The number of many matinee and prime-time movie tickets were sold that day are
What is defined as the linear equation in two variables?A linear equation in two variables is one that is written in the form ax + by + c = 0, where a, b, and c are real numbers and also the coefficients of x and y, i.e. a and b, are not equal to zero.
If there is only one solution, the given lines are intersecting; if no solution is possible, the given equations have been of parallel lines. If there are an infinite number of solutions, it means that given equations form coincident lines.For the given question.
Let 'x' be the number of matinee showings.
Let 'y' be the number of prime-time showings.
Then. the total ticket sold are 1,411.
Thus, x + y = 1,411.
or, x = 1,411 - y
The cost of one matinee showings is $9.
The cost of one prime-time showings is $13.50.
Now, the total cost earned is $17,149.50.
So,
9x + 13.5y = 17,149.50
Put the value of the 'x' in the above equation.
9(1,411 - y) + 13.5y = 17,149.50
Simplifying;
12699 - 9y + 13.5y = 17,149.50
4.5y = 4450.5
y = 989.
Calculate x;
x = 1,411 - 989
x = 422
Therefore, the number of matinee and prime-time movie tickets were sold that day are 422 and 989.
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(√14 + √10i)(√14 - √10i)
Answer:
24
Step-by-step explanation:
You want the value of the product ...
(√14 + √10i)(√14 - √10i)
Difference of squaresThe factoring of the difference of squares is ...
a² -b² = (a +b)(a -b)
Here, we have a=√14 and b=√10i. The product of the sum and difference of these values is ...
(√14 + √10i)(√14 - √10i) = (√14)² -(√10i)²
= 14 -(10(-1)) = 24
The product is 24.
-4x + y = 5. Solve for y
A. y = -4x + 5
B.y = 4x + 5
C. y = 4x - 5
D. y = -4x - 5
Answer:
y = 4x + 5
Step-by-step explanation:
-4x + y = 5
-4x + 4x + y = 5 + 4x
y = 5 + 4x
Hope this helps! :)
Write the following in simplest form
in parenthesis negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end parenthesis
three over 6 times x plus 8
three over 6 times x plus negative 20
negative five sixths times x plus eight
negative five sixths times x plus negative 8
The simplest form in parenthesis is option C which is negative five sixths times x plus eight (- 5x/6 + 8)
What is the solution for an equation?The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
WE have Given equation as; parenthesis negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end parenthesis,
( -2/3 * x - 6 ) - ( -14 + 1/6 * x)
Now solving the equation will gives;
= ( -2/3 * x - 6 ) - ( -14 + 1/6 * x )
= ( -2x/3 - 6 ) - ( -14 + x/6 )
= -2x/3 - 6 + 14 - x/6
Now collecting like terms;
= -2x/3 - x/6 - 6 + 14
= - 5x/6 + 8
Therefore the correct answer is option C; negative five sixths times x plus eight (- 5x/6 + 8)
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What is the answer ? How do you work this problem out ?
Check the picture below.
Given the graph of a radical function, which statement is correct?
Radical function going from the point negative 3 comma negative 2 up to the right through the point 1 comma 0
R colon open bracket y is an element of all real numbers close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 3 close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to negative 2 close bracket
R colon open bracket y is an element of all real numbers such that y is greater than or equal to 1 close bracket
Greetings from Brasil...
The range will be the region of the Y axis comprised by the function. Looking at the graph, we conclude that:
Range = {Y ∈ ℝ/Y ≥ - 2}A supermarket wants to send code for $.25 off a bag of chips to its rewards members. Each coupon will have one digit followed by four letters the letters D and E, and the digits 0, 5and 8 will not be used so there are 24 letters and 7 digits that will be used assume that the letters can be repeated how many such coupons can be generated.
There are 2322432 coupons generated .
According to the question we have been given that the code contains one digit followed by four letters . That is it can be assumed as
code = D L L L L where D and L represent the digits and letters.
Now total digits we have is = 7
total number of letters we have = 24
So we have to choose the first digit from these 7 digits. Thus there are 7 ways in which we can choose as they are repeated.
Also there are 24 ways to select the 4 letters after the digits as the letters are being repeated, that is ways = 24⁴
Therefore the number of coupons that can be generated from the combination are :
7*24⁴ = 7*331776
= 2322432
Hence the number of coupons generated are 2322432.
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Refer to the number line. Find the coordinate of point K that is 4/5 of the distance from A to F.
Point K coordinate from the given number line is; -1²/₃
How to Partition a Line Segment?Partitioning of a line segment means dividing the line segment in the given ratio. The two numbers in the ratio must add up together to equal the total number of partitions of the line segment. For example: If a line segment AB is divided into a ratio of 2:3, it shows that the line segment can be divided into 5 equal sections. Hence, there are 5 parts in total, in which 2 parts will be before the desired point and 3 parts will be after the desired point.
We are given a line segment A F divided into different parts of points B, C, D and E.
Now, we want to find the point K such that it divides Line segment A F in the ratio 4:5.
Now, from the number line, line A F measures 12 units. Thus;
Point K = (4/5) * 12 = 5¹/₃ from point A
Thus, point K coordinate = -7 + 5¹/₃
Point K coordinate = -1²/₃
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Yuki was curious if △ A B C △ABCtriangle, A, B, C was congruent to △ F E D △FEDtriangle, F, E, D, so she tried to map one triangle onto the other using transformations: A coordinate plane. The x- and y-axes both scale by one. A pre-image Triangle A B C has point A at two, two, point B at five, four, and Point C at eleven, two. Another triangle D E F has point D at three, twelve, point E at nine, ten, and point F at twelve twelve. Triangle A B C is translated four units to the right and six units up to form the image Triangle A prime at six, eight, B prime at nine, ten, and C prime at fifteen, eight. E E D D F F A A B B C C A coordinate plane. The x- and y-axes both scale by one. A pre-image Triangle A B C has point A at two, two, point B at five, four, and Point C at eleven, two. Another triangle D E F has point D at three, twelve, point E at nine, ten, and point F at twelve twelve. Triangle A B C is translated four units to the right and six units up to form the image Triangle A prime at six, eight, B prime at nine, ten, and C prime at fifteen, eight. Yuki concluded: "It's not possible to map △ A B C △ABCtriangle, A, B, C onto △ F E D △FEDtriangle, F, E, D using a sequence of rigid transformations, so the triangles are not congruent." What error did Yuki make in her conclusion? Choose 1 answer: Choose 1 answer: (Choice A) A One more transformation — a rotation — would map △ A B C △ABCtriangle, A, B, C onto △ F E D △FEDtriangle, F, E, D. So the triangles are congruent. (Choice B) B One more transformation — a reflection — would map △ A B C △ABCtriangle, A, B, C onto △ F E D △FEDtriangle, F, E, D. So the triangles are congruent. (Choice C) C There is no error. This is a correct conclusion.
Answer:Nose
Step-by-step explanation:Q es eso
A kite is flying 9.75 feet above a lamp post that is 84 2/3 feet tall. How high is the kitchen flying?
The kite is flying at the height of 94 5/2 feet.
Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
= 9.75 +84 2/3 { 9+0.75 = 9.75 84 2/3}
= 9 + 0.75 +84 2/3 { a+b+c+d = a+c+b+d}
= 9 + 84 + 3/4 + 2/3
=93 + 3*3 / 4*3 + 4*2 / 4*3
= 93 + 9/12 + 8/12
= 93 + 17/12
= 93 + (1 + 5/12)
= 94 + 5/12
=94 5/12 feet
{kite height = (post height + the height of the kite above the post)
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At the end of spring break, Mary left the beach and drove back towards home, driving at a rate of 51 mph. A friend of Mary left the beach for home 0.5 hour later, and drove 66 mph. How long did it take Mary's friend to catch up to Mary?
Answer:
2.2 hours or
2 hours and 12 minutes they will meet.
Step-by-step explanation:
Givens
Mary's speed = 51 mph
Friend's speed = 66 mph
Mary will be on the road for t hours
Her Friend will be on the road t - 0.5. Why minus? Because she was on the road 1/2 hour less than Mary was. Any time you see More or Less in a question, pay attention. usually it is the key to the question.
Equation
d_Mary = d_friend
d = rate * time
Solution
51 * t = 66*(t - 0.5) Remove the brackets.
51*t = 66*t - 66*0.5
51*t = 66*t - 33 Subtract 66t from both sides. Be careful
51t - 66t = - 33 Combine
- 15t = - 33 Divide by - 15
t = - 33/-15
t = 2.2 hours or 2 hours and 12 minutues
Write the following in exponential form:
log3y=x
the equation rewritten in exponential form is:
y = 3^x
How to rewrite the given expression?
Here we start with.
Log₃(y) = x
Remember that we can rewrite:
Log₃(y) = ln(y)/ln(3)
Then we can simplify so we get:
ln(y) = ln(3)*x
Now we just apply the exponential function to both sides:
exp(ln(y)) = exp(ln(3)*x)
y = (e^(ln(3))^x = 3^x
y = 3^x
That is the equation rewritten in exponential form:
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Write the following in algebraic language. x is 0.28 of y.
The mathematical statement in algebraic language is x = 0.28y
How to write the mathematical statement in algebraic language?The mathematical statement is given as
x is 0.28 of y
In mathematics, "of" means multiplication
So, we have
x is 0.28 of y => x is 0.28 * y
Evaluate the product
x is 0.28 of y => x is 0.28y
In mathematics, "is" means equation
So, we have
x is 0.28 of y => x = 0.28y
Hence, the mathematical statement in algebraic language is x = 0.28y
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a bakery has six bags of flour. they are are asked to make four loaves of bread
the first two loaves each require two bags and quarter of another bag
the next loaf requires one bag and two thirds of another bag
the final loaf requires a half bags of flour
write a calculation,using brackets ,to work out how much flour the bakery will have left the bakery will have left after making these loaves
The bakery is short on half a bag of flour.This problem can be solved using fractions . So, first loaf of bread requires 2bags of flour and a quarter which can be written as 2[tex]\frac{1}{4}[/tex]second loaf of bread also requires the same amount which is 2[tex]\frac{1}{4}[/tex]
the third loaf of bread requires one bag and two third of another bag which can be written as 1[tex]\frac{2}{3}[/tex]
And the final loaf of bread requires half bag of flour which is [tex]\frac{1}{2}[/tex]
the total requirement of flour for making the four loaves of bread is
= 2[tex]\frac{1}{4}[/tex] + 2[tex]\frac{1}{4}[/tex]+ 1[tex]\frac{2}{3}[/tex]+[tex]\frac{1}{2}[/tex]
=[tex]\frac{9}{4}[/tex] +[tex]\frac{9}{4}[/tex] + [tex]\frac{5}{3}[/tex] + [tex]\frac{1}{2}[/tex]
= [tex]\frac{27}{12}[/tex]+ [tex]\frac{27}{12}[/tex] +[tex]\frac{20}{12}[/tex] +[tex]\frac{6}{12}[/tex]
= [tex]\frac{80}{12}[/tex]
To work out how much flour the bakery will have left after making these loaves we need to reduce the total requirement with total flour we have = 6 -[tex]\frac{80}{12}[/tex]
=[tex]\frac{72}{12}[/tex] - [tex]\frac{80}{12}[/tex]
=- [tex]\frac{6}{12}[/tex] or- [tex]\frac{1}{2}[/tex]
therefore the bakery is short on half a bag of flour
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For recent year, 31 more Democrats than Republicans were in the US House of Representatives if the total number of representatives in the house from these two parties was 433, find the number of representatives from each party
there were total 201 republicans and 232 democrats .
WHAT ARE LINEAR EQUATIONS ?There is only one or two variables in a linear equation. Nothing can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All the dots fall on the same line when the values that, when added together, make a linear equation true are determined and plotted on a coordinate grid.
CALCULATIONlet no. of republicans be x
then, no. of democrats is x + 30
total no. of members given are = 433
so if we make the equation
x + x + 30 = 433
2x = 403
x = 201 members of republican
democrats = 201 + 30 = 232
therefore , there were total 201 republicans and 232 democrats .
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a duck spends about .45 of a day sleeping. how much hours does a duck sleep each day
Answer:
10.8
Step-by-step explanation:
24 * .45 = 10.8
For the point P(-20,7) and Q(-13,12), find the distance d(P,Q) and the
coordinates of the midpoint M of the segment PQ.
Distance
[tex]d(P,Q)=\sqrt{(-20-(-13))^2+(7-12)^2} \\ \\ =\sqrt{49+25} \\ \\ =\boxed{\sqrt{74}}[/tex]
Midpoint
[tex]M=\left(\frac{-20-13}{2}, \frac{7+12}{2} \right)=\boxed{\left(-\frac{33}{2}, \frac{19}{2} \right)}[/tex]
a phone company offers two monthly plans. A costs $25 plus an additional $0.09 for each minute of calls. Plan B has no initial fee but cost $0.11 for each minute of calls
For 1,250 minutes, both plans will charge the same amount.
For how many minutes both plans charge the same?We know that Plan A costs $25 plus $0.09 per minute, so if you have x minutes of calls, the cost is given by the linear equation:
A(x) = $25 + $0.09*x
And plan B just charges $0.11 for each minute, then here we have the linear equation:
B(x) = $0.11*x
The costs are the same when:
A(x) = B(x)
$25 + $0.09*x = $0.11*x
Now we can solve this for x.
$25 = $0.11*x - $0.09*x = $0.02*x
$25/$0.02 = x = 1,250
We conclude that for 1,250 minutes, both plans will charge the same amount.
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What’s 6 and 2/3 divided by 8
Answer: 5/6
Step-by-step explanation:
Answer:
6 divided by 8 is 3/4 (.78)
2/3 divided by 8 is 1/12 (0.083)
6 2/3 divided by 8 is 5/6 (0.83)
Find the solution of this system of equations
-2x - by =
- 16
4x - 6V
=
-58
The values x and y are found as (x = -7) and (y = 5).
What is defined as the system of equations?When there is more than one unidentified and enough content to set up equations within these unknowns, systems of equations are being used to solve applications. In general, we require sufficient information to established n equations in n unknowns if there are n unknowns.One solution exists for a set of 2 or more equations usually contains a set of common variables. When there is no solution to a system of equations with different slopes.The two given equation are-
-2x - 6y = -16 .......equation 1
4x - 6y = -58 .......equation 2
Multiply equation 1 with -1.
-(-2x - 6y = -16)
Solve by eliminations; subtract equation 2 from 1.
2x + 6y = 16
4x - 6y = -58
Further simplifying;
6x = -42
divide both sides by six
x =- 7
Put the value of x equation 1.
2(-7) + 6y = 16
-14 + 6y = 16
6y = 30
y = 5
Thus the values of the variables are found as (x = -7) and (y = 5).
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The correct question is-
Find the solution of this system of equations.
-2x - 6y = -16
4x - 6y = -58
Amy has three times as many Star Wars toys as Carly. Total they have 232 Star Wars toys. How many Star Wars toys does Amy have?
Answer:
174
Step-by-step explanation:
Since we don't know how many toys Carly has, we'll use a variable (x). The equation would then be:
x+3x=232
We can then combine like terms, and the new equation would be:
4x=232
Now, we have to get x by itself. To do this, divide both sides by 4, and you get:
x=58
But, remember, x is how many Carly has. Amy has three times that, so:
58*3=174
Amy has 174 toys.
Hope this helps!
1.Rahul makes a decorative book mark of dimensions 2
inches x 4 inches. Find the area of the bookmark.
The area of rectangular decorative bookmark prepared by Rahul is 8 square inches
Rahul is making a decorative bookmark whose dimensions are 2 inches× 4 inches which clearly states that the decorative bookmark prepared by Rahul is in the shape of a rectangle whose length is 4 inches and breath is 2 inches
In this question we are told to find out the area of rectangular bookmark So, we have to use the formula of area of rectangle
area of rectangle = length of rectangle × breath of rectangle
= 4 inches × 2 inches
= 8 inches²
Hence the area of rectangular decorative bookmark prepared by Rahul is 8 square inches
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July, May, March, what comes next?
Answer:
January
Step-by-step explanation:
subtract 2 from each numbe(month)
7-2=5-2=3-2=1
7: July
5: May
3: March
1: January
NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t)=−4.9t2+106t+206.
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
The rocket splashes down after
seconds.
How high above sea-level does the rocket get at its peak?
The rocket peaks at
meters above sea-level.
If the function of height in time is h(t)=-4.9[tex]t^{2}[/tex]+106t+206,then the rocket will splash down into the ocean after 23.43 seconds and the rocket will get its peak after 10.82 seconds at a height of 779.26524 meters above the sea level.
Given that the function of height in time is h(t)=-4.9[tex]t^{2}[/tex]+106t+206.
We are required to find the time after which the rocket will splash down into the ocean and the time after which the ocean will get its peak and the height of the rocket.
The rocket will splash down when the height of the rocket is 0.
-4.9[tex]t^{2}[/tex]+106t+206=0
4.9[tex]t^{2}[/tex]-106t-206=0
t={106±[tex]\sqrt{(106)^{2} -4*4.9*(-206)}[/tex]}/2*4.9
t=(106±[tex]\sqrt{15273.6}[/tex])/9.8
We have to ignore the negative sign because the time is always shown in positive signs.
t=(106+123.59)/9.8
t=229.59/9.8
t=23.43 seconds
Rocket will be at its peak when the slope of the equation is 0.
[tex]h^{I}[/tex](t)=-9.8t+106
-9.8t+106=0
-9.8t=-106
t=-106/-9.8
t=10.82 seconds
To find the height we need to use t=10.82 in the equation.
h(10.82)=[tex]-4.9*(10.82)^{2} +106*10.82+206[/tex]
=-573.65476+1353.92
=779.26524 meters.
Hence if the function of height in time is h(t)=-4.9[tex]t^{2}[/tex]+106t+206,then the rocket will splash down into the ocean after 23.43 seconds and the rocket will get its peak after 10.82 seconds at a height of 779.26524 meters above the sea level.
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Find the value of X.
Answer:
It's x+10=5+2x+6=>x=-1
About 1% of the population has a particular genetic mutation. 137 people are randomly selected.
Find the mean for the number of people with the genetic mutation in such groups of 137.
Find the standard deviation for the number of people with the genetic mutation in such groups of 137.
(Round to the nearest 2 decimal places.)
Using the binomial distribution, the mean and the standard deviation of the amounts are given as follows:
Mean: 1.37.Standard deviation: 1.16.What are the mean and the standard deviation of the binomial distribution?The binomial distribution gives the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The mean is given by the following rule:
E(x) = np.
The standard deviation is given by the following rule:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In the context of this problem, the parameters are found as follows:
p = 0.01, as about 1% of the population has a particular genetic mutation.n = 137, as 137 people are randomly selected.Hence the mean and the standard deviation are, respectively, given by:
E(x) = np = 137 x 0.01 = 1.37.[tex]\sqrt{V(X)} = \sqrt{137(0.01)(0.99)} = 1.16[/tex]More can be learned about the binomial distribution at https://brainly.com/question/24863377
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Solve the system of linear equations by graphing.
By using a graphing tool, the point of intersection of the two lines is (x, y) = (7, 0).
How to solve a system of linear equations by graphic approach
In this question we have a system of two linear equations with two variables, which can be represented on Cartesian plane. By geometry it is known that a line can be constructed after knowing the location of two distinct points.
First, we find two distinct points from each line:
x + y = 7: (7, 0), (0, 7)
- x + y = - 7: (7, 0), (0, - 7)
Second, set each pair of points and construct the lines on a Cartesian plane.
Third, mark the point of intersection of the two lines. The result is shown in the image attached aside. The point of intersection of the two lines is (x, y) = (7, 0).
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The diameter of a gold atom is approximately 144 trillionths of a metre. The diameter of an oxygen atom is approximately 0.074 billionths of a metre. Which is larger? How many times larger is it than the other?
The diameter of the gold atom is greater than the diameter of the oxygen atom by 7 x 10^-11 meter
What is a diameter?The diameter of a shape (usually a round shape) is a line that divides the shape to equal parts
Which is larger?The diameters are given as:
Diameter of a gold atom = approximately 144 trillionths of a meter
Diameter of an oxygen atom = approximately 0.074 billionths meter
Using a calculator, we convert the above numbers to scientific numbers
So, we have
Diameter of a gold atom = approximately 1.44 x 10^-10 meter
Diameter of an oxygen atom = approximately 7.4 x 10^-11 meter
The number with the higher exponent is greater than the other number
Hence, the diameter of the gold atom is greater than the diameter of the oxygen atom
How many times larger is it than the other?In (a), we have
Diameter of a gold atom = approximately 1.44 x 10^-10 meter
Diameter of an oxygen atom = approximately 7.4 x 10^-11 meter
Calculate the difference
d = 1.44 x 10^-10 - 7.4 x 10^-11
Evaluate the difference
d = 7 x 10^-11
Hence, the diameter of the gold atom is greater than the diameter of the oxygen atom by 7 x 10^-11 meter
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Points E, D, and H are the midpoints of the sides of ΔTUV. UV=110, TV=140, and HD=110. Find HE.
The required value of HE is 55 units.
What is proportion?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal.
Now it is given that Points E, D, and H are the midpoints of the sides of ΔTUV.
UV = 110,
TV = 140, and
HD = 110
Since the triangles are similar there exists correspondance in the angles, so in order to solve this you just have to clear the function:
HD/HE = TV/(TV/2)
Put the values we get,
110/HE = 140 / 70
⇒ HE = 110*70/140
⇒ HE = 55 units
Thus, the required value of HE is 55 units.
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a pound of chocolate is 6.25. How much of a pound would one dollar buy
Answer:
0.16 of a pound for one dollar
Step-by-step explanation:
all you have to do is 1 ÷ 6.25
[tex]\begin{array}{ccll} \stackrel{chocolate}{lbs}&\$\\ \cline{1-2} 1 & 6.25\\ x& 1 \end{array} \implies \cfrac{1}{x}~~=~~\cfrac{6.25}{1} \\\\\\ 1=6.25x\implies \cfrac{1}{6.25}=x\implies 0.16=x[/tex]
f(x)= -x^2 + 4x +5 and g(x)= -f(x) + k. find the values of k so that g(x) = 0 has no real roots
According to the given quadratic equation the values of k = -1.
In mathematics, what is quadratic equation?A quadratic equation seems to be a second-order polynomials equation with a single variable x ax2+bx+c=0. Ta he fundamental theorem of algebra assures that it has at least one solution because it is second-order polynomial equation.
According to the given data:g(x)= -f(x) + k. given
Putting the value of f(x).
g(x)= - -x^2 + 4x +5 + k
= x^2 - 4x - 5 + k
= 0
When g(x) = 0 has no real roots, Δ < 0 a quadratic equation of one variable has no real roots.
So,
16 - 4(5 + k) = 0
16 - 20 -4k < 0
-4 -4K < 0
4K> -4
k>-1
According to the given quadratic equation the values of k = -1.
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