A function is said to have a constant interval if, for any input, the output is the same. The graph of a function with a constant interval is parallel to the axis of the range, i.e., a horizontal line.
A constant interval refers to a specific type of interval that remains the same or constant over its entire length. In other words, the difference between any two consecutive points or numbers in a constant interval is always the same.
Let's assume that f(x) = c is a function with a constant interval.
Then,
for any [tex]x_1\leq x_2[/tex] or [tex]x_1\geq x_2[/tex],
[tex]f(x_1) = f(x_2)[/tex].
Thus, a function whose output remains constant for every input is called a function with constant intervals.
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Easy math question help asap
Answer:
3/4z-1/4z+1=2/4z+1
Combine like terms to get
1/2z+1=1/2z+1
Subtract one from both sides to get
1/2z=1/2z
Multiply both sides by 2 to get
z=z.
This is D, has infinitely many solutions because any number you enter as z will equal itself.
Ex. 5 as z would be 5=5 which is true with any number.
given that the two triangles are similar, solve x if AU=20x+108, UB= 273, BC= 703, UV= 444, AV= 372 and AC=589.
Zoe is making a quilt using 15 red squares and 30 green squares. Which combination shows the same ratio of red squares to green squares
Three cube-shaped boxes are stacked one above the other. The volumes of two of the boxes are 1,331 cubic meters each, and the volume of the third box is 729 cubic meters. What is the height of the stacked boxes in meters?
Answer: The height of the stacked boxes is 31 meters.
Step-by-step explanation:
Since, the Volume of a cube = (side)³
The volume of first box = 1331 cubic meters,
⇒ (side)³ = 1331
⇒
Similarly, the side of second box = 11 meters ( Because, both boxes have the same volume )
Now, the volume of third box = 729 cubic meters
⇒ ⇒ (side)³ = 729
⇒
Thus, the height of the stacked boxes = Side of first box + side of second box + side of third box
= 11 + 11 + 9
= 31 meters.
From a group of 7 candidates, a committee of 6 people is selected. In how many different ways can the committee be selected?
C(n,r)=C(7,6)
=7!(6!(7−6)!)Final answer:
There are 7 different ways to select a committee of 6 people from a group of 7 candidates, calculated using the combinations formula C(7, 6) = 7! / (6! * (7 - 6)!) = 7.
Explanation:
The question is asking to determine the number of different ways a committee can be selected from a group of candidates, which is a common problem in combinatorics, a branch of mathematics. To find the number of different ways a committee of 6 people can be selected from a group of 7 candidates, you can use combinations. Since the order in which the committee is chosen does not matter, you calculate combinations and not permutations. The formula for combinations is:
C(n, k) = n! / (k! * (n - k)!)
Applying the formula:
C(7, 6) = 7! / (6! * (7 - 6)!) = 7 / 1 = 7
Therefore, there are 7 different ways to select a committee of 6 people from a group of 7 candidates.
Brian needs to paint a logo made using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle? 7.5 cm2 15.0 cm2 19.5 cm2 39.0 cm2
Learning about system of equations, please give a VERY DETAILED explanation! I'm having a lot of trouble with this. :(
Name two fractions that are less than 0.7 ? Plz help
Which is not used to reach a conclusion in a formal proof?
In mathematics especially in verifying certain statements regarding geometry, two column proofs are used. A two-column proof contains a table with a logical series of statements and reasons that reach a conclusion. It is commonly present in geometry. Two column proofs always have two columns: statements and reasons. The other choices don’t fit in the definition of two column proof.
In science, the four ways to incorporate proof into the research paper are:
1. If the research you are investigating has been with other research paper before.
2. There is an experimental proof that the evidence is true.
3. The research published belongs to a reliable source.
4. There are citations of the evidence that you are investigating
A ball is thrown vertically upward from the top of a 100-foot tower, with an initial velocity of 20 ft/sec. Its position function is s(t) = –16t2 + 20t + 100. What is its velocity in ft/sec when t = 1 second? (This is Calculus, involving limits, please help and explain, because I mostly just need to know how to do this. :) )
Final answer:
The velocity of the ball at t = 1 second is found by taking the derivative of the position function s(t) and evaluating it at t = 1. The derived velocity function is v(t) = -32t + 20, and the velocity at t = 1 second is 8 ft/sec.
Explanation:
The student wants to find the velocity of a ball at t = 1 second when thrown vertically upward from the top of a 100-foot tower with an initial velocity of 20 ft/sec. The position function given is [tex]s(t) = -16t^2 + 20t + 100[/tex]. To find velocity, we need to take the derivative of the position function with respect to time, which represents the velocity function v(t).
The derivative of the position function is:
v(t) = −32t + 20.
To find the velocity at t = 1 second, substitute 1 for t:
v(1) = −32×1 + 20 = −12 + 20 = 8 ft/sec.
Therefore, the velocity of the ball at t = 1 second is 8 ft/sec.
For how many positive integer values of x is the sum x^2+4x+4 less than 20?
Answer:
2 times
Step-by-step explanation:
Note that since we can only use positive integers for , the minimum will be x = 1. Testing x = 2, we get . Since , we know that only will work, thus, there are positive integer values of such that this function is less than 20.
Please help, an explanation would be really helpful too
What is the slope of a line that is perpendicular to the line whose equation is
2y = 3x - 1 ?????
At the fall festival the tennis team is selling hamburgers for $2.00, hotdogs for $1.50, and drinks for $1.00. Half of the money raised will go towards the purchase of team uniforms. If they sell 21 hamburgers, 34 hotdogs, and 65 drinks, how much money will they have to put towards the purchase of uniforms?
Graph the following inequality. Then click to show the correct graph. 3x - 2y ≤ 6
Solution:
The given inequality is :
3 x - 2 y ≤ 6
To draw the graph we will first draw the graph of line : 3 x - 2 y = 6
The graph of this function i.e 3 x - 2 y = 6 will be a straight line.
Then we will check whether origin lies on which side of line .
Put x=0, and y = 0 in the inequality 3 x - 2 y ≤ 6, we obtain
LHS = 0 ≤ 6
It means the line will contain the Origin.
Equation of line in Intercept form is : [tex]\frac{x}{2} -\frac{y}{3}\leq 1[/tex]
If 3 3/4 pounds of candy cost $20.25 how much would 1 pound of candy cost
Find the area of the circle with the given radius or diameter. Use = 3.14.
r = 4
A =
50.24 sq. units
100.48 sq. units
25.12 sq. units
Answer:
50.24 square units
Step-by-step explanation:
Hope this helps.
Hector drove 185 miles to a business meeting. His business partner drove 5/4 of this distance to get to the same
meeting. How many miles did the business partner drive?
An image point after a 180° rotation is Z'(3, 7). What were the coordinates of the pre-image point?
Z(-3, -7)
Z(7, 3)
Z(-7, -3)
Z(7, -3)
Given the function y-4=5/6(x-2), complete the table of values by entering the missing value.
Table:
X: -10 | -4 | -1 | ?
----------------------------
Y: -6 | -1 | 3/2 | 9
And how did you find the that Answer?
The odds against a spinner showing an even number are 3:8. What is the probability of the spinner showing an even number?
Probability is the likelihood or chance that an event will occur. If the probability of the spinner showing an even number if the odds against a spinner showing an even number are 3:8 is 8/11
What is probability?Probability is the likelihood or chance that an event will occur. The formula for calculating probability is expressed as:
Probability = expected/total outcome
If the odds against a spinner showing an even number are 3:8, the total number of spins is 11 spins
From the ratio
Number of odd spin = 3
Number of even spin = 8
Find the probability of spinning even
pr(even spin) = 8/11
Hence the probability of the spinner showing an even number if the odds against a spinner showing an even number are 3:8 is 8/11
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Chang is participating in a 4-day cross-country biking challenge. He biked for 70, 63, and 66 miles on the first three days. How many miles does he need to bike on the last day so that his average (mean) is
65miles per day?
Chang needs to bike 65 miles on the last day to have an average of 65 miles per day.
Explanation:To find how many miles Chang needs to bike on the last day, we need to find the total miles he has biked so far. So, we add up the miles he has biked on the first three days: 70 + 63 + 66 = 199 miles.
To find the average of 65 miles per day, we need to divide the total miles by the number of days: 199 / 4 = 49.75 miles per day.
Since Chang wants to have an average of exactly 65 miles per day, he needs to bike 65 miles on the last day. Therefore, he needs to bike 65 miles on the last day.
A student earned 23 out of 30 points on a quiz. What percent of the points did the student earn?
Julia spent 1/3 of her birthday money then she lost half of the rest now she has only $10 left how much did she get for her birthday
Final answer:
Working backwards from the $10 Julia has left after spending and losing money, we calculate that she initially had $30 for her birthday.
Explanation:
To find out how much birthday money Julia initially had, we can work backwards from the $10 she has left. Julia lost half of her money after spending 1/3 of it, which means that the $10 is half of what remained after spending 1/3. Therefore, before she lost half, she must have had $20 (since $10 is half of $20). We can then calculate the original amount by understanding that $20 is 2/3 (the remaining amount after spending 1/3) of the original amount. To find the full amount, we divide $20 by 2/3.
Here's the calculation step-by-step:
Let the original amount of birthday money be X.
Julia spent 1/3 of X, leaving her with 2/3 of X.
She then lost half of the remaining money, leaving her with (1/2)(2/3)X, which equals $10.
Solving for X: (1/2)(2/3)X = $10 -> (1/3)X = $10 -> X = $10 / (1/3) -> X = $10 × 3 -> X = $30.
Julia originally had $30 for her birthday.
Mike deposited $6500 into two saving accounts bearing simple interest. One of the accounts has an interest rate of 3% while the other rate is 6%. If the total interest earned after one year is $225, find the amount deposited into each of the accounts.
Simplify: (64x^5y^9z^8)^3/7
A $33$-gon $P_1$ is drawn in the Cartesian plane. The sum of the $x$-coordinates of the $33$ vertices equals $99$. The midpoints of the sides of $P_1$ form a second $33$-gon, $P_2$. Finally, the midpoints of the sides of $P_2$ form a third $33$-gon, $P_3$. Find the sum of the $x$-coordinates of the vertices of $P_3$.
1.2, 3, 7.5, 18.75, ...
Which formula can be used to describe the sequence?
f(x) = 1.2(2.5)x – 1
f(x) = 2.5(1.2)x – 1
f(x) = 1.2(2.5)x
f(x) = 2.5(1.2)x
It's geometric sequence:
[tex]a_1=1.2,\ a_2=3,\ a_3=7.5,\ a_4=18.75,\ ....[/tex]
Calculate the common ratio:
[tex]r=\dfrac{a_{n+1}}{a_n}\to r=\dfrac{3}{1.2}=2.5[/tex]
The explicit formula of geometric sequence:
[tex]a_n=a_1r^{n-1}\to f(x)=a_1r^{x-1}[/tex]
Substitute:
[tex]a_1=1.2,\ r=2.5\\\\f(x)=1.2\left(2.5)^{x-1}[/tex]
Answer: "f(x) = 1.2(2.5)x-1"
Answer:
AStep-by-step explanation:
100% righttt
Determine which system below will produce infinitely many solutions.
−6x + 3y = 18
4x − 3y = 6
2x + 4y = 24
6x + 12y = 36
3x − y = 14
−9x + 3y = −42
5x + 2y = 13
−x + 4y = −6
Answer:
The answer is C
[tex]3x-y=14\\-9x+3y=-42[/tex]
Step-by-step explanation:
In order to determine the system, we have to know the condition to produce infinitely solutions. A solution of a system is the coordinate (x,y) which is common between two lines ( in a 2D plane). A system does not have solution when the lines do not intercept each other, that it means, they are parallele. When two lines are coincident in all points, there are infinitely solutions.
I have attached an image that shows different systems of two lines.
So, to find the system, we have to find two equal equation. If we multiply by 3 the third system:
[tex]3x-y=14\\-9x+3y=-42\\\\(-3)*(3x-y)=(-3)*14\\(1)*(-9x+3y)=(1)*-42\\\\-9x+3y=-42\\-9x+3y=-42[/tex]
This system has infinitely solutions.
What is the mean of 82 64 73 91 85