The graphs of absolute value functions are called "V-shaped" or "V-graphs" because their graph is in the shape of a "V".
The graph of an absolute value function is a V-shape that opens upward or downward, depending on the function.
The vertex of the V is the point where the absolute value function equals zero. The two arms of the V extend out from this point, going in opposite directions along the number line.
The absolute value function is defined as |x| where x is any real number and |x| represents the distance of x from zero on the number line, i.e., always non-negative.
Example of an absolute function is f(x) = |x + 3|. The vertex is where
x + 3 = 0
That is at x = -3.
Here the function opens upward, but if the function was -|x + 3|, it will open downward.
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Question
Graph the solution to this inequality on the number line.
−16≥−4p
Answer:
Attached, [tex]p \geq 4[/tex]
Knowledge NeededTo solve, you must isolate the variable. It means moving the variable and it's coefficient to the other side of the equation by itself.
RuleIf you multiply, divide, add, subtract, square root, exponent both sides of the equation by the same value, that end value stays the same. That is how you solve for it.
However, if you divide or multiply by a negative number by both sides in an inequality, you must flip the sign.
For example:
> to <
to
QuestionDivide -4 on both sides.
[tex]\frac{-16}{-4} \geq \frac{-4p}{-4}[/tex]
[tex]4 \geq p[/tex]
Flip the sign.
[tex]4\leq p[/tex]
[tex]p\geq 4[/tex]
When the line is pointing right, it means the variable is greater than the said number. If the dot is filled in, it means greater than or equal to or less than or equal to. If it is not filled in, it means greater than or less then.
The answer is:
4 ≤ p
Work/explanation:
The inequality is:
[tex]\sf{-16\geqslant-4p}[/tex]
To solve, divide each side by -4. Since we're dividing by a negative number, we will reverse the inequality sign.
We end up with:
[tex]\sf{4\leqslant p}[/tex]
Hence, the answer is 4 ≤ p.simple interest 600 at 4% for 9 months
The simple interest amount which applies to the principal given the rate and time as required to be determined is; 18.
What is the simple interest earned on the principal?It follows from the task content that the interest earned on a principal amount of 600 using a rate of 4% per annum over the course of 9 months is to be determined.
Since the interest earned, i is given by the formula;
i = prt
where, p = principal = 600.
r = annual interest rate = 4% = 0.04
t = time = 9 months = 0.75 years.
Hence, the interest earned is;
i = 600 × 0.04 × 0.75
i = 18.
Ultimately, the interest earned is; 18.
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Which point is on the graph of y = -2x + 1?
A. (2, 7)
B. (3, -8)
C. (6, 8)
D. (4, -7)
Answer:
D. (4, -7)
Step-by-step explanation:
To see if a point lands on the graph of a line, substitute the coordinates (x, y) to the x and y in the equation to see if the result is true:
Option A: (2, 7)
Substitute the values in:
[tex]y=-2x+1\\7=-2(2)+1\\7=-4+1\\7=-3[/tex]
Not true.
So option A is out.
Option B: (3, -8)
Substitute the values in:
[tex]y = -2x + 1\\-8=-2(3)+1\\-8=-6+1\\-8=-5[/tex]
Not true.
So option B is out.
Option C: (6, 8)
Substitute the values in:
[tex]y = -2x + 1\\8=-2(6)+1\\8=-12+1\\8=-11[/tex]
Not true.
So option C is out.
Option D: (4, -7)
Substitute the values in:
[tex]y = -2x + 1\\-7=-2(4)+1\\-7=-8+1\\-7=-7[/tex]
True.
So point (4, -7) lands on the graph of the line. You can also see this visually in a graphing calculator:
(See picture)
on a coordinate plane,point A is located at (7,4), and point B is located at (-8,4). What is the distance between the two points ?
The distance between the point A and B is 15 units.
How to find the distance between two points?The distance between two points can be found using Pythagoras's principle.
Point A is located at (7,4), and point B is located at (-8,4). Let's find the distance between point A and B as follows:
Therefore,
d = √(y₂ - y₁)² + (x₂ - x₁)²
Hence, using (7, 4) (-8, 4)
x₁ = 7
x₂ = -8
y₁ = 4
y₂ = 4
Hence,
d = √(4 - 4)² + (-8 - 7)²
d = √(0)² + (-15)²
d = √225
d = 15 units
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What is the diffrent between statistical significance and practical significance
The concept of statistical significance is mathematically defined and widely accepted by those who use it to assess the usefulness of scientific claims.
However, there is no single definition for practical significance. It is subjective in nature, experiential, and each person decides what it is based on their own experiences.
Thus, it is clear that while Practical significance lacks a common definition, statistical significance has a mathematical definition and is widely accepted by those who use it to assess the usefulness of scientific claims. It is a subjective concept that each person decides for themselves based on their personal experiences.
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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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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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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.
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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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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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
Alice is 2 years younger than brian. The sum of their ages is 28. How old are alice and brian
Answer:
brian is 15 and alice is 13
Step-by-step explanation:
just use x+x+2=28 nd u will get the answer
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!
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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Points A, B, and C are placed in alphabetical order on a
line so that 3AB = AC. What is the ratio of AB: BC?
The co-ordinates of a point C on AB produced so that 3AB = AC, where A = (3 ,2) and B = (-2 , 4) is (-13,-2).
What is co-ordinates of a point?The abscissa, or x coordinate of the point, is the distance between a point and the y-axis scaled with the x-axis. Ordinate is the distance between a point and the x-axis scaled with the y-axis. In order to determine a point's coordinates in a coordinate system, you must do the opposite. Start at the point and move in a vertical line in either an upwards or downwards direction to the x-axis. Here is the x-coordinate for you. Next, repeat the process while following a horizontal line to determine the y-coordinate. An exact position of a point in the coordinate plane can be demonstrated using a collection of values called coordinates. Coordination Plane Definition.Using the section formula, if a point[tex]$(\mathrm{x}, \mathrm{y})$[/tex]divides the line joining the points [tex]$\left(\mathrm{x}_1, \mathrm{y}_1\right)$[/tex]and[tex]$\left(\mathrm{x}_2, \mathrm{y}_2\right)$[/tex]externally in the ratio [tex]$\mathrm{m}: \mathrm{n}$[/tex], then
[tex]$(\mathrm{x}, \mathrm{y})=$[/tex][tex]$\left(\frac{m x_2-n x_1}{m-n}, \frac{m y_2-n y_1}{m-n}\right)$[/tex]
Since, , [tex]$3 \mathrm{AB}=\mathrm{AC} \Rightarrow \frac{\mathrm{AB}}{\mathrm{AC}}=\frac{1}{3}$[/tex]
[tex]& \Rightarrow \frac{\mathrm{BC}}{\mathrm{AC}}=\frac{3-1}{3}=\frac{2}{3}[/tex]
Substituting[tex]$\left(\mathrm{x}_1, \mathrm{y}_1\right)=(3,2)$[/tex] and [tex]$\left(\mathrm{x}_2, \mathrm{y}_2\right)=(-2,4)$[/tex]and [tex]$\mathrm{m}=2, \mathrm{n}=3$[/tex] in the section formula, we get
[tex]$$\mathrm{C}=\left(\frac{2(-2)-3(3)}{2-3}, \frac{2(4)-3(2)}{2-3}\right)=(-13,-2)$$[/tex]
The complete question is,
Find the co-ordinates of a point C on AB produced so that 3AB = AC, where A = (3 ,2) and B = (-2 , 4)
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A children’s public library has picture books and chapter books with a ratio of 2 to 3 if there are a total of 500 books in the children’s section, then how many chapter books are there
By using the ratio, we can see that the fraction 3/5 of the total number of books are chapter books, then there are 300 chapter books in the children's section.
How many chapter books are there?We know that the ratio of picture books to chapter books is 2:3
This means that (2/5) of the total books are picture books, and (3/5) of the total books are chapter books (the denominator of these fractions is the sum of the values in the ratio)
Now we know that there is a total of 500 books in the children's section, then the number of chapter books is:
N = (3/5)*500 =300
There are 300 chapter books.
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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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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 lever a person applies 60 n of force and moves the lever 1 m this moves a 200 newton rock at the other end by 0.2 m
Answer:
work output = 40 N*m
Work input = 60 N*m
Efficiency = 66.67%
Step-by-step explanation:
I did this on a paper so Im sorry but it's to complicated to explain the work proof on the computer. I dont want to type all that equation stuff but thats the answer.
annika was having fun playing poker. she needed the next two cards dealt to be diamonds so she could make a flush (five cards of the same suit). there are 15 cards left in the deck, and five are diamonds. what is the probability that the two cards dealt to annika (without replacement) will both be diamonds? answer choices are in percentage format, rounded to the nearest whole number.
Rounded to the nearest whole number, the probability that the two cards dealt to Annika will both be diamonds is 9.52%. The concept that is used to answer this question is probability.
To calculate the probability that Annika gets two diamond cards dealt to her, we need to find the number of favorable outcomes (getting two diamond cards) and divide it by the total number of possible outcomes (getting any two cards from the remaining 15 cards in the deck).
Since the cards are dealt without replacement, the total number of possible outcomes will be (15 choose 2) = 105.
To find the number of favorable outcomes, we need to find the number of ways to choose 2 cards from the 5 remaining diamond cards. This can be calculated as (5 choose 2) = 10.
So the probability of getting two diamond cards dealt to Annika is: (Number of favorable outcomes) / (Total number of possible outcomes) = 10/105
To express the probability in percentage format, we multiply the fraction by 100
10/105 * 100 = 9.52%
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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
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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solve the inequality
Answer:
D.
Step-by-step explanation:
x + 6 ≤ 8
Subtract 6 on both sides.
x ≤ 2
Option D.
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
Twenty-eight players sign up for basketball. The coach puts 7 players on each team. How many teams are there?
Answer:
Step-by-step explanation:
28/7=4
4 teams
Please help. I will reward 30 points.
x+3≤7 solve for x
Move all terms not containing x to the right side of the inequality. Inequality Form:
x≤4
Interval Notation: (−∞,4]
Aaron's weight is $10$ pounds greater than twice Levi's weight. If the sum of their weights is $118$ pounds, how many more pounds is Aaron's weight than Levi's weight?
Aaron's weight is $118$ pounds - $54$ pounds = $64$ pounds more than Levi's weight.
What is weight?Weight is a measure of the gravitational force of attraction between an object and the Earth, or between two objects. It is measured in Newtons (N) or kilograms (kg). Weight is created by the force of gravity that pulls objects toward the center of the Earth. The greater the mass of an object, the greater the force of gravity and thus the greater its weight. Weight is an important factor in determining the motion of an object and its interaction with other objects.
Aaron's weight is $10$ pounds more than twice Levi's weight, so Levi's weight is $\frac{1}{2}(118 - 10) = 54$ pounds. This means that Aaron's weight is $118$ pounds - $54$ pounds = $64$ pounds more than Levi's weight.
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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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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
What is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial?
The method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial is called completing the square.
The steps to complete the square are as follows:
Move any constant term to the right side of the equation by subtracting it from both sides.
Divide the coefficient of the x term by 2 and square that number, add it to both sides of the equation.
Factor the left side of the equation as a perfect square trinomial.
Take the square root of both sides of the equation, and then add or subtract the value from dividing the coefficient of the x term by 2 to the right side to solve for x.
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