Match the vocabulary word to its correct definition,
1. absolute value
2. continuous function
3. step function
4. piecewise-defined function
function whose graph has no breaks
function whose output equals input for non-negative numbers, and whose output is the opposite of a negative input
function defined on different intervals by different domain rules
function whose graph consists of horizontal line segments
Answer:
function defined on different intervals by different domain rules
hope it helps
The terms absolute value, continuous function, step function, and piecewise-defined function are matched with their respective definitions: the absolute value measures distance from zero, a continuous function has a graph without breaks, a step function has a graph with horizontal steps, and a piecewise-defined function has different rules for different intervals.
Matching Vocabulary to Definitions
Let's match each mathematical term to its correct definition:
Absolute value - This is the function whose output equals the input for non-negative numbers, and whose output is the opposite of a negative input. It can be thought of as the distance from zero on the number line, regardless of direction.
Continuous function - A function whose graph has no breaks is known as continuous. It means you can draw the function without lifting your pen off the paper, indicating it has no jumps or holes.
Step function - Such a function has a graph that consists of horizontal line segments. The value of the function changes in 'steps' rather than smoothly.
Piecewise-defined function - When a function is defined on different intervals by different domain rules, it is known as a piecewise-defined function. It's like having multiple functions strung together each applicable to different parts of the domain.
!!need answer asap!!
solve for x
Answer:
X= 0, X=-3, X=1
Step-by-step explanation:
Karen has $800 to open a checking account. She wants an account with the lowest fees. She only writes about five checks per month and her employer has direct deposit. She does not plan on using the ATM or online banking.
Answer:
account c
Step-by-step explanation:
took on quiz 100%
Answer: C. Account C
Step-by-step explanation:
What is the volume of the oblique cone shown? Round the answer to the nearest tenth
Hight of 25
Diameter of 15
Answer:
V=1472.6
Step-by-step explanation:
Volume of a cone=π*r^2*h/3
The volume of an oblique shape is the same as a non oblique shape. Also, 15/2 is our radius
V=π*r^2*h/3
V=π*7.5^2*(25/3)
V=pi*56.25*8.33333...
V=1472.62155637
V=1472.6
If the height and radius of the oblique cone are 25 units and 7.5 units. Then the volume of the oblique cone will be 1472.62 cubic units.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
If the height of the oblique cone is 25 units and the diameter of the cone is 15 units.
Then the volume of the oblique cone will be
Volume = 1/3 (πr²h)
Then the radius of the cone will be
r = 15/2
r = 7.5 units
Then the volume will be
Volume = 1/3 (π × 7.5² × 25)
Volume = 1/3 (4417.86)
Volume = 1472.62 cubic units
More about the geometry link is given below.
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uwu pls help :''( i may cry if you don't
Combine the like terms to create an equivalent expression:
−4q−(−8q)+10
1.So, what you do is remove the () from -8q.
2. Time -8q by one and it equals -8q.
3. Combined -4q and -8q, that equals -12q
4. Once you combine them create the equation which will be -12q+10 And that’s your answer because you can’t combine the 10 with any other number because -12q has a q. Hope this helps. And I’m sorry if I’m wrong >_<4q + 10 is the equivalent expression of −4q−(−8q)+10
What is an algebraic expression?An algebraic expression is one that has been constructed using integer constants, variables, and algebraic operations. For instance, the algebraic formula 3x² + 2xy + c
Given
-4q - (-8q ) + 10
using BODMAS
-4q + 8q +10
4q + 10
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Use common sense to determine whether the given event is impossible; possible, but very unlikely; or possible and likely.
At least two people have the same birthday in a school of 150 students.
Possible, but very unlikely
Impossible
Possible and likely
Answer:
Possible, but very unlikely
Step-by-step explanation:
In a school of 150 students, the probability that at least two people have the same birthday is possible but very unlikely.
In a year, we have 365 total possible birthdays. If one student was born on 1st of January say, then the second student has 364 possible birth-dates assuming that they have different birthdays. This implies there is a higher probability that the second student has a different birthday.
Moreover, considering the school has only 150 students which is less than the total possible birth-days in a year, 365, the chances of two or more students sharing a birthday is possible but would be very unlikely.
Final answer:
The event that at least two people have the same birthday in a school of 150 students is possible and likely, according to the principles of probability theory and the 'birthday paradox'.
Explanation:
In considering whether it is possible and likely that at least two people have the same birthday in a school of 150 students, we can refer to the birthday paradox. This mathematical probability phenomenon shows that, with just 23 people, there is a roughly 50% chance of two individuals sharing a birthday.
The probability increases significantly with each additional person to the point that in a group of 150 students, it is highly likely that at least two people will share the same birthday. This scenario is an interesting application of probability theory where our intuition might not align with the mathematical reality due to the non-intuitive properties of combinatorics and probability.
We do not arrive at this conclusion by adding probabilities of non-mutually exclusive events incorrectly, which would exceed 100% certainty. Instead, we calculate the probability of all students having unique birthdays, and subtract this from 1 to find the complement probability that at least two students share a birthday. This approach correctly keeps the calculated probability between 0 and 1, as per probability theory's third law.
In the case of 150 students, the calculated likelihood is so close to 1 (almost certain) that we can confidently classify the event as possible and likely.
the product of a number and -6 is at least 24. Write an inequality and solve the problem
Answer:
-6x ≥ 24
x = ≤ 4
Step-by-step explanation:
Number = x
The product of the number and -6.
-6x
The product is at least 24.
-6x ≥ 24
Solve the problem
-6x ≥ 24
Divide by -6 and we change the sign
x = ≤ 4
Answer:
Step-by-step explanation:
need help ASAP algebra 2 please !!!
Answer:
The answer is D.
Step-by-step explanation:
This is because the first part of the expression is the conjugate and youre given -5. The second part of the expression is the imaginary part and youre given 4i.
Answer:
C
Step-by-step explanation:
Given a complex number in the form
a + bi then the conjugate is a - bi
Note the real part remains unchanged while the sign of the imaginary part is negated.
Given
- 5 + 4i then the conjugate is - 5 - 4i → C
A spinner is numbered from 1 through 10 with each number equally likely to occur. What is the probability of obtaining a number less than 3 or greater than 8 in a single spin?
Answer:
[tex]P = 0.4[/tex]
Step-by-step explanation:
If each number X has the same probability of occur then the probability for each number is:
[tex]P = \frac{1}{10}[/tex]
Note that X is a discrete random variable, and the probability of obtaining an X number is independent for each trial.
So the probability that X is less than 3 is:
[tex]P (X <3) = P (1) + P (2)[/tex]
But [tex]P (1) = P (2) = \frac{1}{10}[/tex]
So:
[tex]P (X <3) = P (1) + P (2) = \frac{2}{10} = \frac{1}{5}[/tex]
Also
[tex]P (X> 8) = P (9) + P (10) = \frac{1}{10} = \frac{1}{5}[/tex]
Finally
[tex]P (X <3\ or\ X> 8) = \frac{1}{5} +\frac{1}{5} = \frac{2}{5} = 0.4[/tex]
Please help and thank you
Answer:
survey
Step-by-step explanation:
because she wants to know the opinions of the girls
Hi!
I think it would be a survey because then the people would give their opinions, which is what she wants.
Hope this helps!
An object with a mass of 120 kilograms is moving at a velocity of 60 m/s. What is its momentum? A. 2 kg-m/s B. 0.5 kg-m/s C. 7,200 kg-m/s D. 3,600 kg-m/s
Answer:
The correct answer is C) 7,200.
Step-by-step explanation:
In order to find the answer for this, start by using the formula for momentum.
Mo = M*V
Mo = 120 * 60
Mo = 7,200
The momentum is 7200 kg-m/s.
What is a Momentum?It is a product of mass and velocity.It is a vector quantity with both direction and magnitude.
Given: An object
Mass = 120 kg
Velocity = 60 m/s
We have to find the momentum of an object.
We know, momentum is given by:
⇒ Momentum = Mass × Velocity
⇒ Momentum = 120 × 60
⇒ Momentum = 7200 kg-m/s
Therefore, the momentum of an object is 7200 kg-m/s.
Hence, option (C) is correct.
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Use the diagram below to answer questions 1-3
Answer:
1.) ∠GAC and ∠CAF are complementary and acute angles
2.) 27°
3.) m∠CAG+m∠GAD=180°
Step-by-step explanation:
2.) because you solve for x:
63°+x°=90°
x= 27°
An office supply store has five different packages of thumb tacks. Which is the best deal available on thumb tacks at this office supply?
what is the scale factor of ABC XYZ
Answer:
A
Step-by-step explanation:
To calculate the scale factor k, find the ratio of corresponding sides
[tex]\frac{XZ}{AC}[/tex] = [tex]\frac{18}{3}[/tex] = 6
[tex]\frac{YZ}{BC}[/tex] = [tex]\frac{24}{4}[/tex] = 6
Hence the scale factor k = 6 → A
Answer: The correct option is (A) 6.
Step-by-step explanation: We are given to find the scale factor of dilation from triangle ABC to triangle XYZ.
From the figure, we note that
The lengths of the sides of triangles ABC and XYZ are as follows :
AB = 5 units, BC = 4 units, AC = 3 units, XY = 30 units, YZ = 24 units and XZ = 18 units.
We know that
[tex]\textup{Scale factor}=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.[/tex]
Therefore, for the given triangles, we get
[tex]\textup{Scale factor}=\dfrac{XY}{AB}=\dfrac{30}{5}=6.[/tex]
Thus, the required scale factor of dilation is 6.
Option (A) is CORRECT.
Use the remainder theorem to divide 5x^2+9x-2 by x+3. what is the remainder?
A)16
B)-44
C)-20
D)40
Answer:
A)16
Step-by-step explanation:
Given
f(x)=5x^2+9x-2
Remainder theorem states that when f(x) is divided by x-a then the remainder can be calculated by calculating f(a).
Now Using the remainder theorem to divide 5x^2+9x-2 by x+3 to find the remainder:
f(x)=5x^2+9x-2
f(-3) = 5(-3)^2 +9(-3) -2
=5(9) - 27 -2
= 45-29
= 16 !
What is the completely factored form of x4 + 8x2 – 9?
ANSWER
[tex] ( {x}^{2} + 9)({x} - 1)(x + 1)[/tex]
EXPLANATION
The given function is
[tex] {x}^{4} + 8 {x}^{2} - 9[/tex]
Split the middle term
[tex] {x}^{4} + 9 {x}^{2} - {x}^{2} - 9[/tex]
Factor by grouping;
[tex]{x}^{2} ( {x}^{2} + 9) -1 ({x}^{2} + 9)[/tex]
Factor further to get:
[tex] ( {x}^{2} + 9)({x}^{2} - 1)[/tex]
Apply difference of two squares to get:
[tex] ( {x}^{2} + 9)({x} - 1)(x + 1)[/tex]
Answer:
[tex](x^2+9)(x-1)(x+1)[/tex]
Step-by-step explanation:
We would need to let u = x^2 and use middle term factorization first. let's do this:
if u = x^2, then x^4 + 8x^2 – 9 would be
u^2+8u-9
Middle term factorization of this is:
(u+9)(u-1)
now replacing back u = x^2:
(x^2+9)(x^2-1)
Using the formula a^2 - b^2 = (a+b)(a-b), we can write (x^2 - 1) as (x+1)(x-1).
So, the final factored form is: (x^2+9)(x-1)(x+1)
What is the answer to this question????????
Answer:
a.
Step-by-step explanation:
The key thing to look for here is the vertex. The vertex is the middle of the graph. In the graph, the vertex is located as (2,3)
To write your equation, use the formula y = a|x-h|+k. (h,k) is your vertex [h is the x-coordinate k is the y-coordinate]. So, substitute your vertex into the equation.
[Notice the equation says -h, not h. That's why you have to put -2 into the equation, not positive 2.]
So, your equation will be y=|x-2|+3.
I hope this helps!
In the fall you charge people $8 for going to their house to pick fruits, then $5 for every hour you pick. If you make $28 one day, how many hours did you spend picking?
Answer: 4 hours
Step-by-step explanation: 20-8=20
20/5= 4hours
A bike ramp is shown in the figure. What is theta, the bike ramp's angle of elevation? Round your answer to the nearest degree. Enter your answer in the box.
Answer:
Ф = 14° ⇒ to the nearest degree
Step-by-step explanation:
* Lets revise the trigonometry functions
- Assume that we have a right triangle ABC
∵ m∠B = 90°
∴ AC is the hypotenuse ⇒ opposite to the right angle
∴ AB and BC are the legs of the right angles
- Let angle ACB called Ф
∵ sinФ = opposite/hypotenuse
∴ sinФ = AB/AC
∵ cosФ = adjacent/hypotenuse
∴ cosФ = BC/AC
∵ tanФ = opposite/adjacent
∴ tanФ = AB/BC
* Now lets solve the problem
- We will consider the bike ramp is the ΔABC
∵ AB = 1.5 feet
∵ ∠ACB is Ф
∵ The length of the ramp is the hypotenuse
∴ AC = 6 feet
- W have the length of the opposite to Ф and the hypotenuse
∴ We will chose the sin function
∵ sinФ = AB/AC
∴ sinФ = 1.5/6 ⇒ use the inverse of sin to find Ф
∴ Ф = sin^-1 (1.5/6) = 14.47 ≅ 14° ⇒ to the nearest degree
Answer:
14°
Step-by-step explanation:
Looking at the triangle with green border,
with respect to the angle [tex]\theta[/tex], the side 1.5 ft is "opposite" and the side 6 ft is "hypotenuse" of the triangle.
Which trigonometric ratio relates opposite with hypotenuse? It is sine. Thus we can write:
[tex]Sin\theta=\frac{opposite}{hypotenuse}=\frac{1.5}{6}=0.25\\Sin\theta=0.25\\\theta=Sin^{-1}(0.25)=14.48[/tex]
Hence, the angle is 14.48°
rounded to nearest degree, it is 14°
Type the correct answer in each box. A circle is centered at the point (-7, -1) and passes through the point (8, 7). The radius of the circle is units. The point (-15, ) lies on this circle.
Answer:
r = 17 units
Step-by-step explanation:
The radius is the distance from the centre (- 7, - 1) to the point on the circle
(8, 7)
Use the distance formula to calculate the radius (r)
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 7, - 1) and (x₂, y₂ ) = (8, 7)
r = [tex]\sqrt{(8+7)^2+(7+1)^2}[/tex]
= [tex]\sqrt{15^2+8^2}[/tex]
= [tex]\sqrt{225+64}[/tex]
= [tex]\sqrt{289}[/tex] = 17 units
What is the slope of the line that contains the points (-1,2) and (3,3)?
Answer:
1/4
Step-by-step explanation:
To find the slope of a line from two points we use
m = (y2-y1)/(x2-x1)
m = (3-2)/ (3--1)
= (3-2)/(3+1)
=1/4
Step-by-step explanation:
A(-1,2) and B(3,3) then AB=(4,1).
Normal vector
n=(-1,4)
Our line contains point A(-1,2) and has normal vector n=(-1,4) is
[tex](d) : - 1(x + 1) + 4(y - 2) = 0[/tex]
[tex](d ): - x - 1 + 4y - 8 = 0[/tex]
[tex](d) : - x + 4y - 9 = 0[/tex]
an original piece of artwork is 3 feet by 2.5 feet. A reprint of the artwork is 6 inches by 5 inches. Are the pieces similiar? If so, what is the ration of their corresponding side lengths?
Answer:
Yes
Explaination:
They are similar and the ratio is still the same. The artwork's shape didn't change we just resized it by multiplyting its length and width by 2.
In this triangle, cosA/cosB =
Random answers will be reported!
Answer:
cosA/cosB = 1
Step-by-step explanation:
We know that cos = Adjacent Side/hypothenuse.
Then Cos(A)= AC/AB = 3/4.24 = 0.707
Cos(B) = BC/AB = 3/4.24 = 0.707
Then cosA/cosB = 0.707/0.707 = 1
Answer:
The correct answer is
CosA/CosB =1
Step-by-step explanation:
Points to remember
Trigonometric ratios
Cos θ = Adjacent side/Hypotenuse
From the figure we can see a right angled triangle.
To find the value of CosA/CosB
CosA = Adjacent side/Hypotenuse
=AC/AB = 3/4.24
Cos B = Adjacent side/Hypotenuse
= BC/AB = 3/4.24
CosA/CosB = (3/4.24)/(3/4.24) = 1
Therefore the value of CosA/CosB = 1
given that (-4,-4) is on the graph of f(x), find the corresponding point for the function 1/2 f(x)
Answer:
(-4, -2)
Step-by-step explanation:
The x-coordinate would stay the same, but the y-coordinate would be halved. Thus, the corresponding point would be (-4, -2).
The system of equations y=-1/2 x + 4 and y= 2x - 1 is shown on the graph below According to the graph what is the solution to this system of equations?
Answer:
the answer is where the 2 points intersect... A. (2,3)
Step-by-step explanation:
Answer:
The correct option is A.
Step-by-step explanation:
The given system of equations is
[tex]y=-\frac{1}{2}x+4[/tex]
[tex]y=2x-1[/tex]
All the points on a line is are the solutions of the equation of line.
From the graph it is clear that the lines intersect each other at point (2,3). It means both the lines passes through the point (2,3) and point (2,3) is the solution of given system of equations.
Since (2,3) is the solution of given system of equations, therefore the correct option is A.
Luna had $50 when she got to the carnival.After riding 12 rides, she had $26 left. What was the price of each ride?which equation could be used to represent this situation?
Answer:
I'm not sure but I believe it's 50-12p=26
Step-by-step explanation:
Answer:
The third box: (50-12p=26)
Step-by-step explanation:
50-12p=26
-12p=26-50
-12p=-24
p=2
The price of each ride was $2.
Since the other answers gave you a negative, it would not have given you thr right answer.
25% of the students at school A got a score greater than 25 but less than or equal to 28
if you have the total number of students at School A, you can find out how many students scored between 26 and 28 by multiplying that number by 0.25.
To interpret this statement, let's break it down:
1. **25% of the students:** This refers to a percentage of the total number of students at School A. It means that out of all the students at School A, 25% fall into the category described next.
2. **got a score greater than 25 but less than or equal to 28:** This describes a range of scores. Specifically, it indicates that the students in question scored above 25 but equal to or less than 28.
Putting it together, the statement means that among all the students at School A, 25% of them scored between 26 and 28 (inclusive).
If we represent the total number of students at School A as \( N \), then the number of students who scored between 26 and 28 would be [tex]\( 0.25 \times N \)[/tex]since 25% is equivalent to[tex]\( \frac{1}{4} \).[/tex]
Therefore, if you have the total number of students at School A, you can find out how many students scored between 26 and 28 by multiplying that number by 0.25.
complete question:-
25% of the students at School A got a score greater than 25 but less than or equal to 28.
Find the value of each variable
Answer:
The correct answer is option C
a = 10√3, b = 5√3, c = 15 and d = 5
Step-by-step explanation:
Points to remember
The angles of a right angled triangle, 30°, 60° and 90° then sides are in the ratio, 1: √3 : 2
To find the value of variables
From the figure we can see 2 right angled triangle with angle 30, 60 and 90
we get, d= 5 then b = 5√3
b = 5√3 the c = 5√3 * √3 = 15
and a = 2 * 5√3 = 10√3
Therefore the correct answer is option C
a = 10√3, b = 5√3, c = 15 and d = 5
Answer:
d.[tex]a=10\sqrt3,b=5\sqrt3,c=15,d=5[/tex]
Step-by-step explanation:
We have to find the value of each variable.
[tex]\frac{P}{H}=sin\theta[/tex]
[tex]\frac{b}{10}=sin 60^{\circ}[/tex]
[tex]\frac{b}{10}=\frac}\sqrt3}{2}[/tex]
[tex]b=10\times \frac{\sqrt3}{2}=5\sqrt3[/tex]
[tex]\frac{d}{10}=cos 60^{\circ}[/tex] ([tex]cos\theta=\frac{base}{hypotenuse}[/tex])
[tex]d=\frac{1}{2}\times 10=5[/tex]
[tex]\frac{b}{a}=sin30^{\circ}[/tex]
[tex]\frac{5\sqrt3}{a}=\frac{1}{2}[/tex]
[tex]a=10\sqrt3[/tex]
[tex]\frac{b}{c}}=tan 30^{\circ}[/tex] ([tex]tan\theta=\frac{p}{b}[/tex])
[tex]\frac{5\sqrt3}{c}=\frac{1}{\sqrt3}[/tex]
[tex]c=5\sqrt3\times \sqrt3=15[/tex]
[tex]a=10\sqrt3,b=5\sqrt3,c=15,d=5[/tex]
Hence, option d is true.
Identify the corresponding word problem given in the inequality x less than or equal to 4.50
Answer:
[tex]\boxed{x \leq 4.50}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rrcl}\textbf{Words:} & \text{x} & \text{less than or equal to} & \text{4.50}\\\textbf{Symbols:} & x & \leq & 4.50\\\end{array}[/tex]
Answer:
Step-by-step explanation:
Find the missing measurements for the rectangle when the area equals 216 and the perimeter equals 66
[tex]\bf \stackrel{\textit{perimeter of a rectangle}}{P=2(L+w)}~~ \begin{cases} L=length\\ w=width\\ \cline{1-1} P=66 \end{cases}\implies 66=2(L+w) \\\\\\ 33=L+w\implies \boxed{33-w=L} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of a rectangle}}{A=Lw}\qquad \implies 216=Lw\implies 216=(33-w)w \\\\\\ 216=33w-w^2\implies w^2-33w+216=0 \\\\\\ (w-24)(w-9)=0\implies w= \begin{cases} 24\\ 9 \end{cases}[/tex]
now, both values are valid, so if "w" is either one, "L" is the other.