Answers
Answer:
x = 3 ± 2[tex]\sqrt{6}[/tex]
Step-by-step explanation:
x² - 6x = 15
to complete the square on the left side
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 3)x + 9 = 15 + 9
(x - 3)² = 24 ( take square root of both sides )
x - 3 = ± [tex]\sqrt{24}[/tex] = ± [tex]\sqrt{4(6)}[/tex] = ± ([tex]\sqrt{4}[/tex] × [tex]\sqrt{6}[/tex] ) = ± 2[tex]\sqrt{6}[/tex]
add 3 to both sides
x = 3 ± 2[tex]\sqrt{6}[/tex]
then
x = 3 - 2[tex]\sqrt{6}[/tex] , x = 3 + 2[tex]\sqrt{6}[/tex]
Related Questions
What is 20% of 10? Because I can’t do it
Answers
Answer:
2
Step-by-step explanation:
20% = 0.2
What is 20% of 10?
We take
10 times 0.2 = 2
So, 20% of 10 is 2.
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 17.
The range is the best measure of variability, and it equals 4.
The IQR is the best measure of variability, and it equals 4.
The range is the best measure of variability, and it equals 17.
Answers
The IQR is the best measure of variability, and it equals 4.
what is unit vector notation ?
Answers
Unit vector notation is a way of representing vectors in which magnitude of vector is equal to 1. A vector is mathematical object that has both magnitude (length) and direction, and can be represented as an arrow.
In unit vector notation, a vector is represented as a combination of a scalar (a numerical value) and a unit vector (a vector with a magnitude of 1 in the same direction).
The most common notation for unit vectors is to use a hat symbol (^) to indicate that a vector is a unit vector. For example, if we have a vector v, then its corresponding unit vector in the same direction would be represented as v. The unit vector in the x-direction is typically denoted as i, and the unit vector in the y-direction is denoted as j.
Unit vector notation is useful in many applications, including physics and engineering, where it is used to describe the direction of forces, velocities, and accelerations. It is also commonly used in computer graphics and game development, where it is used to represent the direction of movement or rotation of objects in a 3D space.
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4 of 5
Part 1: The function c (m) = 60 + 10m gives the monthly cost "C" of visiting a gym as a
function of the number of visits "m."
What would the inverse function tell us?
O The minimum number of visitis
O The visits for a cost of $60
O The cost in terms of visits "m"
O The number of visits made for a costs of "C"
Answers
Option (4): The inverse of the function tells us the number of visits m that can be made for a cost of c.
What is meant by the inverse of a function?
A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.
A function that can reverse into another function is known as an inverse function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as " f ⁻¹ " or " F ⁻¹."
Given a function,
c(m) = 60 + 10m
where c = cost of visiting the gym
m = number of visits
Then the Inverse function is:
c(m) - 60 = 10m
m = (c(m) - 60) / 10
Therefore the inverse of the function tells us the number of visits m that can be made for a cost of c.
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A coffee shop sells its coffee for $2.50 per cup.
In April they had total sales of $31,250.
In May they sold 10,150 cups of coffee.
Their total sales in June was the average of what they sold in April and May.
How many cups of coffee were sold in April?
What was the total sales ($$$) for May?
How many cups of coffee were sold and what was the total dollars in sales for the month of June?
Answers
Answer:
Step-by-step explanation:
Let's call the number of cups sold in April "x".
The total sales in April were $31,250, so we can set up an equation to find x:
2.50 * x = 31,250
Dividing both sides by 2.50, we get:
x = 12,500
So in April, 12,500 cups of coffee were sold.
The total sales in May were 10,150 cups * $2.50 per cup = $25,375.
The average of the sales in April and May was $31,250 + $25,375 / 2 = $28,312.50.
So in June, they sold $28,312.50 / $2.50 per cup = 11,250 cups of coffee.
Answer: There were 12,500 cups sold in April. In May they made $25,375. They sold 11,325 cups and made $28,312.50 in June.
Step-by-step explanation:
To find the cups of coffee sold in April, we will divide the total sales by price per cup.
$31,250 / $2.50 = 12,500 cups
To find the total sales for May, we will multiply the cups sold by the price per cup.
10,150 * $2.50 = $25,375
If they sold the average of April and May in June, we will find the average of April and May.
12,500 cups in April + 10,150 cups in May = 22,650
22,650 / 2 = 11,325 cups sold in June
Then, to find the dollar sales, we will multiply by the price per cup again.
11,325 * $2.50 = $28,312.50
[tex]1\frac{2}{3} :2\frac{2}{3}[/tex]
Answers
5/3 :8/3= 5/3 X3/8 =5/8
A school orchestra has 60 members 20%of the members are percussionists,how many orchestra members are percussionist
Answers
Answer:
12
Step-by-step explanation:
10% * 60 = 6
20% * 60 = 12
If the sky is clear then we can see the stars at night
Answers
Yes, that is correct; If the sky is clear, we are able to see the stars at night.
A star is a celestial body that maintains its shape thanks to its own gravity. Also, a star has the ability to generate its own light, an example of a star is the Sun.
The stars are always there, but during the day, the brightness of the sun makes it impossible for us to see them. However, at night when the sun is no longer visible, the stars become visible to us. This is why we can see the stars in the sky at night when there are no clouds obstructing our view.
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Answer:
this is true
Step-by-step explanation:
can someone help me with this geometry question
Answers
According to the figure of the rhombus ∠ UTV = 36 degrees
How to find angle UTVAngle UTV is solved learning some property of rhombus
The opposite angles are equal.
∠ TWV = ∠ TUV and ∠ UTW = ∠ UVWThe diagonals divide the angles.
∠ UTV = ∠ UTW / 2
Assuming ∠ UTW = ∠ UVW = x
Given: ∠ TWV = ∠ TUV = 108
2x + 2(108) = 360 sum of angles of a rhombus
x + 108 = 180
x = 180 - 108
x = 72
∠ UTV = 72/2
∠ UTV = 36 degrees
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Here is a grid of squares.write down the ratio of the number of unshaded to shaded squares
Answers
The ratio of the number of unshaded to shaded squares is 7 : 3.
What is Ratio?Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.
It is also defined as the fraction of one quantity with respect to other.
The ratio of a and b is denoted as a : b.
Given is a grid of squares which is given below.
Total number of squares = 10
Of that,
Number of shaded squares = 3
Number of unshaded squares = 7
We have to find the ratio of unshaded to shaded squares in the grid which is 7 / 3 or 7 : 3.
Ratio of unshaded squares to shaded squares = 7 : 3
Hence 7 : 3 is the ratio of unshaded to shaded.
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What type of triangle has angle measured of 24 degrees and 105 degrees? (Two answers)
Answers
Answer:
Obtuse triangle
Step-by-step explanation:
Obtuse triangle has an interior angle measuring more than 90 degrees.
What does the size of stiffness matrix depend on?
Answers
the size of the stiffness matrix depends on the number of degrees of freedom and the type of elements used in the analysis. It is an important tool in structural mechanics and engineering for analyzing the behavior and performance of structures under different loading conditions.
In structural mechanics and engineering, the stiffness matrix is a mathematical representation of the stiffness of a structure, which relates the forces and displacements of the structure. The size of the stiffness matrix depends on several factors, including the number of degrees of freedom and the type of elements used in the analysis. The number of degrees of freedom (DOF) in the system determines the size of the stiffness matrix. DOF refers to the number of independent displacements or rotations that a structure can undergo in response to external forces. For example, a simple beam structure might have two DOF (vertical displacement and rotation), while a more complex structure such as a truss or frame might have many more DOF. The size of the stiffness matrix also depends on the type of elements used in the analysis. Different types of elements have different degrees of freedom and stiffness properties, which affect the size and shape of the stiffness matrix. For example, a truss element has two DOF and a constant axial stiffness, while a beam element has four or six DOF and variable stiffness properties that depend on its geometry and material properties.
In summary, the size of the stiffness matrix depends on the number of degrees of freedom and the type of elements used in the analysis. It is an important tool in structural mechanics and engineering for analyzing the behavior and performance of structures under different loading conditions.
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pls help asap I need to get this done by tmw
Answers
The interest that Marisol will earn in a period of 5 years is C. $ 1, 437. 50
The number of years that Marisol kept the account open, given the amount she receives when she closes her account is 12 years .
How to find the interest ?The simple interest on the account per year is :
= 5, 000 x 5. 75 %
= $ 287. 50
In 5 years, this is:
= 287. 50 x 5
= $ 1, 437. 50
The number of years that Marisol left the account open was :
= ( 8, 450 - 5, 000 ) / 287.50 per year
= 12 years
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The first part of the question is :
Marisol deposits $5,000 in a savings account earning 5.75% simple interest per year.
I don’t get this math problem4/5 + 3/4
Answers
Answer:
AS a fraction: 1[tex]\frac{11}{20}[/tex]
AS a decimal: 1.55
Step-by-step explanation:
4/5 + 3/4
least common multiple of 5 and 4 is 20. Conver [tex]\frac{4}{5}[/tex] and [tex]\frac{3}{4}[/tex] to fractions with denominator 20.
16/20 + 15/20
since [tex]\frac{16}{20} and \frac{15}{20}[/tex] have the same denominator, add them by adding their numerators.
[tex]\frac{16 + 15}{20}[/tex]
Add 16 and 15 to get 31.
[tex]\frac{31}{20}[/tex]
[tex]\frac{31}{2^{2}x5 } = 1\frac{11}{20}[/tex]
Hope that helps and have a great day! =) ~sunshine~
If AC=82 and AE=2x+11 find the value of x
Answers
Take A, B, C, and D as the quadrilateral's vertices, and BA is created to E. The value of x = 40.
What is meant by value?The value describes the value of each digit in relation to its position in the number. The place value and face value of the digit are multiplied to arrive at the answer. Value equals Place Value minus Face Value.Value is concerned with how much something is worth, whether in monetary terms or in terms of significance. It might imply "declare the value of something," as in "a $200 award," or it can mean "hold something in high regard," as in "I cherish our friendship."Draw the above diagram and add the angles that are missing.
To determine the value of x, use the information provided in the accompanying diagram.
Take A, B, C, and D as the quadrilateral's vertices, and BA is created to E. (say).
Observe the illustration.
[tex]$& \Rightarrow \angle \mathrm{EAD}=70 \\[/tex]
[tex]$& \Rightarrow \angle \mathrm{EAD}+\angle \mathrm{DAB}=180 \\[/tex]
[tex]$& \Rightarrow \angle \mathrm{DAB}=180-70=110[\because E A B \text { is a straight line and } \mathrm{AD} \text { stands on it. }] \\[/tex]
Apply the total of internal angles in step two.
We are aware that a quadrilateral's inner angle total is 360.
[tex]& \Rightarrow \angle \mathrm{DAB}+\angle \mathrm{ADC}+\angle \mathrm{DCB}+\angle \mathrm{CBA}=360 \\[/tex]
[tex]$& \Rightarrow 110+80+56+3 \mathrm{x}-6=360 \\[/tex]
[tex]& 0 \quad 0 \quad 0 \quad 0 \quad 0 \\[/tex]
[tex]$& \Rightarrow 3 \mathrm{x}-6=360-110-80-56[/tex]
[tex]\Rightarrow 3 x-6=114 \\0 \\[/tex]
[tex]\Rightarrow x=120 \\[/tex]
[tex]\Rightarrow x=40 \\[/tex]
0
Therefore the value of x = 40. Hence, option A is correct.
The complete question is:
Use the information given in the following figure to find the value of x.
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How do you draw a horizontal line in Matlab?
Answers
The "line" function in MATLAB allows you to create horizontal lines. Drawing horizontal or vertical lines is possible by using the "line" function,
So the "line" function in MATLAB allows you to create horizontal lines. Drawing horizontal or vertical lines is possible by using the "line" function, which creates a line object. You must supply the x-coordinates of the starting and ending points of the line as well as the line's y-coordinate in order to draw a horizontal line. To draw a horizontal line in MATLAB, use the following syntax: CSS Copy Code: x = [x min x max]; percentage of the x-coordinates of the line's beginning and finish points, y = [y value y value]; line(x, y percentage )'s y-coordinate; % Create a horizontal line
The starting and stopping positions of the line are indicated by the x-coordinates "x min" and "x max," respectively, while the line's y-coordinate is shown by "y value." is the "line".
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Please help
Which polygon appears to be regular?
Responses Figure A Figure B Figure C Figure D
I think it might be A or C but I'm not entirely sure.
Answers
None of the given polygons appears to be regular.
Describe Regular Polygon?A regular polygon is a polygon with all sides and angles of equal measure. In other words, a regular polygon is a shape with straight sides that has all angles and sides of equal length.
The simplest example of a regular polygon is a equilateral triangle, which has three sides of equal length and three angles of equal measure. Another example is a square, which has four sides of equal length and four right angles of equal measure.
Figure A is a rhombus, which has opposite sides parallel and all sides equal, but it has two acute angles and two obtuse angles, so it is not regular.
Figure B is a parallelogram, which has opposite sides parallel, but not all sides and angles equal, so it is not regular.
Figure C is a right-angled triangle, which has one right angle, but not all sides and angles equal, so it is not regular.
Figure D is a trapezoid, which has at least one pair of parallel sides, but not all sides and angles equal, so it is not regular.
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You want to solve the following system of equations by addition. What should
you do first, so that one variable is eliminated when you add the equations?
-2x+4y= 10
3x-2y=-7
OA. Multiply the top equation by 2 and the bottom equation by 3.
B. Multiply the top equation by 3 and the bottom equation by-2.
C. Multiply the bottom equation by 2.
D. Multiply the top equation by -3.
SUBMIT
Answers
Answer: C
Step-by-step explanation:
The two variables need to be eliminated. You can do this by multiplication or subtraction.
Multiply by -3 to the top equation will eliminate the x variable in the system
-3(2x - 4y = 5)
6x - 3y = 10
==> -6x + 12y = -15
6x - 3y = 10
adding a top with a bottom will eliminate the x
==> -6x + 6x = 0, 12y + (-3y) = 9y, -15 + 10 = -5
How do you solve this?
72a^3b^4/6a^2b
Answers
The expression (72a³b⁴) / (6a²b) is equivalent to the expression 12ab³.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ (72a³b⁴) / (6a²b)
Simplify the expression, then we have
⇒ (72a³b⁴) / (6a²b)
⇒ 12ab³
The expression (72a³b⁴) / (6a²b) is equivalent to the expression 12ab³.
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The accompanying table shows the number of bacteria present in a
certain culture over a 5 hour period, where x is the time, in hours, and y is the number of bacteria. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest thousandth. Using this equation, determine the number of bacteria present after 14 hours, to the nearest whole number.
Hours (x) Bacteria (y)
0 1353
1 1584
2 2037
3 2248
4 2630
5 3146
Answers
Answer:
Step-by-step explanation:
To find an exponential regression equation for this set of data, we can use a calculator or spreadsheet software with built-in regression functions. Using a calculator, we can input the data points into lists and use the exponential regression function to find the equation:
x y
0 1353
1 1584
2 2037
3 2248
4 2630
5 3146
Using exponential regression, we get the equation y = 1323.119e^(0.216x).
To determine the number of bacteria present after 14 hours, we can plug in x = 14 into the equation:
y = 1323.119e^(0.216 * 14) ≈ 35433
Therefore, the number of bacteria present after 14 hours is approximately 35,433 (rounded to the nearest whole number).
Question 6 of 25
What are the solutions to the system of equations graphed below?
Answers
The solutions to the system of equations are given as follows:
(0, -4) and (2,0).
How to obtain the number of solutions of the system of equations?The number of solutions of the system of equations is given by the number of times which the two functions intersect.
The two intersection points are given as follows for this problem:
(0, -4) and (2,0).
Which are the solutions to the system of equations.
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Simplify: –3|–2|+ 4|–5|
Answers
Simplify the expression. #1-2
Answers
Answer: 1/2
Step-by-step explanation:
PLS HURRY! Swimming pool A started with a depth of 30 inches of water. Pool A was being filled at a rate of 2 inches per minute.
The depth of swimming pool B, as it was being filled, is shown in the table.
(in the attached image)
Write a linear equation in slope-intercept form for both swimming pools, and then determine how many minutes it took for each pool to be filled to a depth of 71 inches.
Answers
Answer:
Equations:
A: y = 2x + 30
B: y = 3x + 6
Time to fill to 71 inches:
A: 20.5 minutes
B: 25.5 minutes
Step-by-step explanation:
Pool A: starts at 30 inches, fills at 2 inches/minute
Equation: y = 2x + 30
Pool B: starts at 20 inches, fills at 3 inches/minute
Pool B slope = filling rate = (26 - 20)/(2 - 0) = 6/2 = 3
Equation: y = 3x + 20
Pool A: y = 71
71 = 2x + 30
2x = 41
x = 20.5
Pool B: y = 71
71 = 3x + 20
3x = 51
x = 25.5
HELP ASAP !!!!!!!PLEASE
Answers
The both are exponential functions from the fact that the both are raised to a give power. The constant and rate of both functions are different.
What is a function?A function is a block of code that performs a specific task. In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
We can see that the two functions that we here are all such that we can be able to see that they are exponential in nature as shown in the image that depicts the question that has been asked.
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Billy deposited $5,000 in an account earning 1% interest compounded annually.
To the nearest cent, how much interest will he earn in 1 year?
Answers
Answer:
$50.00 is the amount of interest
Six miners divide 15 ounces of gold dust equally. How
many ounces of gold dust does each miner receive?
Answers
Answer:
Each miner receive 2.5 ounces of gold dust.
Step-by-step explanation:
15/6= 2.5 ounces
The slope, a, of the inverse function is , and the x-intercept of the inverse function is at x =.
Answers
The inverse function of f (x) = 1/3x - 2 is f⁻¹(x) = 3(x + 2), the value of a is 3, and the value of x-intercept is x = -2.
FunctionThe sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Each element of X receives exactly one element of Y when a function from one set to the other is used.
According to the question,
f (x) = 1/3x - 2
now to find inverse ,
Add 2 to x term and then divide by 1/3 so, we get,
f⁻¹(x) = (x + 2) / 1/3
f⁻¹(x) = 3(x + 2)
now, compare with f⁻¹(x) = a (x + 2)
a = 3
Calculate the x-intercept by putting f(x) = 0
0 = x + 2
x = -2
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of the
sat
5) The senior classes at High School A and High School B planned separate trips to New York City.
The senior class at High School A rented and filled 5 vans and 4 buses with 205 students. High
School B rented and filled 5 vans and 13 buses with 475 students. Each van and each bus carried
the same number of students. How many students can a van carry? How many students can a
bus carry?
Answers
The number of students the van carry is 17
the number of students the bus carry is 30
How to find the number of students can a bus carryLet's assume that a van can carry "v" students and a bus can carry "b" students.
From the information given, we can set up two equations:
5 vans + 4 buses = 205 students
5 vans + 13 buses = 475 students
We can write these equations as
5v + 4b = 205
5v + 13b = 475
solving simultaneously we have
v = 17 and b = 30
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What is an equation of the line that passes through the point (-4, -6) and is
perpendicular to the line 2x - y = 6?
Answers
Answer:
An equation of the line that passes through the point (-4, -6) and is perpendicular to the line 2x - y = 6 is y = -2x + 10.