The slope of the ramp is m = h/√(r² - h²).
What is mean by square root of a number?
A square root of a number is a value that multiplied by itself gives the same number.
Let h = height of the landing.
And, r = the length of the ramp.
Then, the length from the ground where the ramp touches it, to the ground directly below the landing is
⇒ √(r² - h²)
And, The slope of the ramp is m = h/√(r² - h²)
For example, if the ramp is 5 meters long and the landing height is 3 meters high, the slope of the ramp is 3/4.
As, Slope of the ramp (m) = 3/√(25-9) = 3/√16 = 3/4
Thus, The slope of the ramp is m = h/√(r² - h²).
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What are the domain and range of f(x) = 4x – 8?
domain: {x | x is a real number}; range: {y | y > –8}
domain: {x | x is a real number}; range: {y | y > 8}
domain: {x | x > 4}; range: {y | y > –8}
domain: {x | x > –4}; range: {y | y > 8}
The domain and range of this linear function f(x) = 4x – 8 is: A. domain: {x | x is a real number}; range: {y | y > –8}.
What is a linear function?A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate. This ultimately implies that, a linear function is typically used for uniquely mapping an input variable to an output variable.
What is a domain?A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain refers to the set of all possible input numerical values (numbers) to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
In conclusion, the domain of this linear function consist of all real numbers while the range comprises the set of all real numbers on the y-axis that are greater than negative eight (-8).
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Answer:
its a
Step-by-step explanation:
In a certain country 23% of the population has a college degree and 7% of those people have an advanced degree (masters of above). If the country has 3,000,000 people than how many people have advanced degree?
Answer: 48300
Step-by-step explanation:
23 % of 3.000.000 is [tex]\frac{3.000.000*23}{100} = 690.000[/tex]
So, 690.000 have college degree.
7 % of 690.000 is [tex]\frac{690.000* 7}{100} = 48.300[/tex]
So, 48.300 people have advanced degree.
If lines BG↔ and CF↔ are parallel, then ∆JOL and ∆IOM are congruent triangles. Is this statement correct? Explain your answer.
By the degfinition of a congruent triangle, the statement that was made that ∆JOL and ∆IOM are congruent triangles is false.
What is a congruent triangle?The two triangles are said to be congruent triangles based on the fact that all of their corresponding sides are the same and said to be equal. Then all of the corresponding sides of the angles would also have an equa; measure.
Why these triangles are not congruentThe definition that I have given above says that the congruent triangles are those that have the same shapes and also have the same sizes. The corresponding sides of the angles and the sides would also be the same.
In the diagram that we have here, we can see that IOM and JOL do not have the same size. Hence the congruent law is not correct. To be congruent it would have to be that the the corresponding sides are the same and there is the equality in the angles of the triangles.
Since this property is not in the shape we would have to conclyde that the statement is wrong. They are not congruent triangles.
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Convert 2 grams into milligrams.
*Note: you must use these exact conversion factors to get this question right.
1 pound (lb) = 16 ounces (oz)
1 kilogram (kg) = 1000 grams (g)
1 ton (ton) = 2000 pounds (lb)
1 ounce (oz) = 28.35 grams (g)
1 gram (g) = 1000 milligrams (mg)
1 pound (lb) = 0.454 kilograms (kg)
2 grams = 2000 milligrams
Conversion between different units of measurement of the same quantity is called as conversion of units.
The process of conversion depends on the specific situation and the precision and accuracy of measurement.
Conversions from one unit to another should be exact, without changing the precision of the first. This is sometimes called soft conversion. It does not involve changing of the physical configuration of the unit being calculated.
'g' is the same as grams and similarly 'mg' is the same as milligrams.
Thus, when asked to convert 2 g to mg, as in the given question,
first multiply the value in grams by the conversion factor '1000'.
So, 2 grams = 2 × 1000 = 2000 milligrams.
A gram is larger unit than a milligram.
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Players in a racing game earn 3 points for each coin they collect. Each player loses 5 points for each second that he or she finishes after the first-place finisher. The table shows the results of a race.
List the players in order from greatest to least number of points.
If each player loses 5 points for each second that he or she finishes after the first-place finisher. the players in order from greatest to least number of points is: player 4, player 2, player 1, player 4.
Greatest to the least numberPayer 1 :
Player 1 = 3(31) - 5(8)
Player 1 = 93 - 40
Player 1 = 53 points
Player 2 :
Player 2 = 3 (18)
Player 2 = 54 points
Player 3:
Player 3 = 3(24) - 5(3)
Player 3 = 72 - 15
Player 3 = 57 points
Player 4:
Player 4 = 3(27) - 5(6)
Player 4 = 81 -30
Player 4 = 51 points
Now list the players in order from greatest to least number of points.
Player 3 = 57 points
Player 2 = 54 points
Player 1 = 53 points
Player 4 = 51 points
Therefore the player based on ranking is: player 4, player 2, player 1, player 4.
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| x² = 121; x =
What's the answer
Answer:
x = 7
Step-by-step explanation:
To get rid of the x^2, do the opposite of x^2: radicals, or square roots.
x^2 = 121
x = √121
Think about what number can multiply by itself to get 121...
7 • 7 or 7^2 = 121
So, in x^2 = 121, x = 7.
x^2 = 121
x = √121
7 = √121
7 = 7 ✔
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Find the equation of the line with the given slope and the y-intercept.
slope = 1/5; y-intercept = -5
The equation of the line with the given slope and the y-intercept.
slope = 1/5; y-intercept = -5 is y = 1 / 5 x - 5
How to find the equation of a line?The equation of a line can be described as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore,
slope of the line = 1 / 5
y-intercept = - 5
Hence, the equation of the line can be represented as follows:
y = 1 / 5 x - 5
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Calculate the size of all angles marked with variables in the following diagrams. give reasons
The angles are given below
What is an angle?
An angle is a symbol in Euclidean geometry created by two rays, called the flanks of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are placed in the plane having the rays. Angles are also generated when two planes overlap. These are termed as dihedral angles. An angle defined by two overlapping curves is the angle of both the rays falling tangent to the individual curves at their place of junction. Angle can also refer to the measurement of an angle or of a rotation. This measurement is the length of a circular arc divided by its radius.
(a) angle a = 112° (alternate angles)
angle b = angle a = 112° (vertically opposite angles)
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The cost (in dollars) for manufacturing a particular flashdrive is , where x is the number of flashdrives produced. Recall from the previous chapter that the average cost per flashdrive, denoted by , is found by dividing c(x) by x. Find and interpret
The most appropriate choice for cost function and average cost function will be given by -
[tex]\lim_{x \to \infty} \bar{C}(X) = 6[/tex]
The number of flashdrive is very large, the average cost will come down to as low as $6.
What is cost function and average cost function?
Cost function C(x) is a function of x (quantity) which gives the cost of producing x units of the commodity.
Average cost function is the per unit cost of production and can be obtained by dividing the cost function by the quantity of the commodity.
Here,
C(x) = 17000 + 6x
[tex]\bar{C}(x) = \frac{17000 + 6x}{x}\\[/tex]
[tex]= \frac{17000}{x}+ \frac{6x}{x}\\[/tex]
= [tex]\frac{17000}{x}+6[/tex]
[tex]\lim_{x \to \infty} \bar{C}(x)[/tex] = [tex]\lim_{x \to \infty} (\frac{17000}{x} + 6)[/tex]
= 0 + 6
= 6
This means as the number of flashdrive is very large, the average cost will come down to as low as $6
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Complete Question
The cost (in dollars) for manufacturing a particular flashdrive is 17000 + 6x , where x is the number of flashdrives produced. Recall from the previous chapter that the average cost per flashdrive, denoted by , is found by dividing c(x) by x. Find and interpret [tex]\lim_{x \to \infty} \bar{C}(X)[/tex]
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Work out the missing numbers:
a) (-4) x __ = 320
b) __ x 3 = 180
c) __ / (-7) = (-14)
d) __ / (-9) = 6
please help i’m so confused
Sam and his cousin Matt have the same birthday, but Sam is 5 years older than Matt. Let the
variable x represent Sam’s age and y represent Matt’s age. Graph the relationship between
Sam’s age and Matt’s age.
A graph of the relationship between Sam’s age and Matt’s age has been plotted in the graph shown in the image attached below.
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
In order to solve this word problem, we would assign variables to Sam and Matt's age, and then translate the word problem into algebraic equation as follows:
Let the variable x represent Sam’s age.Let the variable y represent Matt’s age.Translating the word problem into an algebraic equation, we have;
x = 5 + y
Re-arranging the algebraic equation, we have;
y = x - 5
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what is the answer to 2 4/5 x 4 1/16
Answer:
91/8
Step-by-step explanation:
[tex]2\frac{4}{5} *4\frac{1}{6}[/tex]
→ Convert to improper fraction
14/5 × 65/16
→ Simplify
7 × 13/8 = 91/8
I NEED HELP
You recently opened your checking account with ReallyAwesomeBank on August 1 using $200.00.
Complete the checkbook register using the following transactions. Then answer the questions/show your work in the space below the register.
August 1 – Opened the checking account with $200.00
August 2 – Purchased Groceries from Shaw’s for $57.91 plus 3.5% tax. (Check 101)
August 2 – Paid $12 for parking using your debit card.
August 4 – Deposited paycheck from work. (15.50/hr for 30 hours)
August 6 – Paid National Grid $47.50. (Check 102)
August 6 – Bought 3 pairs of pants at $25.98 each with a 15% coupon and 6.5% sales tax from Kohls. (Check 103)
August 7 – Bought a bike for $165.00, helmet for $35.12, and gloves for $10.99 from Bikes-R-Us. Used a 15% off coupon and there was 5% sales tax. (Check 104)
August 11 – Deposited paycheck from work, but took out $100.00 cash (15.50/hr for 25 hours)
August 11 – Opened a savings account with $250 transferred from the checking account.
August 12 – Ate lunch at Red Robin for $24.61 plus 5.5% sales tax. Used your debit card to pay for it.
Number
Date
Transaction Description
Payment Fee, Withdrawal (-)
Deposit, Credit (+)
Balance
Use the space below to explain how you completed the first FOUR transactions.
Use the space below to show your work for how you found the total you spent at Kohl’s on August 6.
Use the space below to show your work for how you found the total you spent at Bikes-R-Us on August 7.
What was your final balance on August 12?
Completing the checkbook register using the transactions done on the checking account at Really Awesome Bank shows that the ending balance was $298.12.
What is a checkbook register?A checkbook register records transactions with a bank for a checking account.
The transactions of a checking account include withdrawals or payments, deposits, and bank charges if any.
Checkbook Register:Check Date Description Payments Deposit, Balance
No. Withdrawal (-) Credit (+)
August 1 Initial deposit $200.00 $200.00
101 August 2 Groceries (Shaw’s) $59.94 140.06
August 2 Parking fee $12 128.06
August 4 Paycheck 465.00 593.06
102 August 6 Electricity $47.50 545.56
103 August 6 Pants $70.56 475.00
104 August 7 Bike, Helmet, Gloves $188.42 286.58
August 11 Paycheck $287.50 574.08
August 11 Savings account $250.00 324.08
August 12 Luch (Red Robin) $25.96 298.12
Transaction Analysis:August 2 – $59.94 ($57.91 x 1.035%)
August 4 – $465 ($15.50 x 30) (15.50/hr for 30 hours)
August 6 – $70.56 (3 x $25.98 x 85% x 1.065)
August 7 – $188.42 ($165 + $35.12 + $10.99 x 85% x 1.05)
August 11 – $287.50 (15.50 x 25 - $100)
August 12 – $25.96 (24.61 x 1.055)
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NEED NOW OFFERING 100 POINTS!!
Which of the following expressions is equal 5^8/ 5^2 to?
5 · 5 · 5
5 · 5 · 5 · 5
3
The expression 5^8/ 5^2 is equal to 5×5×5×5×5×5. Option C
What is an algebraic expression?An algebraic expression can be defined as a are mathematical expression with a minimum of two terms containing variables, factors, constants and coefficients.
What is an exponential function?An exponential function is simply defined as a function in which its value is a constant that is raised to the power of a variable or number.
It is a relation or expression that takes the form y = aˣ in mathematics, where x is a independent variable.
Given the expression as;
⇒ 5^8 / 5²
⇒ 5^8-2
⇒ 5^6
⇒ 5×5×5×5×5×5
Hence, the value is 5×5×5×5×5×5
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The complete question;
Which of the following expressions is equal 5^8/ 5^2 to?
A.5×5×5
B. 1/5×5×5×5
C. 5×5×5×5×5×5
D.3
PLEASE HELP
Solve one sixth times quantity x plus 18 end quantity equals negative 5.
x = −48
x = −138
x = 12
x = 18
the answer is x= -48
solve for x by simplifying bith sides of the equation then isolating the variable so the answer is x= -48 your welcome!
In the semi-circle alongside, ACD is a sector of a circle with the center A. Show that the two shaded regions have equal area.
From the figure the shaded parts are two: the quadrant part and the sector part. The solution shows that:
area of the shaded part of the quadrant = area of the shaded part of the sector = ( pi * r^2) / 4 - bh/2
How to show that the two shaded regions are equalgiven data
ACD is a sector of a circle
From the figure we deduce that arc AC with line O is a quadrant of a circle. Hence the area of the shaded part of the quadrant is:
= area of a circle /4 - area of the right angle triangle
where area of a circle = pi r^2
area of triangle = 1/2 * base * height = bh/2
Area of the shaded part of the quadrant
= ( pi * r^2) / 4 - bh/2
base AO = radius of the circle = height CO
this forms an isosceles triangle and base angles of an isosceles triangle are equal. < A = < C = x
< A + < C + 90 = 180
x = 45 degrees
area of sector
= ∅/360 * pi*r^2
= (45 / 360) * (pi*r^2)
= (pi * r^2) / 4
area of the shaded part of the sector = area of sector - area of the right angle triangle
= (pi * r^2) / 4 - bh/2
Comparing both sides that shows that the tow shaded parts are equal hence the shaded part of the quadrant is equal to the shaded part of the sector
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use multiplication to show how how many twenty fourths equal 3/6
Answer:
10 times
Step-by-step explanation:
To figure this out, the first thing we will do is to find the LCM (Least Common Multiple). We will do this by making a list of the denominators that we have right now. Right now we have [tex]\frac{20}{4}[/tex] and [tex]\frac{3}{6}[/tex]. We will use 4 and 6 to make a list to find our multiple that is in both lists. (That comes up first)
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42...
Now, we just realized that we have 24 that are in common with both 4 and 6. Now we will multiply both the numerator and denominator by the same number to have the denominator equal 24.
[tex]\frac{20}{4} * \frac{6}{6}[/tex] = [tex]\frac{120}{24}[/tex] & [tex]\frac{3}{6} * \frac{4}{4}[/tex] = [tex]\frac{12}{24}[/tex]
Now that we have [tex]\frac{120}{24}[/tex] and [tex]\frac{12}{24}[/tex]. We will read the question again about how many [tex]\frac{3}{6}[/tex] equal to [tex]\frac{20}{4}[/tex]. Since we have our fractions, we will add [tex]\frac{12}{24}[/tex] multiple times until we get [tex]\frac{120}{24}[/tex].
[tex]\frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} + \frac{12}{24} = \frac{120}{24}[/tex]
Therefore, [tex]\frac{3}{6}[/tex] equals to [tex]\frac{20}{4}[/tex] 10 times.
EASY POINTS WILL GIVE BRAINLIST TO BEST ANSWER
Determine if the sequence is arithmetic. If it is, find the common difference, the 21st term, the explicit rule, the recursive rule, and the three terms in the sequence after the last one given.
-29, -22, -15, 8,…
Answer:
This is not an arithmetic sequence because -15 + 7 = -8, not 8.
The Scatter Plot represents Cities in North Carolina by Population and the Crime Index Rate.
The slope is 0.416 which represents what information from the Scatter Plot?
The intercept is -669.96 which represents what information from the Scatter Plot?
The information that a slope of 0.416 represents in the scatterplot is the crime index will increase 416 for every 1000 increment in the population.
The information that an intercept of -669.96 represents in the scatterplot is the value of the crime index when the population is zero.
What is graph?A graph is a pictorial representation of data. It is used by as many fields that uses data. Graphs helps to make information that the data represents easier to understand the relationship existing within the variables
The graph plots the crime index against the population. The slope is the represents how the crime index will behave with respect to the population. While the intercept is the point where the graph intercept the y axis which represents the crime index
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A veichle uses 150 litres of petrol in 45 minutes. How many litres of petrol will it use in 1 hour 15 minutes?
The amount of petrol consumed in one hour will be 200 liters.
A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
In 45 minutes, an automobile uses 150 gallons of gasoline.
Consequently, the rate of gasoline consumption in liters per minute will be
= 150 / 45
= 10 / 3 Liters per minute
We are aware that an hour is made up of 60 minutes.
The amount of gasoline that will be used in an hour will then be
= (10 / 3) x 60
= 10 x 20
= 200 liters
Thus, 200 liters of gasoline will be burned in an hour.
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Answer:
there the vehicle uses 250 litres
Step-by-step explanation:
[tex]150 = 45[/tex]
[tex]x = 75[/tex]
[tex]x = 75 \div 45 \times 150[/tex]
[tex]x = 250litres[/tex]
During an experiment, the temperature of a liquid, in degrees Celsius, is given by the function t(m) = 0.2m + 6, where m is the number of minutes since the experiment began. Which graph correctly shows this function?
The graph that correctly represent the experiment that was graphed with the function t(m) = 0.2m + 6 is the first option with points
first point (-30, 0) second point (0, 6)How to match graph to the functiongiven data
t(m) = 0.2m + 6
information deduced from the graph
intercept = 6slope = 0.2examining the graph shows that first graph have the intercept as 6
using the points to calculate slope we have
= (y2 - y1) / (x2 - x1 )
= (6 - 0) / (0 - -30)
= 6 / (0 + 30)
= 6 / 30
= 0.2
Since the points are same with the given information we can conclude that the first option has the graph of the given function
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What is an equivalent expression for −12(8a − 7b) + 8(4x + 3y)?
−96a + 84b + 32x + 24y
−96a − 84b + 32x − 24y
−96a − 7b + 32x + 3y
−96a + 7b + 32x + 3y
The equivalent expression for −12(8a − 7b) + 8(4x + 3y) is represented as - 96a + 84b + 32x + 24y
How to solve equivalent expression?Two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s).
Therefore, the equivalent expression of −12(8a − 7b) + 8(4x + 3y) can be solved as follows:
−12(8a − 7b) + 8(4x + 3y)
open the bracket
−12(8a − 7b) + 8(4x + 3y)
- 96a + 84b + 32x + 24y
Therefore, the equivalent expression of −12(8a − 7b) + 8(4x + 3y) is - 96a + 84b + 32x + 24y
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A particular jury consists of 7 jurors. Each juror has a 0. 2 chance of making the wrong decision, independently of the others. If the jury reaches a decision by majority rule, what is the probability that it will reach a wrong decision?.
The probability that the jury will make a wrong decision when it reaches a decision by majority rule is 0.033
To solve this, the number of jury that makes the wrong decision can be modeled as a binomial random with parameters n=7 and p=0.2. This jury as a whole will make wrong decision if 4, 5, 6, or 7 make the wrong decision.
We denote these events with A, B, C, D for 4, 5, 6, 7 respectively. The probability of this union is the sum of probabilities, so
P(Jury Error) = P(A)+P(B)+P(C)+P(D)
= [tex]\left({{7} \atop {4}} \right.)(0.2)^{4} *0.8^{3} +(\left \({7} \atop {5}} \right)(0.2)^{5} *0.8^{2} +(\left{7} \atop {6}} \right.)(0.2)^{6} *0.8^{1} +(\left{7} \atop {7}} \right.)(0.2)^{7} *0.8^{0}[/tex]
=0.033
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what is 2.6 to the lower bound
Lower bound of 2.6 is 2.5
What is lower bound?An element of K that is greater than or equal to each element of S is referred to as an upper bound or majorant in mathematics, notably in order theory. To determine a rounded number's upper and lower bounds: Determine the place value of the claimed level of accuracy. By two, multiply this place value. Find the upper bound by adding this amount to the provided value, and the lower bound by deducting this amount from the given value.
Given Data
2.6 to the lower bound
Bound of 2.6 is 2.5 to 2.7
Lower bound of 2.6 is 2.
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the 2 boxes are cubiods work out how many of the smaller boxes you would need to completely fill the larger one.
From calculations, we can see that the number of smaller boxes to completely fill the larger one are; 250 boxes
How to find the volume of the cuboid?The volume of a cuboid is given by the formula;
Volume = Length * Width * Height
Looking at the given dimensions of the larger box in the cuboid image attached, we can calculate the volume as;
Volume = 50 * 30 * 20
Volume = 30000 cm³
The length , width and height of smaller box are 10 cm, 3 cm and 4 cm respectively. Thus, the volume of smaller box is;
volume = 10 * 3 * 4
volume = 120 cm³
Thus, the number of smaller boxes to completely fill the larger one are;
n = 30000/120
n = 250 boxes
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The following two triangles are similar. Find the missing side length represented by x.
A. 7
B. 5
C. 6
D. 8
The missing side length that is represented by x in the triangles that are similar is: B. 5.
How to Find the Dimensions of Similar Triangles?According to the similarity theorem, the corresponding side lengths of two triangles that are similar have the same ratio and are therefore proportional to each other.
The two triangles are considered similar to each other, this means that their corresponding side lengths would be proportional to each other and would have the following equal ratio:
45/9 = 25/x
Cross multiply
(45)(x) = (9)(25)
45x = 225
Divide both sides by 45
45x/45 = 225/45
x = 5
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Ms. May invested $8000 at 7%. How much additional money must she invest at 4% in order that her
total annual income (from interest) may equal 5% of her entire investment?
The additional money Ms. May must invest at rate of 4% to get the 5% interest on entire income is $16,000.
What is meant as the rate of interest?The rate of interest is the amount charged by the lender to the borrower in addition to the principal amount. In aspects of the receiver, an individual who deposits money in any bank or financial institution earns extra money due to the time value of money, which is referred to as interest received by depositor.For the given question,
The money invested by Ms. May at 7% rate of interest is $8,000.
Let 'x' be the money invested at the rate of 4%.
The interest for the total annual income is 5%.
Thus,
7%of 8,000 + 4% of x = 5%(8,000 + x)
8,000×0.07 + 0.04×x = 0.05(8,000 + x)
On solving,
560 + 0.04x = 400 + 0.05x
0.01x = 160
x = 16,000
Thus, the additional money Ms. May must invest at rate of 4% to get the 5% interest on entire income is $16,000.
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Please answer the two questions in the photo ( will mark brainliest if correct )
The diagram shows a prism. The cross section of the prisim is a right-angled triangle. The base of the triangle has length 5cm. The prisim has length 25cm. The prisim has volume 750. Work out the height of the prisim.
The height of the triangular prism is calculated as: 12 cm.
How to Find the Height of a Right-Triangular Prism?The volume of a right-triangular prism = 1/2(base of triangular face)(height of triangular face)(length of the triangular prism).
Given the following:
Base length of the triangular face = 5 cmVolume of the right-triangular prism = 750 cubic cmLength of the right-triangular prism = 25 cmHeight of the right-triangular prism (height of the triangular face) = hPlug in all the values into the volume formula for the triangular prism:
750 = 1/2(5)(h)(25)
750 = (1 × 5 × h × 25)/2
750 = (125h)/2
Multiply both sides by 2
750 × 2 = (125h)/2 × 2 [multiplication property of equality]
1,500 = 125h
Divide both sides by 125
1,500/125 = 125h/125 [division property of equality]
12 = h
h = 12 cm
Thus, the height of the prism that has a base of the triangle measuring 5cm, a prism length of 25 cm., and a volume of 750 cubic cm is determined as 12 cm.
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Aubrey‘s car used 2 gallons to travel 90 miles how far can she travel on 11 gallons
Answer: 495
Step-by-step explanation: