Values 4 and 14 will be described as x that are the distance of 5 units from the number 9.
Given that x is a set of numbers such that the distance from x to 9 is 5 units.
so, distance of x, positive or negative, from 9 can be expressed as |x - 9|
since the distance is equal to 5 units therefore the equation can be written using absolute value notation:
|x - 9| = 5
(x - 9) = 5 -> x = 14
or -(x -9) = 5 -> x = 4
Hence, set x = {4,14}
Therefore, set x is {4,14}.
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For what value of k will the following pair of linear equations have infinitely many solutions ∶ 10x 5y − K − 5 0 ∶ 20x 10y − k 0?
The value of k at which there are an infinite number of solutions to the equation is -10.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. a formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 = 2.
Here,
For infinitely many solutions,
a1/a2 = b1/b2 = c1/c2
therefore, 10/20 = 5/10 = (-k-5)/(-k)
⇒1/2 = -(k+5)/-(k)
⇒ 1/2 = k+5/k
⇒ k = 2(k+5)
⇒ k = 2k + 10
⇒ -10= 2k - k
⇒ k = -10
The value of k for which the equation have infinitely many solutions is -10.
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need help asap A gym charges $252 a year for a gym membership. Bradley's membership fee is a constant amount each month. Which equation represents the amount he pays in m months if c represents the total amount he paid
A constant is something that doesn't change overtime; a steady flow that has a fixed value in a given situation.
First, we would need to see how much the gym charges each month for a membership, based on the amount he pays every year.
If we know that a year has 12 months, and every year he pays $252, we can use an equation that looks like this:
252 ÷ 12 = 21
The gym charges $21 every month for a membership.
Given, if m = months, and c = total amount he paid, the equation would look like this:
21 × m = c
Therefore, an equation you can use to figure out how much he pays in (m) months is 21 × m = c.
Jan 17, 3:56:53 PM
What are the coordinates of the point on the directed line segment from (-9, -8) to
(6, 2) that partitions the segment into a ratio of 2 to 3?
xm = (x1 + x2)/2. Determine the average of the y-coordinates of the end-points to obtain the y-coordinate of the mid-point. ym = (y1 + y2)/2.
What is the directed line segment formula?You may determine the coordinates of the point that divides a directed line segment into a specific proportion using the ratios of directed line segments calculator.
This article will go over the definition of a directed line segment, the formula for segment partitioning, examples of how to divide a line segment with a specified ratio, and commonly asked questions. a line section.
A line with AB attached to it has two endpoints.
A andwhere B
A\s=B. A directed line segment, such as AB, is one that has a clear direction; it is a line segment that runs from A to B. The directed line segment AB cannot be written as BA, despite the fact that the line segment AB may. This is due to AB being directed.
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A pilot flying at an altitude of 2.7 km sights two control towers directly in front of her. The angle of depression to the base of one tower is 37°. The angle of depression to the base of the other tower is 58. What is the distance between the two towers? Round to the nearest tenth of a kilometer.
The distance between the two towers is 2285.4 m (2.3 km)
What is an angle of depression?An angle of depression is the angle formed when a given object is viewed below the horizontal plane.
Let the horizontal distance to the base of the first tower be represented by x, so that;
Tan θ = opposite/ adjacent
Tan 37 = x/ 2700
x = Tan 37 * 2700
= 0.7536*2700
= 2034.6
x = 2034.6 m
Let the horizontal distance to the base of the second tower be represented by y, so that;
Tan θ = opposite/ adjacent
Tan 58 = y/ 2700
y = Tan 58 * 2700
= 1.6*2700
= 4320
y = 4320 m
The distance between the two towers = y - x
= 4320 - 2034.6
= 2285.4
The distance between the two towers is 2285.4 m (2.3 km).
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How do you find the unknown measure?
Use the sum of 180 degrees to calculate the unknown angle's measurement. If two angles are specified, add the two together before deducting 180 degrees. Divide by two after removing the known angle from 180 degrees if two angles are the same but unknown.
A figure made up of two rays or line segments is called an angle. Angles on items are visible all around us. The vertex of the angle is the place where the two rays that make up the angle meet. The arms of the angle are the two rays that make up the angle.
Acute, right, obtuse, straight, reflex, zero, and full angles are some of the numerous types of angles based on how they are measured.
Complementary angles are any two angles whose sum of the angles is 90. Complementary angles don't always have to be next to each other; they can be be two independent angles with a sum of 90 degrees.
When two angles sum up to 180, they are referred to as supplementary angles. Supplementary angles don't always have to be next to each other; they can be be two different angles that add up to 180 degrees.
The opposing angles created when two lines connect are known as vertical angles. Angles vertically are consistently equal.
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What is the measure of each
m∠1 =
m∠2 =
m∠3 =
m∠4 =
m∠5 =
The measure of each angles in the diagram showing a pentagon are:
m∠1 = 56°
m∠2 = 82°
m∠3 = 62°
m∠4 = 80°
m∠5 = 80°
What is the Sum of a Pentagon?The sum of the interior angles of a pentagon is equal to (5-2) * 180 degrees = 540°.
x = 540 - 124 - 100 - 100 - 118 (sum of pentagon is equal to 540 degrees)
x = 98°
m∠1 = 180 - 124 = 56°
m∠2 = 180 - 98 = 82°
m∠3 = 180 - 118 = 62°
m∠4 = 180 - 100 = 80°
m∠5 = 180 - 100 = 80°
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In slope intercept form
Answer:
y = mx + b
Step-by-step explanation:
The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.
There were a party of it 19 people each adult ticket was $9 and each child’s ticket was as $5.50 . If the total cost for the party was $150 , then how many adults and how many children attend
Answer:
13 adults; 6 children
Step-by-step explanation:
Let a = number of adults.
Let c = number of children
a + c = 19;
9a + 5.5c = 150
Let's use substitution. Solve the first equation for a.
a = 19 - c
Now substitute 19 - c for a in the second equation and solve for c.
9(19 - c) + 5.5c = 150
171 - 9c + 5.5c = 150
-3.5c = -21
c = 6
Now substitute 6 for c in a = 19 - c and solve for a.
a = 19 - c
a = 13
Answer: 13 adults; 6 children
You make 75 birdhouses and sell them for B dollars each. The table to the right shows the predicted sales for different prices, B. You use the expression B(75-B) to show your income from sales for the different prices. Drag each statement to the term it describes in the table below.
The expression B represents the price of each bird house and 75-B represents the number of birdhouses sold
What is Expression?An expression is combination of variables, numbers and operators.
Given that You make 75 birdhouses and sell them for B dollars each.
The predicted sales for different prices, B.'
The expression B(75-B) to show your income from sales for the different prices.
We need to find what the B represents and what the 75-B represents.
The B represents the price of each bird house and 75-B represents the
number of birdhouses sold
Hence, the expression B represents the price of each bird house and 75-B represents the number of birdhouses sold
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what are the corresponding rectangular coordinates for point q equals the ordered pair 6 comma 5 times pi over 6 given in polar coordinates?
The rectangular coordinates for the point (6, 5π/6) in polar coordinates are (-3√3, 3)
To convert the given polar coordinates (6, 5π/6) to rectangular coordinates, we can use the following formulas:
x = r cos(θ)
y = r sin(θ)
where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line segment connecting the origin to the point.
Plugging in the values, we get:
x = 6 cos(5π/6) = 6 (-√3/2) = -3√3
y = 6 sin(5π/6) = 6 (1/2) = 3
Therefore, the corresponding coordinates for the point q given in polar coordinates as (6, 5π/6) are (-3√3, 3).
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Find the value of each variable in the parallelogram.
72°
2mᵒ n°
Answer:
m = 36 , n = 108
Step-by-step explanation:
• opposite angles in a parallelogram are congruent
2m = 72 ( divide both sides by 2 )
m = 36
• consecutive angles are supplementary, that is sum to 180°
n and 72 are consecutive angles, then
n + 72 = 180 ( subtract 72 from both sides )
n = 108
Write the slope-intercept form of the line that has a slope of -5, and passes through the point (-4,3).
The slope-intercept form of the line is y = -5x + 17.
What is a slope-intercept form?
Using a straight line's slope and the location of its y-axis intersection, the slope-intercept equation can be used to determine the general equation of the line. Y = mx + b is the equation in slope-intercept form.
Here, we have
Given: a slope of -5, and passes through the point (-4,3).
The slope-intercept form of the line : (y-y₁) = m(x-x₁)
Now, we put the given values and we get
m = -5 and point(-4,3).
(y-y₁) = m(x-x₁)
(y-3) = -5(x-(-4))
y - 3 = -5x + 20
y = -5x + 17
Hence, the slope-intercept form of the line is y = -5x + 17.
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The set of integers forms a ring. Select the answer that is also valid. A. The set of integers is also a field because additive identity and additive inverse are defined, multiplication is associative, and multiplication distributes over addition. B. The set of integers is also a field because multiplication is commutative and the multiplicative identity is defined. C. The set of integers is not a field because there is no multiplicative inverse. D. The set of integers is not a field because it does not qualify as a group
C). The set of integers is not a field because there is no multiplicative inverse.
B. A field is a mathematical structure that has two operations: addition and multiplication. The set of integers does have addition and multiplication operations, but not all elements have a multiplicative inverse.
For example, the multiplicative inverse of 2 does not exist in the set of integers. As a result, the integers do not form a field, because one of the field axioms is not satisfied, that is the existence of multiplicative inverse.
Additionally, the set of integers is a commutative ring as it satisfies the commutative and associative laws for addition and multiplication and it has an additive identity and inverse, but not all elements have a multiplicative inverse, hence it can't be a field.
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Which is an algebraic expression for 9 more than V?
Answer:
V+9
Step-by-step explanation:
more than means to add.
Price of Bagels
A shop sells bagels for $5
per dozen. You can use the
table to answer the
questions. Explain your
reasoning.
1. At this rate, how much
would 6 bagels cost?
2. How many bagels can
you buy for $50?
Mathematic
number of bagels price in dollars
12
5
PLEASE HELP MEEE TELL ME THE ANSWERS PLEASE
Answer:
9) $2.5 | 10) 120 Bagels
Step-by-step explanation:
For #9, a dozen equals 12, and 6 is half a dozen, so divide 5 by 2 = 2.5 dollars.
For #10, $5 per dozen, 50 ÷ 5 = 10, so 10 x 12 equals 120 bagels.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Click and place the appropriate equivalent forms of the numbers shown.
64 16/25 0.64
12.5 1/8 0.125
140 1 2/5 1.4
274 2 3/4 2.75
8 2/25 0.08
If you jog 4 times around a track that is 700 meters long how many miles have you covered?
Answer:
Step-by-step explanation:
1 mile = 1609.34 meters
The track is 700 meters, or about 1/2 a mile.
Multiply 700 by 4 to find the meters you ran:
700 * 4 = 2800
Divide this by 1609:
2800 / 1609 = 1.74 miles
So, you approximately covered 1.74 miles.
Let me know if this is correct! It may be incorrect if your teacher told you '1600 m = 1 mil', or another conversion factor. I am just going off of memory here!
OF 100 students 65 are members of a mathematics club and 40 are members of a physics club if 10 are members of neither club how many students are members os a)both clubs b) maths only c)physics only
Answer:
C. physics only
[tex]\it 100-10=90\ students\ are\ members\ of\ the \ clubs\\ \\ 65+40-90=15\ students\ are\ members\ of\ both \ clubs\\ \\ 64-15=50 \ students\ are\ members\ of\ the \ math\ only\\ \\ 40-15=25\ students\ are\ members\ of\ the \ physics\ only[/tex]
A pole that is 2.6 m tall casts a shadow that is 1.58 m long. At the same time, a nearby tower casts a shadow that is 37.75 m long. How tall is the tower? Round
your answer to the nearest meter.
When a neighboring tower produces a shadow that is 37.75 meters long, you get 125.614, rounded to the closest meter, which is 126 of the tower.
what is unitary method ?The unit strategy is an approach to problem-solving that involves first figuring out the value of a single unit, then multiplying that value to figure out the required value. Simply described, the unit method is used to extract a single unit value from a specified multiple. For instance, 40 pens would cost 400 rupees, which is equal to the cost of one pen. This procedure might be standardized. one nation. anything has a distinctive element. Its adjoint and reciprocal are equal in terms of mathematics (algebra), linear algebra, mathematical analysis, or mathematics of matrices or operators.
given
3.2/ 1.14=x / 44.75
Cross Mutliply:
44.75 * 3.2=1.14x
Divide:
143.2 / 1.14=x
When a neighboring tower produces a shadow that is 37.75 meters long, you get 125.614, rounded to the closest meter, which is 126 of the tower.
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raise m to the 8th power, then find the product of the result and n
The correct equation for this given condition is,
⇒ m⁸ n
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The algebraic expression is,
''Raise m to the 8th power, then the product of the result and n.''
Now, We get;
⇒ Raise m to the 8th power
⇒ m⁸
And, The product of the result and n is,
⇒ m⁸ × n
⇒ m⁸ n
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7. A rock that originally had a mass of 1.00 gram of uranium-238 now has only 0.50 grams.
How old is the rock if the half-live of uranium-238 is 4.5 billions of years.
A 1.00 gram sample of uranium will have decomposed into 0.50 grams of U-238 and 0.43 grams of Pb-206 after one half-life by expression .
what is expression ?Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: Number/variable, mathematical operator, and expression Numbers, variables, and functions make constitute a mathematical expression (such as addition, subtraction, multiplication or division etc.) It is possible to contrast phrases and expressions.
given
U-238 has a half-life of 4.5 109 years. Pb-206 is the final byproduct of the disintegration of U-238.
A 1.00 gram sample of uranium will have decomposed into 0.50 grams of U-238 and 0.43 grams of Pb-206 after one half-life.
Uranium-238 has a half-life of approximately 4.5 billion years, uranium-235 of approximately 700 million years, and uranium-234 of around 250 thousand years.
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9. The ordered pairs (1, 8), (2, 16), (3, 24), (4, 32), and (5, 40) represent a function. What is a rule
that represents this function?
A) y=x8
B) y=8
C) y = 8x
D) y=x+8
A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. T
The answer for the first question is c.The answer for the second question is d.What is function?A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. T. Initially, functions were just an idealized representation of the relationship between two changing quantities. A function is a relationship between a set of inputs and a set of potential outputs, where each input is associated to exactly one outcome. An association between members of one set and those of another is known as a A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y.
In order to complete this exercise, you must first evaluate the supplied functions at the locations 1, 2, 3, and 4 (note that these are the x components of the ordered pairs), after which you must rule out all other options.
Because 12=1, rather than 2 (remember the ordered pair (1,2)), the alternative a. cannot be true.Due to the fact that 2*3=6, as opposed to 8, (remember the ordered pair (3,8)), option b. cannot be true.Since 21=2, 22=4, 23=8, 24=16, and 25=32, the solution is choice c.Because 1+2=3 rather than 2 (remember the pair (1,2)), the option cannot be selected.The above both have the same concept.
Due to the difference between 12 and 16 (recall the pair (1,16)), option a. cannot be true.Due to the fact that 2+15=17, rather than 25 (recall the combination (2,25)), the option b. cannot be true.Due to the difference between 2(1+3)=8 and 16 (recall the pair (1,16)), option c cannot be selected.This should be the right response, by elimination. Nevertheless, it is simple to verify that (1+3)2=16, (2+3)2=25, (3+3)2=36, (4+3)2=49, and (5+3)2=64.The complete question is,
The ordered pairs (1,2),(2,4),(3,8),(4,16), and (5,32) represent a function?
a. y=x^2 b. y=2x c. y=2^x d. y=x+2****** The ordered pairs (1,16),(2,25),(3,36),(4,49), and (5,64) represent a function. What is a rule that represents this function?
a. y=x^2 b. y=x+15 c. y=2(x+3)*** d. y=(x+3)^2
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find the mean of the data 30 43 46 46 47 48 50 52
Answer: 45.3
Step-by-step explanation:
Find a domain on which each function f is one-to-one and non-decreasing. Write
the domain in interval notation. Then find the inverse of f restricted to that
domain.
4. f(x) = (x + 7)²
5. f(x)=x²-5
Domain: [−7, ∞) Inverse: f⁻¹(x) = √x - 7 5.Domain: [5, ∞) Inverse: f⁻¹(x) = √x + 5
What is function?A function is a block of code that performs a specific task and is used to execute different processes and operations. Functions allow for code to be reused and make code easier to read and debug. They also make programs more efficient as they allow for smaller chunks of code to be written. Functions are declared with a specific name and parameters, and can be called by other functions. They can also return a value or set of values.
4. Domain: [ -7, ∞ ), Interval notation: (-7, ∞)
Inverse: f^-1 (x) = √(x) - 7
5. Domain: [ 5, ∞ ), Interval notation: (5, ∞)
Inverse: f^-1 (x) = √(x) + 5
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Find the volume of a cylinder with radius 4 inches and height 3 inches.
Answer:
Step-by-step explanation: Volume of cylinder = 1/3 x π x r x h
= 1/3 x π x 4 x 3
= 1/3 x 12 x π
= 4 x π
= 4 x 3.142
= 12.568
What is the maximum amount a bank can create from an initial deposit of $1000 using fractional-reserve banking when the reserve rate is 25%? How about when the reserve rate is 7%? Show your work.
Fractional-reserve banking is a process whereby a bank creates new money by taking deposits from customers and then lending out a portion of those deposits to other customers.
The amount of new money created is determined by the reserve rate—the percentage of deposits held in reserve instead of being loaned out.$1000 x 0.07 = $930
Cost is an expense associated with a purchase or service. It can refer to the monetary value of materials, labor, or other items used in the production of goods or services. It can also refer to the amount of time, effort, or resources required to complete a task. Cost is a fundamental element of any business decision and is typically used to make decisions about pricing, production, and other aspects of operations.
When the reserve rate is 25%, the maximum amount of new money a bank can create from an initial deposit of $1000 is $750. This can be calculated by multiplying the initial deposit by the reserve rate.
$1000 x 0.25 = $750
When the reserve rate is 7%, the maximum amount of new money a bank can create from an initial deposit of $1000 is $930. This can be calculated by multiplying the initial deposit by the reserve rate.
$1000 x 0.07 = $930
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Richard and Teo have a combined age of 37. Richard is 7 years older than twice Teo's age. How old are Richard and Teo?
To express the provided information, we can construct an equation system as follows:
What does the term "system of equations" mean?
system of equations, simultaneous equations Algebraic equations involving two or more must be solved cooperatively (i.e., the solution must satisfy all the equations in the system). For a system to have a single solution, the number of equations must equal the number of unknowns.
Let x = Teo's age
Richard's age = 2x + 7 (since Richard is 7 years older than twice Teo's age)
x + (2x + 7) = 37 (the combined age of Richard and Teo is 37)
Solving for x in the first equation and substituting into the second equation:
x + (2x + 7) = 37
3x + 7 = 37
3x = 30
x = 10
So Teo is 10 years old. We can use this information to find Richard's age:
Richard's age = 2x + 7
Richard's age = 2(10) + 7
Richard's age = 27
So Teo is 10 years old and Richard is 27 years old.
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PLSSS HELPPPP I DONT HAVE A LOT OF TIMEE
Describe at least five things you know about f-¹(x).
Five things about f-¹(x) are discussed below:
The inverse of the function f is what you're referencing, then (x).A function's inverse reverses what it "does" in some way.Another way of looking at it is to say that the input of a function is the output of its inverse function and the opposite is true for the output of a function.According to that notation, f-1(x) is the inverse function of f, to put it simply (x). Allowing g(x) to be the inverse of f(x), or g(x) = f-¹(x) , will make it a little easier to write (x).A function that "undoes" another function in mathematics is known as an inverse. To put it another way, if f(x) yields y, then y entered into the inverse of f creates x.What does f-¹(x) represents?A function is said to be an inverse function if its own inverse is represented by the symbol f⁻¹(x).
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Using a ruler and a protractor, make an accurate drawing of the triangle shown below. Measure length c in your drawing. Give your answer to 1 d.p. C 9 cm 8 cm 20° Not drawn accurately
The Pythagorean theorem is used to determine the length of side c = 12.12cm
How do you use the Pythagorean theorem to solve?According to the Pythagorean theorem, the square of the length of the hypotenuse in a right triangle equals the sum of the squares of the lengths of the other two sides. The hypotenuse is the side that faces the right angle. Consequently, in this instance, c2 = a2 + b2.
given are 20°, 8 cm, and 9 cm.
To determine c's length
replacing the specified values: c^2 = 8^2 + 9^2
c = √(8^2 + 9^2) = √(64 + 81) = √(145)\sc = 12.12 cm
Therefore, side C is 12.12 cm long.
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Answer:
tell me the answer hello tell ne
the length of a room is 4 metres longer its width. find the length of the room if its area is 32cm^2
Answer:
length = 8 m
Step-by-step explanation:
note the area of a room cannot be 32 cm²
so you must mean area = 32 m²
let the width be w then length is w + 4
area (A) of a rectangular room is calculated as
A = length × width
given A = 32 , then
w(w + 4) = 32
w² + 4w = 32 ( subtract 32 from both sides )
w² + 4w - 32 = 0 ← in standard form
(w + 8)(w - 4) = 0 ← in factored form
equate each factor to zero and solve for w
w + 8 = 0 ⇒ w = - 8
w - 4 = 0 ⇒ w = 4
but w must be greater than zero, so w = 4
length = w + 4 = 4 + 4 = 8 m