From the analysis of the discriminant, you obtain that the quadratic function has no real solutions.
In first place, you must know that the roots or solutions of a quadratic function are those values of x for which the expression is 0. This is the values of x such that y = 0. That is, f (x) = 0.
Being the quadratic function f (x)=a*x² + b*x + c, then the solution must be when: 0 =a*x² + b*x + c
The solutions of a quadratic equation can be calculated with the quadratic formula:
[tex]Solutions=\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}[/tex]
The discriminant is the part of the quadratic formula under the square root, that is, b² - 4*a*c
The discriminant can be positive, zero or negative and this determines how many solutions (or roots) there are for the given quadratic equation.
If the discriminant:
is positive: the quadratic function has two different real solutions. equal to zero: the quadratic function has a real solution. is negative: none of the solutions are real numbers. That is, it has no real solutions.In this case, a= -40, b=10 and c= -1. Then, replacing in the discriminant expression:
discriminant= 10² -4*(-40)*(-1)
Solving:
discriminant= 100 - 160
discriminant= -60
The discriminant is negative, so the quadratic function has no real solutions.
The distance between point (3,0) and (7, 2p) is √80. Find the value of p.
Distance = √[ ( 7 - 3 )^2 + ( 2p - 0 )^2 ]
Distance = √(4)^2 + ( 2p)^2
Distance = √16 + 4p^2
As the question said : Distance = √80
√80 = √16 + 4p^2
Thus :
16 + 4p^2 = 80
Subtract both sides 16
16 - 16 + 4p^2 = 80 - 16
4p^2 = 64
Divide both sides by 4
4p^2 ÷ 4 = 64 ÷ 4
p^2 = 16
Thus :
p = 4 or p = - 4
how to work this fraction 4/11+5/22+3/44
Answer:
29/44
Step-by-step explanation:
[tex]\frac{4}{11} +\frac{5}{22} +\frac{3}{44} =\\[/tex]
-find the common denominator
[tex]\frac{4*4}{4*11} + \frac{2*5}{2*22} +\frac{3}{44} =[/tex]
[tex]\frac{16}{44} +\frac{10}{44} +\frac{3}{44} =[/tex]
-add the fractions and solve
[tex]\frac{16+10+3}{44} =[/tex]
[tex]\frac{29}{44}[/tex]
Evaluate the expression 2x - (4y - 3) + 5xz, when x = -3, y = 2, and z = -1.
Answer:
4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
2x - (4y - 3) + 5xz
x = -3
y = 2
z = -1
Step 2: Evaluate
Substitute in variables: 2(-3) - (4(2) - 3) + 5(-3)(-1)(Parenthesis) Multiply: 2(-3) - (8 - 3) + 5(-3)(-1)(Parenthesis) Subtract: 2(-3) - 5 + 5(-3)(-1)Multiply: -6 - 5 + 15Subtract: -11 + 15Add: 4Which of the following is the graph of…
Answer:
A
Step-by-step explanation:
Try graphing the function on desmos
(x + y, 2) = (13, 2x - y)
Answer: (x, y) = (5,8)
Step-by-step explanation:
x + y = 13 2x - y = 2
y = -x + 13
2x - (-x + 13) = 2 3x =15
x=5
x=5 y = -x + 13
y = -(5) + 13 = 8
Chen rode his skateboard 3/3/4 miles in 34 of an hour.
What was his average speed in miles per hour?
_[blank]_ miles per hour
Answer:
5 miles per hour
Step-by-step explanation:
3¾ ÷ ¾ =
15/4 ÷ ¾ =
15/4 x 4/3 =
15/3 = 5
If there is a maximum of 4,000 hours of labor available per month and 300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor, which of the following constraints reflects this situation?
a. 300x1 + 125x2 > = 4,000
b. 300x1 + 125x2 < = 4,000
c. 425(x1 + x2) < = 4,000
d. 300x1 + 125x2 = 4,000
Answer:
b. 300x1 + 125x2 < = 4,000
Step-by-step explanation:
Maximum of 4,000 hours
This means that the the total amount of labor has to be of at most 4,000, that is:
[tex]T \leq 4000[/tex]
300 ping-pong balls (x1) or 125 wiffle balls (x2) can be produced per hour of labor
The total amount of labor is:
[tex]T = 300x1 + 125x2[/tex]
Uniting the two equations:
[tex]T \leq 4000[/tex]
[tex]300x1 + 125x2 \leq 4000[/tex]
And thus the correct answer is given by option b.
a jet flew 2660 miles in 4.75 hours. what is the rate of speed in miles per hour? (the proportion would be 2660:4.75::x:1 set the proportion in fractional form and proceed to find x.)
Set the proportion as shown:
2660/4.75 = x/1
Cross multiply:
4.75x = 2660
Divide both sides by 4.75
x = 560
Answer: 560 miles per hour
lim(x-0) (sinx-1/x-1)
lim ( sinx-1)/(x-1)
x=>0
apply x=0
(sin(0)-1)/(0-1)
(0-1)/(-1)
=1
A hotel has 210 units. All rooms are occupied when the hotel charges $90 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant. Each occupied room costs $24 per day to service and maintain. What should the hotel charge per day in order to maximize daily profit
Answer: [tex]\$162[/tex]
Step-by-step explanation:
Given
There are 210 units of hotel
Each room charge $90 when fully occupied
occupied room charges is $24 per day
Suppose x rooms are vacant, so, there 210-x occupied
Daily expense on maintenance[tex]=(210-x)\times 24[/tex]
Earning from 210-x rooms[tex]=(210-x)(90+x)[/tex]
Profit(P)=Earning - Expense
[tex]\Rightarrow P=(210-x)(90+x)-(210-x)24\\\Rightarrow P=21,600+210x-90x-x^2-5040+24x\\\Rightarrow P=-x^2+144x+16,560\\[/tex]
To get the maximum profit, determine the derivative of P w.r.t. x and equate it to zero
[tex]\Rightarrow \dfrac{dP}{dx}=-2x+144\\\\\Rightarrow -2x+144=0\\\\\Rightarrow x=72[/tex]
Charges for maximum profit is [tex]90+72=\$162[/tex]
Number of occupied rooms are [tex]210-72=138[/tex]
The hotel charge per day will be $162 in order to maximize daily profit.
Given that, Hotel has 210 units
Let us consider that x rooms are vacant.
Total occupied rooms = [tex](210-x)[/tex]
Since, Each occupied room costs $24 per day to service and maintain
So, Total expense = [tex]24*(210-x)=5040-24x[/tex]
Since, For all rooms are occupied when the hotel charges $90 per day for a room. For every increase of x dollars in the daily room rate, there are x rooms vacant.
So, Total earing = [tex](210-x)*(90+x)=-x^{2} +120x+21600[/tex]
Profit = Total earning - Total expense
[tex]P=-x^{2} +120x+21600-5040+24x\\\\P=-x^{2} +144x+16560[/tex]
In order to maximize profit, Differentiate profit expression with respect to x.
[tex]\frac{dP}{dx}=\frac{d}{dx}(-x^{2} +144x+16560) \\\\\frac{dP}{dx}=-2x+144=0\\\\\\x=\frac{144}{2}=72[/tex]
Thus, Hotel charges per day for maximum profit = [tex]90+x=90+72=162[/tex]
Learn more:
https://brainly.com/question/19578119
please help me with this
9514 1404 393
Answer:
92°
Step-by-step explanation:
The "givens" tell you the E and F are midpoints of their respective segments. That means EF ║ AB and angles DBF and EFC are "corresponding" angles with respect to transversal BC and those parallel lines. Corresponding angles are congruent, so ...
m∠DBF = m∠EFC = 92°
What is the mapping for a reflection in the line y=-1
Answer:
0
Step-by-step explanation:
the key mapping for a reflection in the line y=-1 is 0
HELP! NO SCAMS PLZ, i need to know how to write the proportion.
Answer:
Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.
4+z/y = 36/18
Step-by-step explanation:
a) Since both triangles are similar triangles, then the ratio of their similar sides is equal to a constant k. Therefore:
16/4 = 18/y
Note that the arrangement depends on which of the triangles sides cones first.
Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.
b) Same rule in (a) applies to the sum as well. Hence;
4+z/y = 16+20/18
4+z/y = 36/18
To what extent do syntax textbooks, which analyze the structure of sentences, illustrate gender bias? A study of this question sampled sentences from 10 texts.23 One part of the study examined the use of the words "girl," "boy," "man," and "woman." We will call the first two words juvenile and the last two adult. Is the proportion of female references that are juvenile (girl) equal to the proportion of male references that are juvenile (boy)? Here are data from one of the texts:
Answer: Hello your question is incomplete attached below is the complete question
answer:
i) 0.8 , standard error = 0.0516
ii) 0.39, standard error = 0.0425
Step-by-step explanation:
i) proportion of Juveniles reference for females ( f )
= x₁ / n₁ = 48 / 60 = 0.8
standard error = [tex]\sqrt{\frac{0.8(1-0.8)}{60} }[/tex] = 0.0516
ii) Proportion of Juveniles reference for males ( m )
= x₂ / n₂ = 52 / 132 = 0.39
standard error = [tex]\sqrt{\frac{0.39(1-0.39)}{132} }[/tex] = 0.0425
An Experiment to investigate the relation between two physical quantities was performed where 10 data pairs were collected. You are to perform regression analysis to describe the relation between the two quantities using a polynomial. What are the possible values for the order of that polynomial?
a) from 0 to 10
b) from 1 to 9
c) from 1 to 10
d) Any integer
Answer:
d). Any Integer.
Step-by-step explanation:
Regression analysis is characterized as the statistical method that is employed to determine the association between a dependent, as well as, the independent variable(one or more). It
As per the question, the probable values for the arrangement of a polynomial would be 'any integer' in order to determine the relationship among the different variables(the two physical quantities). Since a regression analysis helps in knowing the factors that influence the other and the factors that do not affect much in order to reach a reliable conclusion. Thus, any of the values can be examined to examine the association among them. Hence, option d is the correct answer.
30 is what percent of 44?
Answer:
68.18
Step-by-step explanation:
→ Set up an equation
[tex]\frac{44x}{100} =30[/tex]
→ Times both sides by 100
44x = 3000
→ Divide both sides by 44
68.18
Given the following coordinates complete the glide reflection transformation.
A(−1,−3)
B(−4,−1)
C(−6,−4)
Transformation: Reflection over the x-axis and a translation of shifting right 10 units.
Given:
The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).
Transformation: Reflection over the x-axis and a translation of shifting right 10 units.
To find:
The image after glide reflection transformation.
Solution:
The vertices of a triangle are A(−1,−3) , B(−4,−1) and C(−6,−4).
If a figure is reflected over the x-axis, then
[tex](x,y)\to (x,-y)[/tex]
Using this, we get
[tex]A(-1,-3)\to A'(-1,3)[/tex]
[tex]B(-4,-1)\to B'(-4,1)[/tex]
[tex]C(-6,-4)\to C'(-6,4)[/tex]
If a figure is shifting 10 units right, then
[tex](x,y)\to (x+10,y)[/tex]
Using this we get
[tex]A'(-1,3)\to A''(-1+10,3)[/tex]
[tex]A'(-1,3)\to A''(9,3)[/tex]
Similarly,
[tex]B'(-4,1)\to B''(-4+10,1)[/tex]
[tex]B'-4,1)\to B''(6,1)[/tex]
And,
[tex]C'(-6,-4)\to C''(-6+10,4)[/tex]
[tex]C'(-6,-4)\to C''(4,4)[/tex]
Therefore, the vertices of the image are A''(9,3), B''(6,1) and C''(4,4).
guys help me I really need your help
Answer:
a x^2/2 is a polynomial because the power of x is 2 which is a positive whole number but 2/x^2 is not a polynomial because the power of x is -2 which is negative whole number.
b.in
[tex] \sqrt{2 x} [/tex]
the power if x will be
[tex]x {}^{ \frac{1}{2} } [/tex]
which is not a whole number so it is not a polynomial.
but in
[tex] \sqrt{2} x[/tex]
the power if x is a positive whole number.so it is a polynomial.
c.the greatest power of variable of the term is called degree of polynomial
what number increased by 130% is 69
Answer:
The number is 30.
Step-by-step explanation:
Let the number be x
so
x + (130% of x) = 69
x + 13x/10 = 69
or, (10x + 13x)/10 = 69
or, 23x = 690
or, x = 690/23
so, x = 30
Answer: 30
Step-by-step explanation:
its correct on rsm
help again please i need to pass this
√50x³y
= √5²×2×x²×x×y
= 5x√2xy
d is the correct answer
Answer:
here
Step-by-step explanation:
Describe domain and range of the graph.
which point lies on the line defined by 7x - 7y = -43
Answer:
(-6,0) and (0,-6) are the points on the graph
Find the area of a circle with a radius of 6 ft. Round off your answer to one decimal point. (The formula for the area of a circle is A = ar?)
Answer:
Using 3.14 for pi A = 113.0 ft^2
Using the pi button A = 113.1 ft^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi ( 6)^2
A = 36 pi
Using 3.14 for an approximation for pi
A = 36(3.14) = 113.04
To 1 decimal
113.0
Using the pi button
A = 113.0973355
A = 113.1
X ^2 + 2x + y’ + 6y = 15
Step-by-step explanation:
x^2+2x+7y=15
7y=15-x^2-2x
y=15/7-1/7x^2-2/7x , x ∈ all real numbers
Abigail buys two cartons of strawberries. One carton has 191919 berries and the other carton has 262626 berries. She wants to divide the berries into bags so there are exactly 666 berries in each bag.
How many bags will have 666 berries?
Answer:
682
Step-by-step explanation:
191,919 + 262,626
454545 ÷ 666 = 682.5
Thus meaning 682 bags will have 666 berries and one bag will have 333 berries.
A farmer weighs a dozen chicken eggs. The heaviest egg is 56 g.
Step-by-step explanation:
hi
what is your question?
Step-by-step explanation:
please tell full questions
Find f(2) given f(x) = -3x^2 + 2x+11
Answer:
Answer:f(2)=-3(2)^2+2*2+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11
Answer:f(2)=-3(2)^2+2*2+11 =-3*4+4+11 =-12+4+11 =3
hence, f(2)=3
Question 27 of 58
Select the equation that represents the problem. Let x represent the unknown
number.
Mr. Jefferson bought 336 markers for his class. The
markers came in packs of 12. How many packs did he
buy?
A. 336 - x= 12
B. 12x= 336
O C. 336x= 12
O D. x + 12 = 336
SUBMIT
Answer:
B.
Step-by-step explanation:
The answer is B.
Question 5 plz show steps
Answer:
C
Step-by-step explanation:
Enter the solutions from least to greatest.
f(x) = (x – 3)(2x – 8)
Answer:
The zeroes of the function are: 3 and 4
Step-by-step explanation:
