Find the
1. domain
2. range,
3. x-intercepts,
4. y-intercepts
5. the rate of change on |-1,4|
6.find the interval(s) where the graph is increasing
7. find the interval(s) where the graph is decreasing
8.find the interval(s) where the graph is positive
Answers
Answer:
I dont think you need the answer anymore, the question is from ages ago
Step-by-step explanation:
The absolute value function has a domain of all real numbers, a range of non-negative real numbers, a single x-intercept at (0, 0), no y-intercept, a constant rate of change of 1 over the interval [-1, 4], and is increasing for x greater than 0 and decreasing for x less than 0. Overall, the graph is positive over the entire real number line.
1. Domain:
The domain of a function is the set of all possible input values (x-values) for which the function produces a real output value (y-value). In the case of the absolute value function, the output is always real, so the domain is all real numbers. Therefore, the domain is:
(x) ∈ (-∞, ∞)
2. Range:
The range of a function is the set of all possible output values (y-values) that the function produces. The absolute value function always outputs a non-negative value, so the range is:
(y) ∈ [0, ∞)
3. x-intercepts:
The x-intercepts of a function are the points where the graph of the function crosses the x-axis. This happens when the output value (y) is zero. In the case of the absolute value function, the output is zero only when the input (x) is zero. Therefore, the x-intercept is:
(0, 0)
4. y-intercepts:
The y-intercept of a function is the point where the graph of the function crosses the y-axis. This happens when the input value (x) is zero. In the case of the absolute value function, the output is always non-negative, so there is no y-intercept.
5. Rate of change on |-1,4|:
The rate of change of a function at a point is the slope of the line tangent to the graph of the function at that point. The absolute value function is a piecewise function, so it has different slopes in different intervals. Over the interval |-1, 4| , the function is simply x + 1, so the rate of change is 1.
6. Intervals where the graph is increasing:
The graph of the absolute value function is increasing over the intervals where the expression inside the absolute value bars is positive. In other words, the graph is increasing when x > 0. Therefore, the interval where the graph is increasing is:
(x) ∈ (0, ∞)
7. Intervals where the graph is decreasing:
The graph of the absolute value function is decreasing over the intervals where the expression inside the absolute value bars is negative. In other words, the graph is decreasing when x < 0. Therefore, the interval where the graph is decreasing is:
(x) ∈ (-∞, 0)
8. Intervals where the graph is positive:
The graph of the absolute value function is always non-negative, so it is positive over the entire interval:
(x) ∈ (-∞, ∞)
Related Questions
I need help on number 2.
Answers
Greetings!
This is how your double number line should look:
(lbs) 0 1 2 3 4 5
↓-----↓-----↓-----↓-----↓-----↓
0 3.5 7 10.5 14 17.5 (dollars)
Hope this helps!
Help me please , I don’t seem to get the right answer when I do the check up point
Answers
Order these numbers from Least to Greatest 4,209 2,438 4,703 3,026
Answers
2,438 3,026 4,209 4,703
Answer: 2,438 3,026 4,209 4,703
Step-by-step explanation:
Drag and drop the answers into the boxes to correctly complete the statement.
A sequence of transformations that maps △RST to △R′S′T′ is a _____ followed by a _____
A. reflection across the x-axis
B. Translation 1 unit down
C. Reflection across the y-axis
D. Rotation of 180 degrees about the origin
Answers
Answer:
A sequence of transformations that maps △RST to △R′S′T′ is a Reflection across the x-axis followed by a Translation 1 unit down
Step-by-step explanation:
step 1
Find out the reflection of △RST across the x-axis
we know that
The rule of the reflection of a point across the x-axis is
(x,y) -----> (x,-y)
we have
R(1,3),S(1,1),T(4,1)
Applying the rule of reflection across the x-axis
R(1,3) -----> R''(1,-3)
S(1,1) -----> S''(1,-1)
T(4,1) ----> T''(4,-1)
step 2
Find out the translation of △R''S''T'' 1 unit down
The rule of the translation is
(x,y) -----> (x,y-1)
Applying the rule of the translation
R''(1,-3)-----> R'(1,-3-1)
R''(1,-3)-----> R'(1,-4)
S''(1,-1)----> S'(1,-1-1)
S''(1,-1)----> S'(1,-2)
T''(4,-1) ----> T'(4,-1-1)
T''(4,-1) ----> T'(4,-2)
therefore
A sequence of transformations that maps △RST to △R′S′T′ is a Reflection across the x-axis followed by a Translation 1 unit down
1-5 Skills Practice
Descriptive Modeling and Accuracy
1. TEST SCORES A teacher compares the ratio of the number of questions answered correctly to the
total number of questions on a test as a metric. For a student to earn and A or B on a test, the ratio
must be greater than or equal to 0.8. The last test given by the teacher had a total of 40 questions.
Using this metric, what is the least number of questions a student can answer correctly and earn an
A or B on the test?
number of questions answered correclty
Ratio to earn an A or B - -
number of questions
Answers
Answer:
The least number of questions a student can answer correctly is 32
Step-by-step explanation:
Let
x -----> the number of questions answered correctly
y ----> the total number of questions on a test
[tex]ratio=\frac{x}{y}[/tex]
we know that
For a student to earn and A or B on a test, the ratio must be greater than or equal to 0.8
so
[tex]\frac{x}{y} \geq 0.8[/tex]
For y=40 questions
Find the value of x
substitute
[tex]\frac{x}{40} \geq 0.8[/tex]
solve for x
Multiply both sides by 40
[tex]x \geq 0.8(40)[/tex]
[tex]x \geq 32[/tex]
so
The least number of questions a student can answer correctly is 32
Verify the ratio
For x=32, y=40
[tex]\frac{32}{40}=0.8[/tex]
Compare
[tex]0.8 \geq 0.8[/tex] ----> is ok
Final answer:
This math question involves determining the minimum number of questions a student needs to answer correctly to earn an A or B grade based on a specific ratio criterion.
Explanation:
Mathematics: In this question, we are dealing with a scenario where a teacher evaluates students' test performance based on a specific ratio criterion to determine if they earn an A or B grade. The focus is on determining the minimum number of questions a student must answer correctly to achieve the desired grades.
Step-by-step explanation:
Given that the ratio of correct answers to the total questions must be greater than or equal to 0.8 to earn an A or B.
We know the total number of questions on the test is 40.
To find the least number of questions a student must answer correctly, we calculate 0.8 x 40 = 32.
Therefore, the student needs to answer at least 32 questions correctly to earn an A or B on the test.
Please help very confused
Answers
Answer:
x = -8
QR = 6
PR = 9
Step-by-step explanation:
Alrighty, this one has a lot of steps. We have to think about this logically.
The length of PR is x + 17, and the length of PQ is 3, and the length of QR is 2x + 22.
The length of PR could also be written as the length of PQ + QR, which gives us the formula PR = PQ + QR. This allows us to put all our information into one formula to solve for x.
PR = PQ + QR
x + 17 = 3 + 2x + 22
17 - 3 - 22 = 2x - x
-8 = x
so x = -8
Now we can use that x and plug it into the other two formulas:
QR = 2x + 22
QR = 2(-8) + 22
QR = -16 + 22
QR = 6
And now we plug x into PR:
PR = x + 17
PR = -8 + 17
PR = 9
Alternatively, we can use our other formula, PR = 3 + QR, which gets us the same answer:
PR = 3 + QR
PR = 3 + 6
PR = 9
Find the exact radius of a circle with circumference 28pi meters.
Answers
Answer: The radius is 14 units.
Step-by-step explanation:
Start by finding the diameter, the formula for circumference is πd, So set up an equality:
28π=c
28π=πd
Divide both sides by π:
28π/π = 28πd/π
Cross out π:
28 = d
diameters twices largest radius, divide your diameter by 2 to get radius.
D/2 = r = 28/2 = 14
Therefore, your radius is 14 units.
least to greatest 2/3, 3/5, 13/15, 2/5
Answers
Answer: 2/5 3/5 2/3 13/15
Step-by-step explanation:
2/3, 3/5, 13/15, 2/5
The least common denominator is: 15.
Rewriting as equivalent fractions with the LCD:
10/15, 9/15, 13/15, 6/15
Ordering these fractions by the numerator in order from least to greatest:
6/15 < 9/15 < 10/15 < 13/15
Therefore, your input in order from least to greatest is:
2/5 < 3/5 < 2/3 < 13/15
A phone company uses the equation y = 0.15x + 10 to find y, the monthly charge for a customer sending x text
messages. How many text messages are sent if the monthly charge is $77.50?
Answers
Hey!
---------------------------------------
Solution:
77.50 = 0.15x + 10
77.50 - 10 + 0.15x + 10 - 10
67.50 = 0.15x
0.15x = 67.50
0.15x/0.15 = 67.50/0.015
x = 450
---------------------------------------
Check:
77.50 = 0.15(450) + 10
77.50 = 67.50 + 10
77.50 = 77.50
---------------------------------------
Answer:
450 text messages can be sent when the monthly charge is $77.50!
---------------------------------------
Hope This Helped! Good Luck!
0.282828 to nearest tenth
Answers
Answer:
0.3
Step-by-step explanation:
7 is greater than 5 therefore round the tenths value up to 3
A number of b divided by -3 is greater than or equal to 6
Answers
Answer: b ≤ -18
Step-by-step explanation:
Isolate the variable by multiplying both sides by -3. Remember that when you multiply or divide by a negativem the symbol flips.
[tex]\dfrac{b}{-3}\geq6\\\\\\\dfrac{b}{-3}(-3)\geq6(-3)\\\\\\\large\boxed{b\leq-18}[/tex]
The first term of an AP is -1/2 and it's common difference is 4. Find the 9th term
Answers
Answer:
[tex]\frac{63}{2}[/tex]
Step-by-step explanation:
The n th term of an arithmetic progression is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - [tex]\frac{1}{2}[/tex] and d = 4, thus
[tex]a_{9}[/tex] = - [tex]\frac{1}{2}[/tex] + (8 × 4) = - [tex]\frac{1}{2}[/tex] + 32 = [tex]\frac{63}{2}[/tex]
Beau earns $26.50 per hour for regular hours worked and double
time for any overtime (over 40) he works. He is paid weekly. If he
worked 56.5 hours last week, how much can Beau expect that his
gross pay will be?
Answers
Answer:
$1694.5
Step-by-step explanation:
Hourly rate for Beau = $26.50
Weekly hours = 40 Hours
Basic earning = 26.50 × 40 = $820
Total number of hours Beau worked in week = 56.5 Hours
Overtime = 56.5 - 40 = 16.5 Hours
Overtime rate = 2 × Hourly rate = 2 × 26.50 = $53
Overtime earning = 53×16.5 = $874.5
Total earning for the week = 820 + 874.5 = $1694.5
Four people invested in a restaurant. One person invested $100,000. Two others invested in
the ratio x:2x, and the fourth person invested an amount equal to the other three investors
combined. The total investment was $ 1,100,000.
Part A
Write an expression for the amount invested by the fourth person.
Answers
Answer:
x=$150,000
4th person invested $550,000
Step-by-step explanation:
100,000+x+2x+(100,000+x+2x)=1,100,000
200,000+6x=1,100,000
6x=900,000
x=150,000
The investment of the fourth person is 100,000+3x
=100,000+450,000
=$550,000
The amount invested by the fourth person was $550,000.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
Given that a person invested $100,000. Two others invested in the ratio x:2x and the fourth person invested an amount equal to the other three investors combined.
We have to determine an expression for the amount invested by the fourth person.
The total investment = $1,100,000.
So an expression for the amount invested by all people as:
⇒ 100,000 + x + 2x + (100,000+x+2x) = 1,100,000
⇒ 200,000 + 6x = 1,100,000
⇒ 6x = 900,000
⇒ x = 150,000
So the investment of the fourth person as
⇒ 100,000 + 3x
⇒ 100,000 + 450,000
⇒ $550,000
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Draw a diagram that shows 0.27+0.23= 1/2
Answers
Answer:
The required diagram is shown below:
Step-by-step explanation:
Consider the provided expression.
0.27+0.23= 1/2
We can draw the model of the provided expression.
Step 1: Shade 27 boxes out of 100 boxes,
This will show 0.27
Step 2: Shade 23 more boxes with another color.
This will show 0.23.
The total shaded boxes are 27+23=50.
Which represents 0.27 + 0.23 = 1/2 (1/2=0.50)
The required diagram is shown below:
To visually show the equation [tex]\(0.27 + 0.23 = \frac{1}{2}\)[/tex], see the diagram attached.
What is the diagramTo represent the equation [tex]\(0.27 + 0.23 = \frac{1}{2}\)[/tex], follow the steps:
1. Draw a horizontal line to represent the number line.
2. Label the line with points 0, 0.2, 0.4, 0.6, 0.8, and 1.
3. Mark a point at 0.27, slightly past the midpoint between 0.2 and 0.4.
4. Mark another point at 0.23, slightly before the midpoint of 0.2 and 0.4.
5. Draw a vertical line connecting these two points to represent their sum.
6. Label the top of this line with "0.27 + 0.23."
7. Draw a horizontal line segment from the vertical line's top point to the middle of the line, intersecting at the value 0.5.
8. Label this intersection point as [tex]"\(\frac{1}{2}\)"[/tex] to show that [tex]\(0.27 + 0.23\)[/tex]indeed equals[tex]\(\frac{1}{2}\).[/tex]
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14/49 in lowest terms ?
Answers
Answer: 2/7
Step-by-step explanation: To simplify the fraction 14/49, we need to find the greatest common factor of 49 and 7 and we can divide our fraction by it.
In this case, the greatest common factor of 14 and 49 is 7 so we can divide both our numerator and denominator by 7.
Therefore, 14/49 as a simplified fraction is 2/7.
Image provided.
PLEASE HELP ME WITH THIS AHHHH 15-(21)
Answers
Answer:
-6
Step-by-step explanation:
Answer:
Is it 15 Minus 21 (Or) 15 x -21
Step-by-step explanation:
16. Which number has the greatest value?
A 9.382
B 9.47
© 9.09
D
9.7
ASAP plssss
Answers
Answer:
D. 9.7
Step-by-step explanation:
9.382
9.470
9.090
9.700
Answer:
d. 9.7
Step-by-step explanation:
if you add 0s to each of the answers, itll make sense. For instance:
A. 9.382
B. 9.470
C. 9.090
D. 9.700
After a baseball is hit, the height h (in feet) of the ball above the ground t seconds after it is hit can be approximated by the equation h = -16t² + 64t + 3. Determine how long it will take for the ball to hit the ground. Round your answer to the nearest hundredth... Please help .. It is due tomorrow
Answers
Answer:
The ball will take 4.05 seconds to hit the ground.
Step-by-step explanation:
we have
[tex]h=-16t^{2}+64t+3[/tex]
This is a quadratic equation (vertical parabola) open down
The vertex is a maximum
we know that
The ball hit the ground when h=0
Solve the quadratic equation
For h=0
[tex]-16t^{2}+64t+3=0[/tex]
The formula to solve a quadratic equation of the form
[tex]at^{2} +bt+c=0[/tex] is equal to
[tex]t=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]-16t^{2}+64t+3=0[/tex]
so
[tex]a=-16\\b=64\\c=3[/tex]
substitute in the formula
[tex]t=\frac{-64(+/-)\sqrt{64^{2}-4(-16)(3)}} {2(-16)}[/tex]
[tex]t=\frac{-64(+/-)\sqrt{4,288}} {-32}[/tex]
[tex]t=\frac{64(-)\sqrt{4,288}} {32}=-0.05\ sec[/tex] ---> the time cannot be a negative number
[tex]t=\frac{64(+)\sqrt{4,288}} {32}=4.05\ sec[/tex]
therefore
The ball will take 4.05 seconds to hit the ground.
what is 8 10/27-1 2/9?
Answers
Answer:
193/27
Step-by-step explanation:
8 10/27 - 1 2/9
226/27 - 11/9
= 193/27
a certain fish can swim 6 1/2 times faster than a person. if a person can swim 5 4/7 miles per hour, how fast can the fish swim?
Answers
Answer: 36 3/14 miles per hour
Step-by-step explanation:
multiply the speed of a human (5 4/7) by 6 1/2 or 6.5 and you get your answer
To find the fish's speed, convert the mixed numbers 5 4/7 and 6 1/2 to improper fractions and multiply them. The result, 507/14, converts back to a mixed number as approximately 36.21 miles per hour.
Explanation:To solve this question, we need to multiply the person's swimming speed with the mentioned relative speed of the fish. A person can swim at a speed of 5 4/7 miles per hour, and since the fish can swim 6 1/2 times faster, we multiply 5 4/7 by 6 1/2.
The first step is to convert these mixed numbers to improper fractions. 5 4/7 becomes 39/7 and 6 1/2 becomes 13/2.
Multiplication of fractions involves multiplying the numerators together to get the new numerator and the denominators together to get the new denominator. So the multiplication (39/7)*(13/2) leads to a result of 507/14.
This can be now converted back to a mixed number, giving us an approximate answer of 36.21. Therefore, the fish swims at a speed of approximately 36.21 miles per hour.
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The length of a rectangle is represented by (6x - 2), and the width is represented by (x - 1). Which expression best represents
the perimeter of the rectangle?
Answers
Answer:
2(6x - 2 + x - 1) = 2(7x - 3) = 14x - 6
Convert dotted decimal IP address into binary. 172.61.35.186
Answers
Answer:
10101100.00111101.00100011.10111010
Step-by-step explanation:
The dotted decimal IP address 172.61.35.186 converts to binary as 10101100.00111101.00100011.10111010. Each segment of the IP address is converted separately and reassembled with dots in between the binary segments.
Explanation:To convert a dotted decimal IP address to binary, it is important to understand that each segment of the IP address (divided by dots) is converted separately. Let's take for example the IP address 172.61.35.186.
The first segment is 172. Converted to binary, this becomes 10101100. The second segment is 61. In binary, it is 00111101. The third segment being, 35, turns into 00100011 in binary. Lastly, the fourth segment, 186, is transmuted into 10111010 in binary.
So, the IP address 172.61.35.186, when converted into binary, will be: 10101100.00111101.00100011.10111010.
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Determine the next term in the sequence: 4, 8, 12, ...
Answers
Answer:
Step-by-step explanation:
Are you asking for a pattern? The answer is 16
4+4=8
8+4=12
12+4=16
The given sequence 4, 8, 12, ... is an arithmetic expression thus the next term will be 16.
What is Arithmetic progression?The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
The arithmetic progression has broader use in mathematics for example sum of natural numbers.
As per the given sequence,
4,8,12,..
Now, 8 - 4 = 4
12 - 8 = 4
Since the common difference is the same thus it will be an arithmetic expression.
The nth term of AP is given as,
a(n) = a + (n - 1)d
Here, a is the first term, and d is a common difference.
The fourth term of the given sequence is,
a(4) = 4 + (4 - 1)4
⇒ 4 + 12 = 16
Hence "The given sequence 4, 8, 12, ... is an arithmetic expression thus the next term will be 16".
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Two angles are complementary. If one angle is 4 times larger than other one then what is the measure of the smaller
angle?
Answers
Answer:
The smaller angle is 18 degrees
The larger angle is 72 degrees
Step-by-step explanation:
x = smaller angle
y = larger angle
y = 4x ---> one angle is 4 times larger than other one.
y + x = 90 ----> the sum of complementary angles is 90 degrees
4x + x = 90 ----> plug in 4x for the larger angle (y) and then solve
5x = 90
x = 18 ----> the smaller angle is 18 degrees
y = 90 - 18
y = 72 ----> the larger angle is 72 degrees
The smaller angle is 18.
What is the complementary angle?The complementary angle is the angle that adds up to 90 degrees always, so when we say that two angles are complementary it means that the sum of the angle or the combined angle is equal to ninety degrees.
The solution to the problemThe larger angle is 4 times the smaller angle so let the smaller angle be 'x' and the larger angle be 4x.
Hence the sum of both the angle is 90 degrees from the definition of complementary
so 4x+x=90, 5x = 90
dividing the equation by 5
x = 18
Hence the smaller angle is 18 degrees
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Simplify the expression.
4[(10-4) ²÷4]
a. 6
b. 12
c. 9
d. 36
Answers
Answer:
Step-by-step explanation:
D 36 is the answer
A rectangle has a height of 3 and a width of 4b^4+2b-6.
Express the area of the entire rectangle.
Answers
Answer:12b^4 + 6b - 18
Step-by-step explanation:
Area of a rectangle is width x height
(4b^4 + 2b - 6) x 3
Multiply the coefficients by 3
So you get
12b^4 + 6b - 18
find the area of a circle with a circumference of 37.68 units
Answers
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=37.68 \end{cases}\implies 37.68=2\pi r\implies \cfrac{37.68}{2\pi }=r \\\\\\ \stackrel{assuming~\pi =3.14}{\cfrac{37.68}{2(3.14)}}=r\implies \boxed{6=r} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad A=\pi (6)^2\implies A=36\pi \implies A\approx 113.10[/tex]
Viola and Paige stand next to each other and kick soccer balls in the air. The
path of Viola's ball is described by the equation y=-3x2 + 6x + 3. The path of
Paige's ball is shown by the graph.
In each function, x is the horizontal distance the ball travels in meters, and y
represents the height.
Whose soccer ball reaches a greater height?
O
A. Both soccer balls reach the same height
O
B. Viola's soccer ball
O
C. Paige's soccer ball
Answers
Answer:
C. Paige's soccer ball.
Step-by-step explanation:
When you graph y = 3x^2 + 6x + 3, you can see that the max of the parabola is around 6. This is lower compared to Paige's soccer ball's max height shown in the image.
Answer:
C. Paige's soccer ballStep-by-step explanation:
To solve this problem, we just need to graph Viola's function to know the altitude she reached, and then compare it with Paige's altitude.
So, we know that Viola's function is [tex]y=-3x^{2}+6x+3[/tex], as an extra solution, we can calculate the vertex of this quadratic function, that will give us Viola's max altitude.
[tex]V(v_{x};v_{y})\\V(\frac{-b}{2a};f(v_{x} ))[/tex]
Where b and a are from the general quadratic function: [tex]y=ax^{2} +bx+c[/tex].
So, in this case, a = -3; b = 6. Replacing this values, we find the vertex:
[tex]V(\frac{-b}{2a};f(v_{x} ))[/tex]
[tex]v_{x}= \frac{-b}{2a}=\frac{-6}{2(-3)}=1[/tex]
Then, we use the function to calculate the vertical coordinate of the vertex:
[tex]v_{y}=f(1)=-3(1)^{2}+6(1)+3=-3+6+3=6[/tex]
Therefore, the max altitude reached by Viola is 6 meters.
Now, from the graph, we observe that Paige's max altitude is around 7.5 meters.
Therefore, Paige reached the higher height. The answer is C.
What happens to the graph f(x) = |x/, when f(x) is replaced by 0.3 f(x) +9
Answers
Answer:
Step-by-step explanation:
First, the graph is flattened, and secondly, the whole resulting graph is translated upward by 9 units.