The value of x in the quadratic equation is as follows:
x = 7 and x = 7
How to solve quadratic equation?A quadratic equation is a polynomial equation in one unknown that contains the second degree, but no higher degree, of the variable.
The standard form of a quadratic equation is ax² + bx + c = 0, when a ≠ 0.
Let's solve for x in the quadratic equation 2x² – 28x = –98.
2x² – 28x = –98
2x² – 28x + 98 = 0
divide through by 2
x² - 14x + 49 = 0
The two numbers you can add get -14 and multiply to get 49 are -7 and -7.
Hence,
x² - 14x + 49 = 0
x² - 7x - 7x + 49 = 0
x(x - 7) -7(x - 7) = 0
(x - 7)(x - 7) = 0
Therefore,
x = 7 and x = 7
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How do you dilate a figure by 2 3?
Dilate any given figure by a scale factor 2/3 represents the new image contracted by scale factor 2/3 or 0.667% times image get contracted.
Explanation :
Dilation represents the type of transformation which changes the size of the given image.To dilate any given figure first find the required scale factor and also center of dilation.In the given scale factor 2/3 the new image get changed by scale factor 2/3 or gets contracted by 0.667%.New image ( 2 / 3 ) times contracted in comparison of old image or 0.667% get reduced.Therefore, the dilate a given figure by scale factor 2/3 represents the figure gets contracted by 0.667%.
The complete question is:
How do you dilate a figure by scale factor 2/ 3?
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in a database, a _____________ is a unit of information about one individual or item.
Answer: Record
Step-by-step explanation:
question 31 pts for the data given below, we construct a 90% confidence interval for the population mean. 42.3 59.2 45.4 55.8 49.0 39.7 56.2 54.6 45.8 60.6 55.7 46.1 58.3 44.4 find the upper bound (round off to first decimal place)
the upper bound is 54.2.
What is confidence interval?
A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.
31 pts for the data given below, we construct a 90% confidence interval for the population mean.
42.3 59.2 45.4 55.8 49.0 39.7 56.2 54.6 45.8 60.6 55.7 46.1 58.3 44.4 .
MEAN = 50.94
varience = 48.55
s.d = √48.55 = 6.96.
C=0.90,α= 1-0.90=0.10
t=ta/2.df = 1.771 (using t value table)
90% confidence interval
(47.6378,54.2336)
Hence the upper bound is 54.2.
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please help, answers only!!
The rate of change of the graphs are as follows:
rate of change = 4 / 5rate of change = 3 / 4How to find rate of change?The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.
The rate of change is constant when the ratio of the output to the input stays the same at any given point on the function.
Therefore,
rate of change = change in y / change in x
Hence,
rate of change = y₂ - y₁ / x₂ - x₁
let's find the rate of change of the graphs.
a.
using (-5, -1) and (5, 7)
rate of change = 7 + 1 / 5 + 5
rate of change = 8 / 10
rate of change = 4 / 5
b.
using (0, 3)(-4, 0)
rate of change = 0 - 3 / -4 - 0
rate of change = - 3 / - 4
rate of change = 3 / 4
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Need help with this problem
By using some exponent properties, we will see that the equivalent expression to √(x⁵*y⁶) is:
x²*y³*√x
So the correct option is the first one.
How to simplify the given expression?
Here we need to remember 3 properties about exponents that we will need to use.
These are:
√x = x¹´²
Also remember that:
(xⁿ)ᵃ = xⁿ*ᵃ
And that:
√(a*b) = √a*√b
Well, our expression is:
√(x⁵*y⁶)
We can rewrite this as:
√x⁵*√y⁶
And using the first and second properties we can rewrite.
√x⁵ = x⁵´² = x⁴´²*x¹´² = x²*√x
√y⁶ = y⁶´² = y³
Replacing all that we get:
√(x⁵*y⁶) = x²*y³*√x
Thus, the correct option is the first one.
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a professional basketball player made 51.6% of field goals in one season. if 110 field goals are randomly selected from the season, what is the probability that more than 52 were made?
By using probability, it can be calculated that -
Probability that more than 52 were made = 0.792
What is probability?
At first it is important to know about probability of an event.
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
A professional basketball player made 51.6% of field goals in one season
n = 110
p = 0.516
q = 1 - 0.516 = 0.484
Now,
Mean = 110 [tex]\times[/tex] 0.516 = 56.76
Standard Deviation = [tex]\sqrt{(110\times0.516\times0.484)}[/tex] = 5.24
P(X>52)
P(X>52.5)
z = [tex]\frac{52.5 - 56.76}{5.24}[/tex]
z = -0.8128
P(z<-0.8128) = 0.208
P(X>52) = 1 - 0.208
P(X>52) = 0.792
Probability that more than 52 were made = 0.792
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Find the value of x.
(2x+6)
38°
x = [?]°
The value of x from the expression 2x + 6 = 38 is 16.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
2x + 6 = 38
Subtracting 6 on both sides.
2x = 38 - 6
2x = 32
Divide both sides by 2.
x = 16
Thus,
The value of x is 16.
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What is the equation of the line passing through point 1 2?
The equation of the line will be equal to y = -x + 3.
The equation of the line in slope intercept form is expressed as
y = mx + c
where m is the slope of the line, c is the y-intercept and x and y are independent and dependent variables respectively.
We have the equation of the line as y = x + 5 and we need to find equation of line perpendicular to this line. The slope of the line is 1.
If two lines are perpendicular then the relation in their slope is expressed as
m₁ × m₂ = -1 and we have m₁ = 1 and m₂ = m so we get
1 × m = -1
=> m = -1
Now, the equation of the line will be
y = (-1)x + c
Also, the line passes through (1, 2) so on putting these values
2 = -1 + c
=> c = 3
So, the complete equation of line will be
y = -x + 3
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Complete Question:
Write the equation of a line that passes through the point (1, 2) and is perpendicular to the line y = x + 5.
A bed of roses consists of m roses. The ratio of pink roses to white roses is 2: 3.
Find the number of pink roses expressed in terms of m.
The number of pink roses with given ratio is 0.4m.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, the ratio of pink roses to white roses is 2:3.
A bed of roses consists of m roses.
Here, 2+3=5
So, the number of pink roses
= 2/5 ×m
= 0.4m
Therefore, the number pink roses are 0.4m.
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Which equations are correct?
Select each correct answer.
Answers:
6b4(−3b4)=−18b8
6 b to the power of 4 end power left parenthesis negative 3 b to the power of 4 right parenthesis equals negative 18 b to the power of 8
5x4(4x2)=20x6
5 x to the power of 4 end power left parenthesis 4 x squared right parenthesis equals 20 x to the power of 6
3z7(4z2)=12z9
3 z to the power of 7 end power left parenthesis 4 z squared right parenthesis equals 12 z to the power of 9
6a5(6a5)=36a25
Answer:
Correct - A, B, C,Incorrect - D.---------------------------
Verify the equations:
A) 6b⁴(-3b⁴) = (6*(- 3))b⁴⁺⁴ = - 18b⁸ - correctB) 5x⁴(4x²) = (5*4) x⁴⁺² = 20x⁶ - correctC) 3z⁷(4z²) = (3*4)z⁷⁺² = 12z⁹ - correctD) 6a⁵(6a⁵) = (6*6)a⁵⁺⁵ = 36a¹⁰ ≠ 36a²⁵ - incorrectIra enters a competition to guess how many buttons are in a jar.
Ira’s guess is 200 buttons.
The actual number of buttons is 250.
What is the percent error of Ira’s guess?
The percent error of Ira’s guess for the number of buttons is 25%
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Ira’s guess is 200 buttons but the actual number of buttons is 250.
The net amount error is (250 - 50) = 50 buttons.
Now to obtain percentage change we'll divide the net amount change by the original amount and multiply it by 100% which is,
= (50/200)×100%.
= 25%
So, the percentage error is 25%.
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use tables to find log
(789.5)1/8
The logarithm of (789.5) elevated to the power 1/8 is given as follows:
log(789.5)^(1/8) = 0.36216901679.
How to obtain the logarithm?The logarithm in this problem is defined as follows:
log(789.5)^(1/8).
It has a power, hence the power can be moved to the front of the logarithm expression applying the power rule, as follows:
log(789.5)^(1/8) = 1/8 x log(789.5).
Then a calculator is used to obtain the logarithm of 789.5, which is the number that is elevated to the base 10 to obtain 789.5, hence:
log(789.5) = 2.89735213434.
Thus the numeric value of the logarithmic expression in this problem is calculated as follows:
log(789.5)^(1/8) = 1/8 x log(789.5) = 1/8 x 2.89735213434 = 0.36216901679.
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a woman 5-feet tall casts an 8-foot shadow. at the same time of day, the shadow of a tree nearby is 120 feet long. in feet, how tall is the tree?
A woman 5-feet tall casts an 8-foot shadow. at the same time of day, the shadow of a tree nearby is 120 feet long. in feet, 75 feet tall is the tree.
Let the tree height = x
From the question, we have
5/8 = x/120
x = (5*120)/8
x = 75 feet
Tree height = 75 feet
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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Graph the following function by moving the points to match two ordered pairs, including the x-intercept:
f(x) = log 1/8(x)
The graph of function f(x) = log 1/8(x) is shown in figure with x - intercept
(8, 0).
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
The function is,
⇒ f (x) = log 1/8 (x)
Now,
Since, The function is,
⇒ f (x) = log 1/8 (x)
Hence, The x - intercept = (8, 0)
And, The graph is show in figure.
Thus, The figure is shown in figure.
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sara gets paid 1,500.00 per month plus 5.5% commission on all her sales. how much will sara get apid for the month of November if she sold $35,000 worth of merchandies
Answer: $1925 is the commission she gets from the merchandise, which means if you add 1,500 + 1925 = $3425. $3425 is what she got for that month.
Step-by-step explanation: if its wrong tell me
  Is it true that 7w + 4 = 5w + 12.
A. Write three more equations that you know are true based on this information.
B. Find the value of 2w.
C. Find the value of w.
Answer:
A. Here are three more equations that are true based on the information you provided:
1. 3w + 2 = 2w + 6
2. 5w - 6 = 4w - 8
3. 7w - 5 = 6w - 7
B. To find the value of 2w, we need to first solve for w in the original equation 7w + 4 = 5w + 12. We can do this by subtracting 5w from both sides of the equation, which gives us 2w + 4 = 12. Then we can subtract 4 from both sides to get 2w = 8. Therefore, the value of 2w is 8.
C. To find the value of w, we can divide both sides of the equation 2w = 8 by 2, which gives us w = 4. Therefore, the value of w is 4.
PLEASE HELP
Graph g(x) = −4x + 8 and identify its x-intercept.
(0, 2)
(0, 8)
(2, 0)
(8, 0)
The x-intercept is (2,0). And the correct option is C: (2,0).
What are intercepts?The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
We have the standard form of the slope-intercept form:
y = mx + b,
where m is the slope and b is the intercept.
In order to find the x-intercept,
substitute y=0 to the equation.
And solve for x.
Given equation is;
g(x); y = -4x+8
y = -4x+8
The slope of the equation is -4.
To find the x-intercept,
Now, -4x + 8 = 0
-4x = -8
x = 2
And the graph is given in the image.
Where (2,0) is the x-intercept.
The point (2,0), where a line crosses x-axis, is known as the x-intercept.
Therefore, the x-intercept is (2,0).
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Answer: (2, 0)
Step-by-step explanation: I took the test and got it right.
I promise it is right!
Just make sure it is the same problem!!
Good luck!!!!! ;)
I need help please it’s ASAP
The interquartile range of the data is equal to 2.18.
What is an interquartile range?The interquartile range is a measure of where a data set's "middle fifty" is located. Whereas a range is a measure of where the start and end of a set are, an interquartile range is a measure of where the majority of the values are.
Given data is { 1.56,1.77,2.22,2.35,2.45,2.77,3.26,4.35,5.23,6.02}.
The upper limit is, and the median is 2.22.
{ 1.56,1.77,2.22,2.35,2.45,2.77}
The lower limit is, and the median is 4.35.
{2.77,3.26,4.35,5.23,6.02}
The interquartile range will be calculated as,
IQR = 4.35 - 2.22
IQR = 2.18
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Given the following formula, solve for v.
8 = 1/2 a^2v + c
Answer:
[tex]v = \frac{16-2c}{a^{2} }[/tex]
Step-by-step explanation:
Original equation
[tex]8 = \frac{1}{2}a^{2} v + c[/tex]
Multiply both sides by 2 to get rid of fraction
[tex]16 = a^{2}v + 2c[/tex]
Get constant on right, [tex]a^{2} v[/tex] on left
[tex]-a^{2}v = 2c - 16[/tex]
Divide both sides by [tex]a^{2}[/tex]
[tex]v = \frac{16 - 2c}{a^{2} }[/tex]
A hot air balloon exert an 800-lb pull on a tether line at a 60-degree angle with the horizontal. Reolve the vector into horizontal and vertical component
Using Vector Decomposition in vertical and horizontal axis, The Horizontal component is 400-lb and Vertical component is 692.82-lb.
What do you mean by vector?An item with both magnitude and direction is referred to be a vector. A vector can be visualized geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.
What is the formula for vertical and horizontal component of vector?The required formulas are:
Horizontal Component = [tex]A \cos \alpha[/tex]
Vertical Component = [tex]A \sin \alpha[/tex]
pull(A) = 800 -lb
[tex]\alpha = 60^{o}[/tex]
Horizontal Component = 800 * cos60
= 400-lb
Vertical Component = 800 * sin60
= 692.82-lb
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Find the result graphically. Click and drag the arrows to represent each term. Type in the result. 7-5
7 is initially represented by 7 units to the right, Now, if we remove 5 from 7, we must move 5 units to the left, arriving at unit 2.
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
On the number line, 7 is represented 7 units right from the origin.
Now subtracting 5 from 7 implies we have to go 5 units to the left so we end up in unit 2.
The graphical representation is illustrated in the attached image.
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Write an expression for "the quotient of z
and 4.”
Answer:
z/4 or 4/z i think or z divided by 4
Step-by-step explanation:
Bella's Pizza Shop charges $4.50 for a small pizza, $7.00 for a medium pizza,and $9.00 for a large pizza. Additional toppings cost extra depending on the size of the pizza ordered. Bruce ordered a large pizza with three toppings that cost a total of $12.60.
Answer:
1.20
Step-by-step explanation:
To determine how much Bruce's large pizza with three toppings would cost without the additional toppings, you would need to know the base price of a large pizza at Bella's Pizza Shop. Based on the information you provided, a large pizza at Bella's Pizza Shop costs $9.00. To determine the cost of the additional toppings, you would need to know the cost of each topping and the number of toppings ordered. Since this information is not provided, it is not possible to determine the cost of the additional toppings or the total cost of Bruce's order.
The large pizza costs $9.00 without any toppings.
The additional toppings cost $12.60 - $9.00 = $<<12.60-9.00=3.60>>3.60.
Therefore, each topping costs $3.60 / 3 = $<<3.60/3=1.20>>1.20. Answer: {1.20}.
Answer:
$1.20
Step-by-step explanation:
Assuming the question is "how much does each topping cost", you could solve it like this:
Total - large pizza price.
12.6 - 9 = 3.6.
Since Bruce got 3 toppings you'll want to do 3.6/3 which will give you 1.2.
If you add it all back up it should give you 12.60 again.
1.2(3)+9=12.6
y = 3/2x + 3 y determine the slope and y intercept
Answer:
if you mean y=3/2x + 3 then the slope (m) is 3/2 and the y-intercept (b) is 3
Step-by-step explanation:
BRAINLIEST!!!
find the slope of the line that passes through the given two points:
(1,-4) and (-4,-6)
Answer:
2/5
Step-by-step explanation:
(y1-y2)/(x1-x2) is the formula
(-4+6)/(1+4) Set up
2/5 Simplify
The time Mo takes to mow the lawn is between 45 minutes and 75 minutes, inclusive.
Does this statement represent a union or an intersection?
Write the statement as a compound inequality with t as your variable of time.
A compound inequality 45 ≤ t ≤ 75 which represents the union of all values larger than or equal to 45 minutes and less than or equal to 75 minutes is the time, denoted by the notation t.
The time Mo takes to mow the lawn is between 45 minutes and 75 minutes, inclusive, which means that the time is either 45 minutes, 46 minutes, 47 minutes, and so on, up to and including 75 minutes. This is a range of values that includes all the times from 45 minutes to 75 minutes.
This statement represents a union, which is the combination of two or more sets of values. In this case, the union is the combination of all the values from 45 minutes to 75 minutes.
To write this statement as a compound inequality, you can use the symbols "≥" (greater than or equal to) and "≤" (less than or equal to) to indicate that the time is greater than or equal to 45 minutes and less than or equal to 75 minutes:
45 minutes ≤ t ≤ 75 minutes
This compound inequality can also be written as:
45 ≤ t ≤ 75
This means that the time, t, is a member of the union of all values that are greater than or equal to 45 minutes and less than or equal to 75 minutes.
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At 0845 hours, a lorry leaves Town A for Town B at an average speed of 52 km/h. It arrives at Town S at 1230 hours. On the return journey, the lorry leaves Town B at 1455 hours and arrives at Town A at 1815 hours. Find the average speed of the lorry on the return journey.
The average speed of the lorry on the return journey is 58.5 km. If At 0845 hours, a lorry leaves Town A for Town B at an average speed of 52 km/h. It arrives at Town S at 1230 hours. On the return journey, the lorry leaves Town B at 1455 hours and arrives at Town A at 1815 hours.
Define speed.The speed of an object can be determined by calculating the distance it covers in a given length of time. For instance, if a car goes 70 miles in an hour, it is doing so at a pace of 70 miles per hour (miles per hour).
Given,
At 0845 hours, a lorry leaves Town A for Town B at an average speed of 52 km/h. It arrives at Town S at 1230 hours.
On the return journey, the lorry leaves Town B at 1455 hours and arrives at Town A at 1815 hours.
distance = speed × time
Average speed from town A to town B is 52 km/h at 3 3/4 hrs.
Distance = 52 km/h × 3 3/4 hrs ...eq1
Let speed in return journey = r
Then distance = r × 3 1/3 hrs ...eq2
From eq1 & eq2
52 ×3 3/4 = r × 3 1/3
52 ×15/4 = r × 10/3
r = (52×15×3)/(4×10) km
r = (13×3×3)/2 km
r = 117/2 km
r = 58.5 km
The average speed of the lorry on the return journey is 58.5 km.
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if each of 20 people generated a random sample of shole numbers and constructed a 95% confidence interval for the proportion that are odd, how many intervlas are expected to contain the true proportion
The control limits that include 95% of the sample means be,
(19.9671 , 20.0329).
Given, each of 20 people generated a random sample of whole numbers and constructed a 95% confidence interval for the proportion that are odd.
we have to find the confidence interval under confidence of 95%.
Subtract 1 from your sample size. 25 – 1 = 24. This gives you degrees of freedom.
Subtract the confidence level from 1, then divide by two.
(1 – 0.95) / 2 = 0.05
For 24 degrees of freedom (df) and α = 0.05, the result is 1.645.
Divide your sample standard deviation by the square root of your sample size.
0.1 / √(20) = 0.02
Now, 0.02 × 1.645 = 0.0329
The lower end of the range
20 – 0.0329 = 19.9671
The upper end of the range
20 + 0.0329 = 20.0329
Hence, the confidence interval be, (19.9671 , 20.0329)
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A car salesperson is paid a base salary of $17,000 a year plus 15% commission on all car sales. What are the sales needed to ensure an annual income greater than $60,000?
Answer:
The salesperson would need to sell a minimum of $286,666,.67 to meet his income goal.
Step-by-step explanation:
y = total income
x = car sales
y = .15x + 17000
60000 = .15x + 17000 Solve for x. Subtract both sides by 17000
43000 = .15x Divide both sides by .15
286,666.67 Rounded to the nearest penny.
Heyy I need help please ^^. Could you also show me how to work this out as well? Thanks! (Both of those equations are supposed to be in 1 curly bracket btw.)
Which ordered pairs are solutions to this system of inequalities?
{5x−4y≥9
{6x+8y≤10
The ordered pair which is solution to this system of inequalities is (1.75, -0.0625).
The system of inequalities are 5x−4y≥9 and 6x+8y≤10.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The intersection consists of the elements that are contained in all of the intervals.
Here, 5x−4y≥9 -------(I) and 6x+8y≤10 -------(I)
Now, y ≤ 5/4 x+(-9/4); y ≤ -3/4 x+5/4
⇒ 5/4 x+(-9/4) ≤ -3/4 x+5/4
⇒ 5/4 x+3/4 x ≤ 5/4+9/4
⇒ 2x≤ 3.5
⇒ x≤ 1.75
Substitute x=1.75 in y ≤ 5/4 x+(-9/4), we get
y ≤ 1.25(1.75)-2.25
y ≤ 2.1875-2.25
y ≤ -0.0625
Two inequalities are intersect at (1.75, -0.0625)
Therefore, the ordered pair which is solution to this system of inequalities is (1.75, -0.0625).
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