solve the quadratic equation 3x^2 - 9x + 1 = 0 Give answer to 3 significant figures
Answer:
Either, (9+√69)/6 or (9-√69)/6
Step wise:
3x²-9x+1=0-------------------(i)
comparing equation onw with (ax²+bx+c=0), we get,
a=3, b=-9, c=1
now,
using Quadratic Formula,
(-b±√b²-4ac)/2a=x
{-(-9)±√(-9)²-4.3.1}/2.3=x
(9±√81-12)/6=x
(9±√69)/6=x
Taking +(ve) sign Taking -(ve) sign
(9+√69)/6=0 (9-√69)/6=0
∴(9+√69)/6=0 ∴(9-√69)/6=0
[∵They cannot be further solved]
The solutions to the given quadratic equation are x = 2.884 and
x = 0.116.
What is a quadratic equation?The equation of the form ax² + bx +c is known as a quadratic equation.
The given equation is 3x² - 9x + 1 =0.
Solve the equation as follows:
3x² - 9x + 1 =0
Use the quadratic formula to solve the equation:
[tex]x = \frac{-(-9)\pm\sqrt{(-9)^2-4(3)(1)}}{2(3)}\\\\x= \frac{9\pm\sqrt{81-12}}{6}\\\\x=\frac{9\pm\sqrt{69}}{6}\\\\x = \frac{9\pm8.306}{6}\\\\x=\frac{9+8.306}{6}\quad\text{ or }x=\frac{9-8.306}{6}\\\\x=2.884\quad\text{ or }x=0.116[/tex]
Hence, the solutions to the given quadratic equation are x = 2.884 and
x = 0.116.
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which of the following scenarios could be modeled by the expression 3/2 divided by 1/4
Answer:
I believe C.
Explanation:
I am pretty sure it's C but I don't really see it too well so I can't read the top two the best.
I GIVE BRAINLILSET
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
Answer:
(C) $1.5
Step-by-step explanation:
Profit Percent * Cost Price = Profit
20% * $1.25 =
20/100 = .2 * $1.25 =
$.25
Selling Price = Profit + Cost Price
$.25 + $1.25 = $1.5
There are 120 students and 23 teachers going on a class trip. The buses used for the class trip hold at most 45 passengers. How many buses will be needed?
Answer: 4 busses if each bus only hold 45 passengers at most.
Step-by-step explanation:
120 students
23 teachers=143 people
143 divided by 3 busses is only 47 so 3
busses wouldn’t be enough
The variables y and x have a proportional relationship, and y = 7 when x = 2 What is the value of x when y = 212 Enter your answer in the box x = 1
Answer:
proportional relational ship
y= kx
7 = k2
solve for k
7/2 =k
y = 7/2 x
if y = 21
21 =7/2 x
solve for x
multiply by 2/7 on each side
21* 2/7 = 2/7*7/2 x
6 =x
$75 lunch; 18% tip what is the total
Answer:
88.5
Step-by-step explanation:
75 x .18
tip= 13.5
75 + 13.5 = 88.5
the question: a computer manufacturer built a new facility for assembling computers. there were construction and new equipment cost. the company paid for these cost and made combined profits of $80 million after four years as shown in the graft.
answers:
a: f(x)=60x-160
b:f(x)=-60x+160
c:f(x)=-80x +4
d: f(x)= 80x -4
Answer:
The equation that closely represents the graph is [tex]\mathbf{y=60x-160}[/tex]
Option A is correct.
Step-by-step explanation:
We need to find equation that represents the graph.
We can write equation in slope-intercept form: [tex]y=mx+b[/tex] where m is slope and b is y-intercept.
For finding the equation we need to find slope and y-intercept
Finding slope
The slope can be found using formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we can find [tex]x_1=0, y_1=-160, x_2=1, y_2=-100[/tex]
Putting values and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-100-(-160)}{1-0} \\Slope=\frac{-100+160}{1}\\Slope=-100+160\\Slope=60[/tex]
We get Slope = 60
Finding y-intercept
Using point (0,-160) and slope m = 60, we can find y-intercept
[tex]y=mx+b\\-160=60(0)+b\\b+0=-160\\b=-160[/tex]
Writing the equation
So, the equation for given graph having slope m = 60 and y-intercept b =-160 is:
[tex]y=mx+b\\y=60(x)+(-160)\\y=60x-160[/tex]
So, The equation that closely represents the graph is [tex]\mathbf{y=60x-160}[/tex]
Option A is correct.
Need help will mark Brainliest no explanation needed
What is the "quotient" of two numbers?
Answer:
Result of a division
Step-by-step explanation:
Example
x / y = z
z is the quotient
Given g(x)=−x2+10x−3, find the following.
g(9)=
Question 14 options:
-174
-111
6
138
Answer:
g(9) = 6
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
g(x) = -x² + 10x - 3
g(9) is x = 9
Step 2: Evaluate
Substitute in x: g(9) = -(9)² + 10(9) - 3Exponents: g(9) = -(81) + 10(9) - 3Multiply: g(9) = -81 + 90 - 3Add: g(9) = 9 - 3Subtract: g(9) = 6Need this ASAP please help
Answer:
Step-by-step explanation:
b
Answer:
Option b) 3x - 22 = 38 should be the correct answer.
Step-by-step explanation:
If we solve the equation, we get:
x = 20
So each bag had 20 apples. In total, 3 bags held 60 apples. If he gives away 22 apples to his friends, he has 38 remaining and this satisfies the discription given in the question.
Therefore, option B) 3x -22 = 38 should be your answer.
Write an inequality with the same meaning as the following
16 > x
Answer:
16>x/2
Step-by-step explanation:
Put these numbers from least to greatest 0.51, 3/4, 0.59, 3/8, 0.24, 0.517
Answer: 0.24, 3/8, 0.51, 0.517, 0.59, 3/4
Step-by-step explanation:
First you will have to convert the 3/4 and 3/8 to a decimal number. By doing this 3/4 turns into 0.75 and the 3/8 becomes 0.375. After this step you then arrange the numbers for the lowest of 0.24 then the 3/8 (0.375) next 0.51 after that is 0.517 then 0.59 and final after that 3/4
Solve for x
-2(x+6) =-36
Answer:
x= 12
Step-by-step explanation:
Answer:
x=12
Step-by-step explanation:
-2(x+6)=-36
distribute the -2
-2x-12=-36
add 12 to both sides
-2x=-24
divide both sides by -2
x=12
if x,4x+3 and 7x+3 are geometric sequence. find the value of x
please help me
Answer:
x = [tex]\frac{-6}{7+\sqrt{13}}[/tex]
r = [tex]\frac{1+\sqrt{13} }{2}[/tex]
Step-by-step explanation:
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-one number called the common ratio.
For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2.
-----
Let's take r=ratio of the geometric sequence
in first term, x is multiplied by [tex]r^{0}[/tex]
First term: x [tex]r^{0}[/tex]
Second term: 4x+3 = x [tex]r^{1}[/tex]
Third term: 7x+3 = x [tex]r^{2}[/tex]
From the last 2 equation, we have to obtain r and x values.
Second equation - First equation:
3x = x r (r - 1)
Let's state: x different from 0, so we can simplify x, obtaining:
3 = [tex]r^{2}[/tex] - r
0 = [tex]r^{2}[/tex] - r - 3
r = [tex]\frac{1+\sqrt{13} }{2}[/tex] (only the positive value of r counts)
so, going to second term of the sequence:
4x+3 = x [tex]r^{1}[/tex] => x (4 - [tex]\frac{1+\sqrt{13} }{2}[/tex] ) = -3
x ([tex]\frac{7+\sqrt{13} }{2}[/tex] ) = -3 => x = [tex]\frac{-6}{7+\sqrt{13}}[/tex]
hope it helps..
Using the graph, determine the coordinates of the x-intercepts of the parabola.
Y
Answer: -2 and 4
Step-by-step: You see the horizontal line? now look at the the numbers -2 and 4 on that line. Notice how the line passes through them? those are your x-intercepts.
The required coordinates of the x-intercepts of the parabola are (0, -2) and (0, 4).
What is x-Intercept?The x-intercept is defined as an intercept that is located at the x-axis of the plane, which is the location or coordinates from where the line crosses.
We have to determine the coordinates of x-intercepts and y-intercepts that would function in the given graph.
The parabola of the graph is given in the question
A horizontal axis, or x-axis, and a vertical axis, or y-axis, are present in a 2-dimensional coordinate graph. Intercepts are the points (0, -2) and (0, 4) here lines representing a range of values intersect these axes.
Therefore, the required coordinates of the x-intercepts of the parabola are (0, -2) and (0, 4).
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find the domain of the graphed function
Answer:
Domain= [0, 13]
Step-by-step explanation:
Domain refers to the possible input values on the x-axis.
HELP ASAP giving brainlist!!!
Answer:
I would say its given because all of the sides are the same
Step-by-step explanation:
what is the estimate of 210 x 733
Answer:
153,930 that is the answer hope it is right
Answer:
about 1,400
Step-by-step explanation:
its about 1,400 because you would round 210 to 200, and 733 to 700.
please give brainliest :))
Sanda withdrew $14.50 from his bank account for 6 weeks. What was the total change in his bank account after six weeks?
Answer:
87 is what he took out after six weeks is that it or?
Solve for the value of n.
(9n)
(8n+8)
This question is based on the given solving an equation. Therefore, the value of n for (9n) (8n+8) is 0 and -1.
Given:
(9n) (8n+8)
We need to determined the value of n.
According to the question,
It is given that, expression (9n) (8n+8).
For finding the value of n, we would be equate the given expression is equal to zero.
⇒ (9n) (8n+8) = 0
Now, calculating the value of n. We get,
⇒ (9n) (8n)+(9n) (8)
Then, solving above expression further. We get,
⇒ [tex]\bold{72 n^2+ 72n = 0}[/tex]
Now, taking common 72 n. We get,
⇒ 72n (n + 1) = 0
⇒ 72 n = 0 and (n+1) = 0
We get,
n = 0 , -1
Therefore, the value of n for (9n) (8n+8) is 0 and -1.
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The measures of the angles of a quadrilateral are 3:8:7:2 find the measure of each angle
Answer:
Angle 1= 54°
Angle 2= 144°
Angle 3 = 126°
Angle 4 = 36°
Step-by-step explanation:
We are given measures of the angles of a quadrilateral are 3:8:7:2
Let the common ratio = x
The angles will be:
Angle 1= 3x,
Angle 2= 8x,
Angle 3 =7x
Angle 4 =2x
We know that sum of all angles of quadrilateral = 360°
We can write as: [tex]3x+8x+7x+2x=360[/tex]
Solving to find x,
[tex]3x+8x+7x+2x=360\\20x=360\\x=\frac{360}{20}\\x=18[/tex]
We get value of x = 18
Now, finding angles:
Angle 1= 3x = 3(18) = 54°
Angle 2= 8x = 8(18) = 144°
Angle 3 =7x = 7(18) = 126°
Angle 4 =2x = 2(18) = 36°
How many laps would be 50 miles on a 1 1/2 mile track?
Answer:
34 laps
Step-by-step explanation:
the specific answer is 33.3 but u have to round the whole number
Rebecca has 6 yards of ribbon. It takes 3/8 yard to wrap one package. How many packages can rebecca wrap
Answer:
16
Step-by-step explanation:
6 x 8 = 48
48 / 3 = 16
Rebecca can only wrap 16 packages with 6 yards of ribbon.
Dejah is proving that perpendicular lines have slopes that are opposite reciprocals. She draws line s and labels two points on the line as (−a, 0) and (0, b).
Enter the answers, in simplest form, in the boxes to complete the proof.
Answer:
math is hard :(
Step-by-step explanation:
What system of equations is shown on the graph below?
On a coordinate plane, 2 lines intersect around (1.8, negative 0.8).
2 x + y = 3 and 3 x minus 4 y = 8
2 x minus y = 3 and 3 x + 4 y = 8
2 x + y = 3 and 3 x minus 4 y = 2
2 x minus y = 3 and 3 x minus 4 y = negative 2
Answer:
i thnk it is c correct me if i am rong
Step-by-step explanation:
Answer:
(C) I got it right
Step-by-step explanation:
on edge
x + 8 + 2x <= 2x + 13
Answer:
X = 15
Step-by-step explanation:
We move all terms to the left:
x+8+2x-(2x+13)=0
We add all the numbers together, and all the variables:
3x-(2x+13)+8=0
We get rid of parentheses:
3x-2x-13+8=0
We add all the numbers together, and all the variables:
x-5=0
We move all terms containing x to the left, all other terms to the right:
x=5
Find the length x.
5
X
45
PLS THIS IS ERGENT
Answer:
X = 7.5
Step-by-step explanation:
First, divide 5 by 3 to find the scale factor:
5/3 = 1.667
Now, multiply 4.5 by 1.667 to find x:
x = (4.5)(1.667)
x = 7.5
Therefore, x is equal to 7.5.
I hope this helps!!
- Kay :)
How you express the average of five quizzes is 85 in mathematical expression
Determine the shaded areas part 2
9514 1404 393
Answer:
(a) cannot be determined
(b) 44 cm^2
(c) 87 m^2
(d) 180 m^2
(e) 132 m^2
Step-by-step explanation:
(a) missing a horizontal dimension
__
(b) The difference between the bounding rectangle and the lower-left cutout is ...
(8 cm)(7 cm) -(3 cm)(4 cm) = (56 -12) cm^2 = 44 cm^2
__
(c) The difference between the bounding rectangle and the center cutout is ...
(13 m)(7 m) -(4 m)(1 m) = (91 -4) m^2 = 87 m^2
__
(d) The difference between the bounding rectangle and the two cutouts is ...
(20 m)(25 m) -(16 m)(20 m) = (20 m)(25 -16) m = (20 m)(9 m) = 180 m^2
__
(e) The difference between the bounding rectangle and the two cutouts is ...
(14 m)(12 m) -(12 m)(3 m) = (12 m)(14 -3) m = (12 m)(11 m) = 132 m^2