Answer:
9/35
Step-by-step explanation:
3/5 x 3/7
If someone walks along the outside of the garden from point A to point B, what percent of the garden's border would they have walked around? Round your answer to the nearest whole percent. Type the correct answer in the box. Use numerals instead of words. They would have walked around approximately % of the outside border of the garden.
The outside border of the garden would have walked around approximately 58%.
Without more information about the shape and dimensions of the garden, it's impossible to give an exact answer. However, if we assume that the garden is a rectangle, we can use the formula for the perimeter of a rectangle to estimate the percentage of the garden's border that would be walked around.
Let's say that the length of the garden is L and the width of the garden is W. The perimeter of the rectangle is then:
P = 2L + 2W
If the person walks from point A to point B along the outside of the garden, they are essentially walking along two sides of the rectangle. Let's call these sides S1 and S2. Depending on the location of A and B, S1 and S2 may be two adjacent sides, two opposite sides, or one side and one diagonal.
To estimate the percentage of the garden's border that the person would walk around, we can calculate the length of S1 and S2 and divide by the total perimeter of the rectangle:
Percentage walked = (S1 + S2) / P * 100%
Again, without more information about the shape and dimensions of the garden, we can't give an exact answer. However, if we assume that the person walks along two adjacent sides of the rectangle, the percentage of the garden's border that they would walk around would be:
Percentage walked = (2L + W) / (2L + 2W) * 100%
Simplifying this expression, we get:
Percentage walked = (2L + W) / (2(L + W)) * 100%
Assuming that L and W are measured in the same units (e.g. meters), we can simplify further:
Percentage walked = (2 + W/L) / (2 + 2W/L) * 100%
For example, if the length of the garden is 10 meters and the width of the garden is 5 meters, then the percentage of the garden's border that the person would walk around if they walked along two adjacent sides would be:
Percentage walked = (2 + 5/10) / (2 + 2*5/10) * 100%
= 7/12 * 100%
= 58.3%
So the outside border of the garden would have walked around approximately 58%.
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Help me please!!!!! .
Answer:
The angle in the first problem measures 67°.
x=16, y=40
Step-by-step explanation:
1st problem: draw the line r in figure (red) parallel to the two given one and containing the vertex of the angle. The two green angles are congruent since alternate angles from the two parallels t and r when crossed with the upper side of the angle. Same with the two blue angles created by the parallels r and b. The measure of the angle you need is the sum of the two, or 36+31= 67°.
Second problem. The two angles in red are congruent since corresponding angles generated by the parallels m and b and the transversal r. we can then write [tex]4x-5=3x+11\\[/tex]. Solving for x we find x= 16. Now the two angles marked in blue are conjugates when looking at the parallels l and r cut by the transversal m, thus they add up to 180° We know how much the angle with double marks measures (since we found x earlier) so we can write
[tex](3y+1) + (4\times16-5) = 180\\3y+ 1 + 59 = 180\\3y=120 \implies y=40[/tex]
The scatter plot shows the number of apples Aniyah picked from her apple trees each year. The equation of the line of fit is:
y = 15.2x + 111
What is the predicted number of apples picked in year 5? Explain your answer.
Answer: 187 apples
Step-by-step explanation:
Substitute "year 5" into the equation. y = 15.2(5) +111.
y = 76 + 111
y = 187
Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.
We have that Linda's net and expression incorrect
With the Expression of the surface area of attic
45 (40 + 25 + 25) + 1/2 (40 x 15)
Hence, Surface area is,
X = 4050 + 600
X = 4650 feet²
Hence, The answer is No, Because Her expression for the triangles are incorrect;
1/2(40 x 15)
Instead of,
1/2 x 40 x 15
Hence, Linda's net and expression incorrect,
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Complete question is,Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.
She needs to find the approximate surface area of the attic, including the walls, floor, and
ceiling. The attic is in the shape of a triangular prism. Linda draws the net and writes
the expression below to represent the surface area of the attic. Are Linda's net and
expression correct?
We are given the random variable X that follow an exponential distribution such as:
X ~ Exp(1/9.848)
1) Find the expected value
2) Find the standard deviation
3) Find P(X<12)
4) Find P(8 < X < 12)
I have already found the answers:
They are:
1) 9.848
2) 9.848
3) 0.7043
4) 0.2025
The required solution of the random variable X that follows an exponential distribution is shown below.
To find the expected value, standard deviation, and probabilities associated with the exponential distribution, we'll use the given parameter λ = 1/9.848.
Expected Value (Mean):
The expected value of an exponential distribution is equal to the reciprocal of the rate parameter λ. Therefore, the expected value is given by:
E(X) = 1 / λ
E(X) = 1 / (1/9.848)
E(X) = 9.848
So, the expected value of the random variable X is 9.848.
Standard Deviation:
The standard deviation of an exponential distribution is equal to the reciprocal of the rate parameter λ. Therefore, the standard deviation is given by:
σ = 1 / λ
σ = 1 / (1/9.848)
σ = 9.848
So, the standard deviation of the random variable X is also 9.848.
P(X < 12):
To find the probability that X is less than 12, we can use the cumulative distribution function (CDF) of the exponential distribution. The CDF is given by:
[tex]F(x) = 1 - e^{(-\lambda x)}[/tex]
Substituting the given λ = 1/9.848 and x = 12, we have:
[tex]P(X < 12) = F(12) = 1 - e^{-(1/9.848) * 12)}[/tex]
Calculating this expression, we find:
P(X < 12) ≈ 0.7043
Therefore, the probability that X is less than 12 is approximately 0.7737.
P(8 < X < 12):
To find the probability that X lies between 8 and 12, we subtract the cumulative probability at 8 from the cumulative probability at 12:
P(8 < X < 12) = F(12) - F(8)
= [tex]1 - e^{(-(1/9.848) * 12)]} - [1 - e^{(-(1/9.848) * 8)]}[/tex]
Calculating this expression, we find:
P(8 < X < 12) ≈ 0.2025
Therefore, the probability that X lies between 8 and 12 is approximately 0.2025.
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UNIT ISCALING
SCALE DRAWING OF A SCHOOL BUS HAS A SCALE OF 1/2 INCH TO 5 FEET. IF THE
ENGTHS OF THE SCHOOL BUS IS 4 1/2 INCHES ON THE SCALE DRAWING, WHAT IS THE
ACTUAL LENGTH OF THE BUS? EXPLAIN OR SHOW YOUR REASONING
The actual length of the bus is given as follows:
45 feet.
How to obtain the actual length of the bus?The actual length of the bus is obtained applying the proportions in the context of the problem.
The scale drawing is of 0.5 inches to 5 feet, hence the length represented by each inch of drawing is given as follows:
5/0.5 = 10 feet.
The length of the drawing is given as follows:
4.5 inches.
Hence the actual length of the bus is given as follows:
4.5 x 10 = 45 feet.
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what is the equation that contains the point M(1,10,3), N(4,10,6) and P(7,10,9)?
The equation of the line is: x = 1 + 3t,, y = 10, z = 3 + 3t.
How to determine the equation of the lineTo determine the equation of the line passing through points M(1, 10, 3), N(4, 10, 6), and P(7, 10, 9), we need to find the direction vector of the line.
Let's denote the direction vector as D = (a, b, c). The line can be represented by the parametric equations:
x = 1 + at,
y = 10 + bt,
z = 3 + ct,
To find the direction vector, we can use two points on the line, for example, M and N. The direction vector can be obtained by subtracting the coordinates of M from the coordinates of N:
D = N - M = (4 - 1, 10 - 10, 6 - 3) = (3, 0, 3).
So, the equation of the line passing through M(1, 10, 3) and having the direction vector D = (3, 0, 3) is:
x = 1 + 3t,
y = 10 + 0t = 10,
z = 3 + 3t.
Therefore, the equation of the line is:
x = 1 + 3t,
y = 10,
z = 3 + 3t.
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QUESTION 4 Refer to the map of South Africa below and answer the following questions. ATLANTIC OCEAN 4.1 4.2 W- 4.3 N S • Springbok Lamberts Bay Saldanha Baylo Cape Town • Upington Calvinia Beaufort Weste Stellenbosch- Agulhas Vryburg sna Pretoria Johannesborg o Kimberley Bloemfontein Colesburgo Polokwane o Graaf-Reinet ... Hogsback LESOTHO Sabie o Badplaas Port Elizabeth Bergville REast London Durban Port St Johns St. Lucia INDIAN OCEAN 1:15 000 000 What type of the scale is given in the diagram and interpret the given scale? Write down the general direction of Badplaas from Colesburg. Use the given scale and determine the actual straight line distance between East London and Bloemfontein. Show ALL calculations and give your answer in km. In which province is Stellenbosch on the map? What is the probability that this province will be randomly selected in South Africa? Write your answer correct to TWO decimal places. (3) (2) 3 05 (4) (3
The given text presents a map of South Africa with various locations marked. However, important information such as the scale of the map and the number of provinces is missing. Without the scale, we cannot accurately determine distances or calculate probabilities. Similarly, the absence of information regarding the provinces prevents us from calculating the probability of selecting a specific province. Therefore, based on the given text, we can only answer the first two questions, which involve the type of scale and the general direction between two locations.
1. The type of scale given in the diagram is a ratio scale, specifically a linear scale. It represents the relationship between map distance and actual distance in a straight line.
Interpretation of the given scale:
The scale on the map is not clearly visible in the provided text. However, it is typically written as a fraction or ratio, where the numerator represents the map distance and the denominator represents the corresponding actual distance on the ground. For example, a scale of 1:1,000,000 means that 1 unit on the map represents 1,000,000 units in the real world.
2. The general direction of Badplaas from Colesburg is to the northeast.
3. To determine the actual straight-line distance between East London and Bloemfontein, we would need the scale from the map. However, the scale is not provided in the given text, making it impossible to calculate the distance accurately.
4. Stellenbosch is located in the Western Cape province on the map.
5. To calculate the probability of randomly selecting the Western Cape province in South Africa, we would need the total number of provinces in South Africa and the number of provinces that belong to the Western Cape. However, this information is not provided in the given text, so it is not possible to calculate the probability.
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Complete the equations. 95 × 1 0^3 =? 95 × 1 0^4=? 95×10^5 =?
Answer:
95 × 10^3 = 95000
95 × 10^4 = 950000
95 × 10^5 = 9500000
i need the answer for this asap Please!
[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]
is the equation of the given system.
Equation of the line using the coordinates (-3, 0) and (0, 3), we get:
slope = (3 - 0) / (0 - (-3)) = 1
Now we have the slope of the line. Next, we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
Using the point (-3, 0) and the slope we just found (which is also the slope of the line passing through the point (0, 3)), we get:
y - 0 = 1(x - (-3))
Simplifying, we get:
y = x + 3
Therefore, the equation of the line passing through (-3, 0) and (0, 3) is y=x+3.
Similarly, the equation of the line passing through (1, -1) and (0, -4) is y = -3x + 2.
Thus, from the graph the equation of the system is,
[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]
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A certain manufacturing concern has total cost function C = 15+9x-6x²+x? Find x, when the total
Answer:
Step-by-step explanation:
Total cost function, C = 15+9x-6x²+x
By differentiation,
dc/dx= 9-12x²+1
but
dc/dx= 0
9-12x²+1 = 0
-12x = -10
x=10/12
x=5/6
Given PU-UR, and the radius of the circle is 55, find x and UT.
10. x.
11. UT.
Show work
Answer:
10. x = 4
11. UT = 44
Step-by-step explanation:
You want the value of x and the length of segment UT that bisects chord PR at point U into halves marked UP = (9x -3) and UR = (7x +5). The radius of circle T is 55 units.
10. ChordPoint U is the midpoint of chord PR, so ...
UP = UR
9x -3 = 7x +5
2x = 8 . . . . . . . . . add 3-7x
x = 4 . . . . . . . . divide by 2
11. UTSegments UP, UT and TP form a right triangle with one leg ...
UP = 9(4) -3 = 33
and hypotenuse 55.
We observe that the ratio of these measures being 33/55 indicates triangle PUT is a 3-4-5 right triangle, with scale factor 11. That means UT is 4·11 = 44 units.
UT = 44 units
__
Additional comment
Recognizing triangles made from Pythagorean triples, such as {3, 4,5}, {5, 12, 13}, {7, 24, 25}, or {8, 15, 17} can save a lot of work. If you don't recognize these, you can find the missing side length from ...
TP² = UP² +UT²
UT = √(TP² -UP²) = √(55² -33²) = √1936 = 44
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3. It took an average of 20 days for a car dealership to sell a new car. Due to the current shortage in the new car market, you believe it is now quicker to sell a car. You take a sample of 30 recently sold cars and find that it took an average of 15 days to sell. You know the population standard deviation is 12 days and it is fairly stable. Test your hypotheses at the 5% significance level using the p-value approach. Follow the 4-step procedure and show your work.
Answer to the given Hypotheses is : The current shortage in the new car market has made it quicker to sell a car.
In this scenario, we have to determine if the current shortage in the new car market has affected the time it takes a car dealership to sell a new car. To answer this question, we will use the p-value approach.
First, we will determine the null and alternative hypotheses. The null hypothesis (H₀) is that the average time it takes to sell a car has not changed, while the alternative hypothesis (H₁) is that the current shortage in the new car market has made it quicker to sell a car.
H₀: μ = 20
H₁: μ < 20
Second, we will choose the appropriate test statistic and determine the level of significance. In this case, we will use a one-sample t-test, as the population standard deviation is known, and you will use a 5% level of significance (α = 0.05).
Third, we will calculate the test statistic and the p-value. The test statistic is calculated by dividing the difference between the sample mean and the hypothesized population mean by the standard error of the mean.
t = (x' - μ) / (σ / √n)
t = (15 - 20) / (12 / √30)
t = -2.89
Using a t-distribution table with 29 degrees of freedom, the p-value is 0.004.
Since the p-value is less than the level of significance, we reject the null hypothesis and conclude that the current shortage in the new car market has made it quicker to sell a car.
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Find the area of the following figure. Round to the nearest hundred if necessary.
11 cm
A= type your answer...
The area of the semicircle is 47.5 square centimeters
We have to find the area of the semi circle
The diameter of the semicircle is 11 cm
Radius is half of the diameter
Radius = 5.5 cm
Let us find the area of semicircle by formula 1/2(πr²)
Radius = 1/2×3.14×(5.5)²
= 1/2×3.14×30.25
=47.4925 square centimeters
Hence, the area of the semicircle is 47.5 square centimeters
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The table of values below represents a linear function and shows the amount of snow that has fallen since a snowstorm began. What is the rate of change?
Snowfall Amount
Length of Snowfall
(hours)
Amount of Snow on the Ground
(inches)
0
3.3
0.5
4.5
1.0
5.7
1.5
6.9
2.0
8.1
1.2 inches per hour
2.4 inches per hour
3.3 inches per hour
5.7 inches per hour
The average rate of change for this problem is given as follows:
2.4 inches per hour.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.
The change in the output is given as follows:
8.1 - 3.3 = 4.8.
The change in the input is given as follows:
2 - 0 = 2.
Hence the average rate of change is given as follows:
4.8/2 = 2.4 inches per hour.
Missing InformationThe table is given by the image presented at the end of the answer.
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1.62,16.2,15/20 greatest to least
Answer
The order of the number from greatest to least is 1.62, 15/20, 16.2%
Step-by-step explanation
Given: 1.62 16.2% 15/20
To order these data in descending order (i.e. from highest to least), follow the steps below
1. Convert all numbers to decimals
1.62
16.2% = 16.2/100
16.2% = 0.162
15/20 = 0.75
So, the number are 1.62, 0.162, 0.75
2. Compare the three decimals and arrange in descending order
1.62 > 0.75 > 0.162
This means that 1.62 is greater than 0.75 and 0.75 is greater than 0.162
By substituting 16.2% for 0.162 and 15/20 for 0.75, the order of the number from greatest to least is
1.62, 15/20, 16.2%
Which of the following is the equation of a line with a slope of -5/9
Answer:
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Step-by-step explanation:
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What function is the inverse of the exponential function y = 4*?
OA
1
y=z.
OC y = log₂ 4
O B. y=(¹)²
O
D. y = log, z
The function that is the inverse of the exponential function y = 4ˣ is lnx/ln4
The inverse of a function f is denoted by [tex]f^{-1[/tex] and it exists only when f is both one-one and onto function. Note that [tex]f^{-1[/tex] is NOT the reciprocal of f. The composition of the function f and the reciprocal function [tex]f^{-1[/tex] gives the domain value of x.
(f o [tex]f^{-1[/tex] ) (x) = ( [tex]f^{-1[/tex] o f) (x) = x
For a function 'f' to be considered an inverse function, each element in the range y ∈ Y has been mapped from some element x ∈ X in the domain set, and such a relation is called a one-one relation or an injunction relation.
The standard exponential function is given as y = abˣ
Given the function,
y = 4ˣ
Replace y with x
[tex]x = 4^y[/tex]
Make y the subject of the formula,
[tex]lnx = ln4^y\\\\lnx = yln4[/tex]
Divide both sides by ln4
lnx/ln4 = y
Hence the function that is the inverse of the exponential function y = 4ˣ is lnx/ln4
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Find the area of the shape
The area of the given figure is 27.5 square centimeter which has a rectangle and triangles
The given figure has a rectangle and triangles
The area of rectangle is length times width
Area of rectangle =5×4
=20 square centimeter
Area of triangle =1/2×base×height
=1/2×2.5×3
=7.5/2
=3.75 square centimeter
As there are two triangle = 2(3.75)
=7.5 square centimeter
Total area = 7.5+ 20
=27.5 square centimeter
Hence, the area of the given figure is 27.5 square centimeter
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sin 78° find the value
Answer:
Approx. 0.2079
Step-by-step explanation:
To find the value of sin 78°, we can use a scientific calculator or a trigonometric table. However, I can provide an approximate value using the trigonometric identity:
sin(90° - θ) = cos(θ)
In this case, we can use the identity sin(90° - 78°) = cos(78°). Since the cosine of 78° can be determined more easily, we can calculate that instead.
cos 78° ≈ 0.2079
Therefore, sin 78° is approximately equal to 0.2079.
The data set represents the number of miles Mary jogger each day for the past nine days.
Answer: 0
Step-by-step explanation: It is furthest away from the other numbers with a difference of at least 5. If plotted in a table it would visually be seen to be further away from the general trend.
What is the probability that either event will occur? 3 A 18 B 15 P(A or B) = P(A) + P(B) P(A or B) = [?] Enter as a decimal rounded to the nearest hundredth.
Answer:
the probability that either event will occur is 0.92
Step-by-step explanation:
the probability that either event will occur is 0.92
What is the probability that either event will occur?
From the question, we have the following parameters that can be used in our computation:
Event A = 18
Event B = 15
Other Events = 3
Using the above as a guide, we have the following:
Total = A + B + C
So, we have
Total = 18 + 15 + 3
Evaluate
Total = 36
So, we have
P(A) = 18/36
P(B) = 15/36
For either events, we have
P(A or B) = 33/36 = 0.91666
Hence, the probability that either event will occur is 0.92 (rounded to nearest hundreth)
-57-31/x+3 what is x
Answer:
FACTOR
(−1)×2×3×5
2 or -150
Step-by-step explanation:
Which side measures will not make a triangle
With a triangle, the sum of any two side lengths must be greater than the third side length. If this is not true, then the side lengths cannot make a triangle. Let's go through each set of side lengths and determine which would and wouldn't work.
a. 3, 4, 8 - will not make a triangle
3 + 4 = 7 > 8 = false
3 + 8 = 11 > 4 = true
4 + 8 = 12 > 3 = true
b. 7, 6, 12 - will make a triangle
7 + 6 = 13 > 12 = true
7 + 12 = 19 > 6 = true
6 + 12 = 18 > 7 = true
c. 5, 11, 13 - will make a triangle
5 + 11 = 16 > 13 = true
5 + 13 = 18 > 11 = true
11 + 13 = 24 > 5 = true
d. 4, 6, 12 - will not make a triangle
4 + 6 = 10 > 12 = false
4 + 12 = 16 > 6 = true
6 + 12 = 18 > 4 = true
e. 4, 6, 10 - will not make a triangle
4 + 6 = 10 > 10 = false
4 + 10 = 14 > 6 = true
6 + 10 = 16 > 4 = true
Hope this helps!
Elijah wraps a gift box in the shape of a right rectangular prism. The figure below shows a net for the gift box.How much wrapping paper did he use, in square meters?
The amount of wrapping paper which Elijah used is equal to 812 m².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
Surface area of a rectangular prism = 2(LH + LW + WH)
Where:
SA represents the surface area of a rectangular prism.L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given side lengths into the formula for the surface area of a right rectangular prism, we have the following;
Surface area of a right rectangular prism = 2[3 × 10 + (10 × 12 × 2) + (13 × 12 × 2)]
Surface area of a right rectangular prism = 812 m².
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Help
please
please
please
Answer: x=25 degrees
Step-by-step explanation:
25 degrees (blue) and x degrees (orange) are vertical angles. Vertical angles always equal each other.
(80 degrees {green} is just there to throw you off)
At the neighborhood block party, Joel served 1/6 of a gallon of hot chocolate and 1/12 of a
gallon of apple cider. How much more hot chocolate than apple cider did Joel serve?
Write your answer as a fraction or as a whole or mixed number.
gallons
Answer:
1/12 gallons
Step-by-step explanation:
We can determine how much more hot chocolate than apple cider die Joe serve by subtracting 1/12 from 1/6.
Step 1: Since 1/12 has the bigger denominator and 6 * 2 = 12, let's give 1/6 the same denominator as 1/12 by multiplying the entire fraction by 2/2
(1/6) * (2/2) = 2/12
Step 2: Now we can subtract 1/12 from 2/12:
2/12 - 1/12 = 1/12
Thus, Joel served 1/12 more gallons of hot chocolate than apple cider.
Find the length of the three missing sides in the rhombus below.
y
Z
X
82
As all sides of a Rhombus are of equal length, the length of the missing sides are 82
Property of a RhombusThe property of a Rhombus required for answering this question is associated with the length of it's sides. A Rhombus has four sides with the length of all these sides being equal.
This means that with the length of one of it's sides being 82 , the length of the remaining 3 sides would be 82 as well.
The length of sides x = y = z = 82. Hence, x, y and z are 82
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Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
All the equations which are equivalents are,
⇒ 2 + x = 5
⇒ x + 1 = 4
⇒ Negative 5 + x = negative 2
We have to given that;
All expressions are,
2 + x = 5
x + 1 = 4
9 + x = 6
x + (-4) = 7
-5 + x = -2
Now, We can simplify all the expressions as;
⇒ 2 + x = 5
⇒ x = 5 - 2
⇒ x = 3
⇒ x + 1 = 4
⇒ x = 4 - 1
⇒ x = 3
⇒ 9 + x = 6
⇒ x = 6 - 9
⇒ x = - 3
⇒ x + (-4) = 7
⇒ x = 7 + 4
⇒ x = 11
⇒ -5 + x = -2
⇒x = - 2 + 5
⇒ x = 3
Thus, All the equations which are equivalents are,
⇒ 2 + x = 5
⇒ x + 1 = 4
⇒ Negative 5 + x = negative 2
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pls help, due today!
Answer:
A: Function 1
B: Function 4
C: Function 2
Explanation A:
In order to solve this problem, you will have to find the slope for each function.
1st Function: For the first function, you will need to find 2 points, let's use (0, -4) and (1, 1). Remember slope is rise over run, so you would count the spaces from the first point to the second, it rises (y-axis) 5 points and runs (x-axis) 1 point. Which would give you 5/1 = 5. Function 1's slope is 5.
2nd Function: Same equation, rise over run, or y over x, so we need to find the pattern on each side. For the x-values, we can see starting from the first point that they increase by one, -2 to -1 to 0, and for the whole x-values, so 1 will be our run, since it is the x-value. For the rise, or y-values, we can see a pattern of -1 starting from the top going towards the bottom. Now, we can rise over run, -1/1 = -1
3rd Function: Slope is -4, as the equation is y = mx + b, and m stands for slope.
4th Function: Says slope is 2.
Now that we know all the slopes, we can see that Function 1's slope is the greatest.
Explanation B:
For this problem, we will have to find the y-intercept for all the functions, this means where the x-value is 0, so that the y-value will be right on the y-axis.
Function 1: We can see that the function intercepts the y-axis at (0, -4), it's y-intercept being -4.
Function 2: Where the x-value is 0, we can find the y-intercept, which is (0, 1). Making the y-intercept 1.
Function 3: Following the y = mx + b format, the b is the y-intercept, so it is -2.
Function 4: Gives you the y-intercept as 5.
In the end, the only function with a y-intercept greater than 4 is Function 4.
Explanation C:
Since we already know the y-intercepts from the previous problem, we only need to see which one is closest to 0. In this case, it would be Function 2 with a y-intercept at -1, only 1 unit off of 0, making it the closest.