[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-4 +3}{2} \implies \cfrac{ -1 }{ 2 } \implies - \cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{1}) \implies y +3 = - \cfrac{ 1 }{ 2 } ( x -1) \\\\\\ y+3=- \cfrac{ 1 }{ 2 }x+\cfrac{1}{2}\implies y=- \cfrac{ 1 }{ 2 }x+\cfrac{1}{2}-3\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 2 }x-\cfrac{5}{2} \end{array}}[/tex]
Answer: First, let's find the slope of the line:
slope = (change in y) / (change in x)
slope = (-4 - (-3)) / (3 - 1)
slope = -1/2
Now, let's choose one of the points, say (1,-3), and use the point-slope formula:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) are the coordinates of the point.
So, substituting in the values we get:
y - (-3) = (-1/2)(x - 1)
Simplifying this equation, we get:
y + 3 = (-1/2)x + 1/2
Subtracting 3 from both sides, we get:
y = (-1/2)x - 5/2
Therefore, the equation of the line that passes through the points (1,-3) and (3,-4) is y = (-1/2)x - 5/2.
Your welcome.
Step-by-step explanation:
What is the prisms volume? Show work
The volume of the triangular prism is 32.8 m³.
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
To find the volume of the triangular prism, we need to use the formula:
Volume = (Area of base) x Height
We are given the surface area of the prism, which includes the area of all five faces. However, we only need the area of the two triangular faces, since the base of the prism is a triangle.
The area of a triangle is given by the formula:
Area = (base x height) / 2
Substituting the given values, we have:
Area of each triangular face = (4.1 m x 2 m) / 2 = 4.1 m²
The total area of the two triangular faces is therefore:
2 x 4.1 m² = 8.2 m²
Now, we can use the formula for the volume of a prism:
Volume = (Area of base) x Height
Substituting the given values, we have:
Volume = (8.2 m²) x 4 m = 32.8 m³
Therefore, the volume of the triangular prism is 32.8 m³.
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i really need help on this please
The value of r(s(4)) is -33.
What is a function?
In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output.
To find the value of r(s(4)), we first need to find the value of s(4), and then use that as the input for the function r.
To find s(4), we substitute x = 4 into the expression for s(x):
s(4) = 3(4) - 1 = 12 - 1 = 11
Now that we have the value of s(4), we can use it as the input for the function r:
r(s(4)) = r(11) = -3(11) = -33
Therefore, the value of r(s(4)) is -33.
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Determine the lateral area of a triangular prism with a height of 20 centimeters (cm) and whose base is a right triangle with side lengths of 8cm,15cm, and 17cm. 416cm^(2) 675cm^(2) 731cm^(2) 800cm^(2)
A right triangle at the base of the a spherical structure with such a height of twenty centimeters (cm) has a lateral area of [tex]= 416 cm^2[/tex].
What distinguishes a triangular prism?There are 6 vertices, 9 edges, and 5 faces in a triangular prism. It contains 3 rectangle faces as addition to a pair of triangle-shaped faces. It is a polyhedron. The two triangle-shaped bases are parallel to one another.
How can we recognise a prism?A three-dimensional form with flat sides is referred to as a prism. It features two identically shaped and sized ends. From one end of the form to the other, it shares a comparable cross-section.
The triangle base's perimeter must be determined. The length of all 3 sides are added to determine the perimeter:
[tex]8 + 15 + 17 = 40[/tex]
The lateral area is,
[tex]2(8 * 20) + 2(15 * 20) + 2(17 * 20)[/tex]
[tex]= 416 cm^2[/tex]
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Urgent help is needed
The volume of the hemisphere with diameter 9 is approximately 76.0435 cubic units.
What is hemisphere ?
A hemisphere is a three-dimensional geometric shape that consists of half of a sphere. It is formed by slicing a sphere into two equal parts along a plane that passes through its center. The term "hemisphere" comes from the Greek words "hemi," meaning half, and "sphaira," meaning sphere.
A hemisphere has a curved surface that is a portion of a sphere's surface, as well as a flat circular base that is formed by the plane of the cut. The diameter of the base is equal to the diameter of the original sphere, and the radius is half of the diameter.
To find the volume of the hemisphere, we first need to know its formula. A hemisphere is half of a sphere, so its volume is half of the volume of a sphere with the same radius.
The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume and r is the radius.
Since the hemisphere has diameter 9, its radius is half of the diameter, which is:
r = 9/2 = 4.5
Substituting the value of r in the formula for the volume of a sphere, we get:
V = (4/3)π(4.5)³
V = (4/3)π(91.125)
V = 152.087
Since the hemisphere is half of a sphere with radius 4.5, its volume is half of the volume of that sphere, which is:
V_hemisphere = (1/2)V_sphere
V_hemisphere = (1/2)(4/3)π(4.5)³
V_hemisphere = 76.0435
Therefore, the volume of the hemisphere with diameter 9 is approximately 76.0435 cubic units.
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The school offered a chess club after school. In one class, 15 of the 25 students in the class signed up
for the club. If the rate stays constant across the school, how many students are in the whole school if 210 signed up for chess club?
The total number of students is calculated by dividing the total number of chess club sign ups by the proportion of students who signed up Therefore, 210/0.6 = 840 students in the school.
15 students out of 25 signed up for chess club.
Therefore, 15/25 = 0.6 of the students signed up for chess club.
Therefore, 0.6 x total number of students = 210 (the number of students who signed up for chess club).
Therefore, 210/0.6
= 840 students in the school.
In one class, 15 out of 25 students signed up for the chess club. This means that 0.6 (or 60%) of the students in the class decided to join. If this rate stays constant across the entire school, then it is possible to calculate the total number of students in the school by using the proportion of students who signed up for the chess club. To calculate the total number of students, we use the equation: 0.6 x total number of students = 210 (the number of students who signed up for chess club). By dividing both sides of the equation by 0.6, we get 210/0.6 = 840 students in the school. Therefore, there are 840 students in the whole school if 210 signed up for chess club.
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what is the HCF of 144 and 360
Find the arc length of the partial circle
Answer: 3π
Step-by-step explanation:
360 - 90 = 270°
Perimeter of full circle = πd = 4π
Arc length = [tex]\frac{270}{360}[/tex] × 4π = 3π
In a lab experiment, the decay of a radioactive isotope is being observed. At the
beginning of the first day of the experiment the mass of the substance was 300 grams
and mass was decreasing by 6% per day. Determine the mass of the radioactive
sample at the beginning of the 16th day of the experiment. Round to the nearest tenth
(if necessary).
Answer:
To solve this problem, we can use the formula for exponential decay:
m = m0(1 - r)^t
where:
m0 = initial mass (300 grams)
r = decay rate (6% per day, or 0.06)
t = time in days
We want to find the mass at the beginning of the 16th day, so t = 15:
m = 300(1 - 0.06)^15
m ≈ 107.4
Therefore, the mass of the radioactive sample at the beginning of the 16th day of the experiment is approximately 107.4 grams.
NEED HELP PLEASE HELP
The difference in the average rate of change of Chris' savings and Lily's savings in the period from Month 3 to Month 12 is given as follows:
A. $5.
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. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.
Chris savings increased from 35 to 170 in the period from Month 3 to Month 12, hence the average rate of change is given as follows:
(170 - 35)/9 = $15.
Lily's Savings increased from 30 to 120 in the period from Month 3 to Month 12, hence the average rate of change is given as follows:
(120 - 30)/9 = $10.
Hence the difference is of:
15 - 10 = $5.
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find arc length of the partial circle
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =90 \end{cases}\implies s=\cfrac{(90)\pi (8)}{180}\implies s=4\pi[/tex]
Trapezoids 1 and 2 are similar. The perimeter of Trapezoid 1 is 240 centimeters and the perimeter of Trapezoid 2 is 150 centimeters. What is the ratio x:y ?
The answer of the given question based on perimeter of trapezoid the ratio will be x:y is 8:5.
What is Trapezoid?A trapezoid is quadrilateral with at least one pair of the parallel sides. The parallel sides are called bases of trapezoid, and non-parallel sides are called legs.
Let's denote the lengths of the four sides of Trapezoid 1 as a, b, c, and d, and the lengths of the corresponding sides of Trapezoid 2 as m, n, p, and q, respectively. Then we have:
a + b + c + d = 240 (perimeter of Trapezoid 1)
m + n + p + q = 150 (perimeter of Trapezoid 2)
Since Trapezoid 1 and Trapezoid 2 are similar, we can write:
m = ax
n = bx
p = cy
q = dy
where x and y are the ratios of the longer and shorter bases of Trapezoid 1 to Trapezoid 2, respectively.
Substituting these expressions into the equations for the perimeters of the trapezoids, we get:
a(x+y) + b(x+y) + c(x+y) + d(x+y) = 240
(ax+bx+cy+dy) = 150
Simplifying these equations, we get:
(a+b+c+d)(x+y) = 240
(a+b+c+d)(x+y)(x/y) = 150
by Dividing second equation by first, we will get:
x/y = 240/150 = 8/5
Therefore, the ratio x:y is 8:5.
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Find the sum or type
"impossible"
[3 -8] +[4 -5 -6]
These matrices have various dimensions, making it difficult to determine their total. Because of this, the sum of these matrices is either undefinable or unattainable.
Due to their various dimensions, it is difficult to find the sum of these matrices.
One row and three columns make up the second matrix, whereas two rows and one column make up the first matrix. Two matrices can only be added if they share the same dimensions. To be more precise, two matrices can only be added if they have the same number of rows and columns.
The matrices [3 -8] and [4 -5 -6] cannot be added together since they have different numbers of rows and columns. Because of this, the sum of these matrices is either undefinable or unattainable.
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PLEASE SHOW WORK!!!!!!!!!
The midpoint of the line segment is (-2, 2). The correct answer is F. (-2, 2).
What is the equation of the line?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula:
((x1 + x2)/2, (y1 + y2)/2)
Using this formula, we can find the midpoint of the line segment that has endpoints (-10,-4) and (6,8):
Midpoint = ((-10 + 6)/2, (-4 + 8)/2) = (-2, 2)
Therefore, the midpoint of the line segment is (-2, 2). The correct answer is F. (-2, 2).
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What is the angle of elevation of the sun when a 42-ft mast casts 15 ft shadow?
The angle of elevation of the sun is approximately 71.56 degrees when a 42-ft mast casts a 15-ft shadow.
We can use trigonometry to determine the angle of elevation of the sun. Let's call the angle we're looking for "theta".
We know that the tangent of theta is equal to the opposite side (the height of the mast) divided by the adjacent side (the length of the shadow):
tan(theta) = height of mast / length of shadow
tan(theta) = 42 / 15
Now we can use a calculator to find the inverse tangent of both sides of the equation:
theta = [tex]tan^{-1}(42/15)[/tex]
theta ≈ 71.56 degrees
So the angle of elevation of the sun is approximately 71.56 degrees.
If you want to verify the solution, you can use the following diagram to better understand the problem and see how the angle of elevation is related to the height of the mast and the length of the shadow:
In this diagram, the angle theta represents the angle of elevation of the sun, the height of the mast is 42 ft, and the length of the shadow is 15 ft. We can see that the tangent of theta is equal to the height of the mast divided by the length of the shadow, which is what we used in our calculation:
tan(theta) = height of mast / length of shadow
tan(theta) = 42 / 15
We can then solve for theta using inverse tangent:
theta = [tex]tan^{-1}(42/15)[/tex]
theta ≈ 71.56 degrees
As a result, the sun is elevated at a about 71.56 degree angle.
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Please help me answer my homework in the image question 5
Answer:
C) trapezoid
Step-by-step explanation:
See attached image. The shape formed from the lines is a trapezoid, for the reasons listed.
1.
2.
Solve the system of equations using elimination.
3x + by=18
-3x+4y=218
(3x+6y=18
1-3x+4y= 2
10g = 20
10 10
-3+9/21=2
- 3+by=2
x=2
y=2
(2,2)
Verify the solution from question 1 algebraically using substitution,
The system of equations solved by elimination has its solution to be (2, 2)
How to solve the system of equations using elimination.From the question, we have the following parameters that can be used in our computation:
-3x + 4y = 2
3x + 6y = 18
When the above equations are added, the variable x is eliminated
Using the above as a guide, we have the following:
4y + 6y = 2 + 18
Evaluate
10y = 20
So, we have
y = 2
Recall that
-3x + 4y = 2
So, we have
-3x + 8 = 2
Evaluate
-3x = -6
Divide
x = 2
Hence, the solution is (2, 2)
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how many minutes was Samuel 2 blocks from his house?
Answer:
Maybe like 10-15 minutes away
what is the volume of a ceral box with a surface area of 250
Answer:
[tex]125cm^{3}[/tex]
Step-by-step explanation:
TSA of a Cuboid= 2LW x 2LH x 2WH
250 = 2 ( L X W X H)
250 / 2 = L X W X H
125 = L X W X H
The volume of a cuboid = L X W X H
125 = L X W X H
Volume = 125cm3
1 point) (a) Find the discriminant of the equation 5x−9x²+6=0Discriminant =(b) Use the discriminant to say whether the equation has two (distinct) solutions, one solution, or no solutions.The equation has
Using the discriminant of the given equation 5x - 9x² + 6 = 0 which is 241, we can say that the the equation has two real and distinct solutions.
The mentioned equation is 5x - 9x² + 6 = 0. Now we have to find the discriminant of the equation.
Discriminant: ax² + bx + c = 0 is b² - 4ac. The discriminant is used to determine the nature of the roots of the quadratic equation. It can be categorized as the following: If b² - 4ac > 0, the quadratic equation has two real and distinct roots.If b² - 4ac = 0, the quadratic equation has one real and repeated root.If b² - 4ac < 0, the quadratic equation has no real roots or two complex roots.
In the given equation 5x - 9x² + 6 = 0, the coefficients are as follows:
a = -9, b = 5, and c = 6.
Now, we can find the discriminant: Discriminant = b² - 4ac= (5)² - 4(-9)(6)= 25 + 216= 241.
Thus, the discriminant of the given equation is 241. As the discriminant is greater than 0, the quadratic equation has two real and distinct roots.
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Two storage sheds are to have the same area. One is square and one is regtangular. The rectangular she is 4 meters wide and 16 meters long
As per the given question, the length of the square shed is 8 meters.
Length of the sheet = 4m
Width of the sheet = 16m
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Since a rectangle's opposite sides are both equal and parallel, a parallelogram is another name for this geometric shape.
Using the formula for the area of the rectangle -
Area = Length x Width
Now,
Let the length of the square shed be x, therefore -
x² = 4(16) = 64
x = √64
= 8
Complete Question:
Two storage sheds are to have the same area. One is square and one is rectangular. The rectangular she is 4 meters wide and 16 meters long. What is the length of the square shed?
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Question two, please help
2/10
What steps should be taken to calculate the volume of the right triangular prism? Select three options. A triangular prism. The triangular base has a base of 8 meters and height of 14 meters. The height of the prism is 7 meters. Use the formula A = one-half b h to find the area of the base. Use the formula A = b h to find the area of the base. The area of the base, A, is One-half (7) (8) = 28 meters squared. The area of the base, A, is One-half (8) (14) = 56 meters squared. The volume of the prism, V is (56) (7) = 392 meters cubed.
Use the formula A = one-half b h to find the area of the base. The area of the base, A, is One-half (8) (14) = 56 meters. The volume of the prism, V is (56) (7) = 392 meters cubed.
What is a right triangular prism?A prism is a solid figure having two bases that are the same in size and shape, flat sides, and a continuous cross-section. The two bases of a prism, which might be triangles, rectangles, or any other polygon, determine the name of the prism in question. Prisms having triangle bases, for instance, are referred to as triangular prisms, whereas those with square bases are referred to as square prisms, and so on. Three rectangle lateral sides and two triangular bases make up a triangular prism.
Given that the figure is a right triangular prism with, base 8 meters and 14 m, also the height of the prism is 7 m.
Thus, the correct steps to calculate the volume of the right triangular prism are:
Use the formula A = one-half b h to find the area of the base.
The area of the base, A, is One-half (8) (14) = 56 meters.
The volume of the prism, V is (56) (7) = 392 meters cubed.
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Find the height of a cone with a radius of 12 inches and a volume of 1,281.12 cubic inches.
[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=12\\ V=1281.12 \end{cases} \implies 1281.12=\cfrac{\pi (12)^2 h}{3} \\\\\\ (3)(1281.12)=144\pi h\implies \cfrac{(3)(1281.12)}{144\pi }=h\implies 8.50\approx h[/tex]
A beg of corn can feed 100 chickens for 12 days . For how many days would the same bag feed 80 chickens
Answer:
9.6 days
Step-by-step explanation:
100 chickens, 12 days
find the days for 10 chickens: 1.2 days (to get 10 you have to divide 100 by ten, so divide 12 by ten too)
times by 8 to get the days for 80 chickens: 9.6 days
Answer: Let's assume that the bag of corn contains "C" units of corn. We know that this amount of corn can feed 100 chickens for 12 days.
To determine how long the same bag of corn would feed 80 chickens, we can use the following proportion:
(Corn units)/(chickens * days) = (Corn units)/(chickens * days)
We can set up two ratios, one for the original situation and one for the new situation, and then cross-multiply to solve for the unknown value:
C/100 * 12 = C/80 * d
where "d" is the number of days that the same bag of corn would feed 80 chickens.
Simplifying the equation, we get:
C/10 = C/80 * d
Multiplying both sides by 80, we get:
8C = Cd
Dividing both sides by "C", we get:
8 = d
Therefore, the same bag of corn would feed 80 chickens for 8 days.
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Mike's Bakery recently spent a total of $392 on new equipment, and their average hourly operating costs are $9. Their average hourly receipts are $10. The bakery will soon make back the amount it invested in equipment. What would the total expenses and receipts both equal? How many hours will that take?
For Mike's Bakery the total expenses will be $3528 and the total receipts will be $3920 and it will take 392 hours.
Let number of hours the bakery needs to operate in order to make back the amount it invested in equipment be = "h".
To find "h", we need to find the profit per hour,
The profit per hour is = difference between hourly receipts and hourly operating costs;
Profit per hour = Hourly receipts - Hourly operating costs
Profit per hour = $10 - $9
Profit per hour = $1
The total profit required to make back the $392 investment is = $392,
We know that,
⇒ Total profit = (Profit per hour) × (Number of hours)
⇒ $392 = $1 × h
⇒ h = $392/$1
⇒ h = 392
So, bakery needs to operate for 392 hours to make back the amount it invested in equipment.
To calculate the total expenses and receipts, we can use the following formulas:
⇒ Total expenses = (Operating costs) × (Number of hours)
⇒ Total expenses = $9 × 392
⇒ Total expenses = $3528
⇒ Total receipts = (Hourly receipts) × (Number of hours)
⇒ Total receipts = $10 × 392
⇒ Total receipts = $3920
Therefore, the total expenses is $3528 and total receipts is $3920.
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MULTIVARIATE STATISTICS
(a) What are the two ways in which the exploratory factor
analysis (EFA) can be useful?
(b) Differentiate between principal component method
and factor analysis
(a) The exploratory factor analysis (EFA) can be useful in two ways: Dimensional Reduction: The dimensionality of a set of data can be reduced by exploratory factor analysis. Rather than dealing with several variables, it identifies the basic factors that describe the data set. This can be achieved by extracting factor information that shows the covariance structure of the variables that underlie the observations. Investigation of latent variables: Exploratory factor analysis can be used to determine whether an underlying dimension, such as depression or anxiety, underlies a collection of observable variables, such as feelings of depression, nervousness, or irritability. Latent variables are those that cannot be observed directly. (b) Factor analysis and principal component analysis are two techniques for data reduction that are frequently confused. The principal component analysis, on the other hand, is a technique that creates uncorrelated variables to replace the original variables. It can be viewed as a special case of factor analysis in which all of the extracted factors are used. It includes the raw data's total variance, which is defined by a few components. Principal component analysis is a method of data reduction that extracts uncorrelated factors from the original variables. The correlation structure of the original variables is utilized in factor analysis to define the underlying factors.
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Find the remainder of (x^10 + 2x^9 + 3x^8 +...+ 9x^2 + 10x + 11) ÷ (x-1)
Answer:
66
Step-by-step explanation:
You want the remainder from (x^10 +2x^9 +3x^8 +...+10x +11)/(x -1).
RemainderThe remainder from dividing polynomial f(x) by (x-a) is the value f(a). Here, that means we can find the remainder by evaluating (x^10 +2x^9 +3x^8 +...+10x +11) for x=1. When we do that, we see the value is simply the sum of the coefficients:
f(1) = (1 + 2 + 3 + ... + 10 + 11) = (11)(11 +1)/2 = 66
The remainder from dividing by (x-1) is 66.
__
Additional comment
The sum of integers 1..n is (n)(n+1)/2.
4) What is the value of v?
Answer:
v = 110
Step-by-step explanation:
The big line is a 180 degree line. We need to find the value of the missing side so we take 70 degrees and subtract it from the total angle 180 degrees. That leaves us 110 degrees, so v = 110 degrees.
Spencer is researching the cost to rent office space in the Brookton Office Center. Office space is rented based on
the square footage of an office's floor area. A linear relationship exists between the square footage of the floor and
the yearly cost to rent that square footage, as shown in the table below.
Brookton Office Center
Yearly Rental Costs
Square
Footage
500
600
800
1,200
Yearly
Rental
Cost
$9,250
$11,100
$14,800
$22,200
Spencer budgeted $20,720 for his yearly office rental cost. The office space can be customized to the size needed.
What is the maximum amount of square footage he can rent in the Brookton Office Center?
Answer:
Step-by-step explanation:
Which set of points includes all of the solutions for y = five halves times x plus three halves?
line going through negative 1 comma negative 1 and 1 comma 4
(x, five halves times x plus three halves) for all real numbers
(−1, −1), (0, 1. 5), (1, 4)
(x, y) for all real numbers
(−3, −6), (−2, −3. 5), (0, 1. 5), (2, 6. 5), (3, 9)
The set of points that includes all of the solutions for [tex]y = 5/2x + 3/2[/tex] is [tex](x, 5/2x + 3/2)[/tex] for all real numbers.
The set of points that includes all of the solutions for the given equation is [tex](x, 5/2x + 3/2)[/tex] for all real numbers. This is because any point on this line will satisfy the equation [tex]y = 5/2x + 3/2[/tex], which means that any solution to the equation will be included in this set of points.
Alternatively, we can find the equation of the line passing through the points (-1, -1) and (1, 4) and confirm that it is the same as the equation [tex]y = 5/2x + 3/2[/tex].
Using the two-point form of a linear equation, the slope of the line passing through the two points is:
[tex]m = (y2 - y1) / (x2 - x1) = (4 - (-1)) / (1 - (-1)) = 5/2[/tex]
Using the point-slope form of a linear equation with the slope and one of the points:
[tex]y - y1 = m(x - x1)[/tex]
[tex]y - (-1) = (5/2)(x - (-1))[/tex]
[tex]y + 1 = (5/2)(x + 1)[/tex]
[tex]y = (5/2)x + (5/2) - 1[/tex]
[tex]y = (5/2)x + (3/2)[/tex]
This is the same equation as [tex]y = 5/2x + 3/2[/tex], so we know that the set of points that includes all of the solutions is [tex](x, 5/2x + 3/2)[/tex] for all real numbers.
Learn more about linear equation here:
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