfrac{3.98}{4.19}[/tex]
[tex]\textrm{The P terms cancel and } \dfrac{(1 + r)^2}{(1+r)} = 1 + r[/tex]
==> [tex]1 + r = \dfrac{3.98}{4.19}\\\\1 + r = 0.94988\\\\[/tex]
Plugging this value of 1 + r into equation (2):
[tex]P( 0.94988) = 4.19\\\\P = \dfrac{4.19}{0.94988}\\\\P = 4.411\\\\[/tex]
So the equation is
[tex]g(m) = 4.411 (0.94988)^m[/tex]
We can verify this is correct for m = 2, 3 and 4
[tex]m\quad\quad g(m) = 4.411(0.94988)^m\\\------------------\\2\quad\quad 4.411(0.94988)^2 = 3.97992 \approx 3.98\\\\3\quad\quad 4.411(0.94988)^3 = 3.78044 \approx 3.78\\\\3\quad\quad 4.411(0.94988)^4 = 3.59097 \approx 3.59\\\\[/tex]
BIG IDEAS MATH
K
Tell whether the information in the figure allows you to conclude that point P lies on the perpendicular bisector of
LM.
L
P
M
Yes
O No
N
Explain your reasoning.
Note that it is correct to state that LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK. See attached image.
What is a perpendicular bisector?A perpendicular bisector is a line that cuts another line segment across the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The phrase bisect implies dividing evenly or uniformly.
A simple technique to determine a perpendicular bisector is to measure the line segment you need to bisect. Then, divide the measured length by two to determine the midway. Draw a line at a 90-degree angle out from this middle.
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Full Question:
Tell whether the information in the diagram allows you to conclude that point P lies on the perpendicular bisector of LM. Explain your reasoning. See attached image.
A) No. You would need to know that LK ⊥ MK
B) No. You would need to know that KP ⊥ LM
C) Yes, t LN ≅ MN and Nk ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK
D) Yes, NK ⊥ LM, so NK is the perpendicular bisector of LM and P is on NK
32 thousands 6 hundreds 8 ones
32 thousands 6 hundreds 8 ones can be rewritten as 32608
What is the BODMAS rule?According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.
Given here: 32 thousands 6 hundreds 8 ones
Thus we can rewrite as 32×1000+6×100+8×1=32608
Numbers in words are written using the English alphabet. Numbers can be expressed both in words and figures. For example, 100,000 in words is written as One Lakh or One hundred thousand. Numbers in words can be written for all the natural numbers, based on the place value of digits, such as ones, tens, hundreds, thousands, and so on.
Hence, 32 thousands 6 hundreds 8 ones can be rewritten as 32608
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The sum of two complementary angles is 90°. For one pair of complementary angles, the measure of the first angle is 15 less than twice the measure of the second angle. Write a system of equations that can be used to determine the measure of the first angle, a, and the measure of the second angle, b.
Es el valor del numero que ocupa el lugar de las centenas en 25 450
The value of the number that occupies the hundreds place in 25,450 is 400
What is Counting?Calculating a set's size, or the number of elements in a finite collection of objects is the process of counting.
In a counting sequence, there are different units used such as:
TensHundredsThousandsTens of thousands, etcHence, in the value of 25,450,
The value that is found in the hundreds place is 400
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The English translation is:
What is the value of the number that occupies the hundreds place in 25,450
Question 4 (Essay Worth 10 points)
(05.06 HC)
Michael has $16 and wants to buy a mixture of cupcakes and fudge to feed at least 4 siblings. Each cupcake costs $4, and each piece of fudge costs $2.
This system of equations models the scenario:
4x+2y = 16
x+y=4
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution set.
Part B: Is the point (2, 3) included in the solution area for the system? Justify your answer mathematically
Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context.
The graph is the graph of straight lines
The point (2, 3) is not included in the solution area
How to describe the graphFrom the question, we have the following parameters that can be used in our computation:
4x+2y = 16
x+y=4
The equations are linear equations
This means that they are straight linesA different solution is 4 cupcakes and 0 fudgeIs the point (2, 3) included in the solution areaWe have
(x, y) = (2, 3)
This gives
4(2) + 2(3) = 16 -- false
2 + 3 = 4 -- false
Hence, it is not in the solution
Interpret a different solution setWe have
4x+2y = 16
x+y=4
This gives
4x+2y = 16
4x + 4y=16
So, we have
2y = 0
And:
y = 0
This means that
4x + 2(0) = 16
x = 4
So, the solution set is (4, 0)
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Mitchell plans to use ASA to prove that two triangles made from a rectangular piece of wood are the same. Which diagram would support his plan to use ASA?
The solution is given below.
What is triangle?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
Remember that the Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
According to this, the correct answer is: given below.
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The length of a rectangle is eight meters more than the width. Write an Algebraic Expression to find the area.
I kinda think that this Question is incomplete but this is what my teacher gave me. Thank you for Solving.
Answer: 8xw=a
Step-by-step explanation:
w=width
a=area
y 10- 9 8 -NW AGO J 7 6 5 4 3 2 A В. 0 1 2 3 4 5 6 7 8 9 10 a) What are the coordinates of A? b) What are the coordinates of B? X
The coordinates of point A' and B' are A'(-12,8) and B'(20, 0)
How to determine the coordinates of point A' and B'?A dilation is a transformation that changes the size of a figure but not its shape.
In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.
In this case, the point A (-3, 2) and B (5, 0) are transformed under a dilation of 4 with respect to the origin.
So the images are
A' = (kx, ky) = (-3*4, 2*4) = (-12, 8)
B' = (kx, ky) = (5*4, 0*4) = (20, 0)
So the image point of A(-3,2) under a dilation of 4 with respect to the origin is A'(-12,8)
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Complete question
The triangle ABC is dilated by a scale factor of 4 with the center of dilation at the origin.
a) What are the coordinates of A?
b) What are the coordinates of B?
if A (-3, 2) and B (5, 0)
The function y = -4(x - 3)^2 + 8 shows the daily profit (in hundreds of dollars) of a taco food truck, where x is the price of a taco ( in dollars). Find and interpret the zeros of this function. Select two answers: one for the zeros and one for the interpretation.
The zeros of the function y = -4(x-3)² + 8 are -1 and 7 and the intercept is 13
What are zeros of a function?The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.
when y = 0
-4(x-3)² +8 = 0
expanding the equation
-4( x²-6x +9)+8 = 0
-4x² +24x -36 +8 = 0
-4x²+24x -28 = 0
divide through by 4
-x²+6x-7 = 0
-x²+7x -x -7 = 0
(-x²+7x)(-x-7) = 0
-x( x-7) 1(x-7)
1-x = 0 or (x-7 )= 0
x = -1 or 7
therefore the zeros are -1 and 7
to find the intercept:
x= 0
y = -4(0-3)²+8
y =-4+9+8
y = 13
therefore the intercept is 13
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A person cycles from their home to a library which is 8 kilometers away. It takes them 20 minutes to reach the library. They stay there for 30 minutes to read, and then
walk to their friend's home which is 4 kilometers from the library and reach there in 20 minutes. Which graph best represents this situation?
The graph that best represents the situation, given the person cycling from home to the library, is Graph C.
Which graph is best ?The graph that would best represent the situation would show that the person cycling, stopped moving after 8 kilometers because they were at the library.
The graph should also show that after 30 minutes, the person left the library which is shown in Graph C as:
= 50 - 20 minutes
= 30 minutes
The best graph is therefore Graph C.
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PLEASE HELM ME ASAP!!! THANKS
The distance betwen the spots are
AD = 2DF = 4EG = 4AC = 5BD = 6How to determine the distance between the spotsFrom the question, we have the following parameters that can be used in our computation:
The coordinates of the spots
The distance between them is then calculated as
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Using the above as a guide, we have the following:
AD = √[(-4 + 4)² + (3 - 1)²] = 2
DF = √[(-4 + 4)² + (1 + 3)²] = 4
EG = √[(5 - 5)² + (1 + 3)²] = 4
AC = √[(-4 - 1)² + (3 - 3)²] = 5
BD = √[(2 + 4)² + (1 - 1)²] = 6
The above values represent the distance betwen the spots
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Find the value of x.
D
168°
y
x = [? ]°
Enter
Answer: It is 84 degrees
Un gerente de oficina pide una calculadora o un calendario para cada uno de los 60 empleados de la oficina. Cada calculadora cuesta $15 y cada calendario cuesta $10. El pedido total ascendió a $800. Parte A: Escribe el sistema de ecuaciones que modela este escenario. (5 puntos) Parte B: Utilice el método de sustitución o el método de eliminación para determinar el número de calculadoras y calendarios pedidos. Mostrar todos los pasos necesarios. (5 puntos)
The system of equations is
15x + 10y = 800
x + y = 60
and the solution to these equations is
x = 40
y = 20
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 that an office manager requests a calculator or calendar for each of the 60 office employees. Each calculator is $15 and each calendar is $10. The total order amounted to $800.
We can write the system of equations as -
15x + 10y = 800
x + y = 60
We can write -
y = 60 - x
So, we can write -
15x + 10(60 - x) = 800
15x - 10x + 600 = 800
5x = 200
x = 40
Then -
y = 20
Therefore, the system of equations is
15x + 10y = 800
x + y = 60
and the solution to these equations is
x = 40
y = 20
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{Question in english is -
An office manager requests a calculator or calendar for each of the 60 office employees. Each calculator is $15 and each calendar is $10. The total order amounted to $800. Part A: Write the system of equations that models this scenario. (5 points) Part B: Use the substitution method or the elimination method to determine the number of calculators and calendars ordered. Show all the necessary steps. (5 points)
}
Jeff purchased 7 gumballs for $0.25 each and 3 pieces of gum. He spent a total of $2.05. How much did each piece of gum cost?
Write the equation for this
problem.
Answer:
Each piece of gum is 10cents
Step-by-step explanation:
7 x 0.25 then subtract that from 2.05 then divide by the 3pieces of gum
Answer: (0.25 x 7) + 3x = 2.05 and $0.10 per piece of gum
Step-by-step explanation:
Jeff purchased 7 gumballs for $0.25 each, which is [tex](0.25*7)[/tex]
Jeff then purchased 3 pieces of gum, but we don't know for how much so the cost becomes [tex]x[/tex] and then [tex]3x[/tex]
The final cost then comes down to $2.05, therefore [tex](0.25*7)+3x=2.05[/tex] and solve for [tex]x[/tex] to find the cost of each piece of gum
[tex]1.75+3x=2.05[/tex]
[tex]3x=0.3[/tex]
[tex]x=0.1[/tex]
31. Let A be a set. Show that ∅ × A = A ×∅=∅.
Answer:
Rational number
Step-by-step explanation:
because all rational number multiple by0 is 0
Law of Exponents: Power to a Power & Power of a product rules, I’m not understanding how is this the correct answer. Explanation Please & Show all Work!
The expression (3a⁸)⁹ * (3b⁵)² is solved to get 3¹¹a⁷²b¹⁰
How to solve the expressionpower or exponents as used in mathematics are number written on top of a base number. The power says how many times the base number multiplies itself.
The problem is solved as follows
= (3a⁸)⁹ * (3b⁵)²
raising the terms by power of 9 and 2 accordingly
= (3^9 * a^(8 * 9)) * (3^2 * b^(5 * 2) )
= (3^9 * a^(72)) * (3^2 * b^(10) )
collecting base 3
= (3^9 * 3^2 * a^(72) * b^(10))
= (3^(9 + 2) * a^(72) * b^(10))
= (3^(11) * a^(72) * b^(10))
rewriting the expressions
= 3¹¹a⁷²b¹⁰
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Let f(x) = x ¹/2 and g(x) = 2x² . Find (fg) (x) then evaluate the
product when x=9.
Answer:
see explanation
Step-by-step explanation:
using the rules of exponents/ radicals
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
• [tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a} )^m[/tex]
then
(fg)(x)
= f(x) × g(x)
= [tex]x^{\frac{1}{2} }[/tex] × 2x²
= 2 × [tex]x^{(\frac{1}{2}+2) }[/tex]
= 2[tex]x^{\frac{5}{2} }[/tex]
when x = 9 , then
= 2 × [tex]9^{\frac{5}{2} }[/tex]
= 2 × [tex](\sqrt{9})^5[/tex]
= 2 × [tex]3^{5}[/tex]
= 2 × 243
= 486
In Exercises 17–20, u is an acute angle and sin u and cos u are
given. Use identities to find tan u, csc u, sec u, and cot u. Where
necessary, rationalize denominators
20.
Answer:
Tan u = sin u/cos u, csc u = 1/sin u, sec u = 1/cos u, and cot u = cos u/sin u. The denominators of the fractions can be rationalized by multiplying the numerator and denominator by the conjugate of the denominator.
Step-by-step explanation:
In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive x = 11 miles closer to the mountain, the angle of elevation is 9°. Approximate the height of the mountain. (Round your answer to one decimal place.)
Answer:
3.2 miles
Step-by-step explanation:
To approximate the height of the mountain, we need to use the tangent function in trigonometry. We have two angles of elevation and the distance between the observer and the mountain, which we can use to create a right triangle.
Let h be the height of the mountain and d be the distance from the observer to the foot of the mountain.
At the first observation, we have:
tan(3.5°) = h/d
And at the second observation, when the observer is 11 miles closer to the mountain:
tan(9°) = h/(d-11)
Dividing the two equations, we have:
tan(9°) / tan(3.5°) = h/(d-11) / h/d
Solving for h, we have:
h = (d * tan(9°)) / (tan(3.5°) + 1)
We don't have an exact value for d, so we can use an estimate based on the difference in distance between the two observations.
Since d-11 = 11 miles, we have:
d = 11 * 2 = 22 miles
Using this estimate and the given angles, we can approximate the height of the mountain:
h = (22 * tan(9°)) / (tan(3.5°) + 1) = (22 * 0.156434465) / (0.066012183 + 1)
= 22 * 0.156434465 / 1.066012183 = 22 * 0.146838446 = 3.23 miles
The height of the mountain is approximately 3.2 miles to one decimal place.
3 c ≈ how many mL? Round to the nearest hundredth if necessary.
Answer: It is not possible to convert 3 c to mL without a conversion factor. There are several different units of measurement for volume, including cubic centimeters (cc), milliliters (mL), and cubic meters (m^3). To convert from one unit to another, you need to know the conversion factor.
The conversion factor between cubic centimeters (cc) and milliliters (mL) is 1:1, meaning they are equivalent units of measurement. So, 3 cc is equal to 3 mL.
Step-by-step explanation: