The ordered pairs that are solutions of the given system of equations are:
(a) (0,−4)
What are ordered pairs?The ordered pairs are a numerical value that occupies a specific position in the Cartesian plane, these pairs can have at least two components and these are:
P = (x, y)
x is the numerical value on the x-axisy is the numerical value on the y-axisFirst we will write the equations in a more organized way, then we will evaluate each of the pairs and validate that the equality is fulfilled.
[tex]y = -4e^{x}[/tex]
[tex]7x - y = 4[/tex]
(a) (−4,0)
y = -4e⁻⁴
y = -0.0732
Not true since the value of "x" does not make the value of "y" zero.
(b) (0,−4)
y = -4e⁰
y = -4
7(0) - y = 4
0 - y = 4
y = -4
If it complies
(c) (0,−2)
y = -4e⁰
y = -4 This pair is not a solution
(d) (−1,−3)
y = -4e⁻¹
y = -1.47 This pair is not a solution
Learn more about ordered pairs in:
https://brainly.com/question/10526274
#SPJ4
a spinner has 20 equally sized sections, 2 of which are green and 18 of which are blue. The spinner is spun and, at the same time , a fair coin is tossed. what is the probability, that the spinner lands on green and the coin toss is tails?
Answer:
The probability of getting the spinner to land on green and coin to show Tails is 1/20
Step-by-step explanation:
p(E) = p(spinner landing on green) = 2/20
p(F) = p(Coin lands on Tails) = 1/2
p(E and F) = p(E) . p(E/F)
p(E and F) = 2/20 . 1/2
p(E and F) = 1/20
The probability of getting the spinner to land on green and coin to show Tails is 1/20
What is the selling price of the bonds?
This announcement is not an offer of securities for sale or an offer to buy securities.
New Issue October 15, 2021
$750,000,000
CRAFT FOODS, INC.
7.75% Debentures Due October 1, 2031
Price 100.5%
1. Is the market rate of interest higher or lower than 7.75% when the Craft Foods bonds were issued.
2. What is the selling price of the bonds?
Answer:
1) It is not specified in the given information whether the market rate of interest is higher or lower than 7.75% when the Craft Foods bonds were issued.
2) The selling price of the bonds is determined by multiplying the face value of the bonds by the price percentage. In this case, the face value of the bonds is $750,000,000 and the price percentage is 100.5%, so the selling price would be:
$750,000,000 x 100.5% = $757,500,000
It's worth noting that the price percentage being 100.5% means that the bonds are being sold at a slight premium (i.e. above face value) and that the yield to maturity is lower than 7.75%.
Chrissy says her book is 12 inches long Jessie says that it is 1 foot long if both of them are correct why do their measurements seem different
12 inches is equal to one foot. 12 inches seems like more because 12>1, but they are really equal.
A city park is in the Shape of a triangle where the sides have lengths 172m, 186m, and 123m. If a fence was built around the perimeter of the park,how long would the fence need to be
To figure out the perimeter of a triangle, we add up all of the sides.
172 + 186 + 123 = 481
The perimeter is equal to 481m.
If a fence were to be built around the perimeter of the park, it would need to be a length of 481m.
A triangle has coordinates F(−2, 3), G(−4, 1), and H(−2, −2). The triangle is translated and its image has coordinates F’(0, 0), G’(−2, −2), and H’(0, −5). What is the correct rule for the translation? (x, y) Right-arrow (x + 2, y + 3) (x, y) Right-arrow (x + 2, y – 3) (x, y) Right-arrow(x – 2, y + 3) (x, y) Right-arrow (x – 3, y+ 2) Use the figure to identify the correct rule for the translation. (x, y) Right-arrow (x – 3, y + 4) (x, y) Right-arrow (x + 3, y – 4) (x, y) Right-arrow (x – 4, y + 3) (x, y) Right-arrow (x + 4, y – 3)
The rule for the translation is (x, y) Right-arrow (x + 2, y – 3).
What is Transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Given;
A triangle has coordinates F(−2, 3), G(−4, 1), and H(−2, −2)
. The triangle is translated and its image has coordinates F’(0, 0), G’(−2, −2), and H’(0, −5).
If a point A(x, y) is translated a units right and b units down, the new point is at A'(x + a, y - b)
Therefore, the translation of FGH to F'G'H' will be (x + y) ⇒ (x + 2, y - 3).
Find out more on Transformation at;
brainly.com/question/1462871
#SPJ1
The cost to produce x monitors is represented by the expression 350x + 1500. The cost to
produce t x chairs is represented by the expression 175x - 50. Write and simplify an expression
to represent
the cost of x monitors and chairs.
The expression to represent the cost of x monitors and chairs is 525x + 1450.
What is system of equation?A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
Given that:
The cost to produce x monitors is:
350x + 1500
The cost to produce x chairs is:
175x - 50
We have to find the total cost of x monitors and chairs.
Total cost of x monitors and chairs = cost to produce x monitors + cost to produce x chairs
Substitute the equations:
Total cost of x monitors and chairs = (350x + 1500) + (175x - 50)
Total cost of x monitors and chairs = 350x + 1500 + 175x - 50
Total cost of x monitors and chairs = 525x + 1450
Hence, the expression to represent the cost of x monitors and chairs is 525x + 1450.
Learn more about system of equation here:
https://brainly.com/question/24065247
#SPJ1
use the shell method to find the volume generated by revolving the shaded regions bounded by the curves and lines in exerciss 7-12about the y-axis
The answer is 1) V = [tex]2\pi\int\limits(2)+ {x} \, dx[/tex]; 2) V = [tex]2\pi \int\limits(1 - 2x) - 2x dx[/tex]; 3) V =[tex]2\pi \int\limits {\sqrt{2} } \, dx[/tex] ; 4) V = [tex]2\pi\int\limits {\sqrt{(-2/2)(2-2)} \ dx[/tex] .
1) The volume of the shell is then given by the product of the area of its curved surface and its height. The height is equal to 2 - (-2) = 4, and the radius is equal to the minimum of the distances from x = 2 to the two curves, which is x = 2 - () = 2 + . The volume of the solid is then given by the definite integral:
V = [tex]2\pi\int\limits(2)+ {x} \, dx[/tex] = [tex]2\pi [(/3) + 2x][/tex] evaluated from 0 to 1 = (4/3)π.
2) The height of the region is equal to - (2x) = -2x, and the radius is equal to the minimum of the distances from x = 1 to the two curves, which is x = 1 - (2x) = 1 - 2x. The volume of the solid is then given by:
V = [tex]2\pi \int\limits(1 - 2x) - 2x dx[/tex]=[tex]2\pi [/5 - 2/3 + /2][/tex] evaluated from 0 to 1 = (8π/15).
3) The height of the region is equal to (2-x) - = 2-x. The radius is equal to the minimum of the distances from x = 0 to the two curves, which is x = The volume of the solid is then given by:
V =[tex]2\pi \int\limits {\sqrt{2} } \, dx[/tex] = [tex]2\pi [(x^4/4)][/tex] evaluated from 0 to √2 = (π/2).
4) The height of the region is equal to () - (2-) = 2 - 2. The radius is equal to the minimum of the distances from x = 0 to the two curves, which is x = √((2-)/2). The volume of the solid is then given by:
V = [tex]2\pi\int\limits {\sqrt{(-2/2)(2-2)} \ dx[/tex] = [tex]4\pi [(2/3)\± (2\sqrt{2} /3)][/tex]
The complete Question is:
Use the shell method to find the volumes of the solids generated by revolving the regions bounded by the curves and lines in about the
1. y = x, y = -x/2, and x = 2
2. y = 2x, y = x/2, and x = 1
3. y = x/2, y = 2-x, and x = 0
4. y = 2-x/2, y = x/2, and x = 0
To know more about Shell Methods:
brainly.com/question/17074517
#SPJ4
Apple = 7, solve for ?
Using historical records, the personnel manager of a plant has determined the probability of XX, the number of employees absent per day. It isX 0 1 2 3 4 5 6 7P(X) 0.0046 0.0248 0.3098 0.3399 0.219 0.0798 0.019 0.0031Find the following probabilities.A. P(2≤X≤5)P(2≤X≤5)Probability =B. P(X>5)P(X>5)Probability =C. P(X<4)P(X<4)Probability =
The probability in each case is:
A. P(2≤X≤5) = 0.5945 (0.3098 + 0.3399 + 0.219) B. P(X>5) = 0.019 (0.0798 + 0.019) C. P(X<4) = 0.3614 (0.0046 + 0.0248 + 0.3098 + 0.3399)The probabilities provided are the probabilities of each value of X. For example,
P(X=0) is 0.0046, which means that there is a 0.0046 probability that exactly 0 employees will be absent per day.Similarly,
P(X=1) is 0.0248, which means that there is a 0.0248 probability that exactly 1 employee will be absent per day. P(X=2) is 0.3098, which means that there is a 0.3098 probability that exactly 2 employees will be absent per day, and so on.When finding probabilities for a range of X values, you need to add up the individual probabilities of all the values in the range. For example, if you are looking for
P(2≤X≤5), then you need to add the individual probabilities for X = 2, 3, 4, and 5, which is 0.3098 + 0.3399 + 0.219 + 0.0798 = 0.5945. Similarly, if you are looking for P(X>5), then you need to add the individual probabilities for X = 6 and 7, which is 0.019 + 0.0031 = 0.0221. Finally, if you are looking for P(X<4), then you need to add the individual probabilities for X = 0, 1, 2, and 3, which is 0.0046 + 0.0248 + 0.3098 + 0.3399 = 0.3614.Learn more about probabilities:
https://brainly.com/question/24756209
#SPJ4
what is the definition of holy
Answer: dedicated or consecrated to God or a religious purpose; sacred.
or used in exclamations of surprise or dismay.
How do I find my MLE given some values for x_i?
(a) The likelihood function for this sample is given by:
L(λ) = λ^2 * exp(-λ * (5 + 3 + x))
where x is the third observation, X₃, which is larger than 10.
What is the MLE for λ?(b) To find the MLE for λ, we take the derivative of the log-likelihood with respect to λ and set it equal to zero:
d/dλ ln(L(λ)) = 2/λ - (5 + 3 + x) = 0
Solving for λ, we find that the MLE for λ is λ = (2) / (5 + 3 + x).
Since x is greater than 10, the MLE for λ is positive and less than 2/(5 + 3 + 10) = 2/18
Therefore, the correct answer is as given above
learn more about MLE for exponential distribution: https://brainly.com/question/15173860
#SPJ1
90 n degrees clockwise about vertex l (-4,1)(-2,1)(-4,-3)
For the 90° clockwise rotation, the coordinate (x, y) becomes (y, -x).
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a point is rotated 90 degrees about the origin.
Assume the point to be -
P(x, y)
For the 90° clockwise rotation, the coordinate (x, y) becomes (y, -x).
Therefore, for the 90° clockwise rotation, the coordinate (x, y) becomes (y, -x).
To solve more questions on algebraic expressions, visit the link below-
brainly.com/question/1041084
#SPJ1
Find the area of the yellow triangle shown below.
I have added a screenshot.
The probability of getting someone who is a woman or a heavy drinker is,
0.546 to three decimal places.
None of the above is the correct option.
What is the probability?The Probability in mathematics is possibility of an event in time. In simple words how many times that incident is happening in any given time interval.
Given:
The table lists the drinking habits of a group of college students.
If a student is chosen at random,
then the probability of getting someone who is a woman or a heavy drinker,
=P(woman) + P(heavy drinker) - P(woman and heavy drinker)
= 216/405 + 13/405 - 8/405
= 221/405
= 0.546 to three decimal places.
Therefore, the probability is 0.546.
To learn more about the probability;
brainly.com/question/11234923
#SPJ1
Select all correct responses (more than one may be correct):Which of the following characteristics of a dataset indicate that linear regression (the kind we know how to do) may NOT be appropriate?Group of answer choices1. A scatterplot of the data looks like a U2. The data are drawn from 2 or more distinct groups3. A scatterplot of the data exhibits a strong negative correlation4. A scatterplot of the data looks like a V
The characteristics of a dataset indicate that linear regression (the kind we know how to do) may NOT be appropriate are, The data are drawn from 2 or more distinct groups, and A scatterplot of the data looks like a V.
These two characteristics indicate that linear regression may not be appropriate because the linear regression model assumes a linear relationship between the independent variable(s) and the dependent variable.
If the data are drawn from two or more distinct groups, this may indicate multiple relationships; therefore, a linear model may not be appropriate. If the scatterplot looks like a V, this may indicate a non-linear relationship, so a linear regression model may not be appropriate either.
To know more about linear regression, here
https://brainly.com/question/29665935
#SPJ4
A triangle has two sides of length 12. which of the following could be the length of the third side?
As a result, the third side's length might be any value higher than 0 and less than 12, or any number bigger than 12 and less than 24.
Hence, option (c) is correct choice.
The length of a triangle's third side must meet the triangle inequality theorem, which says that the total of the lengths of the triangle's two sides must be higher than the length of the triangle's third side.
As a result, the length of the third side of a triangle with two sides of length 12 must be between 0 and 24, omitting 12.
The third side can have the following lengths:
0 < length < 12
12 < length < 24
For more questionsTraingle inequality theorem
https://brainly.com/question/12252201
#SPJ4
The missing option may be:
(a) 6 < length < 12
(b) 2 < length < 4
(c) 12 < length < 24
(d) 15 < length < 30
You have $400,000 saved for retirement. Your account earns 7% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 20 years?
Answer:
you would be able to pull out $1,933.33 each month for 20 years if you have $400,000 saved for retirement and it earns 7% interest.
An exponential function f(x) has f (2) = 36
and f (3) = 216. What is f (4)?
When dividing two exponential functions with the same base, the second law states that the exponents must be subtracted
f(4) = (6)⁴ = 1296
What is meant by exponential function?According to the first law, adding the exponents will multiply two exponential functions with the same base. According to the second law, we must subtract the exponents when dividing two exponential functions with the same base. The third law indicates that we must multiply the exponents in order to increase a power to a new power.
Here,
Given :
=>f(2) = 36
=> f(3) = 216
So,
=> f(x) = (6)ˣ
=>f(4) = (6)⁴ = 1296
If f(x) = , where b > 0 and b 1, is the formula for an exponential function. B is referred to as the base and x is referred to as the exponent, just like in any exponential expression. Bacterial proliferation is an illustration of an exponential function. Some bacteria grow by two folds per hour.
To learn more about exponential function refer to:
brainly.com/question/2456547
#SPJ1
ab³c² and a²b²c
Find the GCF
Written without exponents, you'd have
abbbcc and aabbc
Both have one a, two b's, and one c.
The GCF is [tex]ab^2c[/tex], since those are the greatest factors they all have in common.
find the value of x in both of the problems
Answer:
x = 127°
x = 36
Step-by-step explanation:
For the question 5:The sum of interior angles for the given geometrical figure is calculated with the following formula:
(s-2) × 180
s is the number of sides/angles.3 × 180 = 540
Find the sum of all angles.90 + 143 + 77 + 103 + x = 540
Add like terms.413 + x = 540
Subtract 413 from both sides to isolate x.x = 127°
For the question 6:The given is a hexagon. The sum of its exterior angles is equal to 360.
Find the sum of the given angles to find the value of x.80 + 59 + 2x + 59 + 54 + x = 360
Add them up.252 + 3x = 360
Subtract 252 from both sides to isolate x.3x = 108
Divide both sides by 3.x = 36
Simplify and order the following functions from smallest to largest (in the asymptotic sense) with respect to n. Group functions f(n) and g(n) together if f(n) = O(g(n))). Logarithms are base 2 unless stated otherwise. log 24n, log² (4n²), 210logn, log10 n12, 4logn², 47, √8n, (2), n²/logn, 4²n, n² + 64n1.89
The functions can be simplified and ordered as follows (from smallest to largest):
1. O(1) = constant functions
2472. O(log n) = logarithmic functions
log10 n¹²4 log n3. O(√n) = square root functions
√(8n)O(n) = linear functions210 log n4. O(n log n) = log-linear functions
log² (4n²)log 24n5. O(n²) = quadratic functions
n² + 64n^1.894²n6. O(n² / log n) = "quasi-quadratic" functions
n² / log nSimplifying Ordering FunctionsThis is a description of the concept of big-O notation and asymptotic analysis in computer science. Big-O notation is used to describe the upper bound of the growth rate of a function. It provides a way to classify functions based on how quickly they grow relative to the input size. Asymptotic analysis, on the other hand, is the study of the behavior of functions as the input size approaches infinity.
The purpose of this analysis is to determine which algorithms are the most efficient for a given problem. By understanding the asymptotic behavior of functions, we can make informed decisions about the trade-offs between different algorithms and choose the one that is best suited for a particular problem.
Learn more about Simplifying Ordering Functions here:
https://brainly.com/question/21864792
#SPJ4
A student states
that -x is always equal to a negative
integer. Is the student correct? Justify
your reasoning.
Answer:
Step-by-step explanation:
−x is always equal to a negative integer is an incorrect statement.
The student is not correct.
What is Number system?
A number system is defined as a system of writing to express numbers.
−x is always equal to a negative integer when x is positive integer
Homer ate 12 more donuts than Bart. Together, they ate 26 donuts. How many donuts did Homer eat?
Answer:
14
Step-by-step explanation:
26-12
what's the constant of proportionality/unit rate.
The Constant of proportionality is [tex]\frac{1}{2}[/tex].
What is constant of proportionality?
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
Here to find constant of proportionality we need to divide y by x. Then,
=> constant of proportionality = [tex]\frac{y}{x}[/tex]
Here put x=10 and y=5 then
=> [tex]\frac{5}{10} = \frac{1}{2}[/tex]
Now put x=20 and y=10 then
=> [tex]\frac{10}{20} = \frac{1}{2}[/tex]
Hence the constant of the proportionality is [tex]\frac{1}{2}[/tex].
To learn more about constant of proportionality refer the below link
https://brainly.com/question/28413384
#SPJ1
there are occasions when the forcing term q1x2 in a linear equation fails to be continuous because of jump discontinuities. fortunately, we may still obtain a reasonable solution imitating the pro- cedure discussed in problem 31. use this procedure to find the continuous solution to the initial value problem.
Ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.
How does one determine the beginning value of an equation?A function’s initial value is its value when x equals zero. This is equivalent to the y-intercept. The graph shows that our line crosses the y-axis at point zero, eight. As a result, the starting value is eight. We’ll use SymPy’s solution() function to solve the two equations for the two variables x and y. The solution() method accepts two arguments: a pair of equations (eq1, eq2) and a pair of variables to solve for (x, y). A Python dictionary serves as the SymPy solution object.
The initial value, also known as the y-intercept, is the output value of a linear function when the input is 0.
The continuous solution to the initial value issue given by the linear equation with a forcing component q1x2 is one that meets the starting conditions and holds true across the whole range of x values. The equation's answer is provided by:
C1e(q1x2) + C2x + C3 = y(x).
Where C1, C2, and C3 are starting conditions-determined constants. To obtain the answer, use the beginning conditions to solve for C1, C2, and C3.
To learn more about initial value, visit
brainly.com/question/4469685
#SPJ1
The complete question is: What is the continuous solution to the initial value problem given by the linear equation with a forcing term q1x2?
PLEASE HELP
Value Rent-A-Car rents a luxury car at a daily rate of $37.33 plus 25 cents per mile. A business person is allotted $110 for car rental each day. How many miles can the business person travel on the $110?
The number of miles the business person can travel with 110 dollars is 290 miles.
How to find the number of miles a business person can travel?Value Rent-A-Car rents a luxury car at a daily rate of $37.33 plus 25 cents per mile. A business person is allotted $110 for car rental each day.
Therefore, the number of miles the business person can travel on 110 dollars can be calculated as follows;
Using equations,
Therefore,
y = 0.25x + 37.33
where
x = number of milesy = total costTherefore, let's find the distance he can travel for 110 dollars.
110 = 0.25x + 37.33
110 - 37.33 = 0.25x
72.67 = 0.25x
x = 72.67 / 0.25
x = 290.68
Therefore,
number of miles he can travel = 290 miles
learn more on equation here: https://brainly.com/question/14707938
#SPJ1
A, B & C lie on a straight line. D, C & E lie on a different straight line. Angle y = 109° and angle z = 58°. Work out x , explaining each stage of your working in the comment box.
A, B & C lie on a straight line.
D, C & E lie on a different straight line.
Angle
y
= 109° and angle
z
= 58°.
Work out
x
, explaining each stage of your working in the comment box.
Answer:
The exterior of a triangle is the sum of two of its interior angles except the one adjacent to it. The angle x is evaluated as 135°.
What is a triangle?
A triangle is a two dimensional shape bounded by three sides. The sum of the interior angles of a triangle is 180°. The longest side of a triangle is always less than the sum of other two sides.
Given that,
There is a triangle shown in the figure with following angles,
∠y = 102° and ∠Z = 57°.
Angle x is the exterior angle of the given triangle. Use the property of exterior angle to get,
∠x = ∠B + ∠Z
= (180° - y) + 57°
= (180° - 102°) + 57°
= 135°
Hence, the angle x has been worked out as ∠x = 135°.
To know more about triangle click on,
URGENT!!!
1) Find the domain of ((2a + b)/a - (a + 2b)/b)((a - b)/(b ^ 2 + ab) + (a + b)/(b ^ 2 - ab))
2) Find the domain of the simplified expression.
i believe its a+2b
Step-by-step explanation:
plssss telll me if im wrong
A sine function has the following key features period=12 amplitude=4 midline y=1, y-intercept (0,1)
The sine function is y = 4 sin[ (π/6)x ] + 1.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
1) The parent function is sin(x)
2) sin(x) has:
Middle line: y = 0
Amplitude: 1 because the function goes from 1 unit up to 1 unit down the midddle line.
Period: 2π because sine function repeats every 2π units.
y-intercept: (0,0) because sin(0) = 0.
Now look how these changes in the function reflect on the parameters:
A sin (ωx + B) + C:
That function will have:
amplitude A, becasue the amplitude is scaled by that factor
Period: 2π / ω, because the function is compressed horizontally by that factor.
It will be translated B units to the left
It will be translated C units up.
And you need
Period = 12 => 2π / ω = 12 => ω = π/6
A = 4
Translate the midline from y = 0 to y = 1 => shift the function 1 unit up => = 1.
Translate the y-intercept from y = 0 to y = 1, which is already accomplished when you translate the function 1 unit up.
So, the is the function searched>
y = A sin (ωx + B) + C = 4 sin[ (π/6)x ] + 1
Now you can check the amplitude, the period, the middle line and the y-intercept of that y = 4 sin[ (π/6)x ] + 1.
Hence, the sine function is y = 4 sin[ (π/6)x ] + 1.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ1
find the set values of k for which the curve y=(k+1)x^2 - 3x + (k+1) lies below the x-axis
The values for k for which the given curve y = (k + 1) x² - 3x + (k + 1) lies below the X axis are k < -5/2 and k > 1/2.
What are Quadratic Functions?Quadratic functions are defined as the kind of polynomial functions with the greatest degree of the independent variable equals 2.
A quadratic function can be generally represented as f(x) = ax² + b x + c.
The given function is y = (k + 1) x² - 3x + (k + 1), which is quadratic.
The graph of a quadratic function is a parabola.
If the curve lies below the X axis, then the curve will not touch the X axis.
Then the graph will be an inverted parabola, which does not touch the X axis.
So the function will not have values equal to zero.
That is y ≠ 0
So the function does not have real roots.
So the discriminant of the function f(x) = ax² + b x + c, which is [tex]\sqrt{b^2-4ac}[/tex] will be negative.
Discriminant of the given function is [tex](-3)^2-[4 (k+1)(k+1)][/tex]. [tex](-3)^2-[4 (k+1)(k+1)][/tex] < 0
9 - 4(k + 1)² < 0
9 - 4(k² + 2k + 1) < 0
9 - 4k² - 8k - 4 < 0
-4k² - 8k + 5 < 0
Dividing throughout by -1,
4k² + 8k - 5 > 0
Let 4k² + 8k - 5 = 0
k = [ -8 ± √[(8)² - (4 × 4 × (-5)] / (2 × 4)
= [ -8 ± √144 ] / 8
= [-8 ± 12] / 8
Zeroes are k = 4/8 = 1/2 and k = -20/8 = -5/2
4k² + 8k -5 = 0 when k = 1/2 and k = -5/2
4k² + 8k -5 > 0, when k > 1/2 and k < -5/2
Hence the set of values of k are k > 1/2 and k < -5/2 for which the given function lies below the X axis.
To learn more about Quadratic Functions, click here :
brainly.com/question/27958964
#SPJ1
