Answers
The solution is listed below
[tex]F(x)=4x+7 \\ \\ y=4x+7 \\ \\ y-7=4x \\ \\ \frac{y-7}{4}=x \\ \\ x= \frac{y-7}{4} \\ \\ f-^{1}(y) = \frac{y-7}{4} \\ \\ f-^{1}(x) = \frac{x-7}{4} \\ \\ [/tex]
Related Questions
What are the lateral area and the surface of the cone shown below?
Answers
[tex]\bf \textit{total surface area of a cone}\\\\ SA=\pi r\stackrel{slant~height}{\sqrt{r^2+h^2}}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ -------\\ r=11\\ \stackrel{slant~height}{\sqrt{r^2+h^2}}=24 \end{cases} \\\\\\ SA=\pi (11)(24)+\pi (11)^2\implies SA=264\pi +121\pi \\\\\\ \boxed{SA=385\pi }[/tex]
simplify this problem
Answers
Rewrite the fraction as division:
[tex]= (49 - \dfrac{1}{r^2}) \div (7 - \dfrac{1}{r} )[/tex]
Make them into single fraction:
[tex]= \dfrac{49r^2 - 1}{r^2} \div \dfrac{7r - 1}{r} [/tex]
Change the divide fraction into multiplication fraction:
[tex]= \dfrac{49r^2 - 1}{r^2} \times \dfrac{r}{7r - 1} [/tex]
Factorise the difference of square a² - b² = (a + b) (a - b) :
[tex]= \dfrac{(7r+ 1)(7r - 1)}{r^2} \times \dfrac{r}{7r - 1} [/tex]
Cancel the common factors:
[tex]= \dfrac{(7r+ 1)}{r}[/tex]
Solution
[tex] \frac{49 - a^2}{7 - a} \\ \frac{(7 - a)(7 + a)}{7 - a}\text{ Notice a cancellation can take place} [/tex]
There is a 7 - a in both numerator and denominator, so that cancel providing a does not equal 7. a cannot equal 7 because that will put a 7 in the denominator and that makes the whole fraction = something over 0 which is undefined.
Answer
So far what we have is
7 + a
But a = 1/r
So the answer can be 7 + 1/r
r can be anything but 0 [for this answer]
and 1/7 for the cancellation.
Greg has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Greg's Jumble has 666 classical songs, 777 rock songs, and 999 rap songs on it. What is \text{P(not a rap song})P(not a rap song)P, left parenthesis, n, o, t, space, a, space, r, a, p, space, s, o, n, g, right parenthesis?
Answers
We have been given that Greg's Jumble has 666 classical songs, 777 rock songs, and 999 rap songs.
Therefore, total number of songs are
[tex]666+777+999\\ =2442[/tex]
The formula for probability is given by
[tex]P(E)=\frac{n(E)}{n(s)}[/tex]
Let us first find the probability for rap song
[tex]P(\text{rap song})= \frac{999}{2442} \\ P(\text{rap song})= \frac{9}{22}[/tex]\\
Therefore, we have
[tex]P(\text{ not rap song})=1- P(\text{rap song})\\ \\ P(\text{ not rap song})=1-\frac{9}{22} \\ \\ P(\text{ not rap song})=\frac{13}{22} =0.59[/tex]
Hence, we have
P(not rap song)=0.59
how many times does 15 go into 46
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y = |x| translated two units to the right.
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So we go from y = |x| to y = |x-2|
please help! i dont understand this.
a 25 gram sample substance that's used for drug research has a k-value of 0.1229. find the substances half-life, in days using the exponential decay formula. round your answer to the nearest tenth
Answers
With a k-value of 0.1229, the half-life is approximately 5.6 days.
The exponential decay formula is given by:
amount remaining = initial amount × e^-(k × t)
For a substance's half-life, the amount remaining is half of the initial amount. The formula to find the half-life (t1/2) is:
t1/2 = ln(2) / k
Here, ln(2) is approximately 0.693 and k is given as 0.1229. Substituting these values in:
t1/2 = 0.693 / 0.1229 ≈ 5.64 days
Rounding to the nearest tenth, the half-life of the substance is 5.6 days.
What is the similarity ratio of the smaller to the larger similar pyramids? Enter your answer as a:b
Answers
What is the equation of the circle shown in the graph ? (Blank)^2 + (Blank)^2 = blank
Answers
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{4}{ k})\qquad \qquad radius=\stackrel{6}{ r} \\\\\\\ [x-(-6)]^2+[y-4]^2=6^2\implies (x+6)^2+(y-4)^2=36[/tex]
The equation of the circle shown in the graph is equal to [tex](x + 6)^2 + (y - 4)^2 = 36[/tex]
Form the graph, we can deduce the following points:
The center of the circle is denoted by the black dot and we can see that the values are -6 and 4 respectively.
Center (h, k) = (-6, 4)Also, the diameter of the circle is:
Diameter = 12 units
Radius = [tex]\frac{Diameter}{2} = \frac{12}{2} = 6 \;units[/tex]
Mathematically, the standard form of the equation of a circle is given by;
.....equation 1
Where;
h and k represents the coordinates at the center.r represents the radius of the circle.Substituting the values into eqn 1, we have:
[tex](x - [-6])^2 + (y - 4)^2 = 6^2\\\\(x + 6)^2 + (y - 4)^2 = 36[/tex]
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Of the 12,000 votes cast in an election, 42% of the votes were for Mr.Jones. How many votes were cast for all the other candidates?
Answers
= 5040
Therefore, Number of Voters left = 12000-5040
= 6960
coordinate grid with plotted ordered pairs, point A at negative 5, 4 point B at 4, 7 point C at negative 2, 7 point D at negative 7, 1 point E at 4, negative 2 point F at 1, negative 6 point G at negative 3, negative 10 point H at negative 4, negative 4 point I at 9, 3 point J at 7, negative 4 and point K at 2, 3
The coordinate grid shows points A through K. Which points are solutions to the system of inequalities listed below?
2x + y ≤ 10
2x − 4y < 8
Answers
_____
Doing all the calculations is fairly tedious, but can be done manually. (It works better, perhaps, to do it on a spreadsheet.) It is convenient to reduce the second equation by a factor of 2 to
x -2y < 4
point A(-5, 4) in the first equation: 2(-5)+(4) = -2 ≤ 10
point A(-5, 4) in the second (reduced) equation: (-5)-2(4) = -13 < 4
point H(-4, -4) in the first equation: 2(-4) +(-4) = -12 ≤ 10
point H(-4, -4) in the second equation: (-4) -2(-4) = 4 < 4 . . . FALSE
Jackson goes to the gym 0, 2, or 3 days per week, depending on work demands. The expected value of the number of days per week that Jackson goes to the gym is 2.05. The probability that he goes 0 days is 0.1, the probability that he goes 2 days is , and the probability that he goes 3 days is .
Answers
1-.1=.9
He needs more time at 3 days so:
3 days > 2 days
The equality has to be bigger on three so It can be .46 or bigger. Yet we want concise, clear answers:
.1 (zero), .23 (two) .67 ( three)
Which five values would be used to graph a box-and-whisker plot for the following set of data? 36, 14, 27, 27, 33, 22, 41, 29
Answers
Q1 Q2 Q3
{14,22,27,(27}{,29),33,36,41}
add/div. by 2 add/div. by 2
28.5 34.5
Minimum: 14 (smallest number)
Quartile 1: 28.5 (middle number of q1)
Quartile 2: 28 (middle number) when you have and even amount of numbers you end up having 2 middle numbers, so you just add them then divide by 2. 27+29=56 56/2=28
Quartile 3: 34.5 (middle number of q3)
Maximum: 41 (biggest number)
I hope this helped you! :)
Answer:
Lower value: 14
Highest value: 41
Lower quartile: 24.5
Upper quartile: 34.5
Median: 28
Step-by-step explanation:
Polygon ABCDEF is the result of a translation of polygon GHIJKL . GL¯¯¯¯¯ is parallel to HI¯¯¯¯¯ in the pre-image. please help
Answers
GL parallel to HI in the pre-image ensures AB remains parallel to FE in the translation.
Given that GL and HI are parallel, we can infer that AB and FE will also remain parallel in the translation. The parallelism of lines GL and HI suggests that their corresponding sides, AB and FE, will exhibit the same parallel relationship during the translation process. This is a consequence of the consistent geometric transformation applied to all points on lines GL and HI. As each point on GL undergoes translation, its corresponding point on HI experiences the same displacement, preserving the parallelism.
Therefore, we can confidently state that AB and FE maintain their parallel orientation, aligning with the geometric properties of the translation that preserves parallel lines. The parallelism observed in the original configuration persists throughout the translation, ensuring that AB and FE remain parallel to each other.
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Part A: Factor 2x2b2 + 5xb2 + 2b2. Show your work. (4 points) Part B: Factor x2 − 8x + 16. Show your work. (3 points) Part C: Factor x2 − 49. Show your work. (3 points)
Answers
[tex]x^2 - 8x + 16 = (x - 4) (x - 4) = (x-4)^2[/tex]
[tex]x^2 - 49 = x^2- 7^2 = (x - 7)(x + 7)[/tex]
find the number of gallons in 6 liters of solution(1gal=3.79l)
Answers
To convert 6 liters of solution into gallons, given that 1 gallon is equivalent to 3.79 liters, you divide 6 by 3.79 which gives you 1.58 gallons of solution.
Explanation:The question is asking to find the number of gallons in 6 liters of a solution, given that 1 gallon is equivalent to 3.79 liters. The conversion from liters to gallons is a basic concept in measurement conversion. Here is a step-by-step explanation to help you understand the process:
You have 6 liters of solution which you want to convert to gallons. We know that 1 gallon is equivalent to 3.79 liters. So, to convert liters to gallons, we divide the number of liters by 3.79. Therefore, you have 6 / 3.79 = 1.58 gallons (rounded to two decimal places) of solution. Learn more about Unit Conversion here:
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PLZ HELP ASAP CIRCLES WILL GIVE BRANLIEST
Answers
If we are to look closely to the figure, angle I intercepted the arc BDR. Also, the angle D intercepted arc BIR. The sum of the measures these two arcs is 360°. Hence, the sum of the measures of the angles intercepting these arcs is 180°.
m∠I + m∠D = 180°
117° + m∠D = 180°
The measure of angle D is 63°.
Answer: 63°
Question 19 find the solution
Answers
x= 5
Using the value of x in first equation we can write:
y = 6(5) + 1
y = 30 + 1
y = 31
So, the solution is (5, 31)
Thus, option 2nd is the correct answer
2. An earthquake was felt throughout a circular area of 1,808.64 square miles. What was the radius of the circular area?
A. 24 miles B. 12 miles C. 576 miles D. 20 miles
Answers
Answer:
A. 24 miles
Step-by-step explanation:
Using 3.14 for π, we have ...
... Area = πr^2
... √(Area/π) = r = √(1808.64/3.14) = √576 = 24 . . . . miles
Answer:
its 24 miles so the correct answer would be A
Step-by-step explanation:
what is the solution -10 + sqrt x+8=-4
Answers
Add 10 to both sides to get:
√(x + 8) = 6
Square both sides to get our binomial out of the square root:
x + 8 = 6²
x + 8 = 36
Subtract 8 to both sides to get:
x = 28
Answer:
[tex]x=28[/tex]
Step-by-step explanation:
[tex]-10+\sqrt{x+8}=-4[/tex]
⭆ Add 10 to both sides:-
[tex]-10+\sqrt{x+8}+10=-4+10[/tex]
[tex]\sqrt{x+8}=6[/tex]
⭆ Square both sides:-
[tex]x+8=36[/tex]
⭆ Subtract 8 from both sides:-
[tex]x+8-8=36-8[/tex]
[tex]x=28[/tex]
OAmalOHopeO
what integer and-8 have the product of -96
Answers
12 times -8 = -96!
:) Have a nice day and maybe consider grading this answer brainliest? <3
12 * (- 8) = - 96.
Terry uses 3 cups of pumpkin seeds to decorate the tops of 12 loaves if bread. She puts an equal amount of seeds on each loaf. How many cups of pumpkin seeds does she put on each loaf of bread?
Answers
In the number 7,777.777, how does the 7 in the hundreds place compare to the 7 in the place to its left?
A.
The 7 in the hundreds place represents of what the 7 to its left represents.
B.
The 7 in the hundreds place represents 10 times what the 7 to its left represents.
C.
The 7 in the hundreds place represents of what the 7 to its left represents.
D.
The 7 in the hundreds place represents 100 times what the 7 to its left represents.
Answers
hgfgjdhsghdfg
After a comparison of the number 7 which is at hundreds of places to the number 7 left off it, it is 10 times of what the 7 to its left represents. Hence, option B is correct
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data provided in the question,
The given number is 7,777.777
Now, we have to compare the number 7 which is at the hundreds place with the 7 in the place left to it.
So, the 7 which is left to the 7 at the hundredth place will be 10 times it. Also, the 7 which is the second left to the 7 at the hundredth place is 100 times and so on it will increase like this.
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Which point best approximates the root of 45
Answers
We rewrite 45 as 3²×5
thus
√45=√(3²×5)
pulling terms out from under the radical we obtain
3√5
thus the exact answer form is:
3√5
or the decimal form is:
6.70820393
what is the surface area of a sphere with a radius of 3m
Answers
Can a chord also be classified as a radius? Explain your answer.
Answers
A chord is a straight sediment that joins two points of the circumference. The radius goes from the center of the circle, which is not on the radius.
Al and Bill each have two bullets. They fire alternately at a glass bottle. Al has hitting probability 1/3 and Bill 1/4. What is the probability that Al smashes the bottle if he is the one who fires the first shot? (Note: Al can smash the bottle even if he misses with his first shot.)
Answers
P(Al misses the first shot but hits on his second shot) =
P( Al misses and bill misses and Al hits) = 2/3 * 3/4 * 1/3 = 1/6
So required probability = 1/3 + 1/6 = 1/2
What is the probability that at least 2 students in a class of 36 have the same birthday?
Answers
[tex]p_{no} (n) = \frac{364}{365} \cdot \frac{363}{365} \cdot ... \cdot \frac{365-n+1}{365} = \frac{364!}{365^{n-1} (365-n)!} [/tex]
Therefore, the probabilty that there are at least 2 students with same birthday is the complementary of this value:
[tex]p_{yes} (n) = 1 -p_{no}(n) =1- \frac{364!}{365^{n-1} (365-n)!}[/tex]
And if we use n=36 (number of students), we find
[tex]p=1- \frac{364!}{365^{36-1} (365-36)!} \sim 0.83[/tex]
So, the probability that there are at least 2 students in a group of 36 with same birthday is approximately 83%.
fresh raspberry contain 80% water.Dried raspberry contain only 20%.how many pounds do you get from 36lb fresh berries
Answers
1 % water = 36 ÷ 80 = 0.45 lb
20% water = 0.45 x 20 = 9 lbs
Answer: You will get 9 lbs of raspberry.
The amount of fresh berries that contain 80% water is 7.2 pounds.
Amount of water in fresh raspberry = 80%
It means the amount of raspberry only in a fresh raspberry =20%
Amount of water in dry raspberry =20%
What is a percentage?A percentage is a value per hundred.
So, the amount of raspberry only in 36 lbs fresh berries = 20% of 36
20% of 36 = (20/100)*36 = 7.2 lbs
So, the amount of raspberry only in 36 lbs of fresh berries = 7.2 lbs
Therefore, we get 7.2 lbs from 36lb fresh berries.
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Adams sister want to watch her intake of fat per day.he estimate that the dinner will have 48grams of fat.what percentage of her total daily allowance of fat will the dinner be round your answer to a whole number.the recommended daily allowance of fat is70g
Answers
Use the formula percent/of = x/100.
So, 48/70 and x/100 you cross multiply the numbers; 48*100 and 70*x and end up with 70x=4800.
Divide both sides by 70, which gives you 68.57.
Round the number up to 69 percent.
Given the least squares regression equation, = 1202 + 1,133x, when x = 4, what does equal?
Answers
This can be done by substituting the value of x for 4 and multiplying it by 1,133 which will eventually give you the answer of 4532.
After this step, all you have to do it add 1202 to 4532, resulting in an answer of 5734.