The function is decreasing on the interval (-∞,∞)
This means that, throughout the whole graph, the slope is negative.
Answer:
g
Step-by-step explanation:
g
PLEASE HELP! DUE TOMORROW 1-8-21 !! Look at these equations. Write each equation in slope-intercept form. Are these equations the same or different? Explain. I don’t know how to do the middle equation so please show work for that.
Answer:
y = 2x-4
all the equations are the same as the slope-intercept form is the same for all the equations
Step-by-step explanation:
slope-intercept form:
\(y = mx + b\)
2x-3 = y+1
i) move y to the left-hand side and change its sign-y+2x-3 = 1
ii) move 2x-3 to the right-hand side and change its sign-y = 1-2x+3
iii) add the numbers-y = (1+3)-2x
-y = 4-2x
iv) change the signs on both sides of the equationy = -4+2x
v) use the commutative property to reorder the terms( commutative property: the number on which we operate can be moved or swapped from their position without making any difference to the answers )
y = 2x-4
Which integer is the square root of 55 closest to
Answer:
7
Step-by-step explanation:
Answer
(b)
Factorise 6ac - 4ad
help me with this pls :)) i really need help :)
Hey there!
In order to factorise an expression, we need to factor out the greatest common factor (divide all the terms in the expression by the greatest common factor):
6ac-4ad
In this case, the greatest common factor is 2a.
Put it outside the parentheses:
2(3c-2d)
That's the answer.
Hope everything is clear.
Let me know if you have any questions!
#LearningDoesn'tEnd
:-)
The equation of this type of line is y = kx. what is special about k? k is the change in the y-values. k is the change in the x-values. k is the slope of the line.
The equation of the line is \(y = kx\) . The special thing about k in this equation is that, it is the slope of the line.
Slope of Line: It is the measure of the steepness. It is calculated as 'rise over run' means change in y divided by x.
Equation of a line using slope-intercept form is:
y = ax + b
where,
a is the slope of the line.b is the y-intercept of the line.Here, in the equation \(y = kx\)
k = slope of the line
and y-intercept is zero
Therefore, the special about k in the equation is that k is the slope of the equation \(y = kx\).
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Arrange these from greatest to least greatest PLEASE HELP ME ANSWER THIS QUESTION
Answer: 37, 15, 12, 0, -6, -8, -23
Step-by-step explanation:
So, the higher the negative number, the lower the value is. Hope this helps!
Pedro jogs 1.45 kilometers on Monday. he jogs 0.5 kilometer more on Tuesday than on Monday. how far does Pedro jog during both days?
Answer:
3.4 kilometers on both days
Step-by-step explanation:
\(1.45+0.5=1.95\)
\(1.45+1.95=3.4\)
The ponderal indexis a measure of the "leanness" of a person. A person who is h inches tall and weighs w pounds has a ponderal index I given by I = a. Compule the ponderal index for a person who is 76 inches tall and weighs 192 pounds: Round to the nearest hundredth. b. What is a man's weight if he is 77 inches tall and has a ponderal index of 11.56 ? Round to the nearest whole number. a. The ponderal index for a person who is 76 inches tall and weighs 192 pounds is (Round to the nearest hundredth as needed.)
The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.
To compute the ponderal index, we need the formula and the value of the constant "a."
a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.
b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.
To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.
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what is the value of x
a) 69
b) 35
c) 14
d) 26
Answer:
50²-48²
solve it you will get answer
Answer:
C) 14
Step-by-step explanation:
(Phytogoras theorem)
\( {50}^{2} = {48}^{2} + {x}^{2} \)
2500 = 2304 + x^2
2500 - 2304 = x^2
X^2 = 196
\(x = \sqrt{196} \)
X = 14
Jonczyk Company is considering two different, mutually exclusive capital expenditure proposals. Project A will cost $454,000, has an expected useful life of 13 years and a salvage value of zero, and is expected to increase net annual cash flows by $68,000. Project B will cost $300,000, has an expected useful life of 13 years and a salvage value of zero, and is expected to increase net annual cash flows by $47,000. A discount rate of 9% is appropriate for both projects. Click here to view PV table.
Calculate the net present value and profitability index of each project. (If the net present value is negative, use either a negative sign preceding the number e.g. -45 or parentheses e.g. (45). Round present value answers to 0 decimal places, e.g. 125 and profitability index answers to 2 decimal places, e.g. 15.52. For calculation purposes, use 5 decimal places as displayed in the factor table provided, e.g. 1.25124.)
Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.
A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.
Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14
Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96
The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.
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How to find a quadratic equation with y-intercept and vertex? Explain with examples.
To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.
To find a quadratic equation with the y-intercept and vertex, we can follow these steps:
Step 1: Identify the coordinates of the y-intercept. The y-intercept has the form (0, c), where c is the y-coordinate.Step 2: Identify the coordinates of the vertex. The vertex has the form (-b/2a, f(-b/2a)), where a, b, and c are the coefficients of the quadratic equation.Step 3: Substitute the coordinates of the y-intercept and vertex into the general form of the quadratic equation, y = ax^2 + bx + c.Step 4: Solve the resulting system of equations to find the values of a, b, and c.Step 5: Substitute the values of a, b, and c back into the general form of the quadratic equation to obtain the final equation.For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:
3 = a(0)^2 + b(0) + c
1 = a(-2)^2 + b(-2) + c
Simplifying these equations, we get:
c = 3
4a - 2b + c = 1
By substituting c = 3 into the second equation, we can solve for a and b:
4a - 2b + 3 = 1
4a - 2b = -2
2a - b = -1
By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:
y = x^2 + x + 3
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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.
Start with the standard form of a quadratic equation: y = ax^2 + bx + c, where a, b, and c are constants.Use the vertex form of a quadratic equation: y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.Substitute the vertex coordinates (h, k) into the equation to obtain the equation in vertex form.Use the y-intercept to find another point on the curve. The y-intercept has the form (0, c), where c is the value of y when x is zero.Substitute the coordinates of the additional point into the equation to obtain a system of two equations. Solve the system to find the values of a, b, and c.Substitute the determined values of a, b, and c into the standard form of the quadratic equation to obtain the final equation.Example:
Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).
Using the vertex form, we have y = a(x - 2)^2 - 1.Substituting the y-intercept coordinates, we get 4 = a(0 - 2)^2 - 1, which simplifies to 4 = 4a - 1.Solving the equation above, we find a = 1.Substituting the values of a and the vertex coordinates into the vertex form equation, we have y = 1(x - 2)^2 - 1.Expanding the equation and simplifying, we get y = x^2 - 4x + 3.The final quadratic equation with the given y-intercept and vertex is y = x^2 - 4x + 3.To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.
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The joint pdf of random variables X and Y is given as [A(x+y) 0
The given joint probability density function of the random variables X and Y is given as\([A(x+y) 0 < x < y < 1; 0 otherwise]\). We need to determine the value of A.
Let us first integrate the joint probability density function with respect to y and then with respect to x as follows:\(∫∫[A(x+y)] dy dx\) (over the region
\(0 < x < y < 1)∫[Ax + Ay] dy dx=∫[Ax²/2 + Axy]\) from \(y=x to y=1 dx∫[Ax²/2 + Ax - Ax³/2] dx from x=0 to x=1=∫[(Ax²/2 + Ax - Ax³/2) dx]\) from \(x=0 to x=1= [A/2 + A/2 - A/2]= A/2\)
We can write the given joint probability density function as follows:A(x+y)/2; 0 < x < y < 1; 0 otherwise.Note that the value of the joint probability density function is zero if \(x > y\).
The region where the joint probability density function is non-zero is the triangle in the first quadrant of the xy-plane that lies below the line y=1 and to the right of the line x=0. The joint probability density function is symmetric with respect to the line y=x.
This means that the marginal probability density function of X and Y are equal, that is, \(fX(x) = fY(y)\). The marginal probability density function of X is given as follows:\(fX(x) = ∫f(x,y) dy = ∫A(x+y)/2 dy\)from \(y=x to y=1= A(x + 1)/4 - Ax²/4\) where\(0 < x < 1\).
The marginal probability density function of Y is given as follows:\(fY(y) = ∫f(x,y) dx = ∫A(x+y)/2 dx from x=0 to x=y= Ay/4 + A/4 - A(y²)/4\)where 0 < y < 1.
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Suzie went to the carnival and spent $2.85 on a lemonade and $3.25 on a hot dog. How much money did Suzie spend in total? (3 points) a $6.10 b $6.50 c $6.85 d $7.10
Answer:
a) 6.10
Step-by-step explanation:
if you want to figure out the total number spent, then you simply add together the two amounts to get:
3.25+2.85=6.10
p.s. dont post such simple questions on brainly
Answer: a. $6.10
Step-by-step explanation:
2.85 + 3.25 = (2+3)+(.85+.25) = (5)+(1.10)=6.10
therefore, $6.10 is the right answer
Find the change in profit P for the given marginal. Assume that the number of units x increases by 5 from the specified value of x. (Round your answer to two decimal places.) Marginal Number of Units, x dP dx = 12.1 60 − 3 x x = 121
The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50
To find the change in profit (ΔP) when the number of units (Δx) increases by 5.
we need to evaluate the marginal profit function and multiply it by Δx.
The marginal profit function is given by dP/dx = 12.1(60 - 3x).
We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.
dP/dx = 12.1(60 - 3(121))
= 12.1(60 - 363)
= 12.1(-303)
= -3666.3
Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.
ΔP = dP/dx×Δx
= -3666.3 × 5
= -18331.5
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what is the answer to 2a - 3 = -5?
Answer:
-1
Step-by-step explanation:
get -3 to the other side of the equation. 2a=-2 so a is -1
A simple interest loan is taken for $5000 at 4% interest for 3 years. What
will the balance of the loan be after the three years?
The outstanding loan sum with simple interest will be $5,600.00
Simple interest: What is it?Simple interest is the amount of interest that solely accrues on the principle during the course of a deposit. There is neither earned nor incurred interest on prior interest. It is the same thing as when interest is withheld at the conclusion of each period.
Simple interest = PRT /100
Calculation:
The first step is to convert r percent to R a decimal,
R/100 = 4%/100 = 0.04 every year.
Now, simple interest is equal to
PRT/100
SI = $5000*0.04*3
SI = 600.
How to resolve our equation
A = P + I
A = $5000 + 600
A = $5,600.00
Simple interest at a rate of 4% per year for three years on a principle of $5,000 has amassed a total of $5,600.00 in principal and interest.
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Se empaquetaron 573 carros de juguete en cajas. Cada uno tiene capacidad para 8 coches de juguete.
A) ¿Cuántas cajas se llenaron?
B) ¿Cuántos carros de juguete sobraron?
Answer
creon queens B. lo siento is me equivoco
Which statement about the location of √ 7 on a number line is true?
The location of √ 7 on a number line between 2 and 3.
What is a number line?A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.
A number line is a long straight line with numbers marked at equal intervals. On a number line, we can argue that as we move to the right, the value of numbers increases. This signifies that the numbers on the right are more than those on the left.
A number line shows how numbers are related. It's a line with check marks next to each number. The numerals get smaller as you move left on the number line. The numbers grow larger as you move closer to the number line.
In this case, ✓7 is 2.65. This number can be found between 2 and 3. This should be the true statement since the options aren't given.
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Write an expression showing the sum of 8 and a number .
Answer:
8+ n
Step-by-step explanation:
my answer got delete so dont think i coped the person who did was user content bot
A triangle has side lengths of (5m - 2n) centimeters, (7m + 10p) centimeters,
and (8p9n) centimeters. Which expression represents the perimeter, in
centimeters, of the triangle?
Step-by-step explanation:
Perimeter is addition of the three sides
P= (5m - 2n) + (7m +10p) + 8p9n
Collect like terms
P = 8p9n +10p +12m - 2n
how to graph it? pls help.
The linear equation is:
y = 2x + 40
And the graph is on the image at the end.
How to write and graph the function?We know that the service costs $40 per mont plus $2 per minute of time used out of the service area.
So, if you use x minutes out of the service area, then the total cost is given by the linear function:
y = 2x + 40
Now we need to graph this, to do so, we need to find two points.
if x = 0
y = 2*0 + 40 = 40
if x = 1
y = 2*1 + 40 = 42
Then we have the points (0, 40) and (1, 42), now we need to graph these two points and connect them with a line.
The graph of the linear equation is on the image at the end.
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How do i simplify Sin(312)?
Answer:
-0.743
Step-by-step explanation:
just plug it into a calculator
Answer:
it is also -sin(48)
Step-by-step explanation:
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x=17 degrees
Step-by-step explanation:
All 3 angles = 180 degrees
So 90 + 54 + (x+19) = 180
Combine like terms
163 + x = 180
Subtract 163 from both sides
x = 180-163
x = 17
How many terms are in this expression?
4c + 7b + d
The terms in the given expression 4c+7b+d are 4c, 7b and d.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
The given expression is 4c+7b+d.
There are three terms in 4c+7b+d, they are 4c, 7b and d
Therefore, the terms in the expression are 4c, 7b and d.
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One-way anova is a procedure for comparing the means of several populations. it is the generalization of what procedure for comparing the means of two populations?
One-way ANOVA is a statistical procedure that is used for comparing the means of several populations. Also, it is the generalization of pooled t-procedure for comparing the means of two populations.
What is a mean?A mean is also referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
What is an ANOVA?ANOVA is an abbreviation for analysis of variance which was developed by the notable statistician Ronald Fisher. The analysis of variance (ANOVA) is a collection of statistical models with their respective estimation procedures that are used for the analysis of the difference between the group of means found in a sample.
This ultimately implies that, the analysis of variance (ANOVA) helps to ensure we have a balanced data by splitting the observed variability of a data set into random and systematic factors.
In Statistics, the analysis of variance (ANOVA) procedure is typically used as a statistical tool to determine whether or not the means of two or more populations are equal, especially through the use of the following:
Null hypothesisF-test.Pooled t-procedureIn this context, we can infer and logically deduce that a one-way ANOVA is a statistical procedure that is used for comparing the means of several populations. Also, it is the generalization of pooled t-procedure for comparing the means of two populations.
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Complete Question:
One-way ANOVA is a procedure for comparing the means of several populations. It is the generalization of what procedure for comparing the means of two populations?
A. nonpooled t-procedure
B. paired t-test
C. pooled t-procedure
D. None of the above
The area of the top side of a piece of sheet metal is given below. The sheet metal is submerged horizontally in 7 feet of water. Find the fluid force on the top side. (The weight-density of water is 62.4 pounds per cubic foot.) 4 square feet lb
The fluid force on the sheet metal's top side when submerged horizontally in 7 feet of water is 12441.6 lb.
Given,
The area of the top side of a piece of sheet metal = 4 square feet
The sheet metal is submerged horizontally in 7 feet of water.
Fluid Force on the top side can be found as follows,
Formula used:
Fluid Force = weight-density × volume × depth of fluid
Fluid Force = 62.4 × volume × 7
As the sheet metal is completely submerged, the volume is equal to the area of the sheet metal.
Volume = Area × Depth
= 4 × 7
= 28
Fluid Force = 62.4 × 28 × 7
= 12441.6 lb
Thus, the fluid force on the sheet metal's top side when submerged horizontally in 7 feet of water is 12441.6 lb.
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Therefore, the fluid force on the top side is 55838.08 lb.
Given, the area of the top side of a piece of sheet metal is 4 square feet and it is submerged horizontally in 7 feet of water.
The weight-density of water is 62.4 pounds per cubic foot.To find: the fluid force on the top side.Solution:Fluid force formula is given by,
F = ρ * g * V
Where, ρ is the density of the fluidg is the acceleration due to gravityV is the volume of the fluid displaced.Furthermore, the volume of fluid displaced is equal to the volume of the metal sheet submerged in the water.
Therefore,Volume of fluid displaced = Volume of metal sheet submerged in the water = area of metal sheet * depth submerged
Volume of metal sheet submerged in the water = 4 square feet * 7 feet
= 28 cubic feet
Now, calculate the fluid force on the top side of the metal sheet by using the fluid force formula.
F = ρ * g * V
Here, the density of water,
ρ = 62.4 pounds per cubic foot
g = 32.2 ft/s² (the acceleration due to gravity)
V = 28 cubic feet∴
F = 62.4 * 32.2 * 28 lb
= 55838.08 lb
Therefore, the fluid force on the top side is 55838.08 lb.
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Select all that apply.
Which numbers are not perfect squares?
36
14
20
O16
25
18
24
Answer:
14
20
18
24
Step-by-step explanation:
36 = 6 x 6
16 = 4 x 4
25 = 5 x 5
All others are not square
In
the one way slab, the deflection on direction of long span is
neglected (T or F)
The statement "In the one-way slab, the deflection in the direction of the long span is neglected" is False.
In a one-way slab, the deflection in the direction of the long span is not neglected. The term "one-way" refers to the way the slab is reinforced. It means that the main reinforcement bars are placed parallel to the short span of the slab. However, this does not mean that the deflection in the direction of the long span is ignored.
When designing a one-way slab, engineers consider the deflection in both directions. The deflection in the direction of the long span is typically larger compared to the short span. This is because the long span has a larger moment and a higher chance of experiencing greater loads. Therefore, it is essential to account for the deflection in both directions to ensure the slab can withstand the imposed loads and maintain its structural integrity.
By considering the deflection in both directions, engineers can accurately determine the required reinforcement and ensure that the slab meets the necessary strength and safety requirements.
In summary, the statement "In the one-way slab, the deflection in the direction of the long span is neglected" is false. Deflection in both directions is taken into account when designing a one-way slab to ensure its structural stability and safety.
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An event called __ if the probability it will occur equals 1, plz help im dying (it has 7 letters)
Answer:
"certain"
Step-by-step explanation:
by definition, any event with a probably of 1 is defined as certain (i.e certain to happen)
by contract any even with a probably of 0 is defined as impossible (i.e impossible to happen)
apply the descriptive statistics tool for subsets of liberal arts colleges and research universities in the excel file colleges and universities. compare the two types of colleges. what can you conclude?
Liberal arts colleges have a higher median SAT score and a lower acceptance rate compared to research universities, while research universities have a higher expenditure per student and a higher percentage of top 10% high school graduates.
Descriptive statistics were calculated for liberal arts colleges and research universities based on the data given in the Excel file. The summary of descriptive statistics for each variable by school type is as shown in the table.
Based on the results, it appears that liberal arts colleges have higher median SAT scores, lower acceptance rates, and lower expenditures per student than research universities. On the other hand, research universities have higher mean expenditures per student and higher median percentages of top 10% high school graduates than liberal arts colleges. Overall, there are differences in the characteristics of these two types of colleges.
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--The complete question is, Compute descriptive statistics for liberal arts colleges and research universities in the Excel file Colleges and Universities. Compare the two types of colleges. What can you conclude?
Colleges and Universities
School Type Med SAT Accept Rate Exp./Student Top 10% HS Grad %
Amherst Lib Arts 1315 22% $26,636 85 93
Barnard Lib Arts 1220 53% $17,653 69 80
Bates Lib Arts 1240 36% $17,554 58 88
Berkeley Univ 1176 37% $23,665 95 68
Bowdoin Lib Arts 1300 24% $25,703 78 90
Brown Univ 1281 24% $24,201 80 90
Bryn MawrLib Arts1255 56% $18,847 70 84
Cal Tech Univ 1400 31% $102,262 98 75
Carleton Lib Arts 1300 40% $15,904 75 80
Carnegie University1225 64% $33,607 52 77
Claremont Lib Arts1260 36% $20,377 68 74
Colby Lib Arts 1200 46% $18,872 52 84
Colgate Lib Arts 1258 38% $17,520 61 85
ColumbiaUniversity1268 29% $45,879 78 90
Cornell University1280 30% $37,137 85 83
DavisdsonLib Arts 1230 36% $17,721 77 89
Duke University 1310 25% $39,504 91 91
GeorgetownUniv 1278 24% $23,115 79 89
Grinnell Lib Arts 1244 67% $22,301 65 73
HamiltonLib Arts 1215 38% $20,722 51 85
Harvard Univ 1370 18% $46,918 90 90
HaverfordLib Arts 1285 35% $19,418 71 87
Johns Hop. Univ 1290 48% $45,460 69 86
MiddleburyLib Arts 1255 25% $24,718 65 92
MIT University 1357 30% $56,766 95 86
Mount Lib Arts 1200 61% $23,358 47 83
NWrn University 1230 47% $28,851 77 82
Oberlin Lib Arts 1247 54% $23,591 64 77
Occidental Lib Arts 1170 49% $20,192 54 72
Pomona Lib Arts 1320 33% $26,668 79 80
Princeton University 1340 17% $48,123 89 93
Rice University 1327 24% $26,730 85 88
Smith Lib Arts 1195 57% $25,271 65 87
Stanford University 1370 18% $61,921 92 88
Swarthnore Lib Arts 1310 24% $27,487 78 88
U of MI University 1195 60% $21,853 71 77
U of Chi University 1300 45% $38,937 74 73
U of Roc University 1155 56% $38,597 52 73
U PA University 1280 41% $30,882 87 86
U Va University 1218 37% $19,365 77 88
UCLA University 1142 43% $26,859 96 61
UNC University 1109 32% $19,684 82 73
Vassar Lib Arts 1287 43% $20,179 53 84
Wash U University 1225 54% $39,883 71 76
Wash & Lee Lib Arts 1234 29% $17,998 61 78
Wellesley Lib Arts 1250 49% $27,879 76 86
Wesleyan Lib Arts 1290 35% $19,948 73 91
Williams Lib Arts 1336 28% $23,772 86 93
Yale University 1350 19% $52,468 90 93--
Dante is solving the system of equations below.
r+S-=-4
2r-35+=1
3r-2s+21= 3
He writes the row echelon form of the matrix. Which matrix did Dante write?
Answer:
The answer is the first matrix. Image attached.
Step-by-step explanation: Given that Dante is solving the system of equations:
In solving the above system of equations, Dante writes the row echelon form of the matrix. We are to select the correct row echelon of the matrix that he wrote.
We know that a matrix is said to be in row echelon form if the leading entry in each nonzero row is a 1 and each column containing a leading 1 has zeros everywhere else.
In the given options, these conditions are satisfied by the first option only. And also, if we write the solution from this matrix, we will have
r = -1, s = 0 and t = 3.
If we substitute these values in the given system, it will get satisfied.
Thus, the first matrix, attached herewith, is the correct matrix.