The solutions to the given quadratic equation 4x² - 4x - 1 = 0 are x = ( 1 - √2 )/2, ( 1 +√2 )/2.
What is the solution(s) to the given quadratic equation?A quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula
x = (-b±√(b² - 4ac)) / (2a)
Given the equation in the question;
4x² - 4x - 1 = 0
Compared to the standard form ax² + bx + c = 0
a = 4b = -4c = -1Plug these values into the quadratic formula above.
x = (-b±√(b² - 4ac)) / (2a)
x = (-(-4) ± √((-4)² - ( 4 × 4 × -1 ))) / (2 × 8)
x = ( 4 ± √( 16 - ( -16) ) / (8)
x = ( 4 ± √( 16 + 16) ) / (8)
x = ( 4 ± √( 32) ) / (8)
32 can be written as 4²×2
x = ( 4 ± √( 4²×2 ) ) / (8)
x = ( 4 ± 4√2 ) / (8)
x = ( 1 ± √2 ) / 2
x = ( 1 - √2 )/2, ( 1 +√2 )/2
Therefore, the solutions to the given quadratic equation 4x² - 4x - 1 = 0 are x = ( 1 - √2 )/2, ( 1 +√2 )/2.
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What is the formula used to arrive at x^2-11x+10
Answer:
Quadratic Formula
Step-by-step explanation:
x^2-11x+10=
x^2-x-10x+10=
x(x-1)-10(x-1)=(x-10)(x-1)
E-7/9|12/5-6R|+50 > or equal to -30
The solution set of the inequality for R is given by [tex]-\frac{1172}{85} \leq x\leq \frac{1228}{55}[/tex] .
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. It is frequently used to compare two numbers on the number line based on their sizes. Different types of inequalities are represented by a variety of notations such as < ,> ,≤ and ≥.
The modulus function takes the absolute value of a function.
To solve the given inequality we have simplify the inequality first.
[tex]x-\frac{7}{9} |(\frac{12}{5} -6x)|+50\ge -30[/tex]
[tex]or, x-\frac{7}{9}\times \frac{6}{5} |(2-5x)|+50\ge -30\\or,x-\frac{14}{15}|2-5x|\ge-80\\[/tex]
Now we separate the inequalities:
[tex]x-\frac{14}{15}(2-5x)\ge-80[/tex] for 2x-5 ≥ 0
[tex]x-\frac{14}{15}(-(2-5x))\ge-80[/tex] for 2x-5 ≤ 0
Now we will solve the two inequalities separate and find the intersection.
[tex]x-\frac{14}{15}(2-5x)\ge-80\\or,15x-28+70x\ge-1200\\or,x\ge -\frac{1172}{85}[/tex]
Again
2x-5 ≥ 0
or, [tex]x\le\frac{2}{5}[/tex]
hence [tex]-\frac{1172}{85}\le x\le\frac{2}{5}[/tex]
Similarly solving the other inequality we get
[tex]\frac{2}{5}\le x\le\frac{1228}{55}[/tex]
Now we find the intersection of the two inequalities:
[tex]-\frac{1172}{85}\le x\le\frac{1228}{55}[/tex]
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30 POINTS Graph the solution to this inequality on the number line. 1/2 x - 3 < -1 3/8
The graphing is achieved as follows:
On the graph the third sign counting from the left is used.
This is placed on the first mark of the three marks between 3 and 4. This point equivalent to 3 1/4 or 3.25
How to find the solution of the equation
Given data
the graph
and the equation 1/2 x - 3 < -1 3/8
solving for x gives
1/2 x - 3 < -1 3/8
1/2 x < 3 -11/8
x/2 < 13/8
x < 13 / 4
x < 3 1/4
On the graph the third sign counting from the left is used.
The arrow is facing left, this is to show the sign less than.
The tail has a hollow not a solid point to show that equality sign is not included.
This is placed on the first mark after point 3 as this is the point equivalent to 3 1/4 or 3.25
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Find the quotient of The quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.. Write the final answer in scientific notation.
6 x 1048
6 x 1024
6 x 100
6 x 10−48
The quotient of the given problem using laws of exponents is; 6 * 10⁰
How to use the law of exponents?We want to express the quotient of the quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.
This is;
(30 * 10⁻²⁴)/(5 * 10⁻²⁴)
Now, we can break this down into like terms to get;
(30/5) * (10⁻²⁴/10⁻²⁴)
= 6 * 1
Now, 1 can also be written as;
10⁰ = 1
Thus, the solution of the given problem is; 6 * 10⁰
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Solve the quadratic equation 2h^2 + 100 = 0. If there is more than one solution, separate them with commas. If there are no solutions type DNE.
Answer:
h=sqrt2*5i, h=-sqrt 2*5i
Step-by-step explanation:
Answer:
DNE
No real solutions
Step-by-step explanation:
This Quadratic Equation: 2h² + 100 = 0
Factor out the common term 2:
A machinist is required to manufacture a circular metal disk with area 600 cm2 . (a) What radius produces such a disk? (b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part (a) must the machinist control the radius? (c) In terms of the limit limx→a f(x) = L, what is f(x)? What is a? What is L?
The required radius and error in radius is 13.8 cm and ± 0.12cm
Given that,
A machinist is required to manufacture a circular metal disk with an area of 600cm².
(a) What radius produces such a disk is to be determined
(b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part is to be determined.
The area of a circle is given by the pie times square of the radius.
Area of circle = πr^2
Here,
a) The given area of disk = 600 cm²
πr² = 600
r = √600/3.14
r = 13.8 cm
b) an error tolerance of ± 5 cm² in the area of the disk,
So the percentage of error is 0.84%
Now, 0.84% of radius = 0.84 *13.8/100 = 0.12
The required error in radius will be ±0.12 cm
Similarly,
c) limx→a f(x) = L
Where a is the area of the disk and L is length, and f(x) is function of area.
Thus, the required radius and error in radius is 13.8 cm and ± 0.12cm.
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-0.75(12x+60) = -x-8x - 15.
Answer:
Step-by-step explanation:
-9x - 45 = -7x - 15 (Distribute -0.75 to (12x+60)) (x-8x = -7x)
-30 = 2x (add 15 to both sides and add 9x to both sides)
-15 = x (divide both sides by 2)
In Exercises 6-10, use the diagram.
6. Find the perimeter of AABC.
7. Find the perimeter of quadrilateral
ACDE.
8. Find the area of AABC.
9. Find the area of quadrilateral
ACDE.
10. Find the area of pentagon ABCDF.
B(-1,5) Y
A(-4, 3)
2
F(-4,-3)
-2-
N
E(-2,-3)
C(2, 3)
2 4 X
D(4,-3)
Answer: 5
Step-by-step explanation:
Find the compound interest and the total amount after three years if the interest is compounded half yearly. if principal is ₹1024 rate of interest 100% per annum
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1024\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{half-yearly, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]A=1024\left(1+\frac{1}{2}\right)^{2\cdot 3} \implies A=1024(1.5)^6\implies A = 11664~\hfill \underset{earned~interest}{\stackrel{11664~~ - ~~1024}{10640}}[/tex]
Given the function f(x) = |x+3|, find each of the following.
f(6), f(- 10), f(0)
f(6) = ?
The value of the functions f(6), f(- 10), f(0) are 9, 7 and 3 respectively.
What is a function?A function can be defined as an expression, rule or law that shows the relationship between a dependent and an independent variable.
Given the function;
f(x) = |x+3|
To determine f(6)
Substitute the value of x as 6
We have;
f(6) = | 6 + 3 |
f(6) = 9
To determine f(-10)
Substitute the value of x as - 10
We have;
f(-10) = | -10 + 3 |
f(-10) = | -7|
f(-10) = 7
To determine f(0)
Substitute the value of x as 0
We have;
f(0) = | 0 + 3|
f(0) = 3
Thus, the value of the functions f(6), f(- 10), f(0) are 9, 7 and 3 respectively.
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Need help with this please
Answer:
HELP WITH WHAT?
Step-by-step explanation:
48 inches long and 36 inches wide. What is the area?
Answer:
1728
Hope this helps :)
"clown juggles 12 bowling for the first 2.5 minutes then he bump it up to an average of 18 bowling pins per minute cor the last 1 1/3 minute. what is the total number if pins"
After juggling for several minutes i.e., 2.5 minutes and [tex]1\frac{1}{3}[/tex] minutes (mixed fraction), the total number of bowling pins by clown is 37 pins
As per the question statement, a clown juggles 12 bowling for the first 2.5 minutes then he bump it up to an average of 18 bowling pins per minute for the last [tex]1\frac{1}{3}[/tex] minute (Mixed Fraction form)
We are supposed to find the total number if pins by the clown.
Let's calculate the total time first that will be 2.5 minutes + [tex]1\frac{1}{3}[/tex] minutes
[tex]1\frac{1}{3} =\frac{3*1 +1}{3} =\frac{4}{3} =1.34[/tex] minutes.
Therefore total time = 3.84minutes
Given that he bumps it up to an average of 18 bowling pins per minute for the last [tex]1\frac{1}{3}[/tex] minute so, the number of pins in the last [tex]1\frac{1}{3}[/tex] minute will be = [tex]18*1.34 = 24.12 = 25[/tex] (approx.)
So total number of bowling pins = [tex]12+25 = 37[/tex] pins
Mixed Fraction: A mixed fraction is one that is represented by both of its quotient and remainder present in a single expression. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.To learn more about such questions, click on the link given below:
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I don’t know this one question
Answer:
v = 13
Step-by-step explanation:
because they are supplementary angles they add up to 180
so
add them
and put them equal to 180
9v + 3 + 60 = 180
combine like terms
9v + 63 = 180
now subtract 63 to both sides
9v = 117
divide 9 to both sides
v = 13
that is your answer
Simplify 12/16 to lowest terms and find an equivalent fraction that has a denominator of 32.
10/00
O
0 / 4
[tex]\cfrac{12}{16}\implies \cfrac{4\cdot 3}{4\cdot 4}\implies \cfrac{4}{4}\cdot \cfrac{3}{4}\implies 1\cdot \cfrac{3}{4}\implies \boxed{\cfrac{3}{4}}~\hfill \cfrac{8\cdot 3}{8\cdot 4}\implies \boxed{\cfrac{24}{32}}[/tex]
(-4, 12) and (-7, -3) write an equation of the line in slope intercept form that passes through the points.
Answer:
The equation in slope-intercept form is: [tex]y=5x+32[/tex]
Step-by-step explanation:
To calculate the slope, [tex]m[/tex], we use the formula [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1} }[/tex] where [tex]y[/tex] are the [tex]y[/tex]-values of the points and [tex]x[/tex] are the [tex]x[/tex]-values.
Pugging our numbers into the formula, we get [tex]\frac{(-3)-12}{-7-(-4)}[/tex]. This simplifies to 5.
To calculate the [tex]y[/tex]-intercept, we first substitute one of our points into the formula. Substituting -4 and 12, we get [tex]12=5(-4)+b[/tex].
Then we can solve for [tex]b[/tex].
[tex]12=5(-4)+b[/tex]
[tex]12=-20+b[/tex]
[tex]32=b[/tex]
So, our slope is 32.
We can then plug these values into the slope-intercept form [tex]y=mx+b[/tex]
27. You are driving on the interstate with your cruise control on at a constant speed of 64 miles per hour.
Use the number lines below to determine how long it will take to drive to the next rest sop that is 16
miles away (see textbook, page 20). Explain the thinking you used to determine your answer.
The car will take 15 minutes to drive to the next stop which is 16 miles away.
As per the question statement, we are supposed to find the time taken by the car to drive to the next stop which is 16 miles away if it is driving on the interstate with cruise control on at a constant speed of 64 miles per hour.
Before solving the question, we need to know the concept of relation between time, distance and speed, which states that
[tex]speed=\frac{distance}{time}[/tex]
In the question [tex]speed = 64 mph\\distance = 16 miles\\time taken = t[/tex]
Substituting values in the formula above,
[tex]64=\frac{16}{t} \\t=\frac{16}{64} \\t=0.25 hours =0.25 *60\\t=15 minutes[/tex]
Hence the time taken by car to drive to the next stop which is 16 miles away is 15 minutes or [tex]\frac{1}{4}[/tex] hours.
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subtract x^2+8x from -3x^2-3x-7.
Answer: -4x²-11x-7
Step-by-step explanation:
[tex]-3x^2-3x-7-(x^2+8x)=\\-3x^2-3x-7-x^2-8x=\\-4x^2-11x-7[/tex]
Each square of a chess board measures 57 millimeters by 57 millimeters. There are 64 squares on a chess board. What is the area of the chess board?
Answer: 207936 millimeters squared
Step-by-step explanation:
57 * 57 = 3249
3249 * 64 = 207936
Answer: 207936 millimeters^2
Step-by-step explanation: 57*57=3249
3249 64 times is 207936.
sorry for the blurry photo
A- -10
B- 15
C- 10
D- -15
Answer: 15
Explanation:
The length of the segment is 10 plus 5 which is fifteen because you need to know how long it is. Just ignore the negatives.
a cat on a table 960m views a piece of meat on the ground 114.4cm away from the foot of the table. find the angle of depression of the meat from the top of the table
The angle of depression of the meat from the top of the table is 40°
This situation makes a right-angle triangle with the height of table being the perpendicular to the right-angle triangle and the distance of meat from the foot of the table becomes the base of the imaginary right-angle triangle
to know the angle of depression of the meat from the top of the table
we need to find the ratio between the perpendicular and the base of the triangle to use trigonometry.
Tan is the ratio of perpendicular and base of the triangle
which is = 96/114.4
tan Ф=0.8392
To solve for Ф , a tan would move from the left-hand side to the right-hand side and would become tan inverse.
Ф = tan-1 0.8392
Ф = 40°
The correct question is a cat on a table 96cm views a piece of meat on the ground 114.4cm away from the foot of the table. find the angle of depression of the meat from the top of the table.
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A hamburger and French fries cost $13. A hamburger and two sodas cost $14. A hamburger, French fries, and a soda costs $16. Write the system of equations that describes this situation, then solve to find the price of each. (PLEASE SHOW WORK)
The cost of each hamburger is $8, the cost of each French fry is $5 while the cost of each Soda is $3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the cost of hamburger, y represent the cost of french fries and z represent the cost of soda, hence:
x + y = 13 (1)
Also:
x + 2z = 14 (2)
And:
x + y + z = 16 (3)
From the three equations:
x = 8, y = 5, z = 3
The cost of each hamburger is $8, the cost of each French fry is $5 while the cost of each Soda is $3.
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help me pleaseeeeeeeeee
Answer:
Step-by-step explanation:
x + x + 16 = 90
2x +16 = 90
2x = 74
x = 37
What two im i missing?
HELP
The scatterplot for age in months and number of diaper changes per day is shown.
Part A: Estimate and interpret the correlation coefficient. (5 points)
Part B: Create an influential point for this graph that would cause the correlation to decrease. Explain your reasoning.
Answer:
Here's an answer to part of your question.
Step-by-step explanation:
The older the kids get, the less you have to change their diapers. Therefore, that is why the graph is going down
What's the correct answer?
Answer- D = (equal sign)
Explanation-
When you see two straight lines in math | | with number inside, regardless if the number inside is positive or negative, the outcome will be positive. This is called the absolute value. After we solve our absolute value however, there is a negative on the outside, which means that 61 will become negative again. Our equation is now -61 _____ -61. Your correct choice will be the equal sign, since -61 is equal to -61.
HOPE THIS HELPS GOOD LUCK!
I’m really not understanding what the next step is or what I did wrong. if anyone could help that would be appreciated:)
The vehicle will get speed of approximately 15 mph and -210 mph.
What is speed?Science's most important concept is measurement. Many measurable quantities are measured in fundamental or base units. One such measurable quantity is speed, which is defined as the ratio of an object's distance travelled to the time required to travel that distance. Let us learn about speed in depth during this session.
The ratio of distance to time taken to cover a distance is used to calculate speed. Because it only has one direction and no magnitude, speed is a scalar quantity.
Given the equation for gas mileage = 0.02x² + 3.9x - 43 where x means speed
We have been asked to find x if gas mileage = 20 that is
0.02x² + 3.9x - 43 = 20
Lets simplify
⇒ 0.02x² + 3.9x - 43 = 20
⇒ x² /50 + 39x/10 - 63 = 0
⇒ x²/ 50 + 195x/50 - 3150 = 0
⇒ 1/50 (x + 195x - 3150 ) = 0
⇒ 1/50 (x + 210x - 15 x - 3150 ) = 0
⇒ 1/50 (x (x+210) −15 (x+210)) = 0
⇒ 1/50 (x−15)(x+210) = 0
⇒ (x−15)(x+210) = 0 × 50
⇒ (x − 15)(x + 210) = 0
⇒ x = 15, x = -210
So, try using 15 mph and -210 mph, that might work.
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Area of arrow
Find the area of the figure below
Please help
Answer:
area of the arrow is 36inches^2
Step-by-step explanation:
Area of rectangle= lw
10x3=30
Area of triangle = bh/2
3x4=12/2=6
30+6=36 inches^2
Jenkins Company uses a job order cost system with overhead applied to jobs on the basis of direct labor hours. The direct labor rate is $20 per hour, and the predetermined overhead rate is $15 per direct labor hour. The company worked on three jobs during April. Jobs A and B were in process at the beginning of April. Job A was completed and delivered to the customer. Job B was completed during April, but not sold. Job C was started during April, but not completed. The job cost sheets revealed the following costs for April:
Job A Job B Job C
Cost of Jobs in Process, April 1, Current Year $ 12,000 $ 1,000 $ 0
Direct Materials Used 2,000 8,000 9,000
Direct Labor 10,000 8,000 3,000
Applied Manufacturing Overhead ? ? ?
Required:
If no other jobs were started, completed, or sold, determine the balance in each of the following accounts at the end of April:
work in progress
finished goods
cost of goods sold
The work in process(Job C) is $14,250
The finished goods(job B) is $23,000
The cost of goods sold(job A) is $31,500
What are work in process, finished goods and cost of goods sold in this case?
The work in process refers to the total costs incurred on Job C, since it was not completed at the end of the month, the finished goods refers to the costs incurred on job B which has been completed but not yet sold and cost of goods sold means the cost incurred on Job A which has been sold since it has been completed.
Job A:
Cost of job in process=$12,000
direct materials used=$2,000
direct labor=$10,000
number of direct labor hours=direct labor cost/ direct labor rate
number of direct labor hours=$10,000/$20=500 hours
Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour
Applied Manufacturing Overhead=500*$15=$7,500
cost of goods sold=$12,000+$2,000+$10,000+$7,500
cost of goods sold=$31,500
Job B:
Cost of job in process=$1,000
direct materials used=$8,000
direct labor=$8,000
number of direct labor hours=direct labor cost/ direct labor rate
number of direct labor hours=$8,000/$20=400 hours
Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour
Applied Manufacturing Overhead=400*$15=$6,000
finished goods=$1,000+$8,000+$8,000+$6,000
finished goods=$23,000
Job C:
Cost of job in process=$0
direct materials used=$9,000
direct labor=$3,000
number of direct labor hours=direct labor cost/ direct labor rate
number of direct labor hours=$3000/$20=150 hours
Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour
Applied Manufacturing Overhead=150*$15=$2,250
work in progress=$0+$9,000+$3,000+$2,250
work in progress=$14,250
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Pls help me understand this.
The area of the polygon is approximately 24.497 square units.
How to determine the area of a polygon
In accordance with the statement, we have a polygon with three vertices set on Cartesian plane, that is, a triangle. We need to find the side lengths first and later to calculate the area by Heron's formula. First, determine the lengths of each line segment by Pythagorean theorem:
JK = √[[4 - (- 3)]² + (4 - 4)²]
JK = 7
KL = √[(3 - 4)² + (- 3 - 4)²]
KL = √[(- 1)² + (- 7)²]
KL = 5√2
JL = √[[3 - (- 3)]² + (- 3 - 4)²]
JL = √85
Second, calculate the area of the triangle:
s = (JK + KL + JL) / 2
s = (7 + 5√2 + √85) / 2
s ≈ 11.645
A = √[s · (s - JK) · (s - KL) · (s - JL)]
A = √[11.645 · (11.645 - 7) · (11.645 - 5√2) · (11.645 - √85)]
A ≈ 24.497
The area of the polygon is approximately 24.497 square units.
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