Find the ranges of the function ƒ(x) = |x + 4| + 1 and the range of the exponential function g(x) represented by the graph below.
Are they the same? Explain.
Answers
One of the ways you can answer this question is to graph both of the functions. You already have the graph of one of them. I've made the other one for you.
They don't look very much alike, do they?
You are asked for the ranges. The range of your graph is ∞ > y ≥ 1 which includes all the reals within that boundary.
The value of the range of the absolute value graph is ∞ > y ≥ 1 which includes all the reals within that boundary.
The graphs are not the same but the ranges are the same are the same <<< answer.
Related Questions
There are 100 students in a drawing contest, and 58 of them are girls. What percent of the students in the contest are girls?
Answers
There are 100 students in a drawing contest and 58 of students are girls. What percent of students in the drawing contest are girls?
The fraction [tex]\frac{58}{100}[/tex] represents the number of girls in the drawing contest out of all the students.
To find out what percent of the students are in the drawing contest, we can change [tex]\frac{58}{100}[/tex] into a percent.
We can first reduce the fraction by dividing both the numerator and denominator by the Greatest Common Factor of 58 and 100 using 2.
58 ÷ 2 = 29
100 ÷ 2 = 50
Our reduced fraction is [tex]\frac{29}{50}[/tex].
29 ÷ 50 = 0.58
0.58 × 100 = 58%
Therefore, 58% of the students in the drawing contest are girls.
Find the equation of the line.
A) y= -3/2 x + 1
B) y= -2/3 x - 1
C) y= 2/3 x + 1
D) y= 3/2 x - 1
Answers
Hope this helps
Answer:
It’s y=2/3x+1 that’s the equation of the line.
Step-by-step explanation:
Kelly wants to know if the number of words on a page in her geometry book is generally more than the number of words on a page in her science book. She takes a random sample of 25 pages in each book, then calculates the mean, median, and mean absolute deviation for the 25 samples of each book.
Kelly claims that because the mean number of words on each page in the science book is greater than the mean number of words on each page in the geometry book, the science book has more words per page. Based on the data, is this a valid inference?
Answers
Answer:
No, because there is a lot of variability in the science book data
Step-by-step explanation:
______________ is process that you can do over and over, where each result does not affect the next.
Ex. Flipping a coin, rolling dice, choosing a card, etc.
Answers
use formulas to find the lateral and surface are of the given prism the numbers are 5.39m 26m 5m 2m
Answers
Total Surface Area:
(add to the above)
2(1/2)(3)(2) = 6m^2 (area of the two triangles)
6 + 149 = 155m^2
The depth of a lake, dd, varies directly with rr, the amount of rainfall last month. if kk is the constant of variation, which equation represents the situation?
Answers
let d be the depth and r be the rainfall amount
dαr
thus
d=kr
where, k is the constant of proportionality, thus the formula will be:
d=kr
A system of equations that has an infinite number of solutions is called a(n) ______ system of equations.
Answers
A system of equations with an infinite number of solutions is known as a consistent and dependent system. These systems occur when equations are essentially the same, leading to all solutions satisfying all the equations, often represented by overlapping graphs in the case of linear equations.
Explanation:A system of equations that has an infinite number of solutions is called a consistent and dependent system of equations. When a system is consistent and dependent, it means that the equations describe the same line or geometric shape, leading to an infinite number of points that satisfy all equations in the system simultaneously. This scenario often arises when the equations in the system are multiple forms of the same equation, or when they can be algebraically manipulated to become the same equation.
In practical terms, if you were to graph the equations in a consistent and dependent system, you would see that they overlap completely. For instance, if two linear equations represent the same line, any point on that line is a solution to both equations, hence the infinite solutions. A key aspect of understanding such systems is realizing that they do not lead to a single unique solution but rather a set of solutions that satisfy all conditions outlined by the equations in the system.
A system of equations with an infinite number of solutions is referred to as a consistent and dependent system, indicating the equations describe the same line.
A system of equations that has an infinite number of solutions is called a consistent and dependent system of equations. This type of system occurs when the equations involved describe the same geometric line, meaning every point on the line is a solution to the system, hence an infinite number of solutions. Such systems often arise in various mathematical contexts, including linear algebra and differential equations, where they indicate a fundamental underlying symmetry or redundancy in the system's constraints.This occurs when the equations are dependent, leading to multiple possible solutions that satisfy all the equations simultaneously.
How to solve this problem
Answers
Solve for y
Cos(A) = adjacent / hypotenuse
Cos(A) = y / 8
y = 8 * cos(A)
y = 8 * cos(73)
y = 8 * 0.2924
y = 2.339
Step Two
Solve for x
Sin(A) = opposite / hypotenuse
Sin(73) = x / 8
x = 8 * sin(73)
x = 8 * 0.9563
x = 7.550
Check
x^2 + y^2 =? 8^2
2.339^2 + 7.55^2 =? 8^2
5.471 + 58.53 =? 64
64.000921 = 64 which is close enough.
The problem is in the first picture and the questions are in the second one. I have no idea how to do any of this.
Answers
You are given that CB = 271 feet. You are also given that <CAB = 30 degrees.
So you can use Sin(<CAB) = opposite / hypotenuse or
hypotenuse = opposite / sin(<CAB)
hypotenuse = 271 / 0.5
hypotenuse (AB) = 542 feet.
Problem B
CD = 772 feet Given in table
<ACD = 74o Given on drawing.
We need to find AC which is not given
Cos 30 = adjacent / hypotenuse.
adjacent = hypotenuse * Cos(30)
adjacent = AB * Cos(30)
Adjacent = 542 * cos(30)
Adjacent = AC = 469.4 feet
Now we need to start again
AC = 469.4
<ACD = 74
CD = 772
AD = ???
AD^2 = AC^2 + CD^2 - 2 * AC * CD * Cos(74)
AD^2 = 595984 + 220336.4 - 399538
AD^2 = 416782.1
AD = sqrt(416782.1)
AD = 645.59
Problem 3
I'll set it up for you. And give you the answer I get, but I'm going to leave it to you mostly. It just follows what I've done above.
DC = 645.59
CE = 561
DE = 543
DC^2 = CE^2 + DE^2 - 2* CE * DE * Cos(E)
645.59^2 = 561^2 + 543^2 - 2*561*543 * Cos(E)
Cos(E) = -0.3164
E = cos-1(0.3164)
E = 108.45 degrees.
The volume of a cylinder is given by the formula v=pi r^2h, where r is the radius of the cylinder and h is the height. Which expression represents the volume of this cylinder? h=2x+7, r=x-3.
Answers
volume = pi (x - 3)^2 * (2x + 7)
= pi* (2x + 7)(x^2 - 6x + 9)
= pi * (2x^3 - 12x^2 + 18x + 7x^2 - 42x + 63)
= (2x^3 - 5x^2 - 24x + 63) pi answer
Chiara pays $21 for 3 DVDs that she finds in a one-price bin. Gunther wants to know how much he would spend for 1 DVD in this bin. Chiara wants to know how many dollars she will need to purchase 9 DVDs the next time she goes.
Answers
If Chiara wants to purchase 9 DVD's next time and needs to know the money, we take our previous information (1 DVD = $7) and input it into this equation.
x (unknown dollars) = 9 (DVD) * 7 ($).
Meaning that 9 * 7 = 63.
It will cost $63 for 9 DVD's, when 1 DVD is $7.
Which compound inequality can be used to solve the inequality |3x+2|>7
Answers
Answer:
x>[tex]\frac{5}{3}[/tex].
Step-by-step explanation:
We have given an inequality |3x+2|>7.
We need to solve this inequality |3x+2|>7, and find the compound which can solve this.
We know that, inequality :
|3x+2|>7
Subtrating 2 from both sides,
|3x+2-2|>7-2
3x>5
Dividing by 3 both sides,
[tex]\frac{3x}{3} > \frac{5}{3}[/tex]
x>[tex]\frac{5}{3}[/tex]
Therefore, we can see that on the inequality |3x+2|>7, we find x>[tex]\frac{5}{3}[/tex] compound.
Answer:
D. 3x + 2 < –7 or 3x + 2 > 7
Step-by-step explanation:
Aaron solved an inequality and then graphed the solution as shown below. Anwser: A
A student found the solution below for the given inequality lx-9l less than 4
Anwser: D
Amber is solving the inequality lx+6l - 12 less than 13 by graphing. Which equations should Amber graph?
Anwser: A
What is the solution, if any, to the inequality l3xl greater than or equal to 0?
Anwser: A
Which compound inequality is equivalent to lax-bl greater than c for all real numbers a, b, and c, where c is greater than or equal to 0?
Anwser: D
Which compound inequality is equivalent to the absolute value inequality lbl greater than 6?
Anwser: D
What is another way to write the absolute value inequality lpl less than or equal to 12?
Anwser: A
What is the solution to the inequality lx-4l less than 3?
Anwser: B
Which inequality is equivalent to lx-4l less than 9?
Anwser: B
Hope This Helps!
if 3x+2y=12 and -4x+6y=24 what is the value of -x+2y
Answers
(2) -4x+6y=24
Solving the system of equations using the method of substitution:
Isolating y in the first equation:
(1) 3x+2y=12→3x+2y-3x=12-3x→2y=12-3x→2y/2=(12-3x)/2→y=(12-3x)/2
Replacing "y" by (12-3x)/2 in the second equation:
(2) -4x+6y=24
y=(12-3x)/2→-4x+6[(12-3x)/2]=24
Solving for x:
-4x+3(12-3x)=24
-4x+36-9x=24
-13x+36=24
-13x+36-36=24-36
-13x=-12
-13x/(-13)=-12/(-13)
x=12/13
Replacing "x" by 12/13 in y=(12-3x)/2
x=12/13→y=[12-3(12/13)]/2
y=(12-36/13)/2
y={[(13)(12)-36]/13}/2
y=[(156-36)/13]/2
y=(120/13)/2
y=(120/13)(1/2)
y=60/13
x=12/13; y=60/13
-x+2y=-12/13+2(60/13)
-x+2y=-12/13+120/13
-x+2y=(-12+120)/13
-x+2y=108/13
Answer: The value of -x+2y is 108/13
Item 18 A spherical ball with a volume of 972π in.3 is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of the ball. What is the volume of the box?
Answers
Volume of the given box is 5832 in³
Volume of the cube:
Given a spherical ball with a volume of 972π in.³,
Since the volume of a sphere is (4/3)πr³, we can find that the radius of the sphere is 9 inches.
The edge length of the cube (box) is twice the radius (diameter of the sphere), so the edge length of the cube is equal to 18 inches.
The volume of the cube is then (18³) in³
Volume of the cube = 5832 in³
Find the base area of a rectangular pyramid whose pyramid height is 5 cm and slant height of one side of the base is 13 cm and another side of the base is 7 cm.
a. 92√6 cm^2
b. 96√6 cm^2
c. 180√6 cm^2
d. 100√6 cm^2
e. 198√6 cm^2
Answers
x------> the larger side of the rectangular base
y-------> the smaller side of the rectangular base
we know that
Applying the Pythagoras theorem
for the larger side of the base
slant height =13 cm
h=5 cm
13²=5²+(x/2)²-----> (x/2)²=13²-5²-----> 144
(x/2)²=144------> x/2=12------> x=24 cm
for the smaller side of the base
slant height =7 cm
h=5 cm
7²=5²+(y/2)²-----> (y/2)²=7²-5²-----> 24
(y/2)²=24------> y/2=√24------> y=4√6 cm
the area of the base is
24*4√6------> 96√6 cm²
the answer is the option
b. 96√6 cm^2
Solve 6,394 divided by 42 =
Answers
The required quotient is [tex]152[/tex] and remainder is [tex]10[/tex].
Given that [tex]6394[/tex] ÷ [tex]42[/tex].
Long division states that [tex]divident= divisor*quotient+remainder[/tex].
Let [tex]a[/tex] and [tex]b[/tex] be any real number. Consider [tex]a[/tex] ÷ [tex]b[/tex] gives
[tex]a=bq+r[/tex], [tex]q[/tex] is quotient [tex]r[/tex] is remainder and its value is [tex]0\leq r < b[/tex].
[tex]\begin{array}{ccccc}42)&006394(152&\\-&42____________&\\&219& \\&\\-&210&\\&0094\\-&0084\\&0010\end{array}\right][/tex]
Hence, the required quotient is [tex]152[/tex] and remainder is [tex]10[/tex].
Learn more about Long division click here:
https://brainly.com/question/28748299
#SPJ6
What is the value of c when the expression 21.2x + c is equivalent to 5.3(4x − 2.6)?
Answers
To find our answer we need to work out the parenthesis. This is for instance possible using rainbow technique.
[tex]5.3(4x - 2.6) = \\ 5.3 \times 4x - 5.3 \times 2.6 = \\ 21.2x - 13.78[/tex]
Therefore the value of c = - 13.78.
~ Hope this helps you!
Comparing with 21.2x + c:-
the value of c = -13.78 Answer
Please help me out here.
Answers
When you multiply two exponents with the same base together, you can add the indexes together. For example, if you had y * y², you could make it y³, by adding the indexes of 2 and 1.
In this scenario, you can look at the last choice, where it has [tex] x^{9} [/tex] * x. You add the indexes of 9 and 1, to get [tex] \sqrt[3]{ x^{10} } [/tex]
That's equivalent to the equation given, so your answer would be the last choice.
A sphere has a diameter of 12 ft. What is the volume of the sphere? Give the exact value in terms of pi
Answers
Radius = 12 ÷ 2 = 6 ft
[tex]\text {Volume = } \dfrac{4}{3} \pi r^3[/tex]
[tex]\text {Volume = } \dfrac{4}{3} \pi (6)^3 = 288 \pi \text{ ft}^3[/tex]
your answer is here..
given the diameter of the sphere is 12 ft.
therefore radius of the sphere = 12/2 = 6 ft
[tex]volume \: of \: the \: sphere = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \pi( {6}^{3} ) \\ \\ = \frac{4}{3} \pi(216) \\ \\ = 288\pi {ft}^{3} \\ \\ cheers...[/tex]
Give the dimensions of a cuboid with a volume of 18cm to the power 3.
Answers
volume of a cuboid=length*width*height
in this problem
we have
volume=(18 cm)³
so
volume=18*18*18 cm³
the dimensions of the cuboid are
length 18 cm
width 18 cm
height 18 cm
18 cm x 18 cm x 18 cm
a glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. if a single marble is chosen at random from the jar, what is the probability that it is red
Answers
[tex] \frac{1}{10} [/tex]
Graph the six terms of a finite series where a1 = −3 and r = 1.5.
Answers
For the given series:
[tex]a_{1}=-3 \\ r=1.5 [/tex]
Each term of the geometric series is obtained by multiplying the previous term by common ratio.
So the next terms will be:
-4.5, -6.75, -10.125, -15.1875, -22.78125
The general formula for the G.P would be:
[tex] a_{n}=-3(1.5)^{n-1} [/tex]
On plotting the series, the result will be like this:
Answer:
the answer is C
Step-by-step explanation:
Divide £770 in the ratio of 4:3 plsss
Answers
[tex]\bf 4:3\qquad \cfrac{4}{3}\qquad \cfrac{4\cdot \frac{770}{4+3}}{3\cdot \frac{770}{4+3}}\implies \cfrac{4\cdot 110}{3\cdot 110}\implies \cfrac{440}{330}[/tex]
The total number of points scored by each player throughout a season are listed on a roster by the player's jersey number. is this a function? explain your reasoning.
Answers
Using ordered pairs to represent this, we would have (jersey #, points). A relation is a function if no element of the domain matches more than one element of the range; in our case, the domain is the jersey number and the range is the number of points.
The jersey number will not match two numbers of points throughout the season; a player will only have one total number of points throughout the season. Therefore no element of the domain matches more than one element of the range, and this is a function.
A)Yes, it is a function because each player's jersey number will have only one number for the points scored during the season.
Each jersey number has exactly one number for the total points scored by the player.
In a function, every input has exactly one output. In this situation, each jersey number is an input, and the total points scored for the season by the player is the output.
A campground owner plans to enclose a rectangular field adjacent to a river. the owner wants the field to contain 180,000 square meters. no fencing is required along the river. what dimensions will use the least amount of fencing?
Answers
The area is the product between the two sizes:
[tex]A=xy[/tex] (1)
While the perimeter is twice the sum of the two sizes:
[tex]p=2(x+y)[/tex] (2)
From (1) we can write
[tex]y= \frac{A}{x} [/tex]
and we can substitute it into (2):
[tex]p=2(x+ \frac{A}{x})=2x+2 \frac{A}{x} [/tex]
To find the minimum value of the perimeter, we have to calculate its derivative and put it equal to zero:
[tex]p'(x)=0[/tex]
The derivative of the perimeter is
[tex]p'(x) = 2 -2 \frac{A}{x^2}= \frac{2x^2-2A}{x^2} [/tex]
If we require p'(x)=0, we find
[tex]x^2=A[/tex]
[tex]x= \sqrt{A} = \sqrt{180000 m^2}=424.26 m [/tex]
And the other side is
[tex]y= \frac{A}{x}= \frac{180000 m^2}{424.26 m} =424.26 m[/tex]
This means that the dimensions that require the minimum amoutn of fencing are (424.26 m, 424.26 m), so it corresponds to a square field.
An artist is creating a large conical sculpture for a park. The cone has a height of 16 m of and a diameter of 25 m. Find the volume the sculpture to the nearest hundredth.
A. 833.33 m3
B. 7,850 m3
C. 2,616.67 m3
D. 209.33 m3
Answers
The volume of the conical sculpture is calculated using the formula for the volume of a cone, 1/3πr²h. Substituting the given values, the volume is found to be approximately 2,616.67 m³.
Explanation:The subject of this question is focused on calculating the volume of a cone. To find the volume of a cone, we apply the formula 1/3πr²h, where r is the radius and h is the height. Given in the question, the height (h) of the cone is 16 m and the diameter is 25 m. The radius is half of the diameter so it is 25/2 = 12.5 m. Substituting these values into the formula gives us:
Volume = 1/3πr²h
= 1/3 * π *(12.5 m)² * 16 m
≈ 2,616.67 m³
So, the volume of the sculpture to the nearest hundredth is approximately 2,616.67 m³. Thus, Option C is the correct answer.
Learn more about volume of a cone here:https://brainly.com/question/29767724
#SPJ12
In 2010, 100 japanese yen purchased .88 u.s. dollars and in 2013, it purchased .93 u.s. dollars. how much was 1 u.s. dollar worth in japanese yen, in 2010 and 2013?
Answers
2010:
100 yen x yen (use cross products to solve for x yen)
$0.88 = $1
100 = 0.88x
0.88 0.88
x = 113.6 yen
In 2010, $1 was worth approximately 114 yen.
2013:
100 yen x yen
$0.93 = $1
100 = 0.93x
0.93 0.93
x = 107.5
In 2013, $1 was worth approximately 108 yen.
ivan began to prove the law of sines using the diagram and equations below. sin(A) = h/b, so b sin(A) = h. sin(B) = h/a, so a sin(B) = h. Therefore, b sin(A) = a sin(B). Which equation is equivalent to the equation b sin(A) = a sin(B)?
edit: the answer is b!
Answers
(B.) sin(A)/a = sin(B)/b
A basketball player has a 50 chance of making each free throw. what is the probability that the player makes at least eleven out of twele free throws
Answers
Two cities are 45 miles apart. Two trains, with speeds of 70 mph and 60 mph, leave the two cities at the same time so that one is catching up to the other. How long after the trains leave will they be 10 miles apart for the first time? How long after the trains leave will they be 10 miles apart for the second time?
Answers
The first time the two trains are 10 miles apart is approximately 16.15 minutes after they start. The second time they are 10 miles apart is about 25.38 minutes after they start.
Explanation:This problem is a relative speed problem in mathematics, specifically in the subsection of algebra known as rate, time, and distance problems. To solve, you should consider that when the two trains move towards each other, their speeds add up. Hence, the relative speed of the two trains is 70 mph + 60 mph = 130 mph.
First, we need to figure out the time it would take for the trains to be 10 miles apart for the first time. This would be when they have collectively traveled 35 miles (45 miles initial separation - 10 miles final separation). To find the time it takes, we use the formula d=rt, where d is distance, r is rate or speed, and t is time. Here, time t = d/r = 35 miles / 130 mph = approximately 0.27 hours, which converts to about 16.15 minutes.
Next, to find the time when they are 10 miles apart for the second time, we need to consider when they have covered the total distance of 45 miles and then kept going until they've covered an additional 10 miles. This is a total of 55 miles. Again, using the time formula t = d/r, we get t = 55 miles / 130 mph = approximately 0.42 hours or about 25.38 minutes.
Learn more about Relative Speed here:https://brainly.com/question/14362959
#SPJ2