Considering the 12-face diagonals of a rectangular block, 30 pairs of these diagonals are skew lines.
In a rectangular block, there are a total of 12 face diagonals. These diagonals are formed by connecting the opposite vertices of each face of the block. To determine the number of pairs of skew lines among these diagonals, we can consider the following:
There are 6 faces in a rectangular block, each with 2 diagonals.
Every diagonal on one face is unique and does not intersect with any other diagonal on the same face.
However, diagonals on opposite faces are parallel to each other and therefore, do not form skew lines.
So, we will be selecting one diagonal from one face, so we have 6 options, then we select another diagonal from another face, which would be 5 options, and we repeat this process until we exhaust all the diagonals. This will give us 6*5 = 30 pairs of skew lines.
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George is building a fence. He builds his fence at a constant rate of 1/3 section of fence every 1/2 hour. At his ate, what fraction represents the section of fence George can build per hour?
someone help me please > .
The fraction of fence that George can build at a constant rate of 1/3 in 1 hour is 2/3.
How is division of fractions performed?Divide implies to distribute anything evenly. After learning about whole number division, let's move on to fraction division. The numerator and the denominator are the two components of a fraction. Fractional division is roughly the same as fractional multiplication. When dividing fractions, we multiply the smaller of the two fractions by their reciprocals.
Given that George builds the fence at a rate of 1/3 section per 1/2 hour.
The fraction of fence that George build per hour can be obtained as:
1/3 = 1/2 hour
x = 1 hour
Using the butterfly method for multiplication we have:
x = (1/3) ÷ (1/2)
x = (1/3) × (2)
x = 2/3
Hence, the fraction of fence that George can build at a constant rate of 1/3 in 1 hour is 2/3.
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A 2. 0\, \text {kg}2. 0kg2, point, 0, start text, k, g, end text cart moving right at 5. 0\,\dfrac{\text m}{\text s}5. 0 s m 5, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction on a frictionless track collides with a 3. 0\,\text {kg}3. 0kg3, point, 0, start text, k, g, end text cart initially at rest. The 2. 0\, \text {kg}2. 0kg2, point, 0, start text, k, g, end text cart has a final speed of 1. 0\,\dfrac{\text m}{\text s}1. 0 s m 1, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction to the left. What is the final speed of the 3. 0\,\text {kg}3. 0kg3, point, 0, start text, k, g, end text cart?
4 m/s is the final speed of the 3.0 kg cart.
When two bodies of different masses move together each other and have a head-on collision, they travel in the same or different directions after a collision. This phenomenon is called the conservation of momentum.
The external force is not working here, so the initial momentum is equal to the final momentum. For elastic collision, the final velocities are different for both bodies.
m₁u₁ +m₂u₂ = m₁v₁ +m₂v₂
A 2.0 kg cart moving right at 5.0 m/s on a frictionless track collides with a 3.0 kg cart initially at rest. The 2.0 kg cart has the final speed of 1.0 m/s to the left.
Substitute the values, m₁ = 2kg, m₂ =3kg, u₁ =5 m/s and u₂ =0 m/s, then the final velocity will be
3x0 +2x5 = -2x1 + 3v₂
v₂ = 4 m/s
Thus, the final velocity 3.0 kg cart is 4 m/s.
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A small business invests $10,000 in equipment to produce
a new soft drink. Each bottle of the soft drink costs $0. 65 to
produce and is sold for $1. 20. How many bottles must be
sold before the business breaks even?
The total number of 18,181 bottles should be sold to break the business even based on the investment.
Firstly calculating the profit earned on each soft drink. Based on this, the formula for profit to be used is -
Profit = Selling price - cost price
Keep the values in formula
Profit = 1.20 - 0.65
Performing subtraction on Right Hand Side of the equation
Profit = $0.55
For the business to break even, the total profit earned by company must be equal to the investment. So, let the number of bottles required to break even the business be x.
0.55 × x = 10,000
Performing multiplication on Left Hand Side of the equation
0.55x = 10000
x = 10,000/0.55
Performing division on Right Hand Side of the equation
x = 18181.8
Rounding off = 18181.
Thus, 18,181 bottles need to be sold.
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An approximate solution to an equation is found using this iterative process.
(x₂)²³-5
and x₁ = -1
10
Xn+1 =
a) (i) Work out the value of x2
(ii) Work out the value of x3
b) Work out the solution to 6 decimal places.
a) (i) Working out the value of x2 gives -6
(ii) Working out the value of x3 gives -11
b) Working out the solution to 6 decimal places is undefined.
How do we determine these values?a) (i) To find the value of x2, we substitute x1 = -1 into the iterative equation:
x2 = ((-1)^(2/3)) - 5 = (-1)^(2/3) - 5 = -1 - 5 = -6
(ii) To find the value of x3, we substitute x2 into the iterative equation:
x3 = ((-6)^(2/3)) - 5 = (-6)^(2/3) - 5 = -6 - 5 = -11
b) To find the solution to 6 decimal places, we would need to continue iterating the process until the desired level of accuracy is reached. But in this case, the equation does not have solution as the equation is not defined for negative values of x. The cube root of a negative number is complex numbers and not real numbers.
Therefore, the values are -6, -11, and undefined respectively.
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If DE = x + 9, EF = 9, and DF = 7x, what is DE?
Answer: 12
Step-by-step explanation:
x + 9 + 9 = 7x
9 + 9 = 6x
18 = 6x
x = 3
DE = x + 9 = 3 + 9 = 12 :>
Answer:
DE = 12
Step-by-step explanation:
DF = DE + EF
7x = x+9 + 9
7x = x + 18
6x = 18
x = 3
DE = 3 + 9
DE = 12
What is the length of every median in an equilateral triangle whose side length is 5?
The length of every median in an equilateral triangle whose side length is 5 is; 4.33
What is the length of the triangle median?In geometry, a median of a triangle is defined as a line segment joining a vertex to the midpoint of the opposite side which therefore bisects that side.
This tells us that every single triangle has exactly three medians, with one from each vertex, and as a result they all intersect each other at the centroid of the triangle.
The median joins a vertex and the opposite side's midpoint. Thus;
side = 5
half side = 5/2 = 2.5
Using Pythagoras theorem;
a² + b² = c²
Thus;
2.5² + b² = 5²
b² = 18.75
b = √18.75
b ≈ 4.33
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you work at a relator firm and your boss asked to pull out information about houses sold in the last week, such as price, size, age, number of rooms, etc. what type of data is this? panel (longitudinal) data time-series data cross-sectional data none of the above all of the above
This type of data is cross-sectional data.
In statistics and econometrics, cross-sectional data, or a cross-section of a study population, is a type of data gathered by monitoring numerous subjects (such as individuals, firms, countries, or regions) at one point or throughout the course of time. It's also possible that the analysis disregards variations in time. Cross-sectional data analysis often entails contrasting the variations among pre-selected respondents.
Time series data, in which the same small-scale or aggregate entity is seen multiple times in time, differs from cross-sectional data. A different kind of data called panel data (also known as longitudinal data) combines the concepts of cross-sectional and time series data and examines how the topics (firms, people, etc.) develop throughout a time series. Panel data differs from cross-sectional data that has been pooled over time.
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witch is cheaper 50 head of cattle for $24,500 or 37 head of cattle for $18,870
Answer: 50 cattle for 24500 is cheaper than 18870 for 37 cattle
Step-by-step explanation: divide 24500/50= $490 per cattle
vs
18870/37= $510 per cattle
proving that 24500 for 50 is overall a better deal
The functions f, g and h on the set of real numbers are defined by f(x) = x² + 1, g(x) = 2x - 3 and h(x) = 4x + 5 respectively. Determine the formulae for the composite functions:
(a) f [g(x)]
(b) g [h(x)]
(c) h [g {f(x)} ]
A metal oxide reacts chemically with water to form a base in the reaction shown below.
If the temperature of the metal oxide and water solution is increased, this will most likely
A.
reverse the chemical reaction.
B.
increase the rate of chemical change.
C.
produce an acid.
D.
decrease the rate of chemical change.
Gabriella and Ian are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Gabriella is 550 miles away from the stadium and Ian is 950 miles away from the stadium. Gabriella is driving along the highway at a speed of 25 miles per hour and Ian is driving at speed of 50 miles per hour. Let � G represent Gabriella's distance, in miles, away from the stadium � t hours after noon. Let � I represent Ian's distance, in miles, away from the stadium � t hours after noon. Graph each function and determine the number hours after noon, � , t, when Gabriella and Ian are the same distance from the stadium.
Answer: Gabriella's distance from the stadium is modeled by the function G(t) = 550 - 25t.
Ian's distance from the stadium is modeled by the function I(t) = 950 - 50t.
To find the number of hours after noon when Gabriella and Ian are the same distance from the stadium, we need to set the two equations equal to each other and solve for t:
G(t) = 550 - 25t = I(t) = 950 - 50t
Combining like terms we get:
25t = 400
t = 16
So, 16 hours after noon, Gabriella and Ian will be the same distance away from the stadium.
To graph the functions, we can substitute different values of t into the equations to find the corresponding values of G(t) and I(t). Then we can plot the points on a coordinate plane and connect them to form the graph of the two functions.
It is important to note that we are assuming that both Gabriella and Ian don't make any stops, so the speed is constant through the whole trip and no time is wasted.
Step-by-step explanation:
what is the constant second difference of f(x) = x^2?
Answer:
Step-by-step explanation: make a table of values, followed be a column for the 1st and another for the 2nd difference
0 0
1 1 -- 1
2 4-- 3 -- 2
3 9 --5 -- 2
4 16 --7 -- 2
5 25 --9 --2
6 36 ------- etc
looks like the 2nd difference is 2
Please Help me!!!!!!!!!!!!!
Answer: You have a 1/6 chance to roll a 2 when you role a dice since there is 6 sides
Step-by-step explanation:
2. MODELING REAL LIFE A dumpster rental fee is $350 for
the first week and $10 for each additional day or any portion
of a day. Write and graph a step function that represents the
cost y (in dollars) to rent the dumpster for x days.
The required function that represent the given situation is y = 10x + 350.
What is equation of line?In order to write the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Find two locations on the line and create a sloping triangle connecting the two places.
According to question:Rental fee is $350 for the first week and $10 for each additional day or any portion of a day.
So, The equation that represent this problem is;
Let cost y (in dollars) to rent the dumpster for x days.
y = 350 + 10x (y in dollar)
y = 10x + 350
Here, slope of function is 10 and y- intersect is 350.
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Where there is a jump at x = 7 from y = 350 to y = 350 + 10 * (x - 7). Before x = 7, the cost would remain constant at $350. After x = 7, the cost would increase by $10 for each additional day.
What is equation of line?In order to write the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Find two locations on the line and create a sloping triangle connecting the two places.The step function representing the cost to rent the dumpster for x days can be defined as follows:y(x) = 350, if 0 < x <= 7y(x) = 350 + 10 * (x - 7), if x > 7The graph of this step function would look like a piecewise function, where there is a jump at x = 7 from y = 350 to y = 350 + 10 * (x - 7). Before x = 7, the cost would remain constant at $350. After x = 7, the cost would increase by $10 for each additional day.To learn more about Equation of line refer::
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24÷h=6
h = 1, 3, 6, 8
an airline runs a commuter flight between two cities that are 720 miles apart. if the average speed of the plane is increased by 40 mph, the travek time is decraesed by 12 minutes. what speed is required to obtain this decrease in travel time?
The speed required to obtain this decrease in travel time is 360 mph.
Formula between speed, distance, and travel time
v = d/t
The formula to calculate distance is
d = v × t
v = the speed (mph)In the first condition
d₁ = v₁ × t₁
720 = v × t₁
t₁ = 720/v
In the second condition
d₂ = v₂ × t₂
720 = (v + 40) (t₁ - 0.2)
720 = (v + 40) (720/v - 0.2)
720 = v (720/v - 0.2) + 40 (720/v - 0.2)
720 = 720 - 0.2v + 28,800/v - 8
0.2v + 8 - 28,800/v + 720 - 720 = 0
0.2v + 8 - 28,800/v = 0
0.2v² + 8v - 28,800 = 0
v² + 40v - 144,000 = 0
Factorize quadratic equations
v² + 40v - 144,000 = 0
v² + 400v - 360v - 144,000 = 0
v (v + 400) - 360 (v + 400) = 0
(v + 400) (v - 360) = 0
v + 400 = 0 or v - 360 = 0
v = - 400 v = 360 mph
(negative speed is impossible)
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Which equation is not a linear function?
Answer: B) 2x²-3y=9
Step-by-step explanation:
This is not a linear function because the equation for a linear function is mx+b=y this means that x cannot have an exponent which in B it does.
What is the slope of the line that passes through the points (1,6) and (1, 31)? Write
your answer in simplest form.
A line passing between the points (1, 6) and (1, 31) has an undefined slope.
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
where m is the slope of the line, (x1, y1) and (x2, y2) are two points on the line.
In this case, we have (x1, y1) = (1, 6) and (x2, y2) = (1, 31). Plugging these values into the formula:
m = (31 - 6) / (1 - 1)
Hence, the denominator is zero, the slope is undefined. This means that the line is a vertical line and has no slope.
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Quadrilateral ABCD has coordinates
A(0,2) B(3,4) C(4.2) D(3,0)
Determine the coordinates of the vertices of A’B’C’D’ after a translation along vector
< 2, -3 >
The coordinates of the vertices of quadrilateral A’B’C’D’ after a translation along vector <2, -3> is: A. A' (-2, 5), B' (1, 7), C' (2, 5), D' (1, 3).
What is a translation?In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.
Note: We would move in the opposite direction of the given vector <2, -3>.
By applying a translation to the pre-image of quadrilateral ABCD vertically up by 3 units and horizontally left by 2 unit, the coordinates of the image of triangle A'B'C' include the following:
(x, y) → (x - 2, y + 3)
Coordinate A = (0, 2) → Coordinate A' (0 - 2, 2 + 3) = (-2, 5)
Coordinate B = (3, 4) → Coordinate B' = (3 - 2, 4 + 3) = (1, 7)
Coordinate C = (4, 2) → Coordinate C' = (4 - 2, 2 + 3) = (2, 5)
Coordinate D = (3, 0) → Coordinate D' = (3 - 2, 0 + 3) = (1, 3)
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let sn be the sum of the first n terms of an arithmetic sequence that has a common difference of 2. the quotient s3n/sn does not depend on n. what is
d=2 and (a-1/2)2=2 hence 2a-1=2 hence a=3/2=first term and the common difference=d=2
S1, S2,... Sn can be written as:
A (first term) (first term)
A+r (r is a common difference) (r is a common difference),
A+2r
A+3r
A +(n-1)r
It is possible to calculate the sum as A +A +... +A (n times) + r +2r +3r.... +(n-1)r.
Giving n*A +r*(1+2+3....+n-1)
1+2+3….+n-1= n*(n-1)/2 =n^2 - n/2
The first N terms are added together as follows: n*A + r/2 *n2 - r*n/2
= r/2 *n^2 + (A - r/2)*n
This equals n2 - 2n for any n given the questions, so
A-r/2 = 2 AND r/2 = 1
=> r = 2 and A = 3 with r = 2
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Full question
The sum of the first n terms of an arithmetic sequence is given by Sn= n^2-2n. What are the first term and the common difference?
In ΔQRS, r = 83 cm, mm∠R=161° and mm∠S=5°. Find the length of q, to the nearest centimeter.
The required value of side q is 117. 05 cm for the triangle ΔQRS.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
Given that,
In triangle ΔQRS, r = 83 cm, mm∠R=161° and mm∠S=5°
To find the length of the side q,
The third angle can be calculated using the angle sum property as;
angle Q + angle R + angle S = 180 degrees
angle Q + 161 degrees + 5 = 180 degrees
angle Q = 180 - (166) degrees
angle Q = 14 degrees
To find the length of q we shall apply the Sine rule.
q / Sin Q = r / Sin R
q / Sin 14 = 83 / Sin 161
Now cross multiplication we will get;
q = (83 x Sin 14 ) / Sin 161
q = 117. 05 cm (approximately)
So, the length of q is 117. 05 cm.
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asap. which is 1/3 + 1/4
A mass is rotated from rest at a radius of 4.0 m from the center of rotation to an angular velocity of 0.80 rad/s in 1.5 s.
a) What is the angular acceleration, α?
b) What is the tangential acceleration, a, at r = 4.0 m?
c) What is the radial (centripetal) acceleration, atang, at r = 4.0 m?
a) Angular acceleration is 0.53 rad/s^2
b) Tangential acceleration is 2.56 m/s^2
c) Centripetal acceleration is 2.56 rad/s^2
What is the angular acceleration?We know that the angular acceleration can be obtained from the equations of circular motion. We know that we have the equation for the circular motion as;
α = ω2 - ω1/t
α = angular acceleration
ω2 = final angular velocity
ω1 = initial angular velocity
α = 0.8 - 0/1.5
= 0.53 rad/s^2
b) The tangential acceleration = v^2/r
But V = ωr
V = 0.8 * 4
V = 3.2 m/s
Then;
(3.2)^2/4
= 2.56 m/s^2
c) Centripetal acceleration = ω^2 r
= (0.8)^2 * 4
= 2.56 rad/s^2
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Which of the folloHow many solutions exist for the given equation?
12x + 1 = 3(4x + 1) – 2wing shows the graph of y = –(2)x – 1?
The equation 12x + 1 = 3(4x + 1) – 2 have infinite solutions
what is an equations?An equation is a mathematical statement that shows that two mathematical expressions are equal. In other terms we say that an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
To solve this problem, we can proceed to solve this equation by collecting like terms and then dividing through to know the coefficient of x.
⇒ 12x + 1 = 3(4x + 1) – 2
⇒ 12x + 1 = 12x + 3 – 2
⇒ 12x + 1 = 12x + 1
So that, The equation have infinite solutions.
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This problem have two question:
1) How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) – 2
2) Which of the following shows the graph of y = –(2)x – 1?
we are giving the answer of question no.1
Write thirty million,two hundred and seventy-one thousand in figures
Answer:
3,271,000
Step-by-step explanation:
There is no explanation for this problem.
Answer: is 3,271,000
it rained on a hot summer afternoon and a puddle formed. after several hours, the puddle was gone. identify and describe the two processes made the puddle form and then disappear?
The two processes that caused the puddle to form and then disappear were evaporation and infiltration.
Evaporation is the process in which liquid water turns into vapor and rises into the atmosphere. It occurs when the air around the puddle is warmer than the liquid, causing the water molecules to move faster and spread out. This allows the water to evaporate into a gas. The rate of evaporation is proportional to the water surface area and the difference in temperature between the air and the water.
Infiltration is the process in which water is absorbed into the ground. It occurs when the water in the puddle is drawn into the soil due to gravity and capillary action. This process is influenced by the soil type, the amount of water, and the soil's porosity. The rate of infiltration is proportional to the soil's permeability, which is a measure of how quickly water can move through the soil.
The combination of evaporation and infiltration caused the puddle to form and then disappear. As the water evaporated, the puddle shrank until it was gone. Simultaneously, the water that remained was absorbed into the ground until all of the puddle was gone.
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Help w math homework pls
The analysis of the figure, comprising of concentric circles, in the shape of a hollow cylinder cross-section is as follows;
12) Part A; The area of the deck is about 691.15 square feet
Part B; The minimum number of treatment gallons needed is four gallons
Part C; The total cost to cover the patio with weather treatment is $143.8
What is the cross-sectional area of the shaded part (material) of a hollow cylinder?The cross-sectional area of a hollow cylinder is; A = π·(R² - r²)
Where;
R = The radius of the outer circle of the cylinder
r = The radius of the smaller (open) circle at the center of the cylinder.
Part A
The outside diameter of the deck, D = 32 feet
The radius of the swimming pool = 6 feet
The area of the deck, A = The area of the circle with diameter 32 feet less the area of the swimming pool
A = π·D²/4 - π·r²
A = π × 32²/4 - π × 6² = 220·π ≈ 691.15
The area of the deck ≈ 691.15 square feetPart B
The area covered per gallon of weather treatment = 204.5 square feet per gallon
The minimum number of gallons of weather treatment, n, that will need to be purchased to cover the deck with weather treatment is therefore;
n ≈ 691.15/204.5 ≈ 3.38
Therefore, the minimum number of gallons that needs to be purchased, since 3 gallons is not enough, is four gallons of weather treatment
4 gallons of weather treatment are neededPart C; The cost per gallon of weather treatment excluding tax = $35.95
The total cost in dollars excluding tax to cover the patio with weather treatment, C, is presented as follows;
C = Number of gallons needed × Cost per gallon
Number of gallons needed to cover the deck = 4 gallons
Cost per gallon = $35.95/gallon
Therefore;
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Belvedere is a personal trainer and uses two different workout plans with his clients. Plan I takes 50 minutes to complete and Plan Il takes 35 minutes. Belvedere trained 6 clients using Plan Il last weekend. How many clients (×) did Belvedere train using Plan I if the total training time was 310 minutes?
The number of clients that Belvedere train using Plan I if the total training time was 310 minutes will be 2 clients
How to explain the equation?From the information, Belvedere is a personal trainer and uses two different workout plans with his clients. Plan I takes 50 minutes to complete and Plan Il takes 35 minutes. Belvedere trained 6 clients using Plan Il last weekend.
The number of clients can be given as x.
The number of clients that Belvedere train using Plan I if the total training time was 310 minutes will be:
50x + 35(6) = 310
50x + 210 = 310
Collect the like terms
50x = 310 - 210
50x = 100
Divide
x = 100 / 50
x = 2
The clients are 2.
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"Graph the following lines on the sketchpad."
hi please explain how i graph this
The graph of equations y - 1 = - 3(x - 2) and y = - 3x + 7 is illustrated below with the attached image.
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, An equation of a line y - 1 = - 3(x - 2) in point-slope form.
y - 1 = - 3x + 6.
y = - 3x + 7.
The next equation is 3y = x - 9.
y = (1/3)x - 3.
Now, The graph of these two equations can be sketched by assuming two or more arbitrary values of 'x' that correspond to different values of 'y'.
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An artist draws a stained glass window to scale. The actual window will have a length of 5ft and a width of 2ft. The scale from the drawing to the window is 2in to 1 ft. What is the width of the drawing?
An artist draws a stained glass window to scale. The actual window will have a length of 5ft and a width of 2ft. The scale from the drawing to the window is 2in to 1 ft. The width of the drawing is 4 inches.
How do you determine the size of the width?To find the width of the drawing, we need to determine how much the width of the window has been scaled down on the drawing.
We know that the scale of the drawing is 2 inches to 1 foot, so for every 1 foot in the window, there are 2 inches in the drawing.
Since the width of the window is 2 feet, and the scale is 2 inches to 1 foot, the width of the drawing is (2 inches/foot) * (2 feet) = 4 inches.
Therefore, the correct answer is as given above 4 inches.
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