[tex] {\large\underline{\sf{Solution-}}}[/tex]
Given function is
[tex]\rm \longmapsto\:y = \sqrt{ {x}^{2} - 4} [/tex]
We know
Domain of a function is defined as set of those real values of x for which function is well defined.
So, y is defined when
[tex]\rm \longmapsto\: {x}^{2} - 4 \geqslant 0[/tex]
[tex]\rm \longmapsto\: {x}^{2} - {2}^{2} \geqslant 0[/tex]
[tex]\rm \longmapsto\: (x - 2)(x + 2) \geqslant 0[/tex]
[tex]\rm\implies \:x \leqslant - 2 \: \: or \: \: x \geqslant 2[/tex]
[tex]\rm\implies \:x \: \in \: ( - \infty , \: - 2] \: \cup \: [2, \: \infty )[/tex]
Now, To find the range of function
We know,
Range of a function is defined as set of those real values which is obtained by assigning the values to x.
So,
[tex]\rm \longmapsto\:y = \sqrt{ {x}^{2} - 4} [/tex]
On squaring both sides, we get
[tex]\rm \longmapsto\: {y}^{2} = {x}^{2} - 4[/tex]
[tex]\rm \longmapsto\: {y}^{2} + 4= {x}^{2}[/tex]
[tex]\rm \longmapsto\:x = \sqrt{ {y}^{2} + 4 } [/tex]
Now, x is defined when
[tex]\rm \longmapsto\: {y}^{2} + 4 \geqslant 0 \: which \: is \: always \: true \: \forall \: y \in \: real \: number[/tex]
But,
[tex]\rm \longmapsto\:y \geqslant 0[/tex]
Hence,
[tex]\rm\implies \:Range \: of \: function \: = [0, \: \infty )[/tex]
So, we have
[tex]\rm\implies \:Domain \: of \: function : x \: \in \: ( - \infty , \: - 2] \: \cup \: [2, \: \infty )[/tex]
and
[tex]\rm\implies \:Range \: of \: function \: = [0, \: \infty )[/tex]
Two farms begin the year with $1,500 of extra saving in case they lose money at the year’s end.
And???? What are we computing, you just gave me a fact.
A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. The 95% confidence interval for the true mean number of pushups that can be done is _____.
Using the t-distribution, we have that the 95% confidence interval for the true mean number of pushups that can be done is (9, 21).
For this problem, we have the standard deviation for the sample, thus, the t-distribution is used.
The sample mean is of 15, thus [tex]\overline{x} = 15[/tex].The sample standard deviation is of 9, thus [tex]s = 9[/tex].The sample size is of 10, thus [tex]n = 10[/tex].First, we find the number of degrees of freedom, which is the one less than the sample size, thus df = 9.
Then, looking at the t-table or using a calculator, we find the critical value for a 95% confidence interval, with 9 df, thus t = 2.2622.
The margin of error is of:
[tex]M = t\frac{s}{n}[/tex]
Then:
[tex]M = 2.2622\frac{9}{\sqrt{10}} = 6[/tex]
The confidence interval is:
[tex]\overline{x} \pm M[/tex]
Then
[tex]\overline{x} - M = 15 - 6 = 9[/tex]
[tex]\overline{x} + M = 15 + 6 = 21[/tex]
The confidence interval is (9, 21).
A similar problem is given at https://brainly.com/question/25157574
Alicia has 7 paintings she wants to hang side by side on her wall.
2. If Alicia only wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display? Show your work.
3. In how many ways can Alicia arrange 4 out of the 7 paintings? Show your work.
The question is an illustration of permutation and combinations.
The number of ways she can choose 4 out of the 7 paintings is 35The number of ways she can arrange 4 out of the 7 paintings is 840The given parameters are:
[tex]\mathbf{n = 7}[/tex]
[tex]\mathbf{r = 4}[/tex]
(a) Choose 4 of 7 paintings
Choosing 4 of 7 paintings implies combination.
So, we have:
[tex]\mathbf{^nC_r = \frac{n!}{(n - r)!r!}}[/tex]
Substitute values for n and r
[tex]\mathbf{^7C_4 = \frac{7!}{(7 - 4)!4!}}[/tex]
[tex]\mathbf{^7C_4 = \frac{7!}{3!4!}}[/tex]
Expand
[tex]\mathbf{^7C_4 = \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times 4 !}}[/tex]
[tex]\mathbf{^7C_4 = 35}[/tex]
Hence, the number of ways she can choose 4 out of the 7 paintings is 35
(b) Arrange 4 of 7 paintings
Arranging 4 of 7 paintings implies permutation.
So, we have:
[tex]\mathbf{^nP_r = \frac{n!}{(n - r)!}}[/tex]
Substitute values for n and r
[tex]\mathbf{^7P_4 = \frac{7!}{(7 - 4)!}}[/tex]
[tex]\mathbf{^7P_4 = \frac{7!}{3!}}[/tex]
Expand
[tex]\mathbf{^7P_4 = \frac{7 \times 6 \times 5 \times 4 \times 3!}{3!}}[/tex]
[tex]\mathbf{^7P_4 = 840}[/tex]
Hence, the number of ways she can arrange 4 out of the 7 paintings is 840
Read more about permutation and combinations at:
https://brainly.com/question/15301090
You are using the equation 4(p – 7) = 44 to determine how many pictures can be saved at one time to the photo stream on your cell phone. Describe the operations in the order that you will perform them to solve the equation.
(i have the solution, but i don't really understand the question, it feel like i need some explanation or something.....i don't know. Cause it ask me "what is p" on next question so i don't really understand what should i do on this question.....please help...)
Answer:
p = 18
Step-by-step explanation:
4(p-7) = 44
The operations in order are to distribute first, 4p - 28 = 44
Isolate the variable, 4p = 72
and divide for the answer, p = 18
P stands for pictures, the number of pictures that can be saved to your photo stream at once is 18.
Anyone know how to solve this? Pease show how you got the answer:)
Suppose you used one quarter of a sheet of paper for each ad and four full sheets for the title banner in Problem 2. How many ads could you make?
- 56 ads
-48 ads
-64 ads
-12 ads
- 56 ads jajjajahahahahajha
Translate the sentence into an equation.
Eight more than the quotient of a number and 2 is 6.
Use the variable b for the unknown number.
Step-by-step explanation:
8 + b/2 = 6
8 more than the quotient of is 6
a number and 2
Please help it’s due today
Answer:
the answer is the 3rd one.
Step-by-step explanation:
easy one - giving brainly! show work.
(double-checking my answer)
Answer:
the height of the parent is 1.95 meters.
Step-by-step explanation:
divide 9 by 6 to get 1.5
multiply 1.5 by 1.3 to get the height of the parent
1.95m
your answer is correct
Answer:
The child's height is 6 cm
The parent's height is 9 cm
And now the child's height again 1.3 cm
And the parents height is 3.9
Step-by-step explanation: I think it's supposed to be that so yeah.
Elena needs to find a table that will fit three cube-shaped cases, each containing a frog. If the volume of each case is 1,000 cubic inches, could she use a table with a top that measures 30 inches long and 18 inches wide? Explain and show your work.
a) Find the length of the side of each case
b) Is the length of the table enough for the 3 cases? Explain
c) Is the width of the table enough for the 3 cases? Explain
Answer:
A is 30 inches
b is Yes
c
Step-by-step explanation:
calcular el valor de la fuerza desconocida en cada gráfico, si el sistema esta en equilibrio (les pongo coronita :c ayuda porfaaa)
Answer:
7. F=24N
8. P=16N
Step-by-step explanation:
the sum of all forces will equals 0
[tex]500+500+500[/tex]
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
: uoᴉʇnlos ɹnoʎ sᴉ ǝɹǝɥ
[tex]500 + 500 + 500[/tex][tex]1500[/tex]solve all these quick and brainliest answer
Answer:
a.
Step-by-step explanation:
25x^2-15x+25
=5(5x^2-3x+5)
b.
14xy-7x
=7x(2y-1)
5.a.
7x-4=24
or,7x=24+4
or,7x=28
or,x=28/7
therefore x=4
b.
4y+4=y+16
or,4y-y=16-4
or,3y=12
or,y=12/3
therefore y=4
Step-by-step explanation:
q 5)
a) as it's an Isosceles triangle so both the given sides are equal
so, a/q
→ 7x - 4 = 24
→ 7x = 24 + 4 = 28
→ x = 28/7 = 4
→ x = 4
therefore, value of x is 4.
b) 4y + 4 = y + 16
→ 4y - y = 16 - 4
→ 3y = 12
→ y = 12/3 = 4
→ y = 4
therefore, value of y is 4.
hope this answer helps you dear!
which square has more white space one big circle or small many circle explain
Answer:
When a circle is inscribed in a square , the diameter of the circle is equal to the side length of the square.
You can find the perimeter and area of the square, when at least one measure of the circle or the square is given.
For a square with side length s , the following formulas are used.
Perimeter = 4s
Area = s2
Diagonal = s2√
Similarly, you can find the circumference and area of the circle , when at least one measure of the circle or the square is given.
For a circle with radius r , the following formulas are used.
Circumference = 2πr
Area = πr2
Example 1:
Find the perimeter of the square.
When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square.
So, the side length of the square is 6 cm.
The perimeter P of a square with side length s is given by P=4s .
Substitute 6 for s in P=4s .
P=4(6) =24
The perimeter of the square is 24 cm.
Example 2:
What is the area of a circle that is inscribed in a square of area 64 square units?
When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is 8 units and therefore the radius is 4 units.
The area of a circle of radius r units is A=πr2 .
Substitute r=4 in the formula.
A=π(4)2 =16π ≈50.24
Therefore, the area of the inscribe circle is about 50.24 square units.
Step-by-step explanation:
3 (1 - 3x) = 2 (- 4x +7)
Answer: x = -11
Step-by-step explanation:
Expand the expression (distributive property): 3 - 9x = -8x + 14
// subtract 14 from both sides = -11
// add 9x on both sides = x
Simplify: x = -11
Answer:
[tex]x=-11[/tex]
Step-by-step explanation:
1) Rearrange Terms
[tex]3(-3x+1)=2(-4x+7)[/tex]
2) Distribute
[tex]-9x+3=2(-4x+7)[/tex]
3) Distribute
[tex]-9x+3=-8x+14[/tex]
4) Subtract 3 from both sides of the equation
[tex]-9x+3-3=-8x+14-3[/tex]
5) Simplify
A. Subtract the numbers
[tex]-9x=-8x+14-3[/tex]
B. Subtract the numbers
[tex]-9x=-8x+11[/tex]
6) Add 8x to both sides of the equation
[tex]-9x+8x=-8x+11+8x[/tex]
7) Simplify
A. Combine like terms
[tex]-x=-8x+11+8x[/tex]
B. Combine like terms
[tex]-x=11[/tex]
8) Divide both sides of the equation by the same term
[tex]\frac{-x}{-1} =\frac{11}{-1}[/tex]
9) Simplify
A. Cancel terms that are in both the numerator and denominator
[tex]x=\frac{11}{-1}[/tex]
B. Divide the numbers
[tex]x=-11[/tex]
(0.027/64000)⅓
guys pls I need help
Answer:
7.5×10^-3
Step-by-step explanation:
[tex] \frac{ 0.027}{64000} = \frac{2.7 \times{10}^{ - 2} }{6.4 \times {10}^{4} } [/tex]
due to the law of indices :
[tex] = 4.21875 \times 10 ^{ - 7} [/tex]
don't forget
(0.027/64000)⅓
so :
[tex] ({4.21875 \times {10}^{ - 7} })^{ \frac{1}{3} } [/tex]
i.e third root of the answer above
[tex] = 7.5 \times {10}^{ - 3} [/tex]
Write the slope-intercept form of the equation of the line perpendicular to the
graph of 2x-y=6 that passes through the point (-4,1).
Answer:
12x=4y........................................
Giving brainliest to the person who answers correctly.
What type of angles are these?
Answer: I believe those would be opposite angles (aka vertically opposite angles).
May I please receive help?
Step-by-step explanation:
the straight angle ;
180 - 42 = 138
The isosceles triangle ;
138 + x + x = 180
2x = 42
x = 21
pllease give me a brainliest answer
z-16z=15 what is z please
Answer:
z is equal to -0.88235294117
Step-by-step explanation:
so you first need to do is z minus 16z which is -17z.
you now have -17z is 15
you need to divide each side by -17z
so -17z divided by -17 is 1 z
and 15 divided by -17 is -0.88235294117
so z is equal to -0.88235294117
Hey there!
z - 16z = 15
-15z = 15
DIVIDE -15 to BOTH SIDES
-15z/-15 = 15/-15
CANCEL out: -15/-15 because that gives you 1
KEEP: 15/-15 because gives you the result of the z-value
SIMPLIFY IT
z = -1
Answer: z = -1
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Solve.
−712x=3.85
Enter your answer as a mixed number in simplest form in the box
Answer:
The answer is -6 3/5! Hope this helps you.
Ally's science class was looking at bacteria through a microscope. Ally's teacher said some bacteria can be as small as 0.00365 cm long. What is the length of the bacteria written in scientific notation?
The length of the bacteria should be written in scientific notation.
0.00365 in scientific notation = 3 × 10^-3
Given.
length of the bacteria in decimal = 0.00365 cm long
Scientific notation is written in the format x × 10ⁿ
where,
x = any number between digit 1 and 10
n = exponent (positive or negative).
To have a negative exponent value, move decimal to the rightTo have a positive exponent value, move the decimal point to the left.In this case, the nearest significant value is 3
So move the decimal point three times to where 3 is
That is,
0.00365 = 3.65
Since the decimal point is moved to the right 3 times, n = - 3
we have 10^-3
Therefore,
0.00365 in scientific notation = 3 × 10^-3
Read more:
https://brainly.com/question/10401258
please help! due tmr
Answer:
One solution
Step-by-step explanation:
3x+x+2=8x-4x+2
Combine like terms.
4x+2=4x+2
Solve for x
4x+(-4x)+2=4x+(-4x)+2
2=2
This equation has one solution because 2 only equals 2 and will not equal any other number.
expand and simplify 5(3x+2) -2(4x-1)
Step-by-step explanation:
5(3x+2)-2(4x-1)
15x+10-8x+2
7x+12
Determine a series of transformations that would map figure L onto figure M
Answer:
Translation followed by a Rotation.
Step-by-step explanation:
Hello! I need help with this question
Determine the inverse of the function f (x) = 3(x − 4)^2 + 5.
Step-by-step explanation:
since g(f(x)) = x g (f (x) )= x, f - 1 (x) = 5x3 + 43 f - 1 (x) = 5 x 3 + 4 3
The inverse of the given function [tex]f(x) = 3(x-4)^{2} +5[/tex] is [tex]f^{-1} (x) = \sqrt{\frac{x-5}{3} } +4[/tex].
What is the inverse of a function?An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by [tex]f^{-1}[/tex] or [tex]F^{-1}[/tex].
According to the given equation.
We have a function.
[tex]f(x) = 3(x-4)^{2} +5[/tex]
The above function can be written as
[tex]y = 3(x-4)^{2} +5[/tex]
Write the above function for x.
[tex]\implies y -5 = 3(x-4)^{2}[/tex]
[tex]\implies \frac{y-5}{3} = (x-4)^{2}[/tex]
[tex]\implies \sqrt{\frac{y-5}{3} } =x-4[/tex]
[tex]\implies \sqrt{\frac{y-5}{3} } +4=x[/tex]
[tex]0r\ x = \sqrt{\frac{y-5}{3}}+4[/tex]
Replace [tex]x[/tex] by [tex]f^{-1}(x)[/tex] and [tex]y[/tex] by [tex]x[/tex].
We get
[tex]f^{-1} (x) = \sqrt{\frac{x-5}{3} } +4[/tex]
Hence, the inverse of the given function [tex]f(x) = 3(x-4)^{2} +5[/tex] is [tex]f^{-1} (x) = \sqrt{\frac{x-5}{3} } +4[/tex].
Find out more information about the inverse of the function here:
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a locker contains 3 pairs of tennis shoes, 1 pair of jogging shoes, and 2 pairs of leather shoes. without looking , what's the probability of pulling out the pair of jogging shoes and then one pair of tennis shoes. (assume that you don't put the first pair of jogging shoes back in the locker.) write your answer as a fraction
Answer:
1/3 chance
Step-by-step explanation:
hoped this helped you!
2 root 5 x 5 root 5 sgsvbhmdhmcbjkd jklcdvncbcbxcvzbvk
Answer:
ummm?
Step-by-step explanation:
Answer:
Something
Step-by-step explanation:
I have no idea what u just asked
A line passes through point N ( -2, 0). Its slope is -3. What is the linear equation for this line?
Answer:
y = -3x - 6
Step-by-step explanation:
Please Help, This is confusing. What is the equation of the line that passes through the point (2,-6) and has a slope of -1?
Answer:
ok ok it is y+6=-1(x-2)
Step-by-step explanation:
brainliest?
Answer:
Firstly, you can use the slope and the first point to find a second point:
2 + 1 = x2 and 6 + 5 = y2 because the slope is 5/1.
Next you can write the equation in point-slope form (remember point-slope form is y - y1 = m(x - x1):
y - 11 = 5(x - 3)
Another equation would be B because B is the correct equation if you choose 2 as x2 and 6 as y2.
Hope this helps!