Answer: A
Step-by-step explanation:
This is a fact.
The absolute value parent or modulus function is f ( x ) = | x |
What is Modulus Function?Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = | x |
The absolute value parent function is f(x) = |x|, which represents the absolute value of x.
Option B, f(x) = 13x1, does not represent the absolute value function, as it has a coefficient of 13, which scales the function vertically.
Option C, f(x) = x-− 1|, represents a translation of the absolute value function. The "-1" shifts the function one unit to the right, and the vertical bar denotes the absolute value of the expression within the bar. While it is related to the absolute value function, it is not the parent function itself.
Option D, f(x) = x+2, represents a linear function with a slope of 1, which is not the absolute value function.
Hence , the absolute value parent function is f ( x ) = | x |
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There’s a garden in the neighborhood, and the number of bushes in the garden can be determined by the equation B = 2s, where B is the number of bushes and s is the number of seeds planted. How many seeds were planted if there are 10 bushes?
Which is the solution set of the compound inequality 3,5x-10 >-3 and 8x-9<397
-2
-2
2
2
Answer:
2
Step-by-step explanation:
the cone shaped game piece is made of metal with a mass of 9.2g/cm3 what is the mass of the game piece
The volume of the piece of the metal Gina is found to be 22.82 cubic cm.
What is volume?Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width and height of cube or cuboid.
Given the density of the metal = 9.2g/cm3
Given the mass of the piece of the metal = 210 g
Assuming the volume of a piece of metal to be V
The expression for the density is shown below:-
Density = Mass / Volume
9.2 = 210 / V
V = 210 / 9
V = 22.82 cubic cm.
Therefore the volume of the piece of the metal Gina is found to be 22.82 cubic cm.
The complete question is given below:-
Gina was given an irregularly shaped piece of metal and was told that the density of the metal was 10 g/cm3. She measured the mass of the piece to be 210 g. What was the volume of the piece of metal Gina was given?
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Willey’s Grill & Restaurant Corporation wholesales ovens and ranges to restaurants throughout the Southwest. Willey’s Grill & Restaurant, which had 335,000 shares of common stock outstanding, declared a 2-for-1 stock split. This information has been collected in the Microsoft Excel Online file. Open the spreadsheet, perform the required analysis, and input your answers in the questions below.
a. The number of shares outstanding after the stock split by Willey’s Grill & Restaurant Corporation is 670,000 (335,000 x 2).
b. If the common stock had a market price of $510 per share before the stock split, the approximate market price per share after the split is $255 ($510/2).
What is a stock split?A stock split is a way that a corporation increases the number of its shares by increasing or decreasing the number of shares outstanding.
When a stock split increases the number of outstanding shares, the market price reduces proportionately.
Question Completion:a. What will be the number of shares outstanding after the split? Round your answer to the nearest whole number.
b. If the common stock had a market price of $510 per share before the stock split, what would be an approximate market price per share after the split? Round your answer to the nearest dollar.
Thus, the stock split increased the outstanding shares to 670,000 while reducing the market price to $255.
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You have learned how to divide polynomials in three different ways: by factoring, by long division, and by synthetic division. Explain in words and with mathematical representations how you would divide this polynomial in each of the three ways:
a) Factoring:
b) Long division:
c) Synthetic division:
d) Now, explain a connection you can see for each pair of methods. How does factoring relate to long division? How does long division relate to synthetic division? How does synthetic division relate to factoring?
The way to solve the polynomial using the methods is given below.
How to explain the polynomial?Polynomial by factoring:
An example is (t² + 5t + 4) / +t + 4)
= (t + 1)(t + 4)/(t + 4)
= t + 1.
Dividing polynomial by long division:
Divide the first term of the dividend by the first term of the divisor.
Put this as the first term in the quotient.
Subtract to create a new polynomial.
Continue until you can't divide anymore.
Dividing polynomial by synthesic division:
Step 1: Set up the synthetic division.
Step 2: Bring down the leading coefficient to the bottom row.
Step 3: Multiply c by the value just written on the bottom row.
Step 4: Add the column created in step 3.
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Solve x2 – 8x + 15 < 0. Select the critical points for the inequality shown. –15 –5 –3 3 5
The critical points are within rthe range 3<x<5
Quadratic equationsThese are equations that has a leading degree of 2. Given the expression below.
x²-8x+15<0
Factorize
x²-3x-5x+15<0
Factor out the GCF
x(x-3)-5(x-3) <0
Group
(x-3)(x-5)<0
Find the solution
x < 3 and x <5
Hence the critical points are within rhe range 3<x<5
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CHECK
n =
Solve the equation.
−4(n − 6)= 12
[tex] - 4(n - 6) = 12 \\ (n - 6) = \frac{12}{ - 4} \\ n - 6 = - 3 \\ n = - 3 + 6 \\ n = 3[/tex]
What is the value of h(a) when a = 2 in the
piecewise function
3a + 2
4a +5
3
h(a) =
when a > 3
when a = 3
when a <3
=========================================================
Explanation:
This is the given piecewise function
[tex]h(a) = \begin{cases}3a+2 \text{ when } a > 3\\4a+5 \text{ when } a = 3\\3 \text{ when } a < 3\\\end{cases}[/tex]
We can rewrite things like this
[tex]\text{when } a > 3, \ \ h(a) = 3a+2\\\text{when } a = 3, \ \ h(a) = 4a+5\\\text{when }a < 3, \ \ h(a) = 3\\[/tex]
I personally prefer this format better because it mentions the inputs first, and that leads to which function definition we go for.
The input a = 2 fits the description of [tex]a < 3[/tex] since [tex]2 < 3[/tex] is a true statement. Therefore we go for the third line and can see that [tex]h(a) = 3[/tex] becomes [tex]h(2) = 3[/tex]
-----------
As another example, if we had the input a = 7, then we'd go for the first line (since 7 > 3) and get
h(a) = 3a+2
h(7) = 3(7)+2
h(7) = 23
Which linear function represents the line given by the point-slope equation y-8=(x-4)?
A) f(x) = x +4
B) f(x) = x+6
C) f(x)=x-10
D) f(x)=x-12
The answer is (A) f(x) = x+4.
Sadie made a playlist for her road trip to Arizona. She added the same number of songs from each of her 6 favorite bands. In all, Sadie added 72 songs to the playlist.
Answer: 12 each
Step-by-step explanation: 72 divided by 6 = 12
Whats the correct answer answer asap for brainlist
The graph of y = |2x – 2| – 4 is shown. On a coordinate plane, an angled line opens up. It approaches the grid line at (negative 4, 6), crosses the x-axis at (negative 1, 0), the y-axis at (0, negative 2), has a vertex of (1, 4), and crosses the x-axis at (3, 0). Which statement about the graph is accurate? An x-intercept of the graph is (0, 3). The graph has two y-intercepts. A y-intercept of the graph is (0, –2). The graph has no x-intercepts.
76.89 sjsbs austere. Sisson whenever. Ebenezer oe eie h rur fuf 8r r earned e 3epoe9 r rur 8e e aonwowne e7 rjr or
A small town's population, P, can be modeled by the equation P (t) = 45,000(2.66), where t is the time in years. Is the statement below true of false. The rate of population growth each year is 166% O True O False
A function assigns the values. The statement "The rate of population growth each year is 166%" is true.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function of the population for the town is [tex]P (t) = 45,000(2.66)^t[/tex], where t is the time in years. Comparing the given function to the general function of the population,
P(x) = a(1+b)ˣ
Then, the value of b will be 166%.
Hence, the statement "The rate of population growth each year is 166%" is true.
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12
intent attribution
QUESTION 5 1 POINT
.
Tickets for a basketball game cost $3 for students and $5 for adults. The number of students was 11 less than 8 times
number of adults. The total amount of money from ticket sales was $895. How many of each ticket were sold?
Provide your answer below:
adult tickets,
FEEDI
student tickets
Answer:
32 adult245 studentStep-by-step explanation:
The given relations between numbers and prices can be used to write a system of equations for the number of each kind of ticket. One equation will describe ticket numbers; the other will describe ticket revenue.
SetupLet x represent the number of adult tickets, and y the number of student tickets. The given relations can be written as the general-form equations ...
8x -y -11 = 0 . . . . . . . . . ticket numbers
5x +3y -895 = 0 . . . . . ticket revenue
SolutionThe setup using general form equations lends itself to solution using the "cross multiplication method." Using this method, we define three numbers used in the solution:
Δ = 8(3) -5(-1) = 24 +5 = 29
Δx = -1(-895) -3(-11) = 895 +33 = 928
Δy = -11(5) -(-895)(8) = -55 +7160 = 7105
And the solutions are ...
x = Δx/Δ = 928/29 = 32
y = Δy/Δ = 7105/29 = 245
32 adult tickets and 245 student tickets were sold.
__
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The sum of product of two and nine and product of two and thirty-six is divided by nine and then the quotient is multiplied by the sum of the first three prime numbers.
The sum of the product of two and nine and the product of two and thirty-six is divided by nine and then the quotient is multiplied by the sum of the first three prime numbers is 100.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The expression can be written as,
[tex]\dfrac{(2 \times 9)+(2 \times 36)}{9} \times (2+3+5)[/tex]
The result of the above expression will be,
[tex]\dfrac{(2 \times 9)+(2 \times 36)}{9} \times (2+3+5)\\\\=\dfrac{18+72}{9} \times (10)\\\\[/tex]
= (90/9) × 10
= 10 × 10
= 100
Hence, the sum of the product of two and nine and the product of two and thirty-six is divided by nine and then the quotient is multiplied by the sum of the first three prime numbers is 100.
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Q.17> In how many ways 4 arts students and 4 science Students be arranged alternative at a round table?
Using the arrangements formula, it is found that there are 1152 ways for the students to be arranged alternatively at the table.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, we have that:
With the art students at the odd numbered places and the science students at the even numbered places, there are 4! x 4! ways.Same number of ways if they exchange, art even and science odd.Hence the number of ways is:
2 x 4! x 4! = 1152
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Which relation is also a function?
O {(1,0), (2,2), (1,3)}
O {(1, 2), (1, 4), (2, 6) }
○ {(2, 1), (2, 2), (2, 3) }
○ { (0, 0), (4, 0), (6, 0) }
Answer: Option 4
Step-by-step explanation:
Each value of x maps onto one value of y, meaning the relation is a function.
Given that sin(90-x)°=0.8. where x is an acute angle.Find without using calculator or mathematical table the value of tan x
By using trigonometric properties, we will see that:
tan(x) = 3/4.
How to find the value of tan(x)?
Remember that the sine of the difference is:
sin(a - b) = sin(a)*cos(b) - sin(b)*cos(a).
Here we have:
sin(90° -x ) = 0.8
Expanding the sine:
sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°)
We know that:
sin(90°) = 1 and cos(90°) = 0, then:
sin(90° - x) = sin(90°)*cos(x) - sin(x)*cos(90°) = cos(x).
Then we have:
cos(x) = 0.8
And we want to find the tangent of x, which is:
[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]
We already know that cos(x) = 0.8
Now, remember that:
[tex]sin(x)^2 + cos^2(x) = 1\\\\sin(x) = \sqrt{1 - cos^2(x)} \\[/tex]
Because x is an acute angle, sin(x) > 0, that is why we choose the positive root.
Replacing cos(x) we get:
[tex]sin(x) = \sqrt{1 - 0.8^2} = \sqrt{1 - 0.64} = \sqrt{0.36} = 0.6[/tex]
Then the tangent of x is:
[tex]tan(x) = \frac{0.6}{0.8} = \frac{6}{10}*\frac{10}{8} = 6/8 = 3/4[/tex]
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Find the coordinates of the intersection of the diagonals of the parallelogram with the vertices W(−2, 5), X(2, 5), Y(4, 0),
and Z(0, 0)
.
Using the midpoint formula, the coordinates of the intersection of the diagonals of the parallelogram is: (1, 2.5).
What are Diagonals of a Parallelogram?The diagonals of a parallelogram bisect each other, therefore, the coordinates of their intersection can be determined using the midpoint formula, which is: [tex]M(\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2})[/tex].
A diagonal is XZ.
X(2, 5) = (x1, y1)
Z(0, 0) = (x2, y2)
Plug in the values
[tex]M(\frac{0 + 2}{2}, \frac{0 + 5}{2})[/tex]
= (1, 2.5).
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Can someone help me?
Answer:
m∠R = 112°
m∠S = 112°
m∠T = 68°
Step-by-step explanation:
Quadrilateral QRST is a cyclic quadrilateral.
A cyclic quadrilateral is a quadrilateral drawn inside a circle where every vertex touches the circumference of the circle.
The opposite angles in a cyclic quadrilateral sum to 180°.
⇒ m∠Q + m∠S = 180°
⇒ m∠R + m∠T = 180°
Given:
m∠Q = 68°m∠R = (3x + 40)°m∠T = (5x - 52)°Measure of angle Q
⇒ m∠Q + m∠S = 180°
⇒ 68° + m∠S = 180°
⇒ m∠S = 180° - 68°
⇒ m∠S = 112°
Measure of angles R and T
⇒ m∠R + m∠T = 180°
⇒ (3x + 40)° + (5x - 52)° = 180°
⇒ )8x -12)° = 180°
⇒ 8x° = 192°
⇒ x = 24
Substituting the found value of x into the expressions for angles R and T:
⇒ m∠R = (3(24) + 40)°
⇒ m∠R = 112°
⇒ m∠T = (5x - 52)°
⇒ m∠T = 68°
please help me with this
Evaluate: 2^-4 =
Answer: [tex]\frac{1}{16}[/tex]
Step-by-step explanation:
Whenever an exponent is negative, you flip the solution.
For this, [tex]2^4 = 2*2*2*2 = 4*4 = 16[/tex], however the exponent is negative, so flip 16 to get your final answer of [tex]\frac{1}{16}[/tex]
Help!! A semi circle sits on top of a rectangle to form the figure below. Find this area in parameter use 3.14 for
The area of the figure in the task content is; 14.28in².
What is the area of the figure in the task content?The area of the figure in the task content can be evaluated as the area of the semicircle and the rectangle.
Hence, the area of the semicircle is; (3.14/2) × (4/2)² = 6.28in².
The area of the rectangle can be evaluated as; 2 × 4 = 8in².
Hence, the area of the entire figure is; 8+ 6.28 = 14.28in².
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please help
f (5) = x2
Answer:
25
Step-by-step explanation:
f(5)=x2
=25
8. Jess walked for 45 minutes at 3 km/h and then ran for half an hour at x km/h. At the end
of that time she was 6 km from the starting point. Find the value of x.
Answer:
x = 7.5 km/h
Step-by-step explanation:
• First calculate the distance covered by walking at 3 km/h for 45 minutes ( 0.75 h):
distance = speed × time
= 3 × 0.75
= 2.25 km
• Therefore, she covered 2.25 km of the total journey by walking. Since she was 6 km from the starting point at the end of the entire journey, we can calculate the distance remaining, which she had to run:
distance she had to run = 6 - 2.25
= 3.75 km
• Now we can calculate the speed of the 30 minute (0.5 h) run:
speed = distance ÷ time
= 3.75 ÷ 0.5
= 7.5 km/h
This means that she ran at 7.5 km/h for half an hour.
∴ x = 7.5
Evaluate x² + 4x + 1 when x = -3
Answer: -2
Step-by-step explanation:
We can combine the fundamentals of mental math and the brain to calculate the problem when x is -2. You wake up noticing x is -2 and you instantly know the answer and solved in less than a second.
You are flying a kite and have let out 30 feet of string but it got caught in an 8ft tree. What is the angle of elevation to the location of the kite? Show your work finding the angle of elevation and state the measure of the angle. You are flying a kite and have let out 30 feet of string but it got caught in an 8ft tree . What is the angle of elevation to the location of the kite ? Show your work finding the angle of elevation and state the measure of the angle .
Answer:
15.47 degrees
Step-by-step explanation:
What is the range of the exponential function shown below?
Answer:
D. y>0.
Step-by-step explanation:
1) the domain of the given function is any real numbers, then
2) if x→+∞, then y→0; if x→-∞, then y→+∞;
3) finally, the required range is y>0; answer D.
The table below shows which hand is favored by each person from a sample of 100 people (50 male and 50 female). Use the information in the table to answer the following questions
Determine the probability that a randomly selected person from the sample will be female or left-handed.
The probability that a randomly selected person from the sample will be female or left-handed will be 0.05.
What is the probability?Probability is synonymous with possibility. It is concerned with the occurrence of a random event.
Probability can only have a value between 0 and 1. Its simple notion is that something is very likely to occur. It is the proportion of favorable events to the total number of events.
Given data;
Total number of sample,n(S) = 100 person
No of female or left-handed is,n(E) =5
P(E) is the probability that a randomly selected person from the sample will be female or left-handed
The probability that a randomly selected person from the sample will be female or left-handed is found as;
P(E) = n(E)/n(S)
P(E) = 5 / 100
P(E) = 0.05
Hence the probability that a randomly selected person from the sample will be female or left-handed will be 0.05.
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The elementary school lunch menu repeats every 20 days; the middle school lunch menu repeats
every 15 days. Both schools are serving pizza today. In how may days will both schools serve pizza
again?
Answer:
60 Days.
Step-by-step explanation:
Alright. We're told that the elementary menu repeats every 20 days. All right. And the middle school repeats every 15 days. And today they're both serving pizza. It asks how long until they're both saving it serving pizza again. Alright. So we can kind of just write them out and say well, if it's every 20 days, it repeats. Well then in 20 days from now we're going to get pizza again. And then after that another 20 days, so 40 days and then after that another 60 days. Okay. And we're just adding 20 each time. Uh you know, to see when would we get pizza again at the elementary school? Well, we can do the same thing here with middle school. And when are they going to get pizza again? Well, in 15 days from now they would get pizza again and then another 15 days from that. So that's 30 And then 45 and then 60 and then 75 and so on. And the first time that they're going to repeat is well, this is the common factor that are the common multiple that they have, which is 60. This is really just a complicated way of asking what is the least common multiple of 20 and 15. Alright. And your answer is going to be 60. So it'll be 60 days until they serve the same pizza again.
What is the measure of n?
28
n = [?]
n
7
3
Answer: 14
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{n}{28}=\frac{7}{n}\\\\n^{2}=196\\\\n=\boxed{14}[/tex]