Answer:
1. Absolute value: function whose output equals input for non-negative numbers, and whose output is the opposite of a negative input
2. Continuous function: function whose graph has no breaks
3. Step function: function whose graph consists of horizontal line segments
4. Piecewise-defined function: function defined on different intervals by different domain rules
Step-by-step explanation:
Answer:
Step-by-step explanation:Absolute value: function whose output equals input for non-negative numbers, and whose output is the opposite of a negative input
2. Continuous function: function whose graph has no breaks
3. Step function: function whose graph consists of horizontal line segments
4. Piecewise-defined function: function defined on different intervals by different domain rules
what is the graph of the function f(x)=3x^2+2x+10/x+3
Answer:
Use Desmos, it is an online graphing calculator. You just input the function and you can play around with the graph.
This screenshot is from that :
A function assigns the values. The graph of the function can be made as shown in the image below.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
For the given function, the graph can be made as shown below. The graph of the function is a parabola with the vertex at (0.215, 3.287).
Also, the parabola opens upwards, this is because the leading coefficient of the function is positive.
Further, the graph never touches the x-axis of the graph because the roots of the parabola are imaginary, which can be known by calculating the discriminant.
Hence, the graph of the function can be made as shown in the image below.
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To make a profit, Ethan knows that his prime cost of producing a part must be no more than $189.27. It takes 2 hours for a machinist to make the part. The direct cost of materials is $98.62. To the nearest dollar, what can he afford to spend on direct labor costs per hour?
Answer:
$45/h
Step-by-step explanation:
So, we have a total maximum cost for the finished product and we have the raw material costs... but we need to figure out the maximum labor cost (for 2 hours).
We can express this as follows (remember it takes 2 hours of labor):
98.62 + 2x <= 189.27
2x <= 90.65
x <= 45.325
Rounded to the nearest dollar: $45
The maximum cost Ethan can afford in labor is $45/h for the 2 hours machining of the parts.
Which function represents the graph of h(x)=2|x+3|−1 after it is translated 2 units right?
pleaseeeeee help me
a. f(x)=2|x+3|−3
b. f(x)=2|x+5|−1
c f(x)=2|x+3|+1
d. f(x)=2|x+1|−1
[tex]\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}[/tex]
[tex]\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}[/tex]
[tex]\bf ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]
now with that template in mind
[tex]\bf h(x)=\stackrel{A}{2}|\stackrel{B}{1}x+\stackrel{C}{3}|\stackrel{D}{-1}\qquad \qquad \stackrel{\textit{C=C-2 a translation to the right}}{h(x)=2|x\boxed{+3-2}|-1} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill h(x)=2|x+1|-1~\hfill[/tex]
Using shifting concepts, it is found that the equation after a translation of 2 units to the right is:
d. f(x)=2|x+1|−1
The parent function is:
[tex]h(x) = 2|x + 3| - 1[/tex]
Shifting a function 2 units to the right, the equivalent function is:
[tex]f(x) = h(x - 2)[/tex]
Then:
[tex]h(x - 2) = 2|x - 2 + 3| - 1[/tex]
[tex]f(x) = 2|x + 1| - 1[/tex]
Thus, the function is:
d. f(x)=2|x+1|−1
A similar problem is given at https://brainly.com/question/24465194
Freya is training for a track race. She starts by sprinting 200 yards. She gradually increases her distance, adding 5 years a day for 21 days. Which explicit formula models this situation?
Freya begins started with 200 yards.
Freya then increased her distance by adding five yards a day for two days.
x = 200 + (n - 1)5.
[x = The distance Freya sprints on day 21]
x = 200 + (21 - 1)5
x = 200 + (20) 5 = 300 yards
Answer:
[tex] a _ n = 200 + ( n - 1 ) 5 [/tex]
Step-by-step explanation:
We are given that initially, Freya started with sprinting 200 yards and then gradually increased the distance by adding 5 yards a day for 21 days.
So our initial value for distance is [tex]a_1=200[/tex]
and since she keeps on adding 5 yards everyday to her distance so this will be our common difference.
Therefore, the explicit formula will be:
[tex]a_n=200+(n-1)5[/tex]
Amy has a box containing 6 white, 4 red, and 8 black marbles. She picks a marble randomly. It is red. The second time, she picks a white marble. In the third attempt, Amy picks a white marble again. Amy has not replaced the marbles she picked.
not really sure what the question is but if your question is but if ur question is asking what the possiblity is, the answer should be a possiblity of 8/15 for picking a black marble. If Amy picks a black marble in the fourth attempt, the probability of the fifth attempt she will pick a red or a black marble is 5/7
What is the slope of the line 2x – 5y = 12 ?
Answer:
2x−5y=12
y = 2/5x + −12/5
Answer is x = 5/2y + 6 because....
First, Add 5y to both sides.
2x − 5y + 5y = 12 + 5y
Then, Divide both sides by 2.
[tex]\frac{2x}{2} = \frac{5y+12}{2}[/tex]
Therefor, your answer is going to be x = 5/2y + 6
* Hopefully this helps:) Mark me the brainliest:)!!!
Answer:
2/5
Step-by-step explanation:
We are given the following equation of a line and we are to tell the slope of the line:
[tex]2x-5y=12[/tex]
We know that the standard equation of a line is given by:
[tex] y = m x + c [/tex] where m is the slope of the line.
So re-writing the given equation in the standard form:
[tex]y=\frac{2}{5} x-\frac{12}{5}[/tex]
Therefore, 2/5 is the slope of the line.
what is 4325000 in scientific notation
It is 4.325 • 10^6 (thats ten to the sixth power :))
Hence 4325000 in scientific notation is [tex]4.325 \times 10^6[/tex]
The standard form of scientific notation is expressed as:
[tex]A \times 10^n[/tex] where:
A is any real number between 1 and 10n is any integerGiven the value 4325000
[tex]4325000 = 4 .324\times 10^6[/tex]
Note that the decimal point was shifted to the left 6 times to have [tex]4.325 \times 10^6[/tex]
Hence 325000 in scientific notation is [tex]4.325 \times 10^6[/tex]
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Which modified box plot represents the data set? 10, 12, 2, 4, 24, 2, 7, 7, 9
The fourth option is the answer. When graphed, Min is 2, Q1 is 3, Median is 7, Q3 is 11, and Max is 24. The fourth option is the one that follow all of those!
Answer:
(D)
Step-by-step explanation:
The given data set is:
10, 12, 2, 4, 24, 2, 7, 7, 9
Firstly arrange the given data set in ascending order, we get
2, 2, 4, 7, 7, 9, 10, 12, 24
Now, the median of the above given data set is:
[tex]Median=7[/tex]
The upper quartile is:
9, 10, 12, 24
thus, [tex]LQ=\frac{10+12}{2}=\frac{22}{2}=11[/tex]
The lower quartile is:
2, 2, 4, 7
thus, [tex]LQ=\frac{2+4}{2}=3[/tex]
The highest value of the given data set is 24 and the lowest value is 2.
Therefore, option D is correct.
3/8 *5/6 pls help asap
Answer:
5/16
Step-by-step explanation:
It's a little easier when you write the problem like this:
3 5
----- · -----
8 6
Now reduce that 3/6 to 1/2:
1 5
----- · ----- = 5/16
8 2
Hello There!
We are given the fraction 3/8 multiplied by 5/6.
Step 1. First, we multiply across so we multiply 3*5 which is 15 and then we multiply 8*6 which equals 48.
Step 2. Both of these can be divided by 3 so we can put the fraction that we already have in simplest form. Dividing 15 by 3 equals 5 and dividing 48 by 3 equals 16.
Final step. We now have our simplified fraction which is 5/16.
Have a great day!
Be safe!
TheBlueFox
someone help me out. i could use it please. O is inscribed in ABC , which has a perimeter of 76 cal. What is the length of CE?
Answer:
C.E=18 cm
Step-by-step explanation:
we know that
If the circle O is inscribed in triangle ABC
then
A.F=A.D=6 cm
B.D=B.E=14 cm
C.F=C.E=?
The perimeter of triangle is equal to
P=2(6)+2(14)+2(C.E)
P=76 cm
so
76=2(6)+2(14)+2(C.E) -----> solve for C.E
76=12+28+2C.E
2C.E=76-40
C.E=36/2
C.E=18 cm
change the mixed expressions into fractions
y-1- 5/y+3
To change the mixed expression into a fraction, rewrite the mixed number as an improper fraction. Find the common denominator and combine the fractions by subtracting the second fraction from the first fraction.
Explanation:To change the mixed expression into a fraction, we need to first rewrite the mixed number as an improper fraction.
The mixed number y-1 can be written as (y-1)/1.
Then, we can rewrite the expression as ((y-1)/1) - (5/(y+3)).
To combine these fractions, we need to find a common denominator.
The common denominator is (y+3), so we need to multiply the first fraction by (y+3)/(y+3) and the second fraction by 1/1.
This gives us ((y-1)(y+3))/((y+3)(1)) - (5/(y+3)).
Now, we can combine the fractions by subtracting the second fraction from the first fraction.
This gives us (((y-1)(y+3))-5)/(y+3).
Final answer:
To change the mixed expression into a fraction, find a common denominator and simplify the expression.
Explanation:
To change the mixed expression into a fraction, we need to find a common denominator.
The common denominator for the given expression y-1 and 5/y+3 is (y+3). To convert y-1 to have the common denominator, we multiply the numerator and denominator by (y+3), resulting in (y+3)(y-1)/(y+3). Next, we can simplify the expression by multiplying out the numerator and combining like terms. The final fraction is (y² + 2y - 3)/(y+3).
Can someone please help me with this
Answer:
No. A y-intercept equation forms a straight line. The points given in the graph do not form a straight line. So the answer is no.
Answer: y = mx + b, i think yes
Step-by-step explanation:
Simplify 4!
A.24
B.10
C.9
D.4
Answer:
The answer would be d
Step-by-step explanation:
The value of given factorial 4! in the given problem is A. 24.
In mathematics, the factorial of a non-negative integer, denoted by the symbol "!", is the product of all positive integers less than or equal to that number. It is a fundamental mathematical operation used in combinatorics, probability theory, and other areas of mathematics.
Factorials have various applications, such as counting the number of permutations and combinations, calculating probabilities, solving equations, and representing coefficients in mathematical series. They are also used in formulae for binomial coefficients, as well as in calculus and other areas of mathematics.
4! = 4 [tex]\times[/tex] 3 [tex]\times[/tex] 2 [tex]\times[/tex] 1
= 24
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Please answer right away
Answer:
20 miles with an error margin of ± 8 miles
Step-by-step explanation:
The margin of error of a result is the range in which an error can vary. To find the margin of error between both distances we have to
28-12 = 16, that is, the variation of the result has a range of 16 miles. So we will look for the midpoint of both distances
(X2-X1)/2+X1=(28-12)/2+12=16/2+12=8+12=20
So from this midpoint the value can vary between 8 points below and 8 points above that would cover the difference of 16 miles that we observed at the beginning
In this way, the correct answer is 20 miles with an error margin of ± 8 miles
Done
There are two numbers whose sum is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers?
18 and 35. The numbers whose sum 53 are 18 and 35.
The key to solve this problem is using a system of equations.
There are two numbers whose sum is 53. This number can be represented as x and y. So:
x + y = 53
Three times the smaller number is equal to 19 more than the larger. Let's set x as the smaller number and y the larger number. So:
3x = 19 + y
Clear y in both equations and let's use the equalization method to solve for x:
y = 53 - x and y = 3x - 19
Then,
53 - x = 3x - 19
53 + 19 = 3x + x ---------> 3x + x = 53 + 19 -------> 4x = 72
x = 72/4 = 18
To find y, let's substitute x = 18 in the equation x + y = 53
18 + y = 53 --------> y = 53 - 18
y = 35
Which function represents g(x), a reflection of f(x) = (3)x across the y-axis?
g(x) = 2(3)x
g(x) = −(3)x
g(x) = (3)−x
g(x) = 2(3)-x
Answer: g(x)=(3)-x
to reflect across the y-axis is to change the x coordinate values to opposite of what it is originally. ie;
f(x)=(3)x Now for a reflection across y-axis
g(x)=(3)-x
Answer:
[tex]g(x)= 3^{-x}[/tex]
Step-by-step explanation:
Given parent function is [tex]f(x)= 3^x[/tex]
we need to find a function that is a reflection across y axis
For f(x) , reflection across y axis
f(x) becomes f(-x)
For reflection across x axis, we multiply negative sign with x
f(x) becomes f(-x)
[tex]f(x)= 3^x[/tex] becomes [tex]f(x)= 3^{-x}[/tex]
Replace f(x) with g(x)
[tex]g(x)= 3^{-x}[/tex]
How does multiplying a vector by a scalar value of -pi / 4 change the vector?
The answer is:
The second option:
The vector will change direction and decrease in magnitude.
Why?Multiplying a vector by a scalar will modify the magnitude of the vector, depending if the scalar is less or greater than "1" also, when a scalar has a negative sign, the direction of the new vector will be the opposite that the original vector.
Solving
We are given that the scalar value is equal to:
[tex]-\frac{\pi }{4}=-0.79[/tex]
Let's use as original vector, the following vector:
[tex]A=(2,2)[/tex]
Calculating its magnitude, we have:
[tex]|A|=\sqrt{2^{2} +2^{2} }=2.83[/tex]
Then, multiplying the vector by the given scalar, we have:
[tex](-0.79A)=((-0.79)*2,-(0.79)*2)=(-1.58,-1.58)[/tex]
As we can see, the vector changed its direction, since both components are negative.
Calculating the magnitude of the new vector, we have:
[tex]|A'|=\sqrt{(-1.58)^{2} +(-1.58)^{2} }=2.23[/tex]
We can see that the given scalar is less than "1", so the magnitude will decrease, also, the direction is the opposite of the original vector direction since both components have changed its sign.
Hence, we have that the magnitude of the new vector is less than the magnitude of the original vector, also, we can see that the direction of the new vector is the opposite of the original vector direction, so, the answer is the second option, the vector will change direction and decrease in magnitude.
Have a nice day!
ANSWER ASAP !! TIMED!! Which property is shown in the matrix addition below?
associative property
identity property
inverse property
commutative property
Answer:
yes inverse property
Step-by-step explanation:
Because they all are inverse to each other or oposite
Plz help me with this
Answer:
x = 2Step-by-step explanation:
Look at the picture.
how do i write a proportion?
Answer:
Ratios and Proportions - Proportions - In Depth. A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d; or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."
Step-by-step explanation:
Please really need help on this
Answer:
x = 8
3rd choice
Step-by-step explanation:
https://mathbitsnotebook.com/Geometry/Trigonometry/TGTrigSineCosine.html
A teacher is randomly calling on students in a class. If there are 6 girls and 6 boys in the class, what is the theoretical probability that the first 3 people called on are all girls?
The probability of calling three girls consecutively in a mixed class will be 1/22.
There are 12 students in total.
The probability of the first student being a girl is 6 / 12 = 1/2.
After one girl has been chosen, there are now 5 girls left and a total of 11 students.
So, the probability of the second student being a girl is 5 / 11.
With one more girl removed, there would be 4 girls left and 10 students in total.
The probability of the third student being a girl then is 4 / 10 = 2/5.
To find the overall probability of all three events happening in sequence, we multiply the probabilities of each event:
Probability = (1/2) x (5/11) x (2/5)
= 1/22
The theoretical probability that the first 3 students called are all girls is: [tex]\[\boxed{\frac{1}{11}}\][/tex].
Given a class of 12 students, consisting of 6 girls and 6 boys, we are to determine the probability that the first 3 students called are all girls.
First, we calculate the total number of ways to select any 3 students out of 12. This is given by the combination formula:
[tex]\[\binom{12}{3} = \frac{12!}{3!(12-3)!} = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220\][/tex]
Next, we calculate the number of ways to select 3 girls out of the 6 available girls:
[tex]\[\binom{6}{3} = \frac{6!}{3!(6-3)!} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20\][/tex]
The theoretical probability that the first 3 students called are all girls is the ratio of the number of ways to choose 3 girls to the total number of ways to choose any 3 students. Thus, the probability \(P\) is:
[tex]\[P = \frac{\binom{6}{3}}{\binom{12}{3}} = \frac{20}{220} = \frac{1}{11}\][/tex]
in one month a store had 1222 in sales but expenses were 2345 how much money did the store lose in that month
Answer:
$1,123
Step-by-step explanation:
Remember that the profit or loses of a business is given by the subtraction between the revenue and the expenses. In our case the revenue is sales, so:
[tex]profit=sales-expenses[/tex]
[tex]profit=1222-2345[/tex]
[tex]profit=-1123[/tex]
Since the profit is negatives, the business is losing money.
We can conclude that the store lose $1,123 that month
The store lost $1,123 in the given month, which is calculated by subtracting their total expenses of $2,345 from their total sales of $1,222.
To calculate the amount of money the store lost in a month, we need to subtract the expenses from the sales. The formula to find the loss or profit is Profit (or Loss) = Sales - Expenses.
In this scenario:
Sales for the month are $1,222.Expenses for the month are $2,345.Subtract the expenses from the sales: Profit (or Loss) = $1,222 - $2,345.When you perform the subtraction: $1,222 - $2,345 = - $1,123.
The store therefore experienced a loss of $1,123 for that month.
Two families go to the cinema.
The Smith family buy tickets for one adult and four children
and pay £19
The Jones family buy tickets for two adults and two children
and pay £17
What is the cost of one child’s ticket?
Answer:
Step-by-step explanation:
x= cost of 1 adult ticket
y=cost of 1 kid ticket
so 1 adult+4 childeren=x+4y=19
2 adults and 2 childern=2x+2y=17
elimination
x+4y=19
2x+2y=17
multiply firest equation by -2
-2x-8y=-38
add to first equatuion
-2x-8y=-38
2x+2y=17 +
0x-6y=21
-6y=-21
multiply -2
6y=21
divide by 6
y=21/6=7/2
subsitute
2x+2y=17
2x+2(7/2)=17
2x+14/2=17
2x+7=17
subtract 7 from both sides
2x=10
divide by 2
x=5
1 adult ticket costs £5
1 kid ticket costs £7/2 or £3 and 1/2 or £3.5
hope this helps and give me brainliest pls
I need help please.
Answer:
5 ≥ 4
Step-by-step explanation:
PLEASE HELP ASAP, I WILL GIVE BRAINLESSLY ANSWER
SHOW WORK PLEASE
Answer:
C. [tex]N(t)=150\cdot 3^t[/tex]
Step-by-step explanation:
You are given the exponential function [tex]n(t)=ab^t.[/tex]
From the table, [tex]N(t)=150[/tex] at [tex]t=0,[/tex] thus
[tex]N(0)=a\cdot b^0\\ \\150=a\cdot 1\ [\text{ because }b^0=1][/tex]
Also [tex]N(t)=450[/tex] at [tex]t=1,[/tex] thus
[tex]N(1)=a\cdot b^1=a\cdot b.[/tex]
Since [tex]a=150,[/tex] substitute it into the second equation
[tex]450=150\cdot b\\ \\b=\dfrac{450}{150}\\ \\b=3[/tex]
and the expression for the exponential function is
[tex]N(t)=150\cdot 3^t[/tex]
Write(3-7i)-(-11+5i) as a complex number in standard form
The answer would be 14-12i. Hope this helps! Please mark brainliest! Thanks v much! :)
A sphere has a diameter of 9 inches.
What is the volume of the sphere rounded to the nearest tenth?
Use 3.14 for pi.
95.4 in:
331 6 in:
763.0 in
3052.1
The volume of a sphere with a diameter of 9 inches, using 3.14 for pi, is calculated using the formula V = (4/3)πr³. The radius is 4.5 inches, leading to a volume of 381.675 cubic inches, which rounded to the nearest tenth is 381.7 cubic inches.
Explanation:The question is asking for the volume of a sphere with a diameter of 9 inches, using 3.14 for pi. To find the volume, we first need to calculate the sphere's radius. Since the diameter is 9 inches, the radius (which is half the diameter) is 4.5 inches. The formula for the volume of a sphere is V = (4/3)πr³. Substituting the radius into the formula, we get:
V = (4/3)(3.14)(4.5³) = (4/3)(3.14)(91.125) = 381.675 cubic inches. When rounded to the nearest tenth, the volume is 381.7 cubic inches.
which graph represents the function
[tex]g(x) = \sqrt{x - 1} + 1[/tex]
Answer:
The bottom-left graph.
Step-by-step explanation:
g(1) = 0+1 = 1 => g(1) = 1
=> (1,1) ∈ Gf
The graph of the square root function is the bottom left graph.
which graph represents the function?We want to see which graph represents the function:
g(x) = √(x - 1) + 1
The first thing we can notice is that the domain of the function is:
x ≥ 1
We can see that when x = 1 the function becomes:
g(1) = √(1 - 1) + 1
g(1) = 1
So the first point of this function is (1, 1), like in the graph in the bottom left, so that is the correct option.
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Joe is riding his bike home. He begins 10 miles away from his house and is riding home at a speed of 0.25 miles per minute. Which function f(m) represents the distance he is away from his house given how many minutes m he has been riding?
Select one:
a. f(m)=10m−0.25m
b. f(m)=10−0.25m
c. f(m)=0.25+10m
d. f(m)=10+0.25m
The answer is:
The correct answer is:
d. [tex]f(m)=10+0.25*m[/tex]
Why?From the statement we know that he begins at 10 miles away from his house riding at a speed of 0.25 miles per hour (h)
We have that:
[tex]x_{f}=x_{o}+v*t[/tex]
Where,
[tex]x=FinalPosition\\x_{o}=InitialPosition\\v=speed\\t=time[/tex]
Now, using the given information we have that=
[tex]x_{f}=x_{o}+v*t[/tex]
[tex]x_{f}=10miles+0.25mph*m[/tex]
We have that:
[tex]x_{f}=f(m)[/tex]
So,
[tex]f(m)=10miles+0.25mph*m[/tex]
Hence, we have that the correct answer is:
d. [tex]f(m)=10+0.25*m[/tex]
Have a nice day!
Final answer:
The function that represents Joe's distance from his house after riding for m minutes is f(m) = 10 - 0.25m. Hence, the answer is B.
Explanation:
The correct function to represent the distance Joe is from his house after riding for m minutes is f(m) = 10 - 0.25m. This is because Joe starts 10 miles away from his house and rides towards it, reducing the distance by 0.25 miles every minute.
To form the function, you need to start with the initial distance, which is 10 miles. Since Joe is moving closer to his house, the distance decreases over time. Therefore, for every minute m that Joe rides, he covers 0.25 miles. Thus, the distance from home after m minutes is the initial distance minus the product of the speed and time, which gives us f(m) = 10 - 0.25m.