Given the function f(x)= (x+3)^2 determine the value of f^-1 (49) include a complete solution
Answer:
Step-by-step explanation:
taking the inverse is essentially saying
x = (f(x) + 3)^2
root(x) - 3 = f(x) and -root(x) -3 = f(x)
(you have to take both the positive and negative roots)
plug in 49 for x and get 4 and -10.
The value of the inverse function, to the function f(x) = (x + 3)², at f(x) = 49, is; f⁻¹(49) = 4
What does the inverse notation f⁻¹(x) represents?The notation f⁻¹(x) represents the inverse of the function f(x). The inverse function, f⁻¹(x) undoes the the effect of the function f(x), meaning, that if y = f(x), then x = f⁻¹(y)
The value of f⁻¹(49) for the function, f(x) = (x + 3)² is the x-value, such that f(x) = 49, which can be obtained by solving the equation f(x) = (x + 3)², for x as follows;
Taking the square root of both sides of the equation, we get;
√(f(x)) = √((x + 3)²)
√(f(x)) = (x + 3)
Subtracting 3 from both sides, we get;
√(f(x)) - 3 = x + 3 - 3 = x
√(f(x)) - 3 = x
The above function is the inverse function, f⁻¹(x) that takes an output value, f(x), to produce the corresponding input value, x of the original function;
The inverse function, f⁻¹(x) = √(f(x)) - 3, takes the original output, f(x) to produce the original input x
When the output value is f(x) = 49 we get;
f⁻¹(49) = √(49) - 3 = ±7 - 3
Restricting the domain of the original function, f(x) to (x + 3) ≥ 0, or x ≥ -3, so that its inverse is also a function and produces only one value, we get;
f⁻¹(49) = 7 - 3 = 4
f⁻¹(49) = 4
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Do Now
a) Write the following expression in word form:
2 (x+8)
Answer:
X plus 8. Multiplied by 2
Step-by-step explanation:
You would follow PEMDAS
Hope this helps. :)
If I'm wrong please correct me.
Answer: Two times the sum of a number and eight.
Explanation: The x+8 portion translates to "the sum of a number and eight". Then we just stick "two times" in front of all that to basically say 2 times (x+8).
Maeve can paint a room in 3 hours, and Maura can paint an identical room in 5 hours. How many hours would it take both of them to paint 1 room if they work together at their respective rates?
Answer:
1.875 hours
Step-by-step explanation:
1/a + 1/b = 1/c where a and b are the times alone and c is the time together
1/3 + 1/5 = 1/c
Multiply by 15c to clear the fractions
15c(1/3 + 1/5 = 1/c)
5c+3c = 15
8c = 15
Divide by 8
8c/8 = 15/8
c = 1.875 hours
If I had to write 2 pages a day, how long would it take me to write 300 pages?
Time required for writing 2 pages = 1 day
So, time required for writing 1 pages
= 1 day/2
= ½ day
So, time required for writing 300 pages
= ½ day × 300
= (300/2) days
= 150 days
Answer:
150 days
Step-by-step explanation:
We can write a ratio to solve
2 pages 300 pages
----------- = ------------
1 day x days
Using cross products
2x = 300
Divide by 2
2x/2 = 300/2
x = 150
150 days
Please help (geometry)
Now,
<2 = <3 [ vertically opposite angle]
Then,
<2 = <8 [corresponding angles]
Again,
<2 + <5 = 180° [straight angle]
◆ True A || B
I hope you understand...
Mark me as brainliest...
Answer:
True
Step-by-step explanation:
∠ 2 and ∠ 5 are same- side exterior angles and are supplementary, sum to 180°
I need help asap I’m overtime
Answer:
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2. A pack of 7 rolls of tape sells for $2.73. If the tape is sold individually at the
same rate, how much would 3 rolls cost?
$1.56
$1.17
$0.78
$0.39
3 rolls would cost $1.17.
What is Concept of Direct Proportion?There exists a direct proportion between two values when one exists as a multiple of the other.
In direct proportion, if one quantity exists increased or decreased then the other quantity increases or declines, respectively. But in indirect or inverse proportion, if one quantity increases then the different quantity decreases and vice-versa.
If 7 rolls of tape cost $2.73,
Then 1 roll of tape would cost $2.73/7 = $0.39
Now, the cost of 3 roll of tapes would be 0.39*3 = $1.17
Therefore, at same rate the 3 rolls of tape would cost $1.17.
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David’s mother gave him $200.00 to buy some carrots at the Blue Market. She will be using the carrots to make juice for her church barbecue on Friday. At the market, David finds two vendors selling carrots. Vendor A has carrots for $40.00 per kilogram, and Vendor B has larger carrots for $50.00 per kilogram. Question: A. From which vendor should David buy the carrots? B. Explain why you have chosen that vendor
Answer:
Assuming that the quality (large vs. small) is the same, and PRICE is the main considerations... The $40 would be a better deal....
This reminds me of the old classic joke (told to me way back when , when I was 5 years old)... Which weighs more a ton of bricks, or a ton of feathers.....
I have to be honest being a five tear old the answer confused me, but I finally
figured it out... THEY BOTH WEIGH THE SAME AMOUNT !!!
Step-by-step explanation:
Mk
From which vendor should David buy the carrotWhich graph shows exponential growth?
On a coordinate plane, a parabola opens up with vertex at (0, 0).
On a coordinate plane, a curve approaches y = 0 in quadrant 2 and curves up into quadrant 1.
On a coordinate plane, a straight line with positive slope crosses the y-axis at (negative 1, 0) and crosses the y-axis at (2, 0).
On a coordinate plane a curve opens down and to the right in quadrants 1 and 4. It crosses the x-axis at (1, 0).
Answer:
its C, the u looking graph
Step-by-step explanation:
The following are the temperatures in °C for the first 10 days in January:
1.4, -8.1, -8.2, -5.2, -3.4, -2.3, 8.3 ,-7.1 ,1.3 ,3.6
Calculate the range.
The highest temperature is 8.3, in which we call the max.
The lowest temperature is -8.2, which is the min.
Subtract those values to get the range.
Range = max - min = 8.3 - (-8.2) = 8.3 + 8.2 = 16.5
Answer: 16.5 degrees CelsiusWhat types of concurrent constructions are needed to find the orthocenter of a triangle?
A. intersection of the lines drawn perpendicular to each side of the triangle through its midpoint
B. intersection of the lines drawn from each vertex of the triangle and perpendicular to its opposite side
C. intersection of the lines drawn to the midpoint of each side of the triangle to its opposite vertex
D. intersection of the lines drawn to bisect each vertex of the triangle
Answer:
B. Intersection of the lines drawn from each vertex of the triangle and perpendicular to its opposite side
Step-by-step explanation:
The orthocenter of a triangle is the point of concurrency of the three altitudes or extensions of the the altitudes of a triangle, each of which are perpendicular lines drawn from a vertex of the triangle to the side opposite the vertex
The type of concurrent construction needed to find the orthocenter of a triangle is the point of intersection of the perpendicular lines drawn from each vertex of the triangle, to the side opposite the vertex
Therefore, the correct option is option B. intersection of the lines drawn from each vertex of the triangle and perpendicular to its opposite side.
What is the value of x in the figure below? In this diagram, ABD ~ CAD. Could somebody help me please? I don't entirely grasp the concept of this.
Answer:
E. [tex]\sqrt{39}[/tex]
Step-by-step explanation:
To find the value of x we can use Euclidian theorem
x^2 = 13x3
x^2 = 39 find the root of both sides
x = [tex]\sqrt{39}[/tex]
What is the value of a?
W
b
O 5 units
4
a
с
oss units
O 6 units
3
z
O 7 units
Answer:
the second option : 5 1/3
Step-by-step explanation:
the height (h) in such a right-angled triangle is based on the 2 segments of the baseline : 3 and a
h = 4
the formula is h = sqrt(a×b)
with a and b being the baseline segments.
so,
4 = sqrt(3×a)
16 = 3×a
a = 16/3 = 5 1/3
m 2 = aº, m 3 = bº, m 41
a
b
a + b
a-b
Answer:
m,4+ a+b
Step-by-step explanation:
an exterior angle equals the sum of the 2 opposite interior angles
Instructions: Find the missing side. Round your answer to the nearest
tenth.
58°
х
22
X=
Answer:
35.2
Step-by-step explanation:
tan(58) = x/22
or, x = 22×tan(58)
or, x = 35.2 (rounded to the nearest tenth)
Answered by GAUTHMATH
pls pls pls help and give the actual answer quickly
Answer:
(Sqrt 3)/2 (5^2) (10) =216.51 in^3
Step-by-step explanation:
Grade improvement and study motivation
Step-by-step explanation:
fng-mrxb-dop p.l.e.a.s.e join
Draw 2 line segments, each 4 cm in length, intersecting at their midpoints. Connect each endpoint to each adjacent endpoint to form a quadrilateral. What is the maximum number of square centimeters possible in the area of the quadrilateral?
Answer:
8
Step-by-step explanation:
The maximum area will be a square. Everything else will have a height less than one of the sides of the square.
Use Pythagoras to find the length of the side of the square.
s^2 = 2^2 + 2^2
s^2 = 8
s = 2sqrt(2)
s^2 = 8
the square will have 8 cm^2
Tony calculates that 3 cubic metres of concrete is enough for the path.
He decides to use a concrete mix which has:
cement = 1 part
sand = 2 parts
gravel = 3 parts
How many cubic metres of gravel does Tony need?
Answer:
Amount cubic metres of gravel need = 1.5 cubic meter
Step-by-step explanation:
Given:
Parts
cement = 1 part
sand = 2 parts
gravel = 3 parts
Find:
Amount cubic metres of gravel need
Computation:
Amount cubic metres of gravel need = 3[Part of gravel / Total of all parts]
Amount cubic metres of gravel need = 3[3 / (1+2+3)]
Amount cubic metres of gravel need = 3[3 / 6]
Amount cubic metres of gravel need = 3[0.5]
Amount cubic metres of gravel need = 1.5 cubic meter
Please help me solve this
Answer:
The 2nd one is 3x+1
The 3rd answer is x+3
Step-by-step explanation:
Given g(x)=4x-1 and f(x)=x-2
Subtracting both
4x-1-(x-2)=4x-1-x+2=x(4-1)+(2-1)=3x+1
The next one is 3x+1-(2x-2)=3x+1-2x+2=x+3
Find the slope
of the line passing through the points (3, 4)
and
(8, -3).
Answer:
-7/5
Step-by-step explanation:
I think let me know
Answer:
7/-5 or -7/5
Step-by-step explanation:
This shall be quite an easy problem, I shall be doubting that this is high school, however, I am happy to aid :)
We shall begin by labeling the points given to us to prepare for inputting the values in the slope formula
(3,4). (8,-3)
x1,y1 x2,y2
Slope Formula:
y1 - y2
x1 - x2
Inputting the values:
4 - (-3)
3 - 8
Solve:
7
-5
The slope of the line passing through the points (3,4) and (8,-3) shall be 7/-5 or -7/5 negatives shall go both ways of fractions
I’m practically begging someone please help me!!
Find the absolute value
[5] = ________
Answer:
5
Step-by-step explanation:
the absolute value of a number is its distance from zero on a number line. so the absolute value of 5 is 5.
Age old help!!!!!!
…….
Answer:
Zoe was 32 years old, which was 4 years ago.
Step-by-step explanation:
When Zoe was 36 years old, her daughter was 1/3 her age, or 12 years old. Therefore, the difference in ages is 24 years.
So, our equation becomes:
4(Z-24) = Z
4Z - 96 = Z
3Z = 96
Z = 32
Assuming Zoe is 36 years old right now, our answer is 4 years ago.
Hope this helped,
~cloud
Since the daughter is 1/3 Zoe's age, she must be 12 since 1/3 of 36 is 12.
Then make a chart like I have done in the image attached.
Since the problem says "how many years ago", we use
our x years ago column in our chart to setup the equation.
If you need any additional help or are confused on a step, let me know!
help please i’ve been in here for hours oookung for answers
Answer:
f(x) = 3.33x - 7
Step-by-step explanation:
We are suppposed to write the slope intercept form of the line . The slope intercept form of the line is ,
[tex]\rm\implies y = mx + c [/tex]
where ,
m is slopec is y intercept .Here we can see that the line is passing through (0,-7) . Therefore ,
[tex]\rm\implies y- intercept = -7[/tex]
Also we can see that the line is passing through (2.1,0) . Therefore we can find the slope as ,
[tex]\rm\implies Slope =\dfrac{y_2-y_1}{x_2-x_1}\\\\\rm\implies Slope =\dfrac{ -7-0}{0-2.1}\\\\\rm\implies \bf Slope = 3.33 [/tex]
Using Slope Intercept Form :-
[tex]\rm\implies y = mx + c \\\\\rm\implies y = 3.33x + (-7) \\\\\rm\implies\underline{\boxed{\rm\blue{f(x) = 3.33x - 7 }}}[/tex]
Without plotting these numbers, decide which inequalities are true. Check all that apply.
Square root of 7 > 2
Square root of 7 <7
Square root of 7< square root of 8
Square root of 8<2
Square root of 8<8
Answer:
1st,2nd,3rd, and 5th option
Step-by-step explanation:
Let convert the intergers into radical numbers
[tex] \sqrt{7} > \sqrt{4} [/tex]
[tex] \sqrt{7} < \sqrt{49} [/tex]
[tex] \sqrt{7} < \sqrt{8} [/tex]
[tex] \sqrt{8 } < \sqrt{4} [/tex]
[tex] \sqrt{8} < \sqrt{64} [/tex]
As radical numbers approaches, positive infinity, the answer of the radical gets bigger. So using this explanation,
The first option, Second Option, Third Option, and Fifth Option are true.
Answer:
A, B, C, E
Step-by-step explanation:
Did on edg. its right
Tiffany drove from New York to California over the course of 8 days. Each day, she took a one- hour lunch break and a two-hour dinner break. What fraction of the total number of hours in these eight days did she spend breaking for lunch and dinner?
A. 1/8
B. 1/6
C. 1/4
D. 3/8
What is the value of s?
____units
Answer:
[tex]\huge\boxed{s=17}[/tex]
Step-by-step explanation:
ΔADB is the right triangle with a right angle in vertex B. We can use the Pythagorean theorem.
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have:
[tex]leg=15\\leg=8\\hypotenuse=s[/tex]
Substitute:
[tex]s^2=15^2+8^2\\\\s^2=225+64\\\\s^2=289\Rightarrow s=\sqrt{289}\\\\s=17[/tex]
Question 2 of 5
Which two ratios represent quantities that are proportional?
Answer: A
Step-by-step explanation:
(22)(21)=(14)(33)
Write an expression equivalent to 6(x+y)-5 and state which property you used to write
Answer:
6x+6y-5 distributive property
Step-by-step explanation:
6(x+y)-5
Distribute using the distributive property
6x+6y-5
