Answer:
The vertex is: [tex](\frac{5}{2} - \frac{17}{4} )[/tex]
The zero is: [tex]\frac{5+-\sqrt{17} }{2}[/tex]
Hope this helps :)
Pls brainliest...
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For this graph, write the limits which describe the end-behavior of this graph.
The limits of the end-behavior of this graph are listed below
The limits which describe the end-behavior of this graph.The limits that describe the end behavior of a graph are the values that the function approaches as x goes to positive or negative infinity.
The graph has a hole at (-4, 2), then the function is not defined at x = -4, but the limit as x approaches -4 exists and is equal to the value of the function at that point (since the function is continuous except at the hole).
The graph touches the x-axis at x = 2 to x = 6, this means that the function has roots or zeros at x = 2 and x = 6.
The horizontal asymptote is y = 1, this means that the function approaches 1 as x goes to positive or negative infinity.
To summarize, the end behavior of the graph can be described as follows:
As x approaches -∝, the function approaches 1 As x approaches -4 from the left, the function approaches 2As x approaches -4 from the right, the function approaches 2As x approaches +∝, the function approaches 1Read more about end-behavior at
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help now please will give brain list
Answer:
? = 7.5
Step-by-step explanation:
the angle between the tangent and the radius at the point of contact is 90°
thus the triangle is right
using Pythagoras' identity in the right triangle
?² = 4.5² + 6² = 20.25 + 36 = 56.25 ( take square root of both sides )
? = [tex]\sqrt{56.25 }[/tex] = 7.5
please help me with my math question thank you
The 7th term of the binomial expression given can be found to be 8.136 × 10^7 × x^(-4)
How to find the term ?To find the 7th term of (3x - 4/x²)¹⁴, we can use the binomial theorem, which states that for any positive integer n and any real numbers a and b:
(a + b)ⁿ = ∑(C(n, k) x a^(n-k) x b^k)
Using the binomial theorem formula, the 7th term can be calculated as follows:
Term_7 = C(14, 6) x (3x)^(14-6) x (-4/x²)^6
First, let's find C(14, 6):
C(14, 6) = 14! / (6! x (14-6)!)
C(14, 6) = 14! / (6! x 8!)
C(14, 6) = 3003
Now, we can put everything together:
Term 7 = 3003 x (3x)^8 x (4096 / x¹²)
Term 7 = 8.136 × 10^7 × x^(-4)
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Can someone please help me
The statements true of function f given by f(Θ) = tan(Θ):
A: f is a periodic function (True)D: The period of f is 2π. (True)How to determine functions?A: Since the tangent function has a repeating pattern, it is a periodic function.
B: The domain of the tangent function is restricted because it has vertical asymptotes at certain values of Θ (specifically, odd multiples of π/2).
C: The range of the tangent function is not all real numbers, but rather all values except for its vertical asymptotes.
D: The period of the tangent function is 2π, because the pattern repeats every 2π radians.
E: The period of the tangent function is not π.
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Determine if XY is tangent to circle Z.
Yes
No
(60 POINTs will give BRAINIEST FOR EFFORT)
The line segment XY is tangent to circle Z by using the Pythagorean theorem to find the radius of the circle, and the formula for the distance between a point and a line to find the distance between the center of the circle and the line.
Now let's look at the information given in the problem. We are given the length of line segment XY, which is 3.6 units. We are also given the lengths of two line segments that connect the endpoints of XY to the center of the circle Z: YZ, which is 1.8 units, and ZX, which is 2.7 units.
To determine if XY is tangent to circle Z, we need to check if it is possible for a circle with center Z and radius r to pass through points X and Y. If it is not possible, then XY must be tangent to the circle.
In this case, we can use the lengths of YZ and ZX as the legs of the right triangle, and r as the hypotenuse. We can set up the following equation:
r² = YZ² + ZX²
Substituting the given values, we get:
r² = 1.8² + 2.7²
r² = 7.29
r = √7.29
r ≈ 2.7
Now that we know the radius of circle Z, we can check if it is possible for it to pass through points X and Y. To do this, we need to find the distance between the center of the circle and the line XY. If this distance is equal to the radius of the circle, then XY is tangent to the circle.
To find the distance between the center of the circle and the line XY, we can use the formula for the distance between a point and a line. This formula is:
distance = |Ax + By + C| / √(A² + B²)
where A, B, and C are constants that depend on the equation of the line, and x and y are the coordinates of any point on the line.
In this case, we can use the equation of line XY, which is:
y = 0
Substituting this into the formula, we get:
distance = |A(0) + B(1) + C| / √(A² + B²)
distance = |B| / √(B²)
distance = 1 / √1
distance = 1
Since the distance between the center of circle Z and line XY is 1 unit, and the radius of circle Z is also 1 unit, we can conclude that XY is tangent to circle Z.
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Guff plc, an all-equity firm, has the following earnings per share and dividend history (paid annually).
Year Earnings per share Dividend per share
This year 21p 8p
Last year 18p 7.5p
2 years ago 16p 7p
3 years ago 13p 6.5p
4 years ago 14p 6p
This year’s dividend has just been paid and the next is due in one year. Guff has an opportunity to invest in a new product, Stuff, during the next two years.
The directors are considering cutting the dividend to 4p for each of the next two years to fund the project. However, the dividend in three years can be raised to 10p and will grow by 9 per cent per annum thereafter due to the benefits from the investment. The company is focused on shareholder wealth maximization and requires a rate of return of 13 per cent for its owners.
Required
a. If the directors chose to ignore the investment opportunity and dividends continued to grow at the historical rate what would be the value of one share using the dividend valuation model?
b. If the investment is accepted, and therefore dividends are cut for the next two years, what will be the value of one share?
c. What are the dangers associated with dividend cuts and how might the firm alleviate them?
The circumference of a circle is 15pi centimeters what is the area of the circle in terms of pi?
[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi[/tex]
Consider the demand for fresh detergent in a future sales period
a) The distance value is the leverage value from the output which is 0.004
b) The 99% prediction interval is [7.676, 9.146]
a) We are interested in finding and reporting the prediction interval on the output.
Thus, the prediction interval on the output is [7.9188, 8.9025]
Let us consider the estimated value for y as yₓ
We have
x₁ = 3.7, x₂ =3.9, x₃ = 6.5, β₀= 7.5891, β₁ = -2.3577, β₂= 1.6122, β₃= 0.5012
We know that yₓ = β₀ +β₁x₁ + β₂x₂ + β₃x₃
By substituting the value
x₁ = 3.7, x₂ =3.9, x₃ = 6.5, β₀= 7.5891, β₁ = -2.3577, β₂= 1.6122, β₃= 0.5012 into the above equation we get
yₓ =7.5891-(2.3577*3.7)+(1.6122*3,9)+(0.5012*6.5) = 8.411
Let us calculate the value for the prediction interval
The 100 (1 - a) \% prediction interval is
yₓ ±(tₐ/₂ * x * s* √ 1+distance value )
The distance value is the leverage value from the output which is 0.004
We have yₓ =8.411, t₀.₀₀₅.₂₆ =3.067 and s = 0.235. By substituting these values we find that the 95% prediction interval is
8, 411 + (2.3788 * 0.235sqrt(1 + 0.04)) = [7.841, 8, 981]
b) If Enterprise Industry's plan to have in inventory of the number of bottles implied by the upper limit of the prediction interval, which is approximately 9, it can be very confident that it will have enough bottles to meet demand for detergent in the future sales period.
Thus, the bottles are approximately 9
By multiplying the number of bottles implied by the lower limit of the prediction interval, that is approximately 8, by the price of the detergent that is $3.7. we get the minimal revenue from detergent in the future sales period that is $29.6
We are interested in calculating a 99% prediction interval for the demand of detergent in the future sales period
We have yₓ =8.411, t₀.₀₀₅.₂₆ =3.067 and s = 0.235 By substituting these values, we find that the 95% prediction interval is as follows
8, 411 ± (3.067 * 0.235sqrt(1 + 0.04)) = [7.676, 9.146]
Therefore the 99% prediction interval is [7.676, 9.146]
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Question 13(Multiple Choice Worth 1 points)
(05.01 MC)
Graph the following system of equations.
y = 3x + 15
3x + 3y = 9
What is the solution to the system?
There is no solution.
There is one unique solution (-3, 6).
There is one unique solution (0, 15).
There are infinitely many solutions.
Thus, the given system of equation has one unique solution (-3, 6).
Explain about the system of equations:Two or even more equations with the same variables are referred to be a system of equations. The intersection of the lines is the location where an equation system has a solution. Systems of equations can be solved using one of four techniques: graphing, substitution, elimination, or matrices.
Given: system of equations:
y = 3x + 15 ...eq 1
3x + 3y = 9 (divide by 3)
x + y = 3
y = 3 - x ..eq 2
equation eq 1 and eq 2
3x + 15 = 3- x
3x + x = 3 - 15
4x = -12
x = -3
y = 3 - (-3) = 3 + 3 = 6
Solution - (-3, 6)
Thus, the given system of equation has one unique solution (-3, 6).
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PLEASE HELP ME! I WILL BE GIVING 50 POINTS!
Answer: B
Step-by-step explanation:
Ex: Shortest to smallest.
If x = 3 units, y = 5 units, and h = 4 units, find the area of the rhombus shown above using decomposition.
The calculated value of the area of the rhombus is 35 sq units
Finding the area of the rhombusFrom the question, we have the following parameters that can be used in our computation:
The rhombus
Also, we have
x = 3, y = 5 and h = 4
Using shape decomposition, we have the following
Shapes = Rectangle and 2 triangles
So, the area is
Area = Rectangle + 2 triangles
Using the area formulas, we have
Area = 1/2 * xy + 1/2 * xy + hy
substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 3 * 5 + 1/2 * 3 * 5 + 4 * 5
Evaluate
Area = 35
Hence, the area is 35 sq units
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Kirsty says,
When you double the size of an acute angle,
you always get an obtuse angle.
Explain why Kirsty is not correct.
Step-by-step explanation:
this is because if the acute angle is equal to or less than 45° it will be less than or equal to 90° but it the angle is more than 45° then it will be a obtuse angle if it is doubled .
eg.
acute angle is 44°
then if it is doubled it will be 44 ˣ 2
= 88°
But if the angle is 46 °
then if it is doubled it will be 46 ˣ 2
= 92°
hope this helps you.
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For this graph, for each vertical asymptote, write down the two limits that describe the graph of the function near the asymptote.
The limits on the vertical asymptotes of the function are given as follows:
[tex]\lim_{x \rightarrow -6^-} f(x) = \infty[/tex][tex]\lim_{x \rightarrow -6^+} f(x) = -\infty[/tex][tex]\lim_{x \rightarrow -2^-} f(x) = \infty[/tex][tex]\lim_{x \rightarrow -2^+} f(x) = -\infty[/tex][tex]\lim_{x \rightarrow 6^-} f(x) = -\infty[/tex][tex]\lim_{x \rightarrow 6^+} f(x) = \infty[/tex]What are the vertical asymptotes of a function?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
On a graph, at the vertical asymptotes, the graph just approaches the point, it does not cross the point.
Hence the vertical asymptotes are given as follows:
x = -6, x = -2 and x = 2.
We must observe the limits to the left(denoted by the - sign) and to the right (denoted by the + sign) of each asymptote.
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The graph shows a proportional relationship. Which equation matches the graph? A: y=1/3x B: y=x C: y=3x D: y=9x
The equation that represent the graph is C) y=3x.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here let us take the two points [tex](x_1,y_1)=(1,3) , (x_2,y_2)=(3,9)[/tex].
Now using slope formula then,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> m = [tex]\frac{9-3}{3-1}=\frac{6}{2}=3[/tex].
Now using equation formula then,
=> [tex]y-y_1=m(x-x_1)[/tex]
=> y-3=3(x-1)
=> y-3 = 3x-3
=> y=3x.
Hence the equation that represent the graph is C) y=3x.
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Solve for x. Enter the solutions from least to greatest.
(x - 10)² - 1 = 0
lesser x =
greater x =
Answer:
lesser x = 9
greater x = 11
Step-by-step explanation:
(x-10)² - 1 = 0
(x-10)² = 1
(x-10) = +- root1 (positive and negative root1)
So (x-10) = +1 and (x-10) = -1
Firstly
X - 10 = 1
X = 11
Secondly
X - 10 = -1
X = 9
So you have x = 9, and x = 11
The smaller one is the lesser x (9)
The larger one is the greater x (11)
A rectangular paperboard measuring 26in long and 16in wide has a semicircle cut out of it, as shown below. What is the perimeter of the paperboard that remains after the semicircle is removed? (Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.)
The perimeter of the paperboard that remains after the semicircle is removed is 93.12 inches
How to solve for perimeterInformation given in the problem includes:
A rectangular paperboard measuring 26in long and 16in wide
information for the semicircle are
Width = 16 inches
Radius = 16 / 2 = 8 inches
Length = 26 inches
Circumference of the semi circle is calculated using the formula
= π * radius
Where the radius is 8 inches and π = 3.14.
Substituting in to the formula and solving for the circumference of the semicircle which same as perimeter of the semicircle gives:
= 8 x 3.14
= 25.12
The perimeter would be
26 inches + 26 inches + 25.12 inches + 16 inches
= 93.12 inches
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For # 1 - 3 Identify each of the following numerical values as
either: (P) Parameter or (S) Statistic
1. of a company's employees the opinion of just
those that were there on time one morning about what they
thought of a new training program.
2. in a study abour a small company of 25
employees, the range of their employees salaries
3. in a study about the value of American homes in
2012, the average decrease of all the homes sold in Gwinnett
Answer:
S - S - P
Step-by-step explanation:
(S) Statistic - The opinion of just those employees who were there on time one morning about a new training program would be a statistic as it represents a sample of the entire population of employees in the company.
(S) Statistic - The range of employees' salaries in a study about a small company with 25 employees would be a statistic as it represents a characteristic of a sample of employees from the company.
(P) Parameter - The average decrease of all the homes sold in Gwinnett in a study about the value of American homes in 2012 would be a parameter as it represents a characteristic of the entire population of American homes in Gwinnett.
the dot plots below show the number of books that emma and mary read each month in last 18 months. on average, which girl read the most number of books each month?
Answer:
**NEED ANSWER ASAP DUE TOMORROW**
What are two observations of quasars that prove they cannot be a part of the milky way galaxy?
Step-by-step explanation:
Use the following amortization chart:
Selling price
of home
$ 74,000
Down payment
$ 5,000
Principal
(loan)
$ 69,000
Rate of
interest
5.08
Years
30
Payment per $1,000
$ 5.3682
Monthly mortgage payment
$ 370.41
What is the total cost of interest?
Note: Do not round intermediate calculations. Round your answer to the nearest whole dollar.
Answer:
Step-by-step explanation:
To find the total cost of interest, we first need to find the total payment over the life of the loan:
Total payment = Monthly payment x Number of payments
Total payment = $370.41 x (30 x 12)
Total payment = $133,347.60
Next, we need to subtract the principal (loan) amount to find the total interest paid:
Total interest = Total payment - Principal
Total interest = $133,347.60 - $69,000
Total interest = $64,347.60
Rounding to the nearest whole dollar, the total cost of interest is $64,348.
Kaitlin is jogging from her house to school. She has gone 1/4 miles so far. Her school is 3 7/8 miles from her house. How many miles does Kaitlin still have to jog? Write your answer as a mixed number in simplest form.
Answer:
3 7/8 - 1/4 = 3 5/8 times mile = 3.625 miles
Thats how its done
Step-by-step explanation:
Trapezoid DEFG is formed when right triangle HGD is cut by line FE such that
FE | GD. Find the volume of the solid generated when the trapezoid is rotated
about side DE. Round your answer to the nearest tenth if necessary.
Volume of solid generated when the trapezoid is rotated about side DE=549.8.
What is trapezoid?A trapezoid is a quadrilateral with only one pair of parallel sides. It is also known as a trapezium in some countries.
Define volume of the solid?The volume of a solid is the amount of space it occupies in three-dimensional space.There are different formulas to calculate the volume of different types of solids, such as cubes, spheres, cylinders, and cones.
Given trapezoid DEFG formed when right angle HGD is cut by line FE.
Volume of solid generated about side DE:
[tex]V_{GDH}[/tex]=1/3×πr²h
=1/3×π(5+5)²(6)
=200π
[tex]V_{FEG}[/tex]=1/3×π×r²h=1/3×π×(5)²×3
=25π
Volume of Solid=[tex]V_{GDH}[/tex]-[tex]V_{FEH}[/tex]
=200π-25π=175π
=549.78 ≈549.8
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Consider the line y = -2x + 6. Find the equation of the line that is parallel to this line and passes through the point (7,-4). Find the equation of the line that is perpendicular to this line and passes through the point (7,-4). Note that the ALEKS graphing calculator may be helpful in checking your answer.
The equation of the line that is parallel to the given line and passes through the point (7,-4) is y = -2x + 10.
The equation of the line that is perpendicular to the given line and passes through the point (7,-4) is y = 1/2x - 15/2.
What is the equation of the line?The equation of a line that is parallel to a given line is calculated as follows;
y = -2x + 6
slope of this line = - 2
Any line that is parallel to this line will also have a slope of -2.
The equation of the line that is parallel to the given line and passes through the point (7,-4):
y - y1 = m(x - x1)
y - (-4) = -2(x - 7)
y + 4 = -2x + 14
y = -2x + 10
The slope of the line perpendicular to the line = 1/2
y - y1 = m(x - x1)
y - (-4) = (1/2)(x - 7)
y + 4 = (1/2)x - (7/2)
y = 1/2x - 7/2 - 4
y = 1/2x - 15/2
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Find the perimeter of quadrilateral PQRS.
Perimeter =
(50 POINTs will give BRAINIEST FOR EFFORT)
The perimeter of the quadrilateral PQRS is calculated as:
= 180 units.
How to Find the Perimeter of the Quadrilateral?Recall that if two tangents meet outside a circle, their length will be the same based on the tangents theorem.
Therefore, note that every line segments that appear tangent and intersect each other outside the circle have the same length.
Thus, we have:
Perimeter of the quadrilateral PQRS = 52.5 + 37.5 + 23 + (37.5 - 23) + 27.1 + (52.5 - 27.1)
Perimeter of the quadrilateral PQRS = 180 units.
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−3z−z :Give answer, please
Answer:
-4z
Step-by-step explanation:
Simply add the z, which is a variable together.
Answer:
-4z
Step-by-step explanation:
A pole that is 3m tall casts a shadow that is 1.17 m long. At the same time, a nearby tower casts a shadow that is 45.5 long. How tall is the tower? Round your answer to the nearest meter.
The proportion is solved and the height of the tower is H = 117 m
Given data ,
A pole that is 3m tall casts a shadow that is 1.17 m long
And , a nearby tower casts a shadow that is 45.5m long
So , the proportion is given by
Let the height of the tower be H
And , 3 / 1.17 = H / 45.5
On simplifying the equation , we get
Multiply by 45.5 on both sides , we get
H = 116.6667 m
H = 117 m
Hence , the height of the tower is H = 117 m
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Find the 50th partial sum of the arithmetic sequence
-6, -2, 2, 6, ...
The 50th partial sum of the given arithmetic sequence is 4600
Calculating partial sum of an arithmetic sequenceFrom the question, we are to calculate the 50th partial sum of the given arithmetic sequence
The given arithmetic sequence is
-6, -2, 2, 6, ...
To find the 50th partial sum of the sequence, we will find the sum of the first 50 terms in the sequence.
The sum of n terms of a sequence is given by the formula,
S = n/2(a + l)
Where a is the first term
and l is the last term
l is given by
l = a + (n - 1)d
Where d is the common difference
In the given series
a = -6
d = -6 -(-2) = -6 + 2 = 4
Thus,
l = -6 + (50 - 1)4
l = -6 + 49×4
l = -6 + 196
l = 190
Then,
S = 50/2(-6 + 190)
S = 25(184)
S = 4600
Hence,
The sum is 4600
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An arrowhead is joined to a kite to form a
rhombus, as shown below. The three acute
angles of the arrowhead are all the same
size.
Work out the size of angle z.
Give your answer in degrees (°).
z 153°
Answer:
Z = 60
Step-by-step explanation:
60+60+z=180
120+z=180
z=180-120
Z = 60
A wildlife group is trying to determine how many wild hogs are in a certain area. They trapped, tagged, and released 20 wild hogs. Later, they counted 8 wild hogs out of the 40 they saw.
What can the wildlife group estimate is the total population of wild hogs in that area?
A. 80
B. 90
C. 100
D. 16
The wildlife group can estimate that there are 100 wild hogs in the area. The answer is C.
Define the capture-recapture method?The basic idea behind this method is that if we capture a random sample of animals from a population, tag them, and release them back into the population, then later capture another sample of animals, the ratio of tagged to untagged animals in the second sample can be used to estimate the total population size.
To estimate the total population of wild hogs in the area, we can use the capture-recapture method.
In this case, the wildlife group tagged and released 20 wild hogs, and later counted 8 wild hogs out of the 40 they saw. We can set up a proportion to estimate the total population size:
(Tagged hogs in first sample) / (Total population size) = (Tagged hogs in second sample) / (Number of hogs in second sample)
Putting the values,
⇒ 20 / x = 8 / 40
Simplifying and solving for x, we get:
⇒ x = (20 × 40) / 8 = 100
⇒ x = 100
Therefore, the wildlife group can estimate that there are 100 wild hogs in the area. The answer is C.
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What are the ordered pair solutions for this system of equations? y = -x² + 2 y = x First, set the equations equal to each other and move everything to one side. A:-x²+x+2=0 C: -x² + 2 = X B:x² + x 2 = 0 D: x² + x + 2 = 0 -
To find the ordered pair solutions for the system of equations y = -x² + 2 and y = x, we can set the two equations equal to each other:
-x² + 2 = x
Now we can rearrange this equation into standard quadratic form by moving everything to one side:
-x² + x + 2 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = -1, b = 1, and c = 2
Plugging these values into the formula, we get:
x = (-1 ± √(1 - 4(-1)(2))) / 2(-1)
x = (-1 ± √9) / (-2)
x = (-1 ± 3) / (-2)
So the solutions for x are x = -1 and x = -2.
To find the corresponding values of y, we can plug these values of x into either of the original equations. Let's use y = x:
When x = -1, y = -1
When x = -2, y = -2
Therefore, the ordered pair solutions for this system of equations are (-1, -1) and (-2, -2).
kiran's cat eat 1/2 cup of food each day how much Kirans cat can eat in a week .
Answer:
If Kiran's cat eats 1/2 cup of food each day, then in a week (7 days), the cat can eat:
1/2 cup/day x 7 days = 3.5 cups
So Kiran's cat can eat 3.5 cups of food in a week.