Answer: x=2±√3
Step-by-step explanation:
[tex]\displaystyle\\x^2-4x+1=0\\\\ax^2+bx+c=0\\\\a=1\ \ \ \ \ b=-4\ \ \ \ \ c=1\\\\D=b^2-4ac\\\\D=(-4)^2-4(1)(1)\\\\D=16-4\\\\D=12\\\\\sqrt{D} =\sqrt{12}\\\\\sqrt{D}=\sqrt{3(4)} \\\\\sqrt{D}=2\sqrt{3}\\\\ Hence,\\\\x=\frac{-bб\sqrt{D} }{2c} \\\\x=\frac{-(-4)б2\sqrt{3} }{2(1)} \\\\x=\frac{4б2\sqrt{3} }{2} \\\\x=\frac{2(2б\sqrt{3}) }{2} \\\\x=2б\sqrt{3}[/tex]
The value of solution of equation is,
⇒ x = (2 ± √3)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
Quadratic equation is,
⇒ x² - 4x + 1 = 0
Now, We can simplify as;
⇒ x² - 4x + 1 = 0
⇒ x = - (-4) ± √(-4)² - 4×1×1 / 2
⇒ x = (4 ± √16 - 4) / 2
⇒ x = (4 ± √12) / 2
⇒ x = (4 ± 2√3) / 2
⇒ x = (2 ± √3)
Thus, The value of solution of equation is,
⇒ x = (2 ± √3)
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Determine whether the following quadratic function has a maximum of a minimum value. Then find the maximum or minimum value and where it occurs.
F(x)=-3x²+18x+3
Select the correct choice below and fill in the answer boxes to complete of
(Simplify your answers.)
The function has a maximum value of ___ at x=____.
The function has a minimum value of ___ at x= ___.
The function F(x) = -3x² + 18x + 3 has a maximum value of 30 at x = 3
How to determine if the quadratic function has a maximum or minimum?From the question, we have the following equation that can be used in our computation:
F(x) = -3x² + 18x + 3
A quadratic function is represented as
F(x) = ax² + bx + 3
By comparison, we have
a = -3
For a quadratic function to have a maximum value, the value of a must be less than 0
This means that the function has a maximum value because -3 is less than 0
Solving further, we have
F(x) = -3x² + 18x + 3
Differentiate and set to 0
-6x + 18 = 0
So, we have
x = 3
Substitute x = 3 in F(x)
F(3) = -3(3)² + 18(3) + 3
Evaluate
F(3) = 30
This represents the maximum value
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A triangle has side lengths of (4m +3n) centimeters, (8m + 10p) centimeters,
and (2p+ 2n) centimeters. Which expression represents the perimeter, in
centimeters, of the triangle?
Answer:
5n + 12p + 12m
Step-by-step explanation:
Perimeter means you are adding up all three sides.
4m + 3n + 8m + 10p + 2p + 2n
= 2n+3n + 10p+2p + 4m+8m
Combine like terms.
= 5n + 12p + 12m
Because it is popular, a store owner increases the cost of a toy by $2.47. The new cost of the toy is $9.98.
A. Write an equation that represents the situation. Use c to represent the original cost of the toy.
B. Solve the equation using a related equation. Show your work.
C. What does the solution of the equation represent.
A. The equation that represents the situation is $9.98 = c + $2.47
B. The solution using a related equation $.7.51
C. The solution of the equation represents the initial cost of the toy before the increment of price.
Equation:
Basically, the equation means the mathematical statement that is made up of two expressions connected by an equal sign.
Given,
Because it is popular, a store owner increases the cost of a toy by $2.47. The new cost of the toy is $9.98.
Here we need to find the following:
A. The equation that represents the situation
B. The solution using a related equation
C. The solution of the equation represent.
Here we know that the new cost of the toy is equal to the original cost of the toy plus the amount by which cost was increased.
So, the equation is written as,
=> New cost of the toy = original cost + amount of increase
=> $9.98 = c + $2.47
Here we need to determine the value of c, make c the subject of the formula by combining similar terms
So, the equation is rewritten as,
=> c = $9.98 - $2.47
=> c = $7.51
Therefore, the initial cost of the toy is $.7,51
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17) Solve the exponential equation 5^x-2 = 6
19) Solve the exponential equation 7^p = 51
By using natural logarithm properties we will see that the solutions of the two equations are:
17) x = 3.11
19) p = 2.02
How to solve the exponential equations?Here we will use the property of natural logarithms:
Ln( a^x) = x*ln(a)
17) We have the exponential equation:
5^(x - 2) = 6
If we apply the natural logarithm in both sides, we will get:
ln( 5^(x - 2)) = ln(6)
(x - 2)*ln(5) = ln(6)
(x - 2) = ln(6)/ln(5)
x = ln(6)/ln(5) + 2
x = 3.11
19) Now the exponential equation is:
7^p = 51
We will do the exact same thing, apply the natural logarithm in both sides:
ln(7^p) = ln(51)
p*ln(7) = ln(51)
p = ln(51)/ln(7) = 2.02
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Find the number of terms in the finite arithmetic sequence:
{ -8, 1, 10, 19, 28, ..., 469 }
n= _________
Hint: Use an = a1 + (n-1) d
The number of terms in the arithmetic sequence {-8, 1, 10, 19, 28, ..., 469} is 54 terms
How to find the number of terms in the sequenceThe number of terms in the sequence { -8, 1, 10, 19, 28, ..., 469 } is calculated from the formula
Un = a1 + (n - 1) d
where a1 = first term
d = common difference
n = number of terms
a = -8
d = second term - first term
= 1 - -8
= 9
solving for n
Un = a1 + (n - 1) d
469 = -8 + (n - 1)9
469 + 8 = (n - 1)9
collecting like terms
(n - 1) = 477 / 9
n - 1 = 53
n = 54
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please i need help with these
( please notice that on the first one there is squares those dont matter dont worry about them please)
Answer:
1. [tex]\frac{4}{27}[/tex]
2. D
Step-by-step explanation:
1. [tex]3^{-2} * 1 * 4^3 * 3^{-1}*4^{-2[/tex]
= [tex]3^{-3} * 4^1[/tex]
= [tex]\frac{4^1}{3^3}[/tex]
= [tex]\frac{4}{27}[/tex]
2. Remember the rule that 1/a^b is equal a^-b, in this case, [tex]\frac{1}{2^3}[/tex] is the same as [tex]2^{-3}[/tex], now 6 + (-3) = 3 -- which will be the exponent. [tex]2^3[/tex] is correct.
Select from the drop-down menus to correctly complete the statement. The expressions 3.2^2−1 and 10−0.33⋅2 should be joined by Choose... to form an Choose... .
Answer:
D)
Can you please mark me as "Brainliest"
35x+15y=1675
solve equation
Answer:
Take a look at the attachments...
Hope this helps! :)
what shape of units would you get for an area of 30 and a perimiter of 22
The shape of units you would get that has a perimeter of 22 and an area of 30 is a rectangle, which is shown in the image below.
What is the Area and Perimeter of a Rectangle?A rectangle is a quadrilateral that has two opposite sides that are equal and are longer than the other two opposite sides that are equal and parallel to each other.
The area of a rectangle = length × width.The perimeter of a rectangle = 2(length + width).Assuming that the shape being referred to is a rectangle that has an area of 30 units² and a perimeter of 22 units, therefore, the dimensions of the rectangle is shown in the image attached below, and they are:
Length of rectangle = 6 units
Width of rectangle = 5 units
Therefore:
Area of the rectangle = 6 × 5 = 30 units².
Perimeter of the rectangle = 2(6 + 5) = 2(11) = 22 units.
This implies that the shape of units with an area of 30 units² and a perimeter of 22 units is most likely a rectangle.
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7. Evaluate (1+r/n)nt when r=0.1 n=12 t=2
Round answer to nearest hundredth.
Answer:
shsjsjsjsjshsh#6#7#7##+-##6#3
The value of expression when r = 0.1 , n = 12 and t = 2 is,
⇒ 24.192
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ (1 + r/n) nt
Now, We can put r = 0.1 , n = 12 and t = 2 in above equation as;
⇒ (1 + r/n) nt
⇒ (1 + 0.1/12) 12 x 2
⇒ (1 + 0.008) 24
⇒ 1.008 x 24
⇒ 24.192
Thus, The value of expression when r = 0.1 , n = 12 and t = 2 is,
⇒ 24.192
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Question 1 (1 point) A small company wants to set up a server that is accessible from the company network as well as the Internet. Which of the following is MOST important to determine before allowing employees to access the server remotely A.The quality of the computer used to connect B.A security method of allowing connections C.The employees' home ISP speeds D.The geographical location of the employees
The most important to determine before allowing employees to access the server remotely is B. security method of allowing connections.
What is a computer network?
Computer networking refers to the interconnection of computing devices that can exchange data and share resources. These networked devices use a set of rules known as communications protocols to transmit data over physical or wireless networks.
A computer network is a collection of computers that share resources that are located on or provided by network nodes. To communicate with one another, the computers use common communication protocols over digital interconnections.
Local-area networks (LANs) and wide-area networks (WANs) are the two basic network types (WANs). LANs connect computers and peripheral devices in a constrained physical area, such as a business office, laboratory, or college campus, using data-transmitting links (wires, Ethernet cables, fiber optics, Wi-Fi).
In this case, it should be noted that the security method that's used for allowing the connection is important. Based on the information illustrated, the correct option is B.
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Question 7
A canoe rental company charges a $10 deposit plus $8.25 per hour to rent a canoe. A second rental company charges a $12.50 deposit pa
$7.85 per hour to rent a canoe. For what number of hours is the cost for the rental the same?
Let h represent the number of hours. Select the correct values to write an equation to represent the situation.
The number of hours at which both companies' rental costs will be the same is nearly 6 hours.
What is an equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions displayed on the left and right sides have an equal connection. To determine the value of an unknown variable that stands in for an unknown quantity, equations can be solved.
Let the number of hours = h The deposit price at the first canoe rental company = $10
Cost per hour to rent a canoe = $8.25/h
The total cost for rental for the first company is given by
C(A) = 10 + 8.25h
The deposit price at the second canoe rental company = $12.50
Cost per hour to rent a canoe = $7.85/h
The total cost for rental for the second company is given by
C(B) = 12.50 + 7.85h
The number of hours at which both company's rental costs will be the same is given as
C(A) = C(B)
10 + 8.25h = 12.50 + 7.85h
8.25h - 7.85h = 12.50 - 10
0.4h = 2.5
h = 2.5/0.4
h = 6.25
h ≈ 6 hours
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A tennis ball can in the shape of a right circular cylinder holds six tennis
balls snugly. If the radius of a tennis ball is 3.2 cm, what percentage of
the can is not occupied by tennis balls?
Answer: 33 1/3 percent
Step-by-step explanation:
First, we need to find the volume of the tennis ball can, which is a cylinder.
The formula for the volume of a cylinder is pi r^2 h.
The radius of a tennis ball is 3.2 cm, so the radius of the cylinder would be 3.2 cm as well.
The height is equivalent to the height of three tennis balls, which is the diameter of 3 tennis balls. The diameter of one tennis ball is 6.4 cm, and we can multiply this by 6 to get 38.4 as our height.
We can plug in these values to our equation for the volume of the cylinder.
pi * 3.2^2 * 38.4
The volume of the cylinder is 393.216 pi.
Now, we need to find the volume of one tennis ball and multiply that by six.
The volume of a sphere is 4/3 pi r^3
We know our radius, 3.2, so we just have to substitute that into the equation.
4/3 pi 3.2^3 = 4/3 * pi * 32.768 = 43.69 and 2/3 pi for the volume of one tennis ball. If we multiply this by six, we get the volume of all the tennis balls, which is 43.6 and 2/3 *3 = 262.144 pi.
Now we have to find the percentage of the cylinder not occupied, so we can find one percent of the container and divide that by 262.144 pi.
1% of 393.216 = 3.93216
262.144 divided by this = 66 and 2/3, so 33 and 1/3 percent of the can is not occupied. The answer depends on how many places to round to, or whether or not to keep the answer as a fraction.
add 5 to a number and divide the whole number with -16,the result is-1
Answer:
(x +5)/-16=-1 this is the answer
A local bookstore is selling each of their books at the same price. Jamal bought 5 books for a total of $64.95.
Which of the following equations represents the cost, C
Answer: 64.95/5= C, C= 12.99
Step-by-step explanation:
If you want to figure out what the cost of 1 book you must divide the total cost of the books ($64.95) by how many books Jamal bought (5).
So the equation should look like this 64.95/5=C. Each book is $12.99.
Hope this helped!
There are numerous reasons to use number lines to teach positive and negative numbers. Which of the following is not one of those reasons?
A. Number lines can be used with non-integer values (for example , -4.5).
B. Number lines match several familiar situations, like altitude, temperature, and football.
C. Number lines can be used to show the relative size of negative numbers.
D. Number lines are easier for students to comprehend because they are familiar.
There are numerous reasons to use number lines to teach positive and negative numbers. But the following which is not used number line is B) Number lines match several familiar situations, like altitude, temperature, and football.
What is number line?
A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it. Just to refresh your memory, the whole number is a collection of numbers that contains both zero (0) and all counting numbers (1, 2, 3,4,5,6), whereas the natural number is a collection of all counting numbers (1, 2, 3,4, 5, 6). Comparing numbers is made simpler by writing them on a number line. As seen in the aforementioned graphic, the integers on the left are smaller than the integers on the right. For instance, 0 is lower than 1 and -1
Here the reasons we use number line for to teach positive and negative numbers is ,
=> Children are taught the fundamentals of addition and subtraction in mathematics using number lines with negative and positive numbers. It can also be used to multiply by skipping counts. The use of positive or negative signs makes it challenging to solve equations involving negative integers on a number line.
=> Number lines can be utilised in a variety of various ways, despite the fact that it may seem like addition, subtraction, and multiplication principles are best taught to children using number lines. The negative number line and positive number line are used by people to compute and measure specifics. These lines display the values' substantial increases and decreases.
Therefore the correct option is B)Number lines match several familiar situations, like altitude, temperature, and football.
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Differentiate the function with respect to x. Shot steps
The derivative of the function is [tex]\frac{dy}{dx}=\frac{9x^2(x^3-4)^2}{1+(x^3-4)^6}[/tex].
What is the chain rule?The chain rule is a method for calculating the derivative of composite functions, which are created by joining one or more functions.
The given function is y = tan⁻¹(x³ -4)³.
The derivative of tan⁻¹(x) is 1/(1+x²).
Use the above fact and the chain rule to differentiate the function as follows:
[tex]y = \tan^{-1}(x^3-4)^3\\\\\frac{dy}{dx} = \frac{1}{1+((x^3-4)^3)^2}\cdot\frac{d}{dx}(x^3-4)^3\\\\=\frac{1}{1+(x^3-4)^6}\cdot3(x^3-4)^2\cdot3x^2\\\\=\frac{9x^2(x^3-4)^2}{1+(x^3-4)^6}[/tex]
Hence, the derivative of the function is [tex]\frac{dy}{dx}=\frac{9x^2(x^3-4)^2}{1+(x^3-4)^6}[/tex].
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Determine the surface area of the cylinder. (Use π = 3.14)
net of a cylinder where radius of base is labeled 4 inches and a rectangle with a height labeled 3 inches
200.96 in2
175.84 in2
138.16 in2
100.48 in2
The total surface area of the cylinder is 175.84 squared inches
Surface Area of CylinderThe surface area of a cylinder can be defined as the amount of space covered by the flat surface of the bases of the cylinder and the curved surface of the cylinder. The total surface area of the cylinder includes the area of the 2 bases of the cylinder which are in the shape of a circle and the area of the curved surface.
The formula is given as
A = 2πrh + 2πr²
π = 3.14r = 4 inh = 3inWe can substitute the values into the equation and solve
A = 2(3.14 * 4 * 3) + 2(3.14 * 4²)
A = 175.84 in²
The cylinder has a surface area of 175.84 in²
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Answer: 175.84
Step-by-step explanation:
(2,3)and(-1,-3) what’s the equation
y=−1/2x+1/2
Step-by-step explanation:
Which of the following describes concrete details
a) Simplify the expression and explain each step. (2 points 4(3x+2)−2
b) Factor the expression completely. (1 point) 20b−16
The simplification form of expression 4(3x + 2) −2 is 12x + 6, and the factor of the expression 20b − 16 is 4 (5b - 4).
The expression is given in the question
4(3x + 2) −2
Apply the distributive property of multiplication,
4×3x + 4 × 2 −2
12x + 8 - 2
Apply subtraction operation,
12x + 6
The expression is given in the question
20b − 16
To determine the factor of the expression
20b − 16
5 × 4 × b - 4 × 4
Factor out 4 in the above expression
4 (5b - 4)
Thus, the simplification form of expression 4(3x + 2) −2 is 12x + 6, and the factor of the expression 20b − 16 is 4 (5b - 4).
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The population of Boca Raton can be predicted using the function p(n)=74,760+1940n, where n is the number of years since 2000. In what year will the predicted population of Boca Raton reach 100,000?
In 2014, the predicted population of Boca Raton will be 100000.
Given that the population function of Boca Raton is,
p(n) = 74760+1940n
So when the population of Boca Raton is 100000, then
p(n) = 100000
So,
100000 = 74760+1940n
1940n = 100000-74760
1940n = 25240
n = 25240/1940 = 14 (approximately)
So, the year in which the predicted population of Boca Raton reach 100000 is = 2000+14 = 2014
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Below are monthly rents paid by 30 students who live off campus.
640 640 640 840 610 500
600 940 650 530 630 595
470 650 560 570 760 830
510 530 670 600 620 410
640 710 730 750 630 655
Which number is the closest approximation to the value 200 ?
(A) 20
B) 10
C) 6
(D) 100
Answer:
the answer is 100...........
Which equations are true equations Select all correct answers. Responses 39−3⋅6=6⋅10/4+4 39 minus 3 times 6 equals fraction numerator 6 times 10 over denominator 4 end fraction plus 4 242^2=50−6^2−8 24 over 2 squared equals 50 minus 6 squared minus 8 56÷8+3^2=2⋅2^3 56 divided by 8 plus 3 squared equals 2 times 2 cubed 8^2−5^2=4^2−7..
The true equations are 24 over 2 squared equals 50 minus 6 squared minus 8 and 56 divided by 8 plus 3 squared equals 2 times 2 cubed.
The equation one is given as
39- 3(6) = 6(10/4)+4
After solving we get,
39 - 18 = 15 +4
21 = 19
Which is not a true equation.
2nd equation we have
24/(2^2)=50 -6^2-8
24/4 = 50 -36 -8
6 = 50 - 44
6 = 6
which is a true equation.
3rd equation we have
56/8+3^2= 2(2^3)
7 +9 = 2(8)
16 = 16
which is true equation.
4th equation, we have
8^2-5^2 = 4^2-7
16-10 = 16-7
6 = 9
Which is not a true equation.
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What fraction is represented in the picture below?
Answer: 6/10
Step-by-step explanation: Six parts are shaded and even though the shaded parts are not touching each other, they will still count as shaded. 4 parts are not shaded and there is a total of 10 parts so the answer would be 6/10.
Hoped This Helped!
Answer:
If it is asking for the fraction of shaded parts the answer is A
If it is asking for the fraction of non-shaded parts the answer is B
Step-by-step explanation:
I would most likely go with A, because I have very rarely gotten a question asking for the non-shaded parts.
Question 14(Multiple Choice Worth 2 points)
(Constant of Proportionality MC)
The equation c = 11.5t represents the total cost (c), in dollars, for a certain number of movie tickets (t).
Which table represents the equation?
Number of Tickets Cost (dollars)
0.09 1
0.17 2
Number of Tickets Cost (dollars)
1 11.50
2 23
Number of Tickets Cost (dollars)
11.5 1
23 2
Number of Tickets Cost (dollars)
1 0.09
2 0.17
For the given equation, c = 11.5t where t is the number of tickets to watch movie and c is the total cost to watch movie then table representing the equation is given by
option B:
Number of tickets : 1 2
Cost in dollars : $11.50 $23
As given in the question,
Given equation to represents the total cost to watch a movie related to number of tickets of movie.
c = 11.5t
Where t is the number of tickets to watch movie and c is the total cost to watch movie.
Table which represents the given situation is given by:
Option A:
Number of tickets cannot be in decimals that is 0.09 and 0.17.
Incorrect.
Option B.
Number of ticket = 1
cost 'c' = 11.5(1)
= $11.5
when t = 2
c = 11.5(2)
= $23
Correct.
Option C:
Number of tickets cannot be in decimals that is 11.5.
Option D:
when t = 1
c = $0.09 is incorrect.
Therefore, For the given equation, c = 11.5t where t is the number of tickets to watch movie and c is the total cost to watch movie then table representing the equation is given by
option B:
Number of tickets : 1 2
Cost in dollars : $11.50 $23
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SOLVE AND GRAPH THE INEQUALITY X + 8 > 9
x>1
below is the graph.
any questions in the comments:
Jaxson has some pennies and some nickels. He has no more than 13 coins worth at least $0.33 combined. If Jaxson has 4 pennies, determine the minimum number of nickels that he could have. If there are no possible solutions, submit an empty answer.
The minimum number of nickels that Jaxson could have is 9.
Given that, Jaxson has some pennies and some nickels.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Let the number of pennies be P and the number of nickels be N.
So, P + N > 13
Therefore
P×0.01 + N×0.05 ≥ 0.33
Because he has at most, $0.33
If P = 4
4×0.01 + N0.05 ≥ 0.33
∵ $0.33 - $0.04 = $0.29
N×0.05≥ 0.29
N = 0.29/0.05 = 5.8
The number of nickels that he might have is 9.6, but because he cannot have 0.6 of a nickel, we have to round the figure down to 9.
Now that we also know that he had at least 15 coins in total, we can use that equation to get the smallest possible number for N.
4 + N > 13
N > 13 - 4
N> 9
So we have the range:
9 < N ≤ 5.8
Therefore, the minimum number of nickels that Jaxson could have is 9.
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Amy has 80 marbles. She gives 20% of her marbles to Jack. How many marbles has she left over?
Answer:
64 marbles
Step-by-step explanation:
hope it helped :)
Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
The equations which have the same value of x as "three-fifth(30x minus 15 ) 72 are "18 x minus 9 = 72", "3 (6 x minus 3) = 72", and "x = 4.5".
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The given equation is Three-fifths(30x - 15) = 72.
Simplify the equation as follows:
Three-fifths(30x - 15) = 72
3/5(30x - 15) = 72
18x - 9 = 72
Which is equivalent to "18x minus 9 = 72".
Solve for the value of x:
18x -9 = 72
18x = 72 + 9
18x = 81
x = 81/18
x = 27/6
x = 4.5
Now, solve the equation in the first option:
18x - 15 = 72
18x = 87
x = 4.83
Solve the equation in the second option:
50x - 25 = 72
50x = 97
x = 1.94
The third equation is already shown to be equivalent to the given equation.
The solution to the fourth equation is:
3(6x - 3) = 72
18x -9 =72
Which is the same as the given equation.
The last equation is x = 4.5
Hence, the equations which have the same value of x as "three-fifth(30x minus 15 ) 72 are "18 x minus 9 = 72", "3 (6 x minus 3) = 72", and "x = 4.5".
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