[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]
It takes 5 minutes for 7 people to drink 25 pints of water.At this rate,how long would it take 15 people to drink 160 pints of water
Answer:
14.9 min
Step-by-step explanation:
r=rate
r25=5*7
r25=35
r=35/25
r=1.4
substitution
r160=t*15
t=time
r=1.4
1.4*160=t*15
224=t*15/15
224/15=t
14.9 min
the achievement first family handbook has 235 Pages Ms. Lieberman and print 450 copies of the document for the Middle School Scholars on Monday and 193 copies on Tuesday how many pages were printed in all
Answer:
151,105 pages
Step-by-step explanation:
(450 + 193) copies * 235 pages / copy = 643 copies * 235 pages = 151,105 pages
If covariance between two variables is near 0, it implies that:
Answer:
If the two random variables are independent, the covariance will be zero. It means they don't have any linear relationship.
Step-by-step explanation:
2x2 + 2x-4?
Which expression is equivalent to
2x2 - 4x + 2
X+2
X-1
X-2
o – 2
x+2
X-2
the quotient of 49 and a number
Answer:
7
Step-by-step explanation:
Which statement BEST compares the growth of the two functions shown in the table?
A
The value of the exponential function will never be greater than the linear
function
B)
The value of the linear function will never be greater than the exponential
function
The value of the linear function will eventually be greater than the
exponential function
D)
The value of the exponential function will eventually be greater than the
linear function
Answer will be (D)
The value of the exponential function will eventually be greater than the
linear function.
and
B)
The value of the linear function will never be greater than the exponential
function
a pole that is 3.3m tall casts a shadow that is 1.77 m long. at the same time , a nearby tower casts a shadow that is 38.5 m long. how tall is the tower? round your answer to the nearest meter
Answer:
21m
Step-by-step explanation:
First, divide 38.5 by 3.3.
Then, multiply that number by 1.77.
You will get 20.65...
Rounded, you will get 21 because .65 is bigger than half of one.
-kiniwih426
Solve for X: square root 2x power of 2 +5 = 2
A. plus and minus 1
B. square root 2
C. plus and minus 2
D. no solution
If there is 15 flowers in 3 pots how many flowers are in one pot
Answer:
5 simple because 5*3 =15Show your work on this I will mark as brainliest as well
Answer:
(-1, -4.5)
(-1.5, -2.5)
Step-by-step explanation:
To find the midpoint add the coordinates and divide by 2
19.( -8,-2) (6,-7)
((-8+6)/2, (-2+-7)/2) = (-2/2, -9/2) = (-1, -4.5)
20. ( 6,5) (-8,-10)
(( 6+-8)/2 , (5-10)/2) = (-3/2,-5/2) = (-1.5, -2.5)
Answer:
19. (-1, -4.5)
20. (-1, -2.5)
Step-by-step explanation:
19.
Use the midpoint formula.
[tex]\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]
Substitute the values.
[tex]\frac{-8+6}{2},\frac{-2-7}{2}[/tex]
Add/Subtract the numerators.
[tex]\frac{-2}{2},\frac{-9}{2}[/tex]
Divide.
-1, -4.5
20.
Use the midpoint formula.
[tex]\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]
Substitute the values.
[tex]\frac{6-8}{2},\frac{5-10}{2}[/tex]
Add/Subtract the numerators.
[tex]\frac{-2}{2},\frac{-5}{2}[/tex]
Divide.
-1, -2.5
(02.01)Which translation will change figure ABC to figure A'B'C'?
3 units right and 3 units up
4 units right and 3 units up
4 units right and 4 units up
4 units left and 3 units down
Answer:
4 units right and 3 units up.
Step-by-step explanation:
The sum of two numbers is 70, and their difference 30. Find the two numbers using the process of substitution. Let the first umber = x and the second number = y.
Answer:
x = 50, y = 20.
Step-by-step explanation:
x + y = 70
x - y = 30
From the second equation x = 30 + y, so substituting this in the first equation:
30 + y + y = 70
2y = 70 - 30 = 40
y = 20
and x - 20 = 30
so x = 50.
Answer:
20 , 50
Step-by-step explanation:
The sum of two numbers is 70 ⇒ x + y = 70 -------------(I)
x = 70 - y
Their difference 30 ⇒ x - y = 30 ----------(II)
Substitute x = 70 - y in equation (II)
70 - y - y = 30
Combine like terms
70 - 2y = 30
-2y = 30 - 70
-2y = -40
Divide both sides by (-2)
y = -40/-2
x = 20
Substitute the value of x in (I)
20 + y = 70
y = 70 - 20
y = 50
Arden has 7/8th yard of ribbon. What is the maximum number of 1/16th yard-long pieces Marilyn can cut from this ribbon?
Answer:
2/8 is the answer
Step-by-step explanation:
I think the answer
Help fasttttt the first correct answer I will give brainliest!!!!
Answer: i belive its 5 1/3 or B
Step-by-step explanation:
sorry if im wrong
Step-by-step explanation:
= ([tex]\frac{8}{3}[/tex])([tex]\frac{4}{3}[/tex])([tex]\frac{3}{2}[/tex]) = [tex]\frac{16}{3}[/tex] or [tex]5\frac{1}{3}[/tex]
please give me a brainliest answer
Find the slope of the line that contains the following pair of
points:
(-3,-4) and (3,-2).
Answer:
1/3
Step-by-step explanation:
gradient or slope = m
m = change in y ÷ change in x
= (-4 - -2) ÷ (-3 - 3)
= (-4 + 2) ÷ (-3 - 3)
= -2 ÷ -6
= 1/3
Rick bought 3 apples and 2 oranges for a cost of $1.55. Kim bought 4 apples and 3
3
oranges for a cost of $2.15. Find the cost of one apple.
someone please help me
Answer:
the slope is -2
Step-by-step explanation:
Answer:
1/1 = 1
Step-by-step explanation:
Use rise/run.
The x value increases by 1 in the same amount of time that the y value increases by 1. This gives you the slope 1/1 (y increase/x increase).
1/1 can then be converted to 1.
Find the measures of the interior angles.
what is angle a, b, and c
Using angle sum property
[tex]\\ \sf\longmapsto x+90+30=180[/tex]
[tex]\\ \sf\longmapsto x+120=180[/tex]
[tex]\\ \sf\longmapsto x=180-120[/tex]
[tex]\\ \sf\longmapsto x=60[/tex]
1x2x2x2x2x2x2x22222x0
Answer:
0
Step-by-step explanation:
Anything times 0 will be 0.
what is 1.07 × 103 in standard form.
Answer:
Multiply 1.07 by 103. 110.21
Step-by-step explanation:
Tell me if i'm wrong. Hope this helps!
Please help me due in an hour
Answer:
Ok so it would be square root 1
Step-by-step explanation:
Point M(-6,8) is dilated from the origin with a scale factor of 1/2. What is the coordinate of M'? *
Point M(-6,8) is dilated from the origin with a scale factor of 1/2, hence the new point is M'(-3, 4)
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and translation.
If a point A(x, y) is dilated by a factor k, the new point is A'(kx, ky).
Given Point M(-6,8) is dilated from the origin with a scale factor of 1/2, hence the new point is at:
M'(-3, 4)
Find out more at: https://brainly.com/question/13176891
A car rental agency charges $75 per day, which includes 100 miles. For each mile over 100 miles, there is an additional cost of $0.35 per mile.
Write an equation relating m, the number of miles driven, if the total cost for a one-day rental was $131.
Answer:
Answer for part b is ≈274 miles
Step-by-step explanation:
No idea what the equation is
Answer:
The number of miles, m driven if the total cost for a one-day rental was $131 is; m = 160
Step-by-step explanation:
A store sells a 3 -pound bag of oranges for $3.60 and a 5 -pound bag of oranges for $5.25 . What is the difference between the price per pound for the 3 -pound bag of oranges and the price per pound for the 5 -pound bag of oranges
Answer:
The price of 3 pounds would be $1.20 per pound and the price of 5 pounds would be $1.05 per pound
So, Five pound would cost 15 cents less than the 3 pounds
Step-by-step explanation:
Divide the price by the pounds
Hope this helps
∠2≅∠4, m∠2=110°. Find the measures of angles 1, 3, and 4 and explain how you know.
∠2 ≅ ∠4 = 110° [exterior alternate angles are equal]
∠1 = 180° - 110° = 70° [since angles on a line have a sum of 180°]
∠1 = ∠3 = 70° [since vertically opposite angles are equal]
if 2 + 2^2 + 2^3 +...+ 2^n = 510 then n = ?
Answer:
N= 8
Step-by-step explanation:
Answer:
n = 8
Step-by-step explanation:
This Geometric series. r = 2 and a = 2
[tex]S_{n}= \dfrac{a(r^{n}-1)}{r-1}\\\\\\\dfrac{2(2^{n}-1)}{2-1}=510\\\\\dfrac{2*(2^{n}-1)}{1}=510\\\\2*(2^{n}-1) = 510\\\\2^{n-1}=\dfrac{510}{2}\\\\2^{n} - 1 = 255\\\\2^{n}=255+1\\\\2^{n} = 256\\\\2^{n} =2^{8}[/tex]
n = 8
see screenshot below/above
Answer:
x-int: (-2,0)
y-int: (0,1.333)
Step-by-step explanation:
Hi I really need help with this question, ANSWERS ONLY, I'll give 35 POINTS, PLEASE
What is the positive conterminal angle to -32° that is between 500° and 1000° and a negative conterminal angle to -32° that is between -500° and -50°?
positive coterminal angle:
negative coterminal angle:
Answer:
0° and 90°, it's Ql. If between 90° and 1800 QQ. ... Find a positive and a negative conterminal angle for the given angle.
Step-by-step explanation:
The positive and negative coterminal angles to -32° are:
Positive coterminal angle = 688°
Negative coterminal angle = -392°
What is a coterminal angle?Coterminal angles are those whose terminal sides and beginning sides coincide.
The given angle measure is -32°.
The positive coterminal angle is:
-32° + 360°
= 328°
Since the angle is not between 500° and 1000°, add 360° one more times:
328° + 360°
= 688°
The negative co-terminal angle is:
-32° - 360°
= -392°
Hence, the positive and negative coterminal angles to -32° are:
Positive coterminal angle = 688°
Negative coterminal angle = -392°
Learn more about coterminal angles:
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The sum of the ages of Alice, Barbie & Cindy is 30. Alice is four times older than Cindy. Barbie is 3 years older than Alice. How old is Cindy?
A. 12
B. 21
C. 9
D. 3
E. 15
D.
Explanationbecause the number have 3
Step-by-step explanation:
A+B+C = 30
A = 4C
B = A+3
=> 4C+4C+3+C = 30
9C + 3 = 30
9C = 30-3
9C = 27
C = 3
Therefore, the age of Cindy is 3 years old
(option D)
What is the product?
(4x) {-3x^8}{-7x^3}
Answer:
[tex]84x^{12}[/tex]
Step-by-step explanation:
Step-by-step explanation:
[tex](4x)( - {3x}^{8} )( - {7x}^{3} ) \\ (4 \times - 3 \times - 7)( {x}^{} \times {x}^{8} \times {x}^{3} ) \\ (81)( {x}^{ 1 + 8 + 3} ) \\ 81 {x}^{12} [/tex]