Answers
For the given functions, we will find the first derivative of each function
Note:
a, and b are constants
y, f, and g are functions
2) y = (a+bf)/g
We will use the quotient rule to find y' as follows:
[tex]y^{\prime}=\frac{g*b\frac{df}{dx}-(a+bf)\frac{dg}{dx}}{g^2}[/tex]=============================================================
3) y = (x+f)/g
We will use the quotient rule to find y' as follows:
[tex]y^{\prime}=\frac{g(1+\frac{df}{dx})-(x+f)\frac{dg}{dx}}{g^2}[/tex]==========================================================
4) y = (x+f)³
We will use the exponent rule to find the derivative as follows:
[tex]y^{\prime}=3(x+f)^2(1+\frac{df}{dx})[/tex]===========================================================
5) y = ax² + bg² + f
so, y' will be as follows:
[tex]y^{\prime}=2ax+2bg\frac{dg}{dx}+\frac{df}{dx}[/tex]==========================================================
Related Questions
A 20-foot ladder is leaning against the side of a house so that the bottom of the ladder is 12 feet from the base of the house. Will the ladder reach a window that is 14.5 feet above the ground?
Yes, because the ladder will reach 32 feet high
Yes, because the ladder will reach 16 feet high
No, because the ladder will only reach 16 feet high
No, because the ladder will only reach 12 feet high
Answers
Yes, because the ladder will reach 16 feet high
what is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem.
According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.
Given:
Hypotenuse= 20 feet
base= 12 feet
Using Pythagoras theorem
H²= P² + B²
20² =12² +P²
P²= 400-144
P²= 256
P= 16 FEET.
Hence, Yes, because the ladder will reach 16 feet high
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The area of the floor of a square play pen is 6 square meters. What is the perimeter of the play pen? Approximate your answer by rounding to the nearest integer.
Help must be done in less than 10 minutes
Answers
Answer:
10 m
Step-by-step explanation:
Area of a square
[tex]A=s^2[/tex]
where s is the side length.
If the area of the floor is 6 m²:
[tex]\begin{aligned}A&=s^2\\\implies 6&=s^2\\\sqrt{6}&=\sqrt{s^2}\\s&=\sqrt{6}\end{aligned}[/tex]
Therefore, the side length of the square is √6 m.
Perimeter of a square
[tex]P=4s[/tex]
where s is the side length.
Substitute the found value for s into the formula to find the perimeter:
[tex]\begin{aligned}P&=4s\\\implies P&=4 \cdot \sqrt{6}\\P&=4 \sqrt{6}\\P&=9.79795897...\\ P&=10 \sf \;m\;(nearest\:integer)\end{aligned}[/tex]
Therefore, the perimeter is 10 m to the nearest integer.
⦁ A room 12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square. Answer the following questions. Assume there is no waste in materials, and round off your answer to the next largest unit. Show both exact and rounded figures in the blanks provided.
Answers
The amount of wall surface in square feet is there to paint is: 364 square ft. While the floor area is 169.58sq ft. See the calculations below:
What is Square Feet?The square foot is an imperial measure of area and a customary unit of area in most countries. It is defined as the area of a square with one-foot sides.
The calculation for the above solution is given as:
Step I - Recall the Given Stats:
Dimensions of the room are:
12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square.
Let Lenght (l) = 13'9" = 13(9/12) ft = 13(3/4) = 55/4 ft.
Let Width(w) = 12'4" = 12(4/12) ft = 12(1/3)ft = 37/3 ft
Let Height h = 8'0" = 8ft.
Recall that we have a door with dimensions 3' x 7' and two windows 4'x4'
Step II - A) Surface area of the wall to be painted is:
Area of 4 walls less (area of door plus area of window)
Surface Area = 2LH + 2WH - ((3 x7) + 2(4x4))
= 2(l +w)h - (21 + 32)
= 2 ((55/4) + (37/3))8 -53
= 220 + 592/3 - 53
= 167 + 592
= (501+ 592)/3
= 1093/3
Hence,
The Surface Area to be painted is = 364.33 Sq ft.
Step III - B) The Area of the Floor = Lx W
= (55/4) x (37/3)
= 2035/12
= 169.583333333
Hence,
Area of the Floor is approximately = 169.58
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Full Question:
A room 12′-4″ by 13′-9″ with an 8′-0″ ceiling height has one door 3′ × 7′ and two windows 4′ square.
Answer the following questions. Assume there is no waste in materials, and round off your answer to the next largest unit. Show both exact and rounded figures in the blanks provided.
A. How much wall surface in square feet is there to paint?
B. What is the floor area?
3/5 × 2/9 and 5/6 × 4/7 and 3/10 × 5/6 and 6/7 × 7/15
Answers
1
Step
Multiple both numerator and both denominator
[tex]\frac{3}{5}\text{ x }\frac{2}{9}\text{ = }\frac{3\text{ x 2}}{5\text{ x 9}}\text{ = }\frac{6}{45}\text{ = }\frac{2}{15}[/tex]2
[tex]\frac{5}{6}\text{ x }\frac{4}{7}\text{ = }\frac{5\text{ x 4}}{6\text{ x 7}}\text{ = }\frac{20}{42}\text{ = }\frac{10}{27}[/tex]3
[tex]\frac{3}{10}\text{ x }\frac{5}{6}\text{ = }\frac{3\text{ x 5}}{10\text{ x 6}}\text{ = }\frac{15}{60\text{ }}\text{ = }\frac{1}{4}[/tex]4
[tex]\frac{6}{7}\text{ x }\frac{7}{15}\text{ = }\frac{6\text{ x 7}}{7\text{ x 15}}\text{ = }\frac{42}{105}\text{ = }\frac{2}{5}[/tex]Use fundamental identities to find the value. Step by step can u explain.
Answers
To answer this question, we will use the following diagram as reference:
To determine the tangent of θ, we have to find the value of x.
To find x, we use the Pythagorean theorem and get:
[tex]4^2=3^2+x^2.[/tex]Therefore:
[tex]x=\sqrt{4^2-3^2}=\sqrt[]{7}.[/tex]Therefore:
[tex]\tan \theta=\frac{3}{\sqrt[]{7}}.[/tex]Answer:
[tex]\tan \theta=\frac{3}{\sqrt[]{7}}.[/tex]Thomas invested $1498 at
6% Sumple interest per annum.
Calculate.
1) The interest, in dollars,
earned after six months
Answers
well, keeping in mind that a year has 12 months, that means 6 months is 6/12 of a year, so
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1498\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\to \frac{6}{12}\dotfill &\frac{1}{2} \end{cases} \\\\\\ I = (1498)(0.06)(\frac{1}{2}) \implies I = 44.94[/tex]
Maria is to weld a support for a 23-m conveyor so that it will operate at a 20 degree angle. What is the length of the support?
Answers
The length of the support when Maria is to weld a support for a 23-m conveyor is 7.87 m.
How to illustrate the information?From the information, Maria is to weld a support for a 23-m conveyor so that it will operate at a 20 degree angle.
Let AB = 23m
Let x = 20°
We can then use the sine rule to find the length. This will be illustrated thus:
Sin x = AC / AB
Sin 20° = AC / 23
AC = 23 × sin 20°
AC = 7.87
The length is 7.87m
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Enter the ratio as a fraction in lowest terms6 ft to 78 in.
Answers
To answer this question, we need to remember that a ratio is a comparison of two or more units. We can also need to have into account that these units must be in the same units.
We have one of the quantities is 6ft, the other is equal to 78 inches. We can convert 6ft to its equivalent in inches, or 78 inches into its equivalent in feet. Then, we have:
[tex]6ft\cdot\frac{12in}{1ft}=72in[/tex]Then, we can conclude that the ratio of 6feet (72 inches) to 78 inches is equivalent to:
[tex]\text{Ratio}=\frac{72in}{78in}=\frac{12}{13}\Rightarrow Ratio=\frac{12}{13}[/tex]tape da grams to
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Question
On Friday, there were 6 snowboarders for every 2 skiers at a local ski resort. Or
Saturday, the ratio of the number of snowboarders to the number of skiers
was 5:3. There were 144 snowboarders at the ski resort on Friday. There were
same number of people at the ski resort on Saturday as there were on Friday
How many more skiers were there than snowboarders at the ski resort on
Saturday?
Answers
As calculated by the given ratios, 36 more skiers were there than snowboarders at the local resort on Saturday.
What is ratio?
A ratio illustrates how two or more values differ in terms of size.
Ratios can be displayed in a variety of ways, including as decimals (after dividing one value by the whole), percentages (after dividing one value by the entire), and using the ":" or "/" to separate values.
As given in the question,
Ratio of Snowboarders to Skiers
On Friday: ratio is 6:2
On Saturday: 5:3
Population = 144
Now, lets calculate the number of snowboarders and skiers at Saturday:
Given ratio: 5:3
total = 5+3
total = 8
No. of skiers is:
= (3/8)(144)
= 54
No. of snowboarders is:
= (5/8)(144)
= 90
Now lets calculate the difference between no. of snowboarders and skiers:
= 90-54
= 36
Hence, there are 36 more snowboarders than skiers.
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4-[x]=1 absolute value equation
Answers
Answer: x=-3, x=3
Step-by-step explanation:
Answer:
4-[x]=1
-4. -4
-[x]=-3
x=3
The hypotenuse of a right triangle is four times the length of one of the legs. The length of the other leg is sqrt(240) feet. Find the lengths of the leg and hypotenuse
Answers
ANSWER
Hypotenuse: 16 ft
Leg: 4 ft
EXPLANATION
Given:
A right angle triangle with only one leg = sqrt(240) feet
Desired Outcomes:
Lengths of the leg and hypotenuse
Declaration of variables
Let x represent the length of leg
Hypotenuse = 4 times the length of leg = 4x
Apply Pythagorean theorem
[tex]\begin{gathered} Hyp^2=Opp^2+Adj^2 \\ (4x)^2=x^2+(\sqrt{240})^2 \\ 16x^2\text{ = }x^2\text{ + 240} \\ 16x^2-x^2\text{ = 240} \\ 15x^2\text{ = 240} \\ x^2\text{ = }\frac{240}{15} \\ x\text{ =}\sqrt{16} \\ x\text{ = 4 ft} \end{gathered}[/tex]Hypotenuse = 4x = 4 (4) = 16 ft
Hence, the Lengths of the leg and hypotenuse are 4 ft and 16 ft respectively.
A worker's salary increased from $750 to $900 per month. Which equation shows the increase of the worker's salary to the nearest percent?
Answers
where A is the first value, B the second value and x the percent
we can solve x
[tex]\begin{gathered} \frac{x}{100}A=B-A \\ x=\frac{100\times(B-A)}{A} \end{gathered}[/tex]this is the equation
and this is the percent:
[tex]\begin{gathered} x=\frac{100\times(900-750)}{750} \\ \\ x=20 \end{gathered}[/tex]the percent is 20%
There are 36 students in s2a some of them usually bring their own lunch and the other buy lunch.if 1/5 of the students who usually bring their own lunch buy their lunch today , the ratio of the number of students bringing their own lunch to number of students buying lunch becomes 1:2. how many students are there who usually bring thier own lunch ?
Answers
The no. of students who usually bring their own lunch is 15.
What is the ratio?The ratio is a comparison between two or more quantities in simplest form.
Given there are 36 students in an s2a class some of them bring their own lunch and the others buy their lunch.
Assuming x students bring their own lunch hence (36 - x) students buy their lunch.
(1/5)th of the student who brings their own lunch is (1/5)×x = (x/5).
∴ x - (x/5) : (36 - x) + (x/5) = 1 : 2. (The reduced students are added to the
other category).
4x/5 : 36 - 4x/5 = 1 : 2.
4x/5 : (180 - 4x)/5 = 1 : 2.
(4x/5)÷(180 - 4x)/5 = 1/2.
(4x/5)×5/(180 - 4x) = 1/2.
4x/(180 - 4x) = 1/2.
4x = (180 - 4x)/2.
8x = 180 - 4x.
12x = 180.
x = 15.
∴ 15 students usually bring their own lunch.
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May I please get help with this for I am confused and have tried many times to re-create the reflection of the triangle
Answers
We have to reflect the triangle across the y-axis.
If we have a point P = (x,y) and we reflect it across the y-axis, we will change the x-coordinate to its opposite value and and the y-coordinate is kept the same.
The image point then is P' = (-x,y).
Then, to reflect the triangle, we have to reflect the three vertices and then join the vertices.
We can then reflect the vertices as:
A box of chocolates contains five milk chocolates and five dark chocolates. You randomly pick a chocolate and eat it. Then you randomly pick another piece. What is the probability that both pieces are milk chocolate?
Answers
SOLUTION
This is a probability question that has to do with the "without replacement" scenario, because every chocolate eaten leaves the box and never returns
The probability that both pieces are milk chocolate is calculated thus:
[tex]\frac{Number\text{ of milk chocoltes}}{Total\text{ number of chocoltes in the box}}\times\frac{Number\text{ of milk chocolates-1}}{Total\text{ number of chocoltes -1}}[/tex]Number of milk chocolates = 5
NUmber of dark chocolates = 5
Total number of chocolates in the box = 5+5 =10
The probability that both pieces are milk chocolate is:
[tex]\begin{gathered} \frac{5}{10}\times\frac{5-1}{10-1}(since\text{ it is without replacement of chocolates)} \\ \frac{5}{10}\times\frac{4}{9} \\ \frac{20}{90} \\ =\frac{2}{9} \end{gathered}[/tex]The probability that both pieces are milk chocolate is:
[tex]\frac{2}{9}[/tex]
Write an equation of function g(x) and describe the effects on the graph of the parent function f(x)=x^2. g(x)=f(x)+d where d=2
Answers
Given:
a.) f(x) = x²
b.) g(x) = f(x) + d
c.) d = 2
To be able to complete the equation of function g(x), let's substitute the function of f(x) and d.
We get,
g(x) = f(x) + d
g(x) = x² + 2
Therefore, g(x) = x² + 2.
Use the slope formula to find the slope of the line through the points (−8,−6) and (0,−7).
Answers
Answer:
Slope formula is given as (y2-y1) ÷ (x2-x1) or (y1-y2) ÷ (x1-x2), where x and y are the coordinates of the points.
Slope = (-7-(-6)) ÷ (0-(-8))
= (-7+6) ÷ (0+8)
= -1/8
Four friends use a spinner to decide the luckiest person. Who is more likely to be the luckiest person?
Answers
The luckiest person is Clinton because it is more likely.
Answer: Clinton
Put the following equation of a line into slope-intercept form, simplifying all fractions.
4x-20y=-160
Answers
The equation of the line 4x-20y = -160 in the slope intercept form is y = x/5 + 8 .
The equation of the line in slope intercept form is written as
y = mx + c ,
where m is the slope of the line , and c is the y intercept .
In the question ,
the equation of the line is given
equation of line is given as 4x-20y = -160
to convert the equation in slope intercept form , we rewrite it as
20y = 4x+160
dividing both sides by 20 ,
we get
20y/20 = 4x/20 + 160/20
y = x/5 + 8
hence ,the slope intercept form is y = x/5 + 8 , where 8 is the y intercept and 1/5 is the slope .
Therefore , the equation of the line 4x-20y = -160 in the slope intercept form is y = x/5 + 8 .
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An anonymous survey of college students was taken to determine behaviors regarding alcohol, cigarettes, and illegal drugs. The results were as follows: 855 drankalcohol regularly, 657 smoked cigarettes, 192 used illegal drugs, 418 drank alcohol regularly and smoked cigarettes, 109 drank alcohol regularly and used illegal drugs,116 smoked cigarettes and used illegal drugs, 88 engaged in all three behaviors, and 251 engaged in none of these behaviors.Answer parts a, b, c, d, e, f, g for this question.
Answers
To solve the question, we will be using a Venn Diagram. Let's list down what's given first:
855 drank alcohol
657 smoked cigarettes
192 used illegal drugs
418 both drank alcohol and smoked cigarettes
109 drank alcohol and used illegal drugs
116 smoked cigarettes and used illegal drugs
88 engaged in all three
and 251 engaged in none of these
We will draw a Venn Diagram with 3 circles, one for each vice. Then we will start with the intersection of all three and the area outside of the circles (for those who do not engage in vices).
Because we know how many engaged in all 3 vices, we can deduct that number from those who belong to the intersection of 2 vices since they have already been counted in that too.
418 - 88 = 330 drank and smoked, but not used drugs
109 - 88 = 21 drank and used drugs, but not smoked
116 - 88 = 28 smoked and used drugs but not drank
Then, we subtract the numbers in each circle from the total for each vice.
855 - (330 + 88 + 21) = 416 drank only
657 - (330 + 88 + 28) = 211 smoked only
192 - (88 + 21 + 28) = 55 used drugs only
To find the total number of surveyed students, we just need to add all the numbers in the Venn Diagram.
416 + 330 + 88 + 21 + 211 + 28 + 55 + 251 = 1,400
Therefore, there were 1,400 students who were surveyed.
In a sample of 30000 first borne babies, 6 were found to have Down syndrome. Find the empirical probability thay a famili’s first child will be born with this sydrome
Answers
The probability that a family’s first child will be born with down syndrome is 1/5000
Number of first borne babies = 30000
Number of first borne babies having Down syndrome = 6
Probability is defined as the ratio of number of favorable outcomes to the total outcome.
Probability = (number of favorable outcomes)/(total outcome)
We have to find the probability that a family’s first child will be born with down syndrome. So, Number of first borne babies having Down syndrome is equal to the total number of favorable outcomes and Number of first borne babies will also be equal to total outcome. Hence we can write,
Probability = (number of favorable outcomes)/(total outcome)
Probability = 6/30000
Probability = 1/5000
So, the required probability is 1/5000.
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Consider the function whose input value is time of day and whose corresponding output value is temperature at that time of day, rounded to the nearest degree. Is this a one-to-one function? Explain why or why not.
Answers
No, a function whose input value is time of day and whose corresponding output value is temperature at that time of day, rounded to the nearest degree is not a one-to-one function.
What is a one-to-one function?A one-to-one function is also referred to as an injective function and it can be defined as special type of function in which every element of the range is mapped to exactly a single element of its domain. This ultimately implies that, the output values (y-values) of a one-to-one function never repeat themselves.
Additionally, a one-to-one function maps distinct elements of its domain (y-values) to distinct elements of the range (x-values) and as such, it connotes the mapping of two (2) sets.
In this context, we can reasonably and logically deduce that this function is not a one-to-one function because it fails the horizontal line test as there could be the same temperature at different times of the day.
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Which of the following is the correct mathematical expression for:
The difference between three times a number and 4
Answers
Answer:
3x - 4
Step-by-step explanation:
"Difference" is a clue word that tells you to use subtraction. The other clue word is "times" but that means times, or multiplication and is pretty straight forward.
"Three times a number" means to multiply a number, but we don't know the number, so we use a variable (a letter). I put x but you could use n or c or almost any letter for the variable.
"the difference of ___ and ___" means to subtract those two things.
So we get 3x - 4
PLEASE HELP ITS DUE SOON! I DONT GET ANY OF THIS! HELP WOULD BE MUCH APPRECIATED! NEED THIS DONE BEEN STUCK ON THIS FOR WAY TO LONG!
YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
Answers
1) [tex]VX=ZX, \angle XVY=\angle XZW[/tex] (given)
2) [tex]\angle X=\angle X[/tex] (reflexive property)
3) [tex]\triangle VXY \equiv \triangle ZXW[/tex] (ASA)
El área de un sector circular de un círculo con radio igual a 8cm y ángulo central igual a 56° es aproximadamente
Answers
The sectorial area of the circle is equal 31.3cm^2
Area of a SectorThe formula for the b of the sector of a circle is /360o (r2) where r is the radius of the circle and is the angle of the sector.
Area of a Sector of Circle = (θ/360º) × πr^2, where, θ is the sector angle subtended by the arc at the center, in degrees, and 'r' is the radius of the circle.
Data;
Radius - 8cmangle = 56 degreesThe area of the sector can be calculated using the formula given
[tex]A = \frac{\theta }{360} * \pi r^2[/tex]
Substituting the values into the formula;
[tex]A = \frac{\theta }{360} * \pi r^2\\A = \frac{56}{360}* \pi * 8^2\\A = 31.27cm\\A = 31.3cm^2[/tex]
The area is equal 31.3cm^2
Translation:
The area of a circular sector of a circle with radius equal to 8cm and central angle equal to 56 degrees.
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A number with an absolute value of 42 was divided by a number with an absolute value of 7 The quotient -6. Write two posibble numeric equations
Answers
Answer:
-42/7 and 42/-7
Explanation:
The absolute value of a number is represented by:
[tex]|x|[/tex]The lines represent absolute value of a number x, and what it does is that it makes everything into a positive number.
For example |-5|=5 and |5|=5, so we always have two options with an absolute value: that it comes from a negative number or that it comes from a positive number.
In this case we have that a number with an absolute value of 42 (it could be |-42|=42 or |42|=42) divided by a number with an absolute value of 7 (it could be |-7|=7 or |7|=7) the quotient is -6.
One possible numberic equation is:
[tex]\frac{-42}{7}=-6[/tex]Since this meets all the above conditions
Another possible numeric equation is:
[tex]\frac{42}{-7}=-6[/tex]Since this too meets all the above conditions.
what function is represented in the table ?- y = 3 (4x )- y = 2 ( .25x )- y = 4 ( .25 ) x - y = 4 ( 3x )
Answers
1) To determine which is the function from the table we need to attentively look for a constant factor in the y-column.
2) As we can see from this table, the factor we can tell that goes from 64 to 16 and then 4 is 1/4. Or in decimal form 0.25. So, we can tell the factor "b" is going to be 1/4 considering this model:
[tex]\begin{gathered} y=a(b)^x \\ y=a(0.25)^x \end{gathered}[/tex]3) Let's pick one point (0,4) and plug it to find the other elements:
[tex]\begin{gathered} y=a(\frac{1}{4})^x,(0,4) \\ 4=a(\frac{1}{4})^0 \\ a=4 \end{gathered}[/tex]And finally, we can tell the function is:
[tex]undefined[/tex]tod has 20 books he donated 2/5 how many books did he donate?
Answers
Given:
Total number of books is, N = 20.
Number of books donated is, d = 2/5 of books.
The objective is to find the number of books donated.
Consider the number of books donated as x.
[tex]\begin{gathered} x=\frac{2}{5}\cdot20 \\ x=8 \end{gathered}[/tex]Hence, the number of books donated is 8.
Name the segments in the figure below.Q R S ISelect all that apply.
Answers
Answer
Options A, F, G, N
The line segments include
QR
QS
QT
RS
RT
ST
Note that the segments only have a dash on top of them and not an arrow.
Explanation
A line segment is a region of a line bounded by two different endpoints and contains all the points on the line that are between the two endpoints.
From the attached image, we can see that there is a line with infinite length (the arrows at the two endpoints indicate that this line continues till infinity), has points Q, R, S and T.
So, the line segments will be any space from one endpoint to another. They'll include
QR
QS
QT
RS
RT
ST
Note that the segments only have a dash on top of them and not an arrow.
Hope this Helps!!!
helllpppppppppppppp.
Answers
Answer:
See below
Step-by-step explanation: