Solving the quadratic function, the sales are of 9 million in the years of 2000 and 2012.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
The number of sales(in millions of dollars), in t years after 2000, is modeled by the following function:
[tex]S(t) = \frac{20t^2 + 800t + 300}{8t^2 + 10t + 100}[/tex]
The sales are of 9 million when S(t) = 9, hence:
[tex]S(t) = \frac{20t^2 + 800t + 300}{8t^2 + 10t + 100}[/tex]
[tex]9 = \frac{20t^2 + 800t + 300}{8t^2 + 10t + 100}[/tex]
[tex]72t^2 + 90t + 900 = 20t^2 + 800t + 300[/tex]
[tex]52t^2 - 710t + 600 = 0[/tex]
Which is a quadratic equation with coefficients a = 52, b = -710, c = 600, hence:
[tex]\Delta = (-710)^2 - 4(52)(600) = 379300[/tex]
[tex]x_1 = \frac{710 + \sqrt{379300}}{104} = 12.7[/tex]
[tex]x_2 = \frac{710 - \sqrt{379300}}{104} = 0.91[/tex]
t is measured in years after 2000, the sales are of 9 million in the years of 2000 and 2012.
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Which expression can be used to determine the volume of water in a rain barrel after days if there were 179.2 gallons of water in the barrel and 10.6 gallons are used each day?
The required expression is given by 179.2 - 10.6d.
There were 179.2 gallons of water in the barrel and 10.6 gallons are used each day
Volume, is defined as the ratio of the mass of object to its density.
the volume of water in a rain barrel after "d"days
When there were 179.2 gallons of water in the barrel and 10.6 gallons are used each day.
since the amount of water is getting consumed day by day
therefore, the expression can be given as
= 179.2 - 10.6d
Thus, the required expression is 179.2 - 10.6d.
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What is the value of x in the figure at the right?
Answer:
b 12
Step-by-step explanation:
62=5x+2(opposite angle are equal)
5x=60
x=12
Which expression is not a polynomial?
A. 4-3x+ 5x6
B. x²-x-12
X+3
C. 5x2 + 4x+1
D. 8x¹0+2x+5
Option b) [tex]x^{2} -x-\sqrt{x} +3[/tex] is not a polynomial
Polynomial equation is equation of dependent variables which is related to the independent variable.
since, the equation ,[tex]x^{2} -x-\sqrt{x} +3[/tex] contains the square root of variable that's why its not a polynomial.
Thus, Option b) [tex]x^{2} -x-\sqrt{x} +3[/tex] is not a polynomial
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Can someone help me out on matching these angles? ASAP, gotta have answers fast pls
Answer:
8. a , c
9. b
10. c
Find the measure of x.
X
56.76°
56.76
x = [?]
Round to the nearest hundredth.
evaluate x+2x+1/x^2-25
The evaluation of the algebraic fraction x+2x+1/x^2-25 is[tex]\mathbf{\implies -\dfrac{3}{5(x+5)} +\dfrac{18}{5(x-5)}}[/tex]
What is the division of algebraic expression?The division of an algebraic expression can be carried out by using the long division method or expansion of the.
Given that:
[tex]\mathbf{\dfrac{x+2x+21}{x^2-25}}[/tex]
where:
x^2 - 25 is the divisor.By expanding the denominator, we have:
[tex]\mathbf{\dfrac{x+2x+21}{(x+5)(x-5)}}[/tex]
[tex]\mathbf{\dfrac{3x+21}{(x+5)(x-5)}}[/tex]
Creating a partial fraction from the denominator, we have:
[tex]\mathbf{\dfrac{3x+21}{(x+5)(x-5)} = \dfrac{a_o}{x+5} +\dfrac{a_1}{x-5}}[/tex]
Multiply the equation by the denominator, and we have:
[tex]\mathbf{\dfrac{(3x+21)(x+5)+(x-5)}{(x+5)(x-5)} = \dfrac{a_o(x+5)(x-5)}{x+5} +\dfrac{a_1(x+5)(x-5)}{x-5}}[/tex]
Simplifying, we have:
3x + 21 = a₀(x-5)+a₁(x+5)
Solve for the unknown parameter by plugging the real roots of the denominator: -5, 5
[tex]\mathbf{a_o =\dfrac{-3}{5}}[/tex]
[tex]\mathbf{a_1 =\dfrac{18}{5}}[/tex]
Replacing the solutions into the partial fractions parameters to obtain the final result, we have:
[tex]\mathbf{\dfrac{-(\dfrac{3}{5})}{x+5} +\dfrac{\dfrac{18}{5}}{x-5}}[/tex]
[tex]\mathbf{\implies -\dfrac{3}{5(x+5)} +\dfrac{18}{5(x-5)}}[/tex]
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Who is the Father of Algebra ?
Answer:
Al- khwarizmiStep-by-step explanation:
that is my
Answer:
Muhammad ibn Musa al-Khwarizmi
محمد بن موسی خوارزمی
If 1600 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
The largest possible volume of the box is 6158.394 cm^3.
Define the dimensions of the box to be L, W, and H.
Square base, L = W
Area: A = L^2 * H
Surface Area (Base + Area of 4 sides):
1600 = L^2 + 4 (L*H) ⇒ H = (1600 - L^2) / (4L)
Area: A = 400L - (1/4)L^3
Maximum (Derivative) A' = 400 - (3/4)L^2
Solving for 0
0 = 400 - (3/4)L^2
L^2 ⇒ (40 * SQRT(3)) / 3 = 23.094 (Maximum)
Solving for dimensions, known L=23.094
L = 23.094 cm
W = 23.094 cm
H ⇒ (1600 - L^2) / (4L) = (20 * SQRT(3) / 3) = 11.547 cm
Volume ⇒ L*W*H = 6158.394 cm^3
To locate the most viable extent, add the greatest viable mistakes to every dimension, then multiply. To find the minimum viable volume, subtract the greatest feasible mistakes from each measurement, then multiply.
Volume is a scalar amount expressing the amount of 3-dimensional area enclosed by a closed surface. For example, the gap that a substance or 3-D shape occupies or consists of.
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2 people can paint a fence in one hour. how long would it take 10 people. give your answer in minuets
Step-by-step explanation:
no of people=2
time taken=1/60mins
no of people=10
time taken=1/x
2=1/60
10=1/x
x=12mins
Which inequality represents Three times a number is greater than 15. a. 3x > 15 b. 3x = 15 c. 3x + 15 d.15 + 3x
Answer:
a.
Step-by-step explanation:
> is a symbol of inequality representing greater than
Need help now.
Someone please.
Answer:
$1,075
Step-by-step explanation:
Simple Intereat Formula:
A = P(1+rt)
where A is the final amount,
P is the principal(original amount invested)
r = annual interest rate
t = time in years
Given P = 1000
r = 2.5/100
t = 3 (Beginning of 4th year means the 4th year is not counted)
A = 1000(1+(0.025)(3))
= 1000(1.075)
=$1,075
PROBLABILITY!!!
(I added the picture needed)
1.Create a sample space and find the product of each combination. What is the probability that a person wins the game? Express your answer as a fraction in lowest terms and as a percent rounded to the nearest tenth.
(answer to this one is 9/28 and 32.1%)
2. You realize a short time into the carnival that you don’t have enough prizes to last the entire event. You call your teacher, and she suggests that you change the winning number so that a participant will win only 25% of the time. What number will that be? Support your answer.
3. Participants achieving a winning score of 36 or higher in four consecutive attempts will receive a large prize! What is the probability of this occurring?
4. After changing the game rules, participants and the crowd are disappointed when the first five games yield scores of 12, 18, 30, 28, and 24. What statement can you recommend the teacher posts to reassure everyone that the game is fair?
Based on the game rules of randomly picking a card and multiplying it by the roll from a number cube, the following are true:
Probability is 3/8 or 37.5%.To win 25% of the time, player needs to get 32 or higher. Probability of a score of 36 or higher in 4 attempts is 1/1,1296.Teacher should remind everyone that all numbers except only 24 and 30 can appear equally.How can the data be represented?There are 6 sides to dice and 4 cards. The sample space is:
Dice Card Product
1 5 5
1 6 6
1 7 7
1 8 8
2 5 10
2 6 12
2 7 14
2 8 16
3 5 15
3 6 18
3 7 21
3 8 24
4 5 20
4 6 24
4 7 28
4 8 32
5 5 25
5 6 30
5 7 35
5 8 40
6 5 30
6 6 36
6 7 42
6 8 48
Frequency table
Product Frequency
5 1
6 1
7 1
8 1
10 1
12 1
14 1
16 1
15 1
18 1
21 1
24 2
20 1
28 1
30 2
32 1
25 1
35 1
40 1
36 1
42 1
48 1
Total 24
The frequency table shows that to get 28 or more, a person will have a relative frequency of:
= 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1
= 9
Probability is:
= 9 / 24
= 3/8
= 37.5%
What product does a player need to win 25% of the time?The number of products required to win 25% of the time is:
= 25% x 24
= 6
To find the winning number, count down from the highest product 6 times to get 32.
How can the larger prize be won?The probability of getting 36 or higher is:
= ∑(Probabability of picking 36 and above numbers)
= 1 / 24 + 1/24 + 1/24 + 1/24
= 1 / 6
The probability of repeating this 4 times is:
= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6
= 1 / 1,296
= 0.0007716
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The function fis given by this table of values.
-1
96
0
48
X
f(x)
Use this table to complete the statements.
1
24
2
12
3
6
The parent function of the function represented in the table is
If function fis vertically compressed by a factor of 4, the
A point in the table for the transformed function is
-values will be
Answer:
no man you should reconsider the question again
try typing again i guess its wrong
Answer: exponential, f(x), divided by 4, 1,6
Step-by-step explanation:
Please help with these 3 questions! Will give brainliest and 25 points.
a. I and II only true statement.
b . ∠3 = 84°
c . m∠KJM = 138° and m∠KLM = 59°
Properties of an Isosceles trapeziumOnly one pair of sides are parallelThe diagonals are equal in measure.The opposite angles are supplementaryThe base angles are equal in measure.Therefore, i and ii are true for an isosceles trapezium.
∠2 ≅ ∠3
∠1 ≅ 96°
Therefore,
∠3 = 180 - 96
∠3 = 84°
m∠KJM = 180 - x - 14
5x - 2 = 180 - x - 14
5x - 2 = 180 - x - 14
5x + x = 180 - 14 + 2
6x = 168
x = 168 /6
x = 28
m∠KJM = 5(28) - 2 = 138°
m∠KLM = 180 - 10y + 29
3y + 14 = 180 - 10y + 29
3y + 10y = 180 + 29 - 14
13y = 195
y = 195 / 13
y = 15
m∠KLM = 3(15) + 14
m∠KLM = 45 + 14
m∠KLM = 59°
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Billy thinks of a number that is not zero.
He multiples his number by -3
Is:
The answer is positive
The answer is negative
The answer could be
positive or negative
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Billy thinks of a nonzero number. He multiplies it by 3. He gets...? 3 options given
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
This problem does not give us the information about the starting number (we can't read Billy's mind).
First, I'm going to assume that the number is positive
[tex]\bf{A\;positive\;number\;multiplied\;by\;-3;\;yields\;a\;negative}[/tex]
Next, I'll assume that Billy's number is a negative one.
[tex]\bf{The\;number\;is\;a\;positive\;one}[/tex].
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=The\;answer\;could\;be\;either\;positive\;or\;negative.\;It\;depends\;on\;the\;sign}\\of\:the\:starting\:number.[/tex]
1.) Find the distance between F( 5, - 2 ) and A( -1, 4)
Answer:
8.49 units
Step-by-step explanation:
1. The distance formula is: [tex]\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]
2. Let's plug in the numbers: [tex]\sqrt{(-1-5)^{2} +(4--2)^{2} }[/tex]
3. [tex]\sqrt{(-6)^{2} +(6)^{2} }[/tex]
4. [tex]\sqrt{36 + 36}[/tex]
5. [tex]\sqrt{72}[/tex] ≈ 8.485
URGENT CAN SOMEBODY PLEASE ANSWER THESE 2 QUESTIONS
Answer:
A: y=2x+4
B. 34° Celsius
Step-by-step explanation:
A:
Since the temperature goes up at a steady rate of 2 degres per minute, we can assume that 2 is our slope. Since the graph shows us that 4 is the y-intercept, we can substitute both the slope and y-intercept into the equation of a line, or y=mx+b. (m is our slope and b is our y-intercept.)
Doing so gives you:
[tex]y = 2x + 4[/tex]
B.
Using the above formula (y=2x+4), we can substitute x with 15 (since x is the minutes that pass).
Doing so gives you y=30+4, the sum of which is 34.
Therefore, the answer should be 34° Celsius.
You have to fill a can of gasoline with a capacity of 12 liters.
The gas pump indicates that gasoline is selling for $1.15/litre.
Which equation allows you to calculate the cost of gasoline C according to the quantity of gasoline in liters n ?
Please choose an answer.
C = 1,15n + 12
C= -1,15n + 12
C = 0,12n - 1,15
C = 1,15n
Answer:
C=0,12N-1,15
Step-by-step explanation:
The vehicle preference of police officers and firefighters is given in the table. Based on the information in the table, which or the following is an example of independent events
Answer:
Step-by-step explanation:
I had this exact question and I figured it out.
the answer is: P(police officer and chooses car)
In order to get this answer I did the P(police officer) X P(choosing car)
It ended up being 36/45 X 15/45. Which is equal to around .2666667.
Now you take the Intersection of police officer and chooses car and you divide it by 45. That value on the chart is 12.
lucky enough, the product of 36/45 and 15/45 is equal to 12/45.
So 0.8 X 0.33 = .26
.26 = .26
Answer:
answer is P(police officer and chooses car)
Step-by-step explanation:
the probability of P(policer officer) and P(choose a car) are independent probabilities ( they are not overlapping probabilities)
Solve the inequality.
-2x + 8 < 14
and -3x - 9 ≥ -12
x>?
and
x≤
Answer:
x > -3 and x ≤ 1
Step-by-step explanation:
[First inequality]
Given:
-2x + 8 < 14
Subtract 8 from both sides:
-2x < -6
Divide both sides by -2, since it's negative we also flip the sign:
x > 3
[Second inequality]
Given:
-3x - 9 ≥ -12
Add 9 to both sides:
-3x ≥ -3
Divide both sides by -3, since it's a negative we also flip the sign:
x ≤ 1
(1+sinA+cosA)^2 = 2(1+sinA) (1+cosA)
Answer:
Step-by-step explanation:
[tex]L.H.S = 1^2+Sin^2A+Cos^2A+2SinA+2CosA+2SinACosA\\ \{(a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca\}\\ = 1 + (Sin^2A+Cos^2A) + 2SinA+2CosA+2SinACosA \\ \{Sin^2A+Cos^2A=1\}\\ = 1 + 1 + 2SinA+2CosA+2SinACosA \\ = 2(1 + SinA+CosA+SinACosA)\\ = 2(1^2 + (SinA+CosA).1+ SinACosA )\\ \{x^2+(a+b)x + ab = (x+a)(x+b)\} \quad here \quad x=1\\ = 2(1+SinA)(1+CosA).\\[/tex]
Problem 11-3 blair & rosen, inc. (b&r) is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. a client who contacted b&r this past week has a maximum of $55,000 to invest. b&r's investment advisor decides to recommend a portfolio consisting of two investment funds: an internet fund and a blue chip fund. the internet fund has a projected annual return of 12%, while the blue chip fund has a projected annual return of 9%. the investment advisor requires that at most $25,000 of the client's funds should be invested in the internet fund. b&r services include a risk rating for each investment alternative. the internet fund, which is the more risky of the two investment alternatives, has a risk rating of 5 per thousand dollars invested. the blue chip fund has a risk rating of 4 per thousand dollars invested. for example, if $10,000 is invested in each of the two investment funds, b&r's risk rating for the portfolio would be 5(10) + 5(10) = 100. finally, b&r developed a questionnaire to measure each client's risk tolerance. based on the responses, each client is classified as a conservative, moderate, or aggressive investor. suppose that the questionnaire results classified the current client as a moderate investor. b&r recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 250.
(a) formulate a linear programming model to find the best investment strategy for this client. let i = internet fund investment in thousands b = blue chip fund investment in thousands if required, round your answers to two decimal places. i + b s.t. i + b available investment funds i + b maximum investment in the internet fund i + b maximum risk for a moderate investor i, b 0
(b) build a spreadsheet model and solve the problem using solver. what is the recommended investment portfolio for this client? internet fund = $ blue chip fund = $ what is the annual return for the portfolio? $
(c) suppose that a second client with $55,000 to invest has been classified as an aggressive investor. b&r recommends that the maximum portfolio risk rating for an aggressive investor is 310. what is the recommended investment portfolio for this aggressive investor? internet fund = $ blue chip fund = $ annual return = $
(d) suppose that a third client with $55,000 to invest has been classified as a conservative investor. b&r recommends that the maximum portfolio risk rating for a conservative investor is 150. develop the recommended investment portfolio for the conservative investor. internet fund = $ blue chip fund = $ annual return = $
Linear programming which shows the best investment strategy for the client is Max Z=0.12I +0.09B and subject to constraints are :I+ B<=25000,
0.005 I +0.004B<=250.
Given maximum investment client can make is $55000, annual return= 9%, The investment advisor requires that at most $25,000 of the client's funds should be invested in the internet fund. The internet fund, which is the more risky of the two investment alternatives, has a risk rating of 5 per thousand dollars invested. the blue chip fund has a risk rating of 4 per thousand dollars invested.
We have to make a linear programming problem.
Let
I= Internet fund investment in thousands.
B=Blue chip fund investment in thousands.
Objective function:
Max Z=0.12I+0.09B
subject to following constraints:
Investment amount: I+ B<=25000
Risk Rating: 5/100* I+4/100*B<=250 or 0.005 I +0.004B<=250
I,B>=0.
Hence the objective function is Max Z=0.12 I+ 0.09 B.
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A rectangular prism has a square base with a width of 6 and a volume of 360 cm3. If a square pyramid has a base with the same width and height, what is the volume of the pyramid?
Which phrase best describes the translation from the graph y = (x + 2)2 to the graph of y = x2 + 3?
The parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3
What is translation?This is a way of changing the position of an object on an xy-plane.
Given the parent function expressed as y = (x + 2^)2
From the resulting image after translation, we can see that the parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3
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Find the area of the segment (unshaded area) of Circle G with radius 4in. Round to the nearest tenth.
Angle is 90°
The sector is 1/4 th of circle
Area of sector
πr²/4π(4)²/44πin²Triangle is right angled
Area
1/2(4)²16/28in²Area of unshaded region
4π-84(π-2)4(3.14-2)4(1.14)4.56in²Answer:
4.6 in² (nearest tenth)
Step-by-step explanation:
To find the area of the unshaded region, subtract the area of ΔAGB from the area of sector AGB.
The measure of an arc is equal to its corresponding central angle measure. Therefore, the central angle of sector AGB is 90°.
As the two sides of ΔAGB adjacent the central angle are the radii of the circle they are therefore equal in length ⇒ ∠GAB = ∠GBA.
Therefore, ΔAGB is an isosceles triangle.
Area of triangle (using the Sine Rule):
[tex]\sf A=\dfrac{1}{2}ab \sin C[/tex]
(where a and b are the side lengths and C is the included angle)
Given:
a = b = radius = 4 inC = 90°[tex]\implies \sf Area\:of\:triangle=\dfrac{1}{2}(4)(4)\sin 90^{\circ}=8\:in^2[/tex]
Area of a sector of a circle
[tex]\textsf{A}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}[/tex]
Substituting the given angle and radius:
[tex]\implies \textsf{A}=\left(\dfrac{90^{\circ}}{360^{\circ}}\right) \pi (4)^2=4\pi\:\: \sf in^2[/tex]
Area of the unshaded region:
[tex]\begin{aligned}\textsf{Area of unshaded region} & =\textsf{Area of sector} - \textsf{Area of triangle}\\& = 4 \pi - 8\\& = 4.566370614...\\ & = 4.6\:\sf in^2\:\:(nearest\:tenth)\end{aligned}[/tex]
Help me pls it is geomerty traingle proof
and here the question
Given: NQ¯¯¯¯¯¯¯¯ is the bisector of ∠MNP and ∠NMQ≅∠NPQ
Prove: △MNQ≅△PNQ
△MNQ ≅ △PNQ by SAS congruence theorem.
What is the SAS Congruence Theorem?If two triangles are congruent by the SAS congruence theorem, then they have two pairs of corresponding congruent sides and a pair of corresponding included sides that are congruent.
∠MNQ ≅ ∠PNQ [congruent angles formed by angle bisector]
Therefore, opposite sides to the angles, MQ and PQ would also be congruent.
Thus, MQ ≅ PQ
NQ ≅ NQ [reflexive property]
This means that both triangles have two pairs of corresponding congruent sides and a pair of corresponding included sides that are congruent.
Thus, △MNQ ≅ △PNQ by SAS congruence theorem.
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Fawzia took a taxi from her house to the airport. The taxi company charged a pick-up
fee of $2.60 plus $1.50 per mile. The total fare was $17.60, not including the tip. How
many miles was the taxi ride?
Answer:
9.375 miles
Step-by-step explanation:
1) Let's set up an equation.
2.60 + 1.50x = 17.60
1.50x = 17.60 - 2.60
1.60x = 15
x = 15/1.60
x = 9.375
a(x + 1) - b(x + 1) - x - 1
Answer:
Step-by-step explanation:
Solution
I'm assuming you want this simplified. If not leave a note.
a(x + 1) - b(x + 1) - x - 1 remove the brackets
ax + a - bx - b - x - 1 gather like terms
ax - bx - x + a - b - 1
x(a - b - 1) + (a - b - 1) Use the distributive property to simplify
Answer
(x + 1)(a - b - 1)
The common factor is (a - b - 1). That can be pulled out on either side of the isolated + sign
If sin theta = 3/4 and is in the first quadrant, then cos theta
Answer:
[tex]\frac{\sqrt{7} }{4}[/tex]
Step-by-step explanation:
since sin theta = 3/4, opposite length = 3 units and hypotenuse length = 4 units
by pythagoras' theorem, adjacent length = [tex]\sqrt{7}[/tex]
thus cos theta = adjacent/hypotenuse = [tex]\frac{\sqrt{7} }{4}[/tex]
Solve the quadratic equation 8x²-5x-4=0
Give your answer to 3 significant figures
The solution of the quadratic equation 8x² – 5x – 4 = 0 will be 1.085 and negative 0.460.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The quadratic equation is given below.
8x² – 5x – 4 = 0
Then we have
a = 8, b = -5, c = -4
Then the solutions will be
[tex]\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}\\\\\\\rm x = \dfrac{-(-5)\pm \sqrt{(-5)^2 - 4 * 8 * (-4)}}{2 * 8 }\\\\\\x = \dfrac{5 \pm 12.37}{16}\\\\\\x = \dfrac{5- 12.37}{16}, \dfrac{5 +12.37}{16}[/tex]
On further solving, we have
x = 1.085, -0.460
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