Which of the following is an example of an inequality?
The equation which is an example of an inequality include the following: C. 4x > -16
What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).In this context, we can reasonably infer and logically deduce that the only equation with an inequality symbol is 4x > -16 and as such, it is an example of an inequality.
By evaluating, we have:
4x > -16
x > -16/4
x > -4
In conclusion, we can logically deduce that x is greater than negative four (-4).
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Complete Question:
Which of the following is an example of an inequality
A. x+5=10
B. 2x-3=7
C. 4x>-16
D. 3x-2
6 foot tall adult casts, a shadow that is 15 feet long estimate the height of a child who cast a 10 foot shadow
By similarity of triangle the height of a children will be 4ft.
What is similarity of triangle?Similar triangles are that kind of triangles that have the same shape, but different sizes. examples of similar objects are All equilateral triangles, squares of any side lengths. In another words, if two triangles having their corresponding angles are congruent and corresponding sides are in equal proportion then two triangles are said to be similar. It is denoted by ‘~’ symbol.
We can use the property of similar triangles to estimate the height of the child:
The ratio of the height of the adult to the length of their shadow is the same as the ratio of the height of the child to the length of their shadow:
height of adult / length of adult shadow = height of child / length of child shadow
Plugging in the values we know:
6 / 15 = height of child / 10
Solving for the height of the child:
height of child = (6 / 15) * 10 = 4 feet
Therefore, the estimated height of the child is 4 feet.
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What is the area of this composite figure? Use 3.14 for pi. Round to the nearest hundredth. Show ALL work.
The composite figure compromising of a sector, a triangle and a trapezoid have a total area calculated to be 15.9 square units.
How to find the area of the composite figureWe can observe from the figure that it is a combination of a sector, a triangle and a trapezoid, so we shall calculate the area of each shape and add their result to get the area of the composite figure as follows:
area of the sector = 135°/360° × 22/7 × 2 × 2
area of the sector = 33/7
area of the sector = 4.7 square units
area of triangle = 2.6 × 1
area of the triangle = 2.6 square units
area of the trapezoid = 1/2 × (2.6 + 6) × 2
area of the trapezoid = 8.6 square units
area of the composite figure = 4.7 + 2.6 + 8.6
area of the composite figure = 15.9 square units
In conclusion, the composite figure compromising of a sector, a triangle and a trapezoid have a total area calculated to be 15.9 square units.
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Explain how you can you prove the Corresponding Angles Theorem using the
Same-Side Interior Angles Postulate and a linear pair of angles.
Answer:
If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. Converse of the Same-Side Interior Angles Postulate: If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.
does anyone know how to solve this problem. (image attached)
The rectangle's area is growing at a pace of 138 [tex]\frac{cm^{2} }{s}[/tex] when its length is 10 cm and its width is 6 cm, this is the case.
What is the rate of change?One quantity's rate of change with regard to another quantity is known as the rate of change function. In order to calculate the rate of change, one simply divides the amount of change in one item by the equivalent amount of change in another.
Let L and W represent the length and breadth of the rectangle, respectively, and A represents the area of the rectangle. Next, we have:
A = L * W
When L = 10 cm and W = 6 cm, we are interested in determining the rate of increase of the rectangle's area with regard to time, or dA/dt.
We can begin by finding the derivative of A = L * W with regard to time t for both sides of the equation:
Derivate the equation by both sides with respective t.
[tex]\frac{d}{dt} (L * W) = \frac{dA}{dt}[/tex]
Using the principle of product rule of derivative, we arrive at:
[tex]L * W + L * \frac{dw}{dt} = \frac{dA}{dt}[/tex]
To determine dA/dt when L = 10 cm and W = 6 cm, we are provided that [tex]\frac{dL}{dt}[/tex] = 8 cm/s and [tex]\frac{dw}{dt}[/tex]= 9 cm/s. Therefore, we replace these numbers in the previous equation to obtain:
[tex]\frac{dA}{dt}[/tex] = (8 [tex]\frac{cm}{s}[/tex]) * (6 cm) + (10 cm * 9 [tex]\frac{cm}{s}[/tex]).
[tex]\frac{dA}{dt} = 48 \frac{cm^{2}}{s} + 90 \frac{cm^{2}}{s} \\[/tex]
[tex]138 \frac{cm^{2} }{s} = \frac{dA}{dt}[/tex]
Since the rectangle's area is growing at a pace of 138 [tex]\frac{cm^{2} }{s}[/tex]when its length is 10 cm and its width is 6 cm, this is the case.
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given the equations below what is the frist x value where g(x)>f(X)
f(X)=4X=25
g(X)=2(5)x
Answer:There seems to be a typo in the equation for f(x). I will assume that the correct equation is:f(x) = 4x - 25To find the first x value where g(x) > f(x), we can set the two equations equal to each other and solve for x:g(x) = f(x)
2(5)x = 4x - 25
10x = 4x - 25
6x = -25
x = -25/6
Step-by-step explanation:However, we need to check if this value satisfies the condition g(x) > f(x):g(-25/6) = 2(5)(-25/6) = -25
f(-25/6) = 4(-25/6) - 25 = -75/3 - 25/1 = -100/3Therefore, g(x) > f(x) is not true for x = -25/6. We need to keep looking for a larger value of x where g(x) > f(x).To do this, we can graph the two functions and look for the point where the graph of g(x) is above the graph of f(x). Alternatively, we can simply plug in some larger values of x and compare the values of g(x) and f(x) until we find the first x value where g(x) > f(x).Let's try plugging in x = 0:g(0) = 2(5)(0) = 0
f(0) = 4(0) - 25 = -25Since g(0) = 0 and f(0) = -25, we have g(x) > f(x) for x > 0. Therefore, the first x value where g(x) > f(x) is x = 0.
a jar contains $3.60 in nickels and quarters. there are 28 coins in all. how many of each coin is in the jar?
In a class of 24 students, 7 students have 2 brothers or sisters. 4 students have 1 brother or sister. 3 students do not have any brothers or sisters. 6 students have 3 brothers or sisters. The remaining students have 4 brothers or sisters.
Samedy says that the total number of brothers and sisters that the class has is 24, because there will be 24 dots above the number line on the line plot. Use the drop-down menus to complete the statement below.
Answer:
Samedy's statement is false. in total the class has 56 brothers and sisters
Step-by-step explanation:
Answer:
A. Samedy's statement is incorrect.
B. In total, the class has 71 brothers and sisters.
To arrive at this answer, we can use the information given in the problem to calculate the total number of brothers and sisters:
7 students have 2 siblings each, so there are 14 siblings in total.
4 students have 1 sibling each, so there are 4 siblings in total.
6 students have 3 siblings each, so there are 18 siblings in total.
The remaining students have 4 siblings each, so there are 4 x (24 - 7 - 4 - 3 - 6) = 4 x 4 = 16 siblings in total.
Adding all of these up, we get a total of 14 + 4 + 18 + 16 = 52 siblings. Therefore, Samedy's statement is incorrect, as the class has 52 siblings and not 24.
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A greengrocer normally sells 20 carrots for £2.80. In a sale, the cost of the carrots is reduced by 30%. Work out how much 180 carrots cost in the sale. Give your answer in pounds
Answer:
Step-by-step explanation:
180 ÷ 20 = 9
Original Price = 9 x £2.80 = £25.2
Discounted price = £25.2 - (£25.2 x 0.30) = £17.55
In a sale, 180 carrots would cost £17.55.
solve the equation
3(3-2x)=2 x-11
Answer:
x = 2,5
Step-by-step explanation:
[tex]3(3 - 2x) = 2x - 11[/tex]
[tex]9 - 6x = 2x - 11[/tex]
Put numbers with x's to the left, and the plain numbers to the right:
[tex] - 6x - 2x = - 11 - 9[/tex]
[tex] - 8x = - 20[/tex]
[tex]x = 2.5[/tex]
Why is the green triangle not possible given an angle of 30°?
The reason why the green triangle is not possible given an angle of 30° and a side length of 8.73 is due to the fact that the green triangle violates the triangle inequality theorem.
What is triangle inequality theorem?According to the triangle inequality theory, any triangle's lengths of any two sides must add up to more than the length of the third side.
The triangle inequality theorem is broken in the instance of the green triangle if the second side is extended to a very long length, making the triangle's lengths of the two shorter sides (7 and 8.73) less than the length of the longer side (24).
The orange triangle, which has side lengths of 7, 15, and roughly 16.16 (determined using the Pythagorean equation), is the only one that can exist because the green triangle is impossible.
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In an Australian netball competition, these teams are tipped to win Round 1 by three experts:
Expert A: NSW, Queensland, WA, Tasmania
Expert B: SA, Victoria, Queensland, WA Expert C: NSW, ACT, WA, Victoria No one tipped the Northern Territory to win. Which team did Victoria play?
Answer:
undetermined or most likely Tasmania
Step-by-step explanation:
Based on the choices of experts in the first round of the Australian netball competition, we can conclude that Victoria played against WA. This is because, out of the common tips, WA was tipped by an expert who also tipped Victoria and didn't tip Queensland. Therefore, WA is the likely team that Victoria played against.
Explanation:To identify which team Victoria played in the Australian netball competition we can reason through our experts' tips. The experts' tips overlap at Queensland and WA as indicated by Expert A and Expert B. However, Expert C tipped Victoria, and they did not tip Queensland which tells us that Victoria did not play against Queensland, leaving us with WA. Hence Victoria must've played against WA.
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Emily and Josie were randomly choosing a colored chip from the ones show below. What is the probability that Emily will choose a blue chip, keep it, and then Josie chooses a red chip?
The probability that Emily chooses a blue chip and Josie chooses a red chip is 3/28.
What is mutually exclusive events?Events that are mutually incompatible cannot take place at the same moment. If one thing happens, the other thing can't happen. For instance, if we flip a coin, receiving heads and getting tails are mutually exclusive events. The likelihood of two mutually exclusive occurrences happening simultaneously is zero.
Events that are independent of one another are said to be independent. The likelihood of the other event happening is unaffected if one event happens.
Given, 3 blue chips and 2 red chip from a total of 8 chip we have:
P(Emily chooses blue and Josie chooses red) = P(Emily chooses blue) × P(Josie chooses red after Emily chose blue)
= (3/8) × (2/7)
= 6/56
= 3/28
Hence, the probability that Emily chooses a blue chip and Josie chooses a red chip is 3/28.
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The complete question is:
Emily and Josie were randomly choosing a colored chip from the ones show below. What is the probability that Emily will choose a blue chip, keep it, and then Josie chooses a red chip?
The number of chips there are 8 chips. 3 are blue, 2 are red.
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What is the image point of (-9,-5) after the transformation T-5,00 D₂?
attempt 11 out of 20/problem 1 out of ma
C
Thus, following the transformation T-5,00 D2, the image point of (-9,-5) is (-8,-10). Hence, choice C is the right response.
What is transformation ?The term "transformations" refers to the movements or adjustments that can be made to a geometric shape or object, such as turning, reflecting, translating, processes in an organization, or resizing. With these procedures, the original form or object can retain its geometry, angles, and other geometric attributes while changing its position, size, and orientation. Geometry, photography, and other disciplines frequently employ transformations to manipulate and examine patterns and shapes.
given
Applying the translation T-5,00 to the point (-9,-5) first yields (-9-(-5),-5+0) =, which we can use to determine the image point of (-9,-5) following the transformation T-5,00 D2 (-4,-5).
Then, we dilate the point (-4, -5) using the formula (2(-4,2(-5)) = (-8,-10).
Thus, following the transformation T-5,00 D2, the image point of (-9,-5) is (-8,-10). Hence, choice C is the right response.
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IF I A LIQUID IS AT A TEMPERATURE OF 16.9 AND RISES AT A RATE OF 2.3 AND A SOLID IS AT A TEMPERATURE OF 30.7 AND DECREASES AT A RATE OF 6.9 how long will it take for them to be at the same temperature in minutes
Answer:
The number of minutes it will take for a liquid and a solid to reach the same temperature is 3 minutes.
Step-by-step explanation:
You know that the temperature of liquid at 16.9°C is decreasing at a rate of 2.3°C per minute. Then, the temperature of the liquid after t minutes, as its value decreases, will be the difference between the initial temperature of 16.9 ° C and the temperature after t minutes. So:
temperature of the liquid= 16.9°C - 2.3 °C/minute * t
On the other side, you know that the temperature of a solid at 30.7°C is decreasing at a rate of 6.9°C per minute. Then, the temperature of the solid after t minutes, as its value decreases, will be the difference between the initial temperature of 30.7°C and the temperature after t minutes. So:
temperature of the solid= 30.7°C - 6.9 °C/minute * t
You want to calculate the number of minutes it will take for a liquid and a solid to reach the same temperature. This is:
temperature of the liquid= temperature of the solid
16.9°C - 2.3 °C/minute * t= 30.7°C - 6.9 °C/minute * t
Solving:
- 2.3 °C/minute * t= 30.7°C - 6.9 °C/minute * t - 16.9°C
- 2.3 °C/minute * t + 6.9 °C/minute *t= 30.7°C - 16.9°C
4.6 °C/minute * t = 13.8 °C
t=3 minutes
So the number of minutes it will take for a liquid and a solid to reach the same temperature is 3 minutes.
Choose the equation that represents the line that passes through the point (6, -3) and has a slope of
1
-İN
2
O
O
y=-x+6
O
y=-x-6
|_y=-x-3
2
|_y=-x+3
Answer:y=-x+6
Step-by-step explanation:
एउटा मोटरसाइकलको मूल्य वि.सं 2070 मा रु. 250,000 थियो र वि.सं. 2072 मा रु. 160,000 छ भने वार्षिक मिश्रह्रास दर पत्ता लगाउनुहोस् । The price of a motorcycle was Rs 250,000 in 2070 B.S. and in 2072 B.S., it is Rs 1,60,000. Find the annual rate of compound depreciation.
Step-by-step explanation:
Solution,
P=2,50,000
T=2072-2070
=2 years
Pt=1,60,000
Pt=P(1-D/100)^2
1,60,000=2,50,000{(100-D)}^2
100
1,60,000/2,50,000={(100-D)}^2
100
0.64={(100-D}^2
100
(0.8)^2={(100-D)}
100
80=100-D
100
80=100-D
D=100-80
D=20%
Hence, the deprecation rate is 20% over the period of 2 years
Help me please. for 65 points and brainly
Answer:
Answer 3
Step-by-step explanation:
Answer: 3
Step-by-step explanation:
help pls show ur work
1. The triangles are not similar because they do not have proportional set of sides.
2. Both triangles are not similar as well.
What is the SSS Similarity Theorem?The SSS similarity theorem states that if three corresponding sides of two triangles are proportional, then the triangles are similar. "SSS" stands for "side-side-side," which refers to the three corresponding sides that are proportional.
More formally, the SSS similarity theorem can be stated as follows:
If ΔABC ~ ΔDEF, then: AB/DE = BC/EF = AC/DF (the sides are proportional)
1. QP/ML = 90/40 = 2.25
RQ/LK = 81/36 = 2.25
PR/MK = 64/28 = 2.29
Thus, this means that QP/ML = RQ/LK ≠ PR/MK. This implies the three sides are of both triangles are not proportional. Therefore, they are not similar by SSS nor any other theorem.
2. Both triangles do not have any set of corresponding angles that are congruent, therefore, they are not similar.
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A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.
Find the probability that the mean actual weight for the 100 weights is greater than 24.9. (Round your answer to four decimal places.)
Thus, the chance according to the equation that the average actual weight for the [tex]100 weights[/tex] is higher than [tex]24.9 pounds[/tex] is roughly [tex]0.9582[/tex]
What is equation?An equation in mathematics is a declaration of the equivalence of two expressions. Two parts of an equation are divided by the algebraic symbol ([tex]=[/tex]). As an example, the assertion "[tex]2x+3=9[/tex]" is supported by the argument that it is true.
Finding the value or values of the variable(s) needed to make the equation correct is the aim of equation solving. It is possible to create regular or nonlinear, straightforward or complex equations that include one or more variables.
For instance, the variable[tex]x[/tex] is raised to the second degree in the equation "[tex]x^{2} +2x-3[/tex]". In many areas of mathematics, such as algebra, calculus, or geometry, lines are used.
The weights are distributed evenly, with a minimum value of [tex]24[/tex] and a highest value of [tex]26[/tex]. The average of the lowest and maximum values, which is the mean weight of a single weight, is
[tex](mean weight)= (24+26)/2 = 25 pounds[/tex]
The standard deviation of a single weight is the difference between the maximum and minimum values divided by[tex]\sqrt{12}[/tex] (since there are [tex]12[/tex]possible values between [tex]24[/tex] and [tex]26[/tex]), which is
[tex]Standard deviation = (24+26)/\sqrt{12}[/tex]
[tex]We know (standard deviation of mean weight ) = 0.57735/\sqrt{100} =0.057735[/tex]
We must standardise this value by taking the mean weight, subtracting it, and dividing the result by the mean weight's standard deviation in order to determine the likelihood that the mean actual weight for the[tex]100[/tex]weights is higher than [tex]24.9 pounds[/tex]:
[tex]( Z- score )= (24.9-25)/0.057735 = -1.7321[/tex]
Probability is [tex]less than[/tex] [tex]-1.7321 in Z- score approx 0.0418[/tex]
However [tex]mean actual weight > 24.9[/tex] which is the complement of the probability i.e, [tex]\leq 24.9[/tex]
After subtracting the probability we found [tex]1[/tex] [tex](mean weight > 24.9)[/tex]
∴[tex]1 -0.0418 = 0.9582[/tex]
Therefore the the average actual weight for the [tex]100 weights[/tex] is higher than [tex]24.9 pounds[/tex] is roughly [tex]0.9582[/tex]
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James starts from point A along the pentagonal path A to B, B to C, C to D,
D to E and finally returns to point A. The distance of side
of pentagon is 8 m .He takes 16
from A to A along the path as said earlier. Write:
Distance covered by him
Displacement
Speed
Answer:
a) Distance is 40m b)0 c)2.5m/min
Step-by-step explanation:
a)8*5=40 b)He went from A to A c)16 min s=d/t 40/16
Rewrite from standard form to vertex form
F(x)=x^2-4x+49
Accοrding tο the given infοrmatiοn, the vertex οf the parabοla is at (2, 45), and the minimum value οf the functiοn is 45, which οccurs at the vertex.
What is the vertex fοrm?The vertex fοrm οf a quadratic functiοn is a way οf writing a quadratic functiοn in the fοrm: f(x) = a(x - h)² + k, where (h, k) is the vertex οf the parabοla, a is a cοefficient that determines the shape and directiοn οf the parabοla, and x is the input variable. This fοrm is called the vertex fοrm because it prοvides direct infοrmatiοn abοut the vertex οf the parabοla, which is the pοint where the parabοla changes directiοn.
Tο rewrite the quadratic functiοn f(x) = x² - 4x + 49 frοm standard fοrm tο vertex fοrm, we need tο cοmplete the square by adding and subtracting a cοnstant term inside the parentheses, such that the functiοn can be expressed in the fοrm a(x - h)² + k.
f(x) = x² - 4x + 49
We can cοmplete the square as fοllοws:
f(x) = (x² - 4x + 4) + 45
= (x - 2)² + 45
Therefοre, the vertex fοrm οf the functiοn f(x) is:
f(x) = (x - 2)² + 45
The vertex οf the parabοla is at (2, 45), and the minimum value οf the functiοn is 45, which οccurs at the vertex.
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Help can someone help me
Answer:
70
Step-by-step explanation:
The weight of 4 hummingbirds is recorded below. The weight of each
1
hummingbird has been rounded to the nearest gram.
2
2
2/1/2
3 31/1 4 4/ 5
Weights of birds (grams)
10
What is the weight of all 4 hummingbirds combined?
grams
Answer: The total amount of the hummingbirds' weight is 15 grams.
Step-by-step explanation:
As it is shown in the dot graph, the four hummingbirds' weigh is recorded to the nearest gram.
Hummingbird 1 - 2 1/2
Hummingbird 2 - 3
Hummingbird 3 - 4 1/2
Hummingbird 4 - 5
2 1/2 + 4 1/2 = 7
3 + 5 = 8
Seven plus eight equals to fifteen. Therefore, the total weight of all four hummingbirds is 15.
Hope this helps coralasting123!i need the answers pls
Step-by-step explanation:
5. Name the Circle.
Ans. Circle C.
6. Name to radii.
Ans. BH, AD
7. Name two chords.
Ans. AD ,BH
8. Name a diameter
Ans. AD
9. Name a secant .
Ans. KG
10.Name a tangent
Ans. GE
Point of tangency = F
More to Know :
• Radii: The distance from the centre of the circle to the circumference.
• Chord: Chord is a line segment that have two end points on the circle
• Secant: It refers to the line that intersect the circle at two points.
• Diameter: The lines that passes from the centre of the circle and meet at both the ends of the circle.
• Point of tagency: It is referred to the point where the tangent meets the circle.
[tex]\\[/tex]
Drag a statement or reason to each box to complete this proof
Drag the following statement, equation or reason to each box to complete this proof accordingly:
2. Multiplication Property of Equality
3. x-2 = 8
4. Addition Property of Equality
5. x = 10 Simplifying
How to complete the proof of the equation with reason?An equation is a mathematical statement that expresses the equality between two expressions. It contains an equal sign "=" that separates the two expressions.
The proof of the equation with reason can be completed as follow:
(x-2)/4 = 2 Given
4(x-2)/4 = 4 * 2 Multiplication Property of Equality
x-2 = 8 Simplifying
x - 2+ 2 = 8 + 2 Addition Property of Equality
x = 10 Simplifying
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A right triangle is drawn on the coordinate plane. Apply a dilation with a scale factor of one over three to this triangle in draw the new triangle on the coordinate plane.
The image of the triangle is attached with coordinates
(0, 0)
(0. 3)
(3, 3)
What is a scale factor?In mathematics, a scale factor is a constant that multiplies every length of an object, changing its size while preserving its shape. In the context of dilation, which is a type of transformation that changes the size of a shape, the scale factor determines the amount by which the shape is enlarged or reduced.
When a shape is dilated with a scale factor greater than 1, the resulting shape is larger than the original. Conversely, when a shape is dilated with a scale factor between 0 and 1, the resulting shape is smaller than the original. If the scale factor is exactly 1, then the shape remains the same size.
In the problem the image is dilated with a scale factor less than one hence the resulting image is lesser
The new coordinates are gotten as follows
(0, 0) * 1/3 = (0, 0)
(0. 9) * 1/3 = (0. 3)
(9, 9) * 1/3 = (3. 3)
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Riley was a spectator at his town's air guitar competition. Contestants were allowed to play either the acoustic or electric air guitar, but not both. Riley recorded which type of guitar each contestant played. He also counted the number of contestants wearing different kinds of pants, as there were some interesting stylistic choices.
What is the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants?
A. 9/25
B. 2/5
C. 3/5
D. 6/25
show all steps
The conditional probability that a randomly selected participant wore leather pants and played an acoustic guitar is 6/25. Therefore, the answer is option D. 6/25.
What is conditional probability?Conditional probability is the probability that an event will occur given that another event has already occurred.
It is denoted by P(A|B), where A and B are events, and the vertical line | indicates "given that" or "conditional on".
The conditional probability of an event A given event B is defined as the probability of both A and B happening divided by the probability of B happening:
P(A|B) = P(A and B) / P(B)
In this case, the event A is playing an acoustic guitar and the event B is wearing leather pants.
We can start by finding the probability of wearing leather pants:
P(B) = (6 + 9) + (3 + 7) = 25
This is because there are a total of 6 contestants wearing leather pants and 19 contestants in total.
Next, we need to find the probability of both wearing leather pants and playing an acoustic guitar:
P(A and B) = 6
This is because there are 6 contestants wearing leather pants and playing an acoustic guitar.
Now we can use the formula to find the conditional probability:
P(A|B) = P(A and B) / P(B) = 6 / 25
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The sum of the ages of two brothers Kofi and Kwaku is 35. Kofi age is 2/3 of Kwaku's age. find their ages.
2/3 of 35 is 23. Kofi is 23.
Which expression is equivalent to (7^3)5 ⋅ 7^4?
Answer: [tex]7^3\cdot7^{-5}=7^{-2}=\dfrac{1}{7^2}[/tex]
Step-by-step explanation: