The domen range of the function y = √(x² - 4) is _____.
Please explain with step i need explanation.
[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]
asap po please thank you po!
Answer:
Step-by-step explanation:
2. Should be 500
8. Should be 290
The rest are correct
Answer:
1. 100 good job
2. 500 round to the nearest hundred either 400 or 500. 500 is closer.
3. 9,000 good job
4. 7,800 good job
5. 250 good job
6. 4,000 good job
7. 6,800 good job
8. 290 round to the nearest 10 either 290 or 300 290 is closer
9. 400 good job
10. 8,000 good job
Step-by-step explanation:
Rounding to the nearest number is up at 5 and below for 4 and less. The same concept applies to larger numbers.
find the measure of the indicated angle
Answer:
Angle A is also the measurement of 48 degrees because the dashes on the triangle lines indicate that they are the same.
Step-by-step explanation:
The energy needs of an eagle range between 350-600 calories per day. If it gets 120 calories from consuming 1 snake, how many snakes can it have
Answer:
3- 5 snakesStep-by-step explanation:
One snake gives 120 calories, so 3 snakes = 360 and 5 snakes = 600 calories.
The eagle can have 3 - 5 snakes per day
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The required number of snakes is ~
[tex]3 \: \: to \: \: 5 \: \: \: snakes[/tex][tex] \large \boxed{ \mathfrak{Explanation}}[/tex]
Minimum number of snakes that the eagle need to eat to maintain its energy level ~
[tex] \dfrac{350}{120} [/tex][tex] \dfrac{35}{12} [/tex][tex] \approx3[/tex]Maximum number of snakes that the eagle should eat to maintain the level of energy ~
[tex] \dfrac{600}{120} [/tex][tex]5[/tex]So,
The Eagle should have 3 - 5 snakes per day ~
Please help I need 6543÷29 options for answers are below in picture
Answer:
6543÷29
=225.620.......
PLEASE HELP.
I’m not good at algebra and I’m stuck.
7/12 divided by 3 3/4
Answer:
The answer is 7/45
Step-by-step explanation:
First you make 3 3 /4 into an improper fraction which becomes 15/4
Next, you do KFC which is keeping 7/12, making the division sign into multiplication, and then finally you flip 15/4 to 4/15.
Your final answer is 7/45
Hope that helped! Can I also get brainliest? I need a few more to advance, if not thank you anyways and have a nice day!!!
factorise the following, with steps
Answer:
Step-by-step explanation:
1) Sum = - 9
Product = -36
Factors = -12 , 3 {-12 + 3 = -9 & -12*3 = -36}
3a² - 9a - 12 = 3a² + 3a - 12a - 12
=3a(a + 1) - 12(a + 1)
= (a + 1) (3a - 12)
2) 4a² + 38a - 20 = 4a² + 40a - 2a - 20
=4a(a + 10) - 2(a + 10)
=(a + 10)(4a - 2)
3) 11a² + 30a - 9 = 11a² + 33a - 3a - 9
= 11a(a + 3) - 3(a + 3)
=(a + 3)(11a - 3)
Drag up the correct symbol to make the following relationships true.
9,100
9,200
42,720
42,650
912
738
Three years after a tree was planted it was 9 feet tall. Seven years after it was planted it was 17 feet tall. a What is the yearly growth rate of the tree? b. Determine the height of the tree when it was planted.
Answer:
your answer i think is 2/3 sorry if i'm wrong
Step-by-step explanation:
Forty-eight divided by one hundred equals what?
Answer:
0.48
Step-by-step explanation:
jou just have move point from right to left like this 48 rite so 48. =because have to zero u hqve move two place left so it will be 0.48
Answer:
0.48
Step-by-step explanation:
48 divided by 100=0.48
Plz help
A)40
B)30
C)24
Answer:
I think its 30 hope this helps and sorry if I get it wrong
Answer:
B) 30
Ok now that you have the answer......
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WHAT AM I???????
why are 4^0 and (-4)^0 is equal to 1,while -4^0 is equal to -1
Step-by-step explanation:
According to the zero property of exponents, any number (other than 0) raised to the power of zero is always equal to 1.
The problem with this question is the simple fact that in this format it is confusing.
So, -(4^0) = -1 × (4^0) = -1x1 = -1
and, (-4)^0 =1
trying to figure it out
I need answers fast plsss
Answer:
1/6
Step-by-step explanation:
the form you're using is slope-intercept. That is
y=mx+b
where y= y coordinate
m=slope
x= x coordinate
and b= y intercept
so, m in that equation is 1/6, so the slope is 1/6
Hope this helps!
Which segment is a dilation of BC using A as the center of dilation and a scale factor of 2/3
Answer: 45
Step-by-step explanation:
Quadrilateral ABCD has both reflection and rotation symmetry. What type of quadrilateral could it
be? Show or explain.
Answer:
Rhombus
Step-by-step explanation:
So if |AB| = |BC| then ABCD is a rhombus and has a second line of reflective symmetry, namely \overleftrightarrow{BD}. Quadrilateral ABCD is what is called a kite.
Since ℓ contains two vertices of ABCD the other two must be reflections of one another about ℓ. In the picture ℓ goes through A and C and D=rℓ(B). So rℓ interchanges AD¯¯¯¯¯¯¯¯ and AB¯¯¯¯¯¯¯¯ and also interchanges CB¯¯¯¯¯¯¯¯ and CD¯¯¯¯¯¯¯¯. So if |AB|=|BC| then ABCD is a rhombus and has a second line of reflective symmetry, namely BD←→. Quadrilateral ABCD is what is called a kite. Note that we have implicitly used the fact that ABCD is convex: without this hypothesis, the vertex C could be reflected over BD←→, giving a non convex quadrilateral with exactly one line of symmetry.
Rectangle has rotational and reflectional symmetry.
What is Quadrilateral?
A quadrilateral is a polygon having four sides, four vertices and four angles.
Given that;
Quadrilateral ABCD has both reflection and rotation symmetry.
Now,
A rectangle ABCD has a reflection symmetry because it has two line of symmetry.
And, Rotational symmetry is defined as the number of times an object is exactly identical to the original object in a complete 360° rotation.
So, Rectangle ABCD has rotational symmetry.
Thus, Rectangle has rotational and reflectional symmetry.
Learn more about the quadrilateral visit:
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Which function is equivalent to g ( x ) = x 2 + 15 x - 54?
Answer:
g(x) = (x+18)(x-3)
Step-by-step explanation:
g(x) = x²+15x-54= x²+18x-3x+54= x(x+18) -3(x+18)g(x) = (x+18)(x-3)The product of four and a number C is decreased by five?
8.8d + 9.65 = –3.01 + 7.2d + 1.46
d= -14 right ?
Answer:
d=-7
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Answer:
d=-23.934375
Step-by-step explanation:
If it is 7:00 AM at letter F, what time is it at letter A?
5:00 AM
5:00 PM
4:00 AM
4:00 PM
Answer:
The aswer is 1:00 AM to 1:00 PM.
Step-by-step explanation:
A lab technician has 40 gallons of a 15% iodine solution. How many
gallons of a 40% iodine solution must he add to make a 20% iodine solution?
Please show work!!
The quantity of a 40% iodine solution that must be added to 40 gallons of a 15% iodine solution to make a 20% iodine solution is: 10 gallons.
According to the question;
We are required to determine how many gallons of a 40% iodine solution must he add to make a 20% iodine solution.Let gallons of a 40% iodine solution to be added be; x gallons.
Therefore, the total gallons of a 20% iodine solution obtained is; (40+x) gallons.
By mass balance of iodine in each solution;
(15% of 40) + (40% of x) = (20% of (40 + x))(0.15 × 40) + 0.4x = 0.2x + 80.2x = 2x = 10 gallons.In essence; 10 gallons of a 40% iodine solution must be added to make a 20% iodine solution.
Read more:
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please help me solve this thank uuu
Answer:
Same Side Interior Angles
Step-by-step explanation:
Angle 7 and angle 14 are both inside of the two transversal lines E and M, and are on the same side of the line Q, making them both same side interior angles
-Chetan K
May I please receive help?
Please?))
Answer:
50°
Step-by-step explanation:
Please leave a “thanks” heart if I helped.
Activity Give the exponential model for the following situation
Answer:
Suppose that a couple invested $50,000 in an account when their child was born, to prepare for the child's college education. If the average interest rate is 4.4% compounded annually, ( A ) Give an exponential model for the situation, and ( B ) Will the money be doubled by the time the child turns 18 years old?
( A ) First picture signifies the growth of money per year.
( B ) Yes, the money will be doubled as it's maturity would be $108,537.29.
a = p(1 + \frac{r}{n} ) {}^{nt}a=p(1+
n
r
)
nt
a = 50.000.00(1 + \frac{0.044}{1} ) {}^{(1)(18)}a=50.000.00(1+
1
0.044
)
(1)(18)
a = 50.000.00(1 + 0.044) {}^{(1)(18)}a=50.000.00(1+0.044)
(1)(18)
a = 50.000.00(1.044) {}^{(18)}a=50.000.00(1.044)
(18)
50,000.00 ( 2.17074583287910578440507440 it did not round off as the exact decimal is needed.
a = 108.537.29a=108.537.29
Step-by-step explanation:
Hope This Help you!!
helppppppppppppppppppppppppppppppp
Step-by-step explanation:
wjjdjrjdjdjdudidjdkdk pick the C
Answer:
D,
Step-by-step explanation:
Step 1: 47-12=27, 27+(-27)=0
step 2: 27/2=13.5, 2c/2=c
step 3, change 13.5 to fraction which is 13 1/2
(hope it's helpful :)
GHD989 guys please you this code for guathmath thank you .
I will do that soon okay I will
f) create a residual plot for your data.
g) does your residual plot show that the linear model from the regression calculator is a good model?
h) using your equation estimate the gpa of a student who studies for 15 hours a week.
PLSSSSS NEED HELP
Answer: Consider the plot created from the residuals of a line of best fit for a set of data. Does the residual plot show that the line of best fit is appropriate for the data? Yes, the points have no pattern.
Step-by-step explanation:
can someone please help me with this
Answer:
Add 8 and 8 and then add 5and 5 and get answer 16
Step-by-step explanation:
write linear equatuon relating x and y for each table x (2,4,6,8). y (5,8,11,14)
Step-by-step explanation:
x increases continuously in steps of 2, y increases continuously in steps of 3.
so the slope of the line is y difference / x difference = 3/2. and the slope is siesta the factor of x in the equation
the line equating looks so far like
y = (3/2)×x + b
to get b we use one of the x and y pairs like (2, 5) and put these values in :
5 = (3/2)×2 + b = 3 + b
b = 2
so, the full equation is
y = (3/2)×x + 2