state the domain, the range, and the intervals on which function is increasing, decreasing, or constant in interval notation
Answers
Answer:
domain (-∞, ∞)range (-∞, 4]increasing (-∞, 0)decreasing (0, ∞)constant (only at x=0, not on any interval)Step-by-step explanation:
The graph is of the equation y = -x^2 +4. It is a polynomial of even degree, so has a domain of all real numbers: (-∞, ∞).
The vertical extent of the graph includes y=4 and all numbers less than that:
range: (-∞, 4]
The graph is increasing to the left of its vertex at x=0, decreasing to the right.
increasing (-∞, 0); decreasing (0, ∞)
There is no interval on which the function is constant. It has a horizontal tangent at x=0, but a single point does not constitute an interval.
Related Questions
One of the legs of a right triangle is twice as long as the other, and the perimeter of the triangle is 35. Find the
lengths of all three sides, to two decimal places.
i would appreciate if you showed work so i know how you did it!
Answers
Answer:
6.68, 13.37, 14.95
Step-by-step explanation:
One of the legs is twice as long as the other.
b = 2a
The perimeter is 35.
35 = a + b + c
The triangle is a right triangle.
c² = a² + b²
Three equations, three variables. Start by plugging the first equation into the second and solving for c.
35 = a + 2a + c
c = 35 − 3a
Now plug this and the first equation into the Pythagorean theorem:
(35 − 3a)² = a² + (2a)²
1225 − 210a + 9a² = a² + 4a²
1225 − 210a + 4a² = 0
Solve with quadratic formula:
a = [ -(-210) ± √((-210)² − 4(4)(1225)) ] / 2(4)
a = (210 ± √24500) / 8
a ≈ 6.68 or 45.82
Since the perimeter is 35, a = 6.68. Therefore, the other sides are:
b ≈ 13.37
c ≈ 14.95
The daily production cost, C, for x units is modeled by the equation: C = 200 – 7x + 0.345x2 Explain how to find the domain and range of C
Answers
range is the set of possible results for c(x), possible costs.
you can derive this from the fact that c(x) is a parabole and you can draw it, for which you can find the vertex of the parabola, the roots, the y intercept, the shape. also limit the costs to be positive.
you can substitute some values for x to help you, for example.
x y
0 200
1 200 - 7 + 0.345 = 193.345
2 200 - 14 + .345(4) = 187.38
3 200 - 21 + .345(9) = 182.105
the function does not have real roots, then the costs never decrease to 0.
the function starts at c(x) = 200, decreases until the vertex, (x = 10, c = 164.5) and starts to increase
then the range goes to 164.5 to infinity, limited to the solution for x = positive integers.
Answer:
This is a quadratic function, which is usually defined on all reals. But, the domain is restricted to x>=0 because it does not make sense to produce a negative number of units.
Find the vertex of the parabola at
(10.14, 164.5)
Since the parabola opens up, the range is y>=164.5
Step-by-step explanation:
PLZ ANSWER QUICKLY, I NEED THIS SOON, thx :) If m∠A = m∠B and m∠A + m∠C = ∠D, then m∠B + m∠C = ∠D. Which property is shown? reflexive property substitution property symmetric property transitive property
Answers
Answer:
Substitution Property
is the answer A),B),C) or D)?
Answers
Answer:
D) 2a-6
Step-by-step explanation:
Graham sold 6 less = -6
Than double what Adriania sold. = 2a
2a - 6
Trapezoid ABCD is reflected over the line y - x. What rule shows the input and output of the reflection, and what is the new coordinate of A (1 point)
B
0
A
(X,Y)--(-x): A is at (1,5)
(X,Y) (YX); A' is at (1-5)
(x,y)--(-x,y); A' is at (5, 1)
(x,y)--(-X, "): A' is at (5, -1)
Answers
Answer:
(x,y)--(-X, "): A' is at (5, -1)
Step-by-step explanat
Answer:
(x,y)→(−x,−y); A' is at (5, −1)
Step-by-step explanation:
F(1)=2
F(n)=-3f(n-1)+[f(n-1)]^2 ?
Answers
Answer:
Step-by-step explanation:
Umm
Whta is 80 - (-9) = explain pls
Answers
Answer:
80 - (-9) = 89.
Explanation:
In math, two negatives next to each other will become a positive. Since a negative number is being subtracted, The negatives will cancel.
So this:
80 - (-9)
Is functionally the same as this:
80 + 9
Therefore, the answer is 89.
A student has 2/3 quart of yellow paint in a container.The student uses 1/2 quart of the yellow paint to make green paint.How many quarts of yellow paint remains in the container after the student makes green paint?
Answers
Answer:
1/6
Step-by-step explanation:
2/3 - 1/2 = 4/6 - 3/6 = 1/6
1/6 quart remains.
Answer:
There are 1/6 quarts left in the container.
Step-by-step explanation:
You need to subtract 1/2 (the paint used) by 2/3 (the paint in the container)
First, find the LCD (lowest common denominator) if you want to subtract.
3 x 2 = 6; you do the same to the numerator 2 x 2 = 4
4/6 (paint in the container)
2 x 3 = 6; you do the same to the numerator 1 x 3 = 3
3/6 (paint used)
Now, you subtract.
4/6 - 3/6 = 1/6 quarts
At a game booth, a student gets a box of candy as the prize for winning a game. The boxes come in four colors: white, red, green, and blue. There are 8 boxes of each color. All the boxes are equally likely to be given away as prizes. Which expression shows the probability of the first winner receiving a white box and the second winner also receiving a box of the same color? (1 point) 8 over 32 multiplied by 8 over 31 8 over 32 plus 8 over 31 8 over 32 plus 7 over 31 8 over 32 multiplied by 7 over 31
Answers
Answer:
32 multiplied by 8 over 31 8 over 32 plus
Step-by-step explanation:
i think this is the answer not quite sure tho
Answer:
32 multiplied by 8 over 31 8 over 32 plus
Step-by-step explanation:
Now, graph the equation x - 2y = 7 below the
equation 8x - 4y = 56
What are the coordinates for x and y at the
intersection of the two lines?
Answers
Answer:
(7,0)
Step-by-step explanation:
2. A line or line segment perpendicular to a line segment at the midpoint of the segment is a...
Answers
Answer:
A segment is called a perpendicular bisector of another segment if it goes through the midpoint and is perpendicular to the segment. While there can be many segments that bisect another segment, only one segment can be the perpendicular bisector.
Step-by-step explanation:
perpendicular bisector
simplify 1/3(6x−12)+4x
Answers
Answer:
não sei....................
Need help answering question 4
Answers
Answer:
(-1,5)
Step-by-step explanation:
To find this, you have to add both "x" coordinates, then divide them by two.
Same thing goes for the "y" coordinates, add them, then divide them by two.
x-coordinates ---> 2+(-4)= -2
y-coordinates ---> 1+9= 10
-2÷2= -1
10÷2= 5
That gives you, (-1,5).
1) Students in Jake's class were numbered in order from 1 to 24. Jake was asked to
choose classmates numbered with multiples of 5 to be in his group. Which
number could be the number of a classmate in his group?
>) 15
>) 16
() 21
>)7
Answers
Answer:
15
Step-by-step explanation:
15 is the only number with a multiple of 5.
The Number of classmates in his group is less than 21
What is an inequality?An inequality is an inequation separated by <,>≥,≤. the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
Given here: Jake's class has 24 students and she is to choose a group which is a multiple of 5
Thus the possible multiples of 5 between 1 and 24 are
5,10,15,20
Therefore all these multiples are less than 21
Hence, The Number of classmates in his group is less than 21
Learn more about inequalities here:
https://brainly.com/question/28823603
#SPJ2
Please help I have this due by tomorrow
Answers
Answer:
1) Linear Pair
2) Adjacent
3) Complmentary
4) Vertical
Perform the indicated row operations
Answers
Answer:
[tex]\begin{bmatrix}2 & -1 & -4 & 7\\ 0 & -30 & 20 & -50\\ 0 & 30 & 24 & 6\end{bmatrix}[/tex]
Step-by-step explanation:
Given matrix is,
[tex]\begin{bmatrix}2 & -1 & -4 & 7\\ 0 & 3 & -2 & 5\\ 0 & 10 & 8 & 2\end{bmatrix}[/tex]
Operations performed,
-10R₂ → R₂
[tex]\begin{bmatrix}2 & -1 & -4 & 7\\ 0 & -30 & 20 & -50\\ 0 & 10 & 8 & 2\end{bmatrix}[/tex]
3R₃ → R₃
[tex]\begin{bmatrix}2 & -1 & -4 & 7\\ 0 & -30 & 20 & -50\\ 0 & 30 & 24 & 6\end{bmatrix}[/tex]
Answer:
the multiple choice is A
Step-by-step explanation:
What’s -86.4 divided by 3.2
Answers
Answer:
-27
Step-by-step explanation:
Answer:-27
Step-by-step explanation:
Miss bird can make 8 sculptures in 6 months. If she prepared 12 sculptures, how much time would she take
Answers
Answer:
9 months
Step-by-step explanation:
8 sculptures....... 6 months
12 sculptures...... X months
X=12 ×6 :8
X=72 :8
X=9 months
If you shift the quadratic parent function, f(x) = x2,right 12 units, what is the
equation of the new function?
A. g(x) = x² + 12
B. g(x) = x2 - 12
ООО
C. g(x) = (x - 12)
D. g(x) = (x + 12)
Answers
What is the value oíz in the equation 3x - y = 13, when y=272
05
45
Answers
I need help on this question please
Answers
Answer:
a, c, and f
Step-by-step explanation:
becuase i took the test
Solve for y in 2y + 5 = - 3y - 10.*
Answers
Answer:
y = -3
Step-by-step explanation:
2y +3y = -10 -5 (collect the terms then calculate)
5y = -15 ( divide both sides )
then you'll get your answer which is y = -3
Sonjesa found a job in advertising that pays a yearly salary of $47,300. What is her weekly salary?
$6,757.14
$909.62
$985.42
$3,941.67
Answers
Answer:
$909.62
Explanation:
If Sonjesa makes $47,300 a year and in a year there are 52 weeks we do the equation...
$47,300 / 52 weeks = weekly salary
47300 / 52 = 909.615
If we round that equals $909.62
Hope this helps!
For questions 12-17, determine whether each statement is always, sometimes, or never true.
12. TQ and QT are the same line.
13. JK and JL are the same ray.
14. Intersecting lines are coplanar.
15. Four points are coplanar.
16. A plane containing two points of a line contains the entire line.
17. Two distinct lines intersect in more than one point.
Answers
The table below shows the total cost of buying printer ink cartridges for both members and nonmembers of a shopping club. Price of Ink at Shopping Club Number of ink cartridges purchased Total cost for members (with membership fee) Total cost for nonmembers 0 $30 0 1 $40 $25 2 $50 $50 3 $60 $75 Which statement is supported by the table?
Answers
Answer:
B
Step-by-step explanation:
Answer:
the answer is a i did the quiz
Step-by-step explanation:
2. Which of these graphs represents a function?
Answers
Answer:
I think the first one.
Step-by-step explanation:
I need help in the simplest way!
Answers
Please include an explanation, i am confused. Thank you
Answers
Explanation:
Let's say,
(x1,y) (x2,y2)
are two points in a
xy
plane. We can find the shortest distance between two point by applying the distance formula stated as:
Distance
=√(x2−x1) 2+(y2−y1) 2
So by putting our given points
(x1,y1)=(6,−5) and (x2,y2)=(−1,−4)
in the distance formula, we have:
¯¯¯¯¯¯CD=√(−1−6)2+(−4−(5)2
Simplify to get:
5√2
The area of the football field is 57,600 square feet. If the width of the field is the length,what is the length of the football field?
Answers
Answer:
240
Step-by-step explanation:
57600=10×24×10×24
Angle 1 and Angle 2 form a linear pair. If m41 = (5x + 9)® and m22 = (3x + 11)", find the measure of
each angle.
Answers
Answer:
2/23/140+50ismmm/50
148/'320"120+4640=%40=40