What is the domain of the function
f(x)= square root of (1/3)x+2?
Answers
Answer:
The domain of f(x) = √[(1/3)x +2] is [-6, ∞).
Step-by-step explanation:
GIven f(x) = √[(1/3)x +2], you have to find the values for which the the expression inseide the square will be possitive (for negative values the function is not defined for Reals.
(1/3)x + 2 = 0 ⇒ (1/3)x = -2 ⇒ x = -2/(1/3) ⇒ x = -6
Finally the domain of f(x) is (-6, ∞).
Answer:
✔️ X [tex]\geq[/tex] -6
Related Questions
an absolute value equation that equals 3 and -3
Answers
Final answer:
The absolute value equation that has solutions of 3 and -3 is |x| = 3. Substituting x = 3 or x = -3 into the equation both result in true statements, confirming they are the correct solutions.
Explanation:
The student is asking about solving an absolute value equation that has solutions of 3 and -3. To tackle this problem, you want to set up an equation where the absolute value is equal to both positive and negative 3. The most straightforward equation that satisfies this condition is |x| = 3. This equation means that the solution, x, can be either 3 or -3 because the absolute value of both numbers is 3. To verify that these are the correct solutions, you can substitute them back into the original equation:
For x = 3: |3| = 3, which simplifies to 3 = 3, confirming the solution.
For x = -3: |-3| = 3, which simplifies to 3 = 3, again confirming the solution.
This absolute value equation is an identity because substituting either solution results in a true statement.
which number is greater or equal or less than
Answers
Find two consecutive even integers whose sum is 126. write an equation.
Answers
Answer: Ist integer = 32
2nd integer = 34
Step-by-step explanation: SEE THE ATTACHED
At King’s Super Market, Clay bought 214 pounds of tomatoes for $13.50. Gabriella bought 112 pounds of tomatoes for $6.75 at the local farmer’s market. Who got the better deal?
At King’s Super Market, Clay bought 214 pounds of tomatoes for $13.50. Gabriella bought 112 pounds of tomatoes for $6.75 at the local farmer’s market. Who got the better deal?
Answers
Gabriella got the better deal, as she paid slightly less per pound for the tomatoes.
To determine who got the better deal, we need to calculate the price per pound of tomatoes for each person.
For Clay:
Price per pound = Total price / Total pounds
Price per pound = $13.50 / 214 pounds ≈ $0.0631 per pound
For Gabriella:
Price per pound = Total price / Total pounds
Price per pound = $6.75 / 112 pounds ≈ $0.0607 per pound
Comparing the two, we see that Gabriella paid approximately $0.0607 per pound, while Clay paid approximately $0.0631 per pound.
Circle the odd number.
2
6
10
17
Answers
Answer:
17
Step-by-step explanation:
17 is the odd number because 17 cannot be split into 2 equal groups. However, 2,6, and 10 can be split into 2 even groups. So therefor, they are even numbers.
.83 is 10 times as much as
Answers
Answer:
.083
Step-by-step explanation:
just divide by the number it says its times as
in this example divide .83 by 10
Answer:
0.083
Step-by-step explanation:
If you move the decimal once to the right from 0.083 you will get the answer .83
What is the value of x?
Plssss help me :(
Answers
Answer:I believe it’s 40 degrees
Step-by-step explanation:
70
-30
=
40
Hope this helped
Please answer this correctly
Is the answer
Blue marble
Pink marble
Yellow marble or
The red marble
Answers
The red marble is farthest from the target.
What is -3t+4=19 someone please help thank you
Answers
Answer:
t = -5Step-by-step explanation:
[tex]-3t+4=19\qquad\text{subtract 4 from both sides}\\\\-3t+4-4=19-4\\\\-3t=15\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3t}{-3}=\dfrac{15}{-3}\\\\t=-5[/tex]
Answer:
-5
Step-by-step explanation:
19-4= 15
15/-3 = -5
t = -5
Find m∠1, If m∠2=136°, m∠3=61°, m∠4=119°. give anws wer quickly pls
Answers
Answer: 44
Step-by-step explanation:
I’m assuming that the shape is a quadrilateral, meaning that it has 4 sides. All quadrilaterals need angles to add up to 360.
what do I do for 1-117? Help please!
Answers
Answer:
Step-by-step explanation:
You give characteristics about the polygons. Then you define then. For example, C is a rectangle because it has 4 right angles, it had 4 sides and corners, and it has two sets of parallel lines. For b, you just organise the polygons into the Venn diagram according to each polygons classification.
You need to count all of the loaves of bread in the front area there are 22 loaves of white bread 17 loaves of wheat bread and 19 Gourmet breads what is the total number of loaves
Answers
Answer:
58 loaves
Step-by-step explanation:
22+17+19= 58
Twenty-seven is
% of 60
help mee asap
Answers
Answer: The answer is: " 45 % " .
________________________________________________
→ " Twenty-seven is 45 % of 60. "
________________________________________________
Step-by-step explanation:
________________________________________________
The question asks:
" 27 is what % {percentage] of 60 " ? ;
________________________
So: " 27 = (n/100) * 60 " ; Solve for "n" ;
________________________________________________
Method 1:
________________________________________________
→ (n/100) * 60 = 27 ;
Divide each side by 60 :
→ [ (n/100) * 60 ] / 60 = 27 /60 ;
to get:
→ (n/100) = 27/60 ;
Now: Cross-factor multiply:
→ 60n = (27)*(100) ;
to get:
→ 60n = 2700 ;
Divide each side by "60" ;
→ 60n = 2700/ 60 ;
to get: n = 45 ;
________________________
→ The answer is: 45 % .
→ " Twenty-seven is 45 % of 60."
________________________________________________
Method 2:
________________________________________________
The question asks:
" 27 is what % {percentage] of 60 " ?
________________________
To solve this problem:
Rephrase this question as:
________________________
" 27 is 60% of what number ? "
→ The answer will be the same!
________________________
→ 27 = (60/100)* n ; Solve for "n" ;
Multiply each side of the equation by "100" ; to eliminate the fraction:
→ 100 * 27 = 100 * [ (60/100)* n ] ;
to get:
→ 2700 = 60n ;
↔ 60n = 2700 ;
Divide Each Side of the equation by "60" ;
→ 60n/60 = 2700 / 60 ;
to get: n = 45 ;
________________________________________________
→ The answer is: 45 % .
→ " Twenty-seven is 45 % of 60."
________________________________________________
Method 2: Variant 1 of 2:
________________________________________________
When we have:
→ 27 = (60/100)* n ; Solve for "n" ;
________________________
Note that: "(60/100) = (60÷ 100) = (6 ÷ 10)" ; since: in "(60/100)" ; the "zero" from the "numerator" cancels out; And: the "last zero" in "100" — from the "denominator" cancels out; since we are dividing "each side" of the fraction by "10" ;
→ "(60÷10) / (600÷10)" = " 6/10 " ;
→ " (6/10)" ; that is; "six-tenths"} ;
→ can be represented by: " 0.6 " ;
→ {by convention; but specifically, here is the explanation} — as follows:
________________________
→ "(6/10)" = " (6 ÷ 10) " ;
Note: When dividing a number by "10" ; we take the original number; and move the decimal point to the left; & then we rewrite that number as the "answer".
Note: When multiplying or dividing by a positive, non-zero integer factor of "10" that has at least 1 (one) "zero" after that particular factor of "10". We can get the answer by taking the original number & moving the decimal point the number of spaces as designated by the number of zeros following the particular [aforementioned factor of "10".].
We move the decimal point to the right if we are multiplying; and to the left if we are dividing. In this case, we are dividing "6" by "10 " :
→ " 6 ÷ 10 = ? " ;
→ " 6. ÷ 10 = ? " ;
We take the: " 6. " ; and move the decimal point "one space backward [i.e. "to the left"]; since we are dividing by "10" ;
→ to get: " .6 " ; & we rewrite this value as "0.6" in a rewritten equation:
________________________
So; we take our equation:
→ 27 = (60/100)*n ; And rewrite—substituting "0.6" for
"(60/100)"— as follows:
________________________
→ 27 = (0.6)n ; ↔ (0.6) n = 27 ;
Multiply each side of the equation by "10" ; to eliminate the decimal:
→ 10 * [ (0.6)n ] = 27 * 10 ;
to get:
→ 6n = 270 ;
Divide each side of the equation by "6" ; to isolate "n" on one side of the equation; & to solve for "n" ;
→ 6n / 6 = 270 / 6 ;
to get: n = 45 ;
________________________________________________
→ The answer is: 45 % .
→ " Twenty-seven is 45 % of 60."
________________________________________________
Method 2 (variant 2 of 2):
________________________________________________
We have the equation: 27 = (60/100)* n ; Solve for "n" ;
________________________
Note: From Method 2 (variant) 1 of 2— see above):
________________________
Note: Refer to the point at which we have:
________________________
→ " { (60÷10) / (600÷10)" = " (6/10) " ; that is; "six-tenths"} ;
________________________
Note that the fraction— "(6/10)" ; can be further simplified:
→ "(6/10)" = "(6÷2) / (10÷2)" = "(3/5)" ;
Now, we can rewrite the equation;
→ We replace "(60/100)" ; with: "(3/5)" :
→ 27 = (3/5)* n ; Solve for "n" ;
↔ (3/5)* n = 27 ;
↔ (3n/5) = 27 ;
Multiply Each Side of the equation by "5" ;
→ 5* (3n/5) = 27 * 5 ;
to get:
→ 3n = 135 ;
Divide Each side of the equation by "3" ; to isolate "n" on one side of the equation; & to solve for "n" ;
→ 3n / 3 = 135 / 3 ;
to get: n = 45 ;
________________________________________________
→ The answer is: 45 % .
→ " Twenty-seven is 45 % of 60."
________________________________________________
Hope this answer is helpful!
Wishing you the best in your academic endeavors
— and within the "Brainly" community!
________________________________________________
Answer and Step-by-step explanation:
[tex]27[/tex] of [tex]60[/tex] is [tex]45[/tex]%
Working out in percentage :
[tex]27[/tex] of [tex]60[/tex] can be written as :
[tex]\frac{27}{60}[/tex]
Multiplying both the numerator and denominator by [tex]100[/tex] :
[tex]\frac{27}{60} *\frac{100}{100}= \frac{45}{100}=45[/tex]%
So the answer to your question is [tex]27[/tex] of [tex]60[/tex] is [tex]45[/tex] %
Which of the following is the inverse to the function f(x)= x^2-10
Answers
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solve for "y".
[tex]\bf \stackrel{f(x)}{y}=x^2-10\implies \stackrel{switcheroo}{x=y^2-10}\implies x+10=y^2\implies \sqrt{x+10}=\stackrel{f^{-1}(x)}{y}[/tex]
Answer as a mixed number (4 1/4) - (7/3
Answers
4 1/4 - 7/3
17/4 -7/3
51/12 - 28/12
23/12 = 1 11/12
Answer: 1 and 11/12
Step-by-step explanation: (4 1/4) - (7/3)= 4 3/12- 2 4/12=1 and 11/12
From least to greatest 1.34,1 1/3,1 6/8,1.034?
Answers
1.034, 1 1/3, 1.34, 1 6/8
Explanation:
1 1/3 = 1.333333333
1 6/8 = 1.75
The sum of two numbers is 61 and the difference is 7. What are the numbers?
Answers
Answer:
ley the different numbers be x&y
x+y=67
x-y=7
2y=54
y=27
substitute for x
x-27=7
x=7+27
x=34
The two unknown numbers 'a' and 'b' are 34 and 27.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let the two numbers be 'a' and 'b'.
Given, The sum of two numbers is 61 which is (a + b) = 61...(i)
Also given the difference is 7 which is (a - b) = 7...(ii)
Adding the equations (i) and (ii) we get,
2a = 68 (+ b and - b cancel out)
a = 34 and hence 34 + b = 61 ⇒ b = 27.
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How is 0.004 the same as and different from 0.444?
Answers
Answer:both are in thousandths place,in the thousandths place both have 4 as a value
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given : 0.004 and 0.444.
To find : How is 0.004 the same as and different from 0.444.
Solution : We have given 0.004 and 0.444.
In 0.004
We can see tenth place digit is 0.
Hundredth place digit is 0
Thousandth place digit is 0.
In 0.444.
We can see here tenth place is 4
Hundredth place digit is 4
Thousandth place digit is 4.
We can conclude that 0.444 is greater than 0.004.
Therefore, 0.444 is greater than 0.004.
Why did the obtuse Angle go to the beach
Answers
An obtuse angle is any angle larger than 90 degrees and less than 180 degrees. In other words, if the angle formed where two line segments meet goes beyond a right angle, it's obtuse.
Angles between 90 and 180 degrees (90°< θ <180°) are known as obtuse angles. Angles that are 90 degrees (θ = 90°) are right angles. Angles that are 180 degrees (θ = 180°) are known as straight angles.A coat hanger as well as the angle of a roof creates an obtuse angle, because they both contain an obtuse interior angle.Learn more:
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The width of a rectangle is 3/4 its length. The perimeter of the rectangle is 420 feet. what is the length, in feet, of the rectangle.
Answers
Answer:
120
Step-by-step explanation:
Length of the rectangle = 120 feet
Given :
The width of a rectangle is 3/4 its length. The perimeter of the rectangle is 420 feet.
Let 'L' be the length of the rectangle
Width of the rectangle is 3/4 of its length
width = [tex]\frac{3}{4} \cdot length[/tex]
Perimeter of rectangle = 2(length ) +2(width )
[tex]P=2L+2W\\P=2L+2(\frac{3}{4}\cdot L) \\P=2L+(\frac{3}{2}t L) \\\\P=\frac{7}{2}L \\[/tex]
Given that perimeter of rectangle is 420 feet
Replace perimeter by 420 feet and solve for L
[tex]420= \frac{7}{2} L\\840=7L\\Divide \; by \; 7\\L=120[/tex]
Length of the rectangle = 120 feet
Width of the rectangle =[tex]\frac{3}{4} \cdot length= \frac{3}{4} \cdot 120=90[/tex]
Width of the rectangle = 90 feet
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Which expression represents the phrase "three times the sum of a number and 4"?
3x + 4
3(x+4)
3(3x+4)
3x−4
Answers
Answer:
The answer is: 3(x+4)
Step-by-step explanation:
Oof
Answer:
The correct option is 2.
Step-by-step explanation:
The given statement is "three times the sum of a number and 4".
We need write the mathematical expression for the given statement.
Let the unknown number be x.
The sign " + " is used for addition and sum.
The sign " × " is used for multiplication, times and product.
Sum of a number and 4 = [tex](x+4)[/tex]
Three times the sum of a number and 4 = [tex]3\times (x+4)=3(x+4)[/tex]
The required expression is 3(x+4). Therefore, the correct option is 2.
Two right triangles are graphed on a coordinate plane. One triangle has a vertical side of 2 and a horizontal side of 6. The other triangle has a vertical side of 10 and a horizontal side of 30.
Could the hypotenuses of these two triangles lie along the same line?
(A) No, because they are not similar triangles
(B) No, because one is larger than the other
(C) Yes, because they are both right triangles
(D) Yes, because they are similar triangles
Answers
Answer:
Consider two right triangles: 1. ΔABC with vertices A(0,0), B(0,2), C(6,0). Then AB is perpendicular to AC and AB=2 units (vertical leg), AC=6 units (horizontal leg).2. ΔXYZ with vertices X(6,-10), Y(6,0), Z(36,-10). Then XY is perpendicular to XZ and XY=10 units (vrrtical leg), XZ=30 units (horizontal leg).The equation of the line BC is Check whether points Y and Z lie on this line:Y(6,0): - true;Z(36,-10): - true.Answer: the hypotenuses of these two triangles could lie along the same line
Please answer this correctly
Answers
Answer:
ok honestly that wus super confusing, but i think its a trick question so the answer is 0
Step-by-step explanation:
What is the value of i20+1?
Answers
The value of i^{20}+1 is 2, which is calculated by recognizing that the powers of i repeat every 4 cycles and that i^20 simplifies to 1.
Explanation:The value of i^{20}+1 can be determined by understanding the properties of the imaginary unit i, which is defined by i^2 = -1.
The powers of i follow a cyclical pattern: i^0 = 1, i^1 = i, i^2 = -1, i^3 = -i, and i^4 = 1, with this pattern repeating every 4 powers.
To find i^{20}, we observe that 20 is divisible by 4 (20 = 4 × 5), so i^{20} = (i^4)^5 = 1^5 = 1.
Add 1 to this result, and we get i^{20} + 1 = 1 + 1 = 2.
3.249 rounded to nearest tenth
Answers
The number 3.249 rounded to nearest tenth is; 3.2
According to the question;
We are required to round off the number 3.249 to nearest tenthAccording to the place value concept in mathematics; the place values after the decimal point in a decimal number are identified from left to right, as tenths, hundredths, thousandths etc.
Evidently, the number which occupies the tenths position in 3.249 is the digit 2.
Consequently, to round the number 3.249 to the nearest tenth; the digit 4 is considered and rounded off to 0 or 1 as the case may be.Since, 4 is less than 5, it is rounded off to 0 and added to the digit, 2 which occupies the tenths position in the number 3.249
Ultimately, the number 3.249 rounded to nearest tenth is 3.2.
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Sara bought a dress on sale for $30. She saved 45%. What was the original cost?
I appreciate any help, thank you.
Answers
Final answer:
Sara paid 55% of the original price of the dress when she bought it for $30. By dividing the sale price by 0.55, we calculate that the original price was approximately $54.55.
Explanation:
To answer the question of what the original cost of Sara's dress was before she saved 45% on the sale, we need to set up a simple percentage calculation. Since Sara saved 45%, this means she paid 55% of the original price (100% - 45% = 55%). The sale price of $30 is what represents this 55%.
To find the original price, we can write the equation:
30 = 0.55 × (original price).
Now we divide the sale price by 0.55 to find the original price:
(original price) = $30 / 0.55 = approximately $54.55.
So the original cost of the dress was approximately $54.55 before the sale.
The original price of the dress is approximately '54.55'
Sara bought a dress on sale for $30 and she saved 45% on the dress
Thus the price she paid for the dress is 100%−45%=55%
Now 55% of the original price of the dress is the amount she paid for the dress
Thus let 'P' be the original price of the dress
We can say that,
55% of P = 30
[tex]55*\frac{P}{100}=30\\ 55*P=30*100\\55*P=3000\\P=\frac{3000}{55}\\ P=54.55[/tex]
Thus '54.55' is the required answer
An art teacher is hosting a summer art
camp. He has a total of $180 to purchase
snacks, drinks, and art supplies. He buys 45
bags of chips at $0.55 each and 45 juice
boxes at $0.80 each. How much money does
he have left to spend on art supplies?
Answers
Answer:
$119.25
Step-by-step explanation:
$0.55.×45= $24.75
$0.80×45= +$36.00
$180.00- $ 60.75= $119.25
Hope it helps :)
The amount of money he has left to spend on art supplies is $119.25.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that an art teacher is hosting a summer art camp. He has a total of $180 to purchase snacks, drinks, and art supplies. He buys 45 bags of chips at $0.55 each and 45 juice boxes at $0.80 each.
$0.55.×45= $24.75
$0.80×45= +$36.00
$180.00- $ 60.75= $119.25
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Find the pay per hour if you earned $120.67 for 16 hours worked.
Answers
Answer:
$7.54 / hour to the nearest cent.
Step-by-step explanation:
This is 120.67 / 16
= $7.54 / hour,
A scuba diver dives down 20 feet into the ocean. He then swims 11 feet back up towards the surface. What is the position of the scuba diver relative to the surface?
Answers
The position of the diver relative to the surface is -9 feets
Using the parameters given for our Calculation;
downward distance = 20Upward distance= 11Difference in distance
20 - 11 = 9Since, we are expressing position relative to the surface , The diver is 9 feets below the surface , which would be expressed as -9 feets.
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help! i need the answer to this
Answers
Answer:
Yes
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 270°
a point (x, y ) → (y, - x )
Thus
A(1, 1 ) → A'(1, - 1 )
B(1, 4 ) → B'(4, - 1 )
C(3, 4 ) → C'(4, - 3 )
D(6, 1 ) → D'(1, - 6 )
These are the correct coordinates for the diagram A'B'C'D'
A translation (x, y ) → (x + 4, y + 1 )
Add 4 to the x- coordinates and add 1 to the y- coordinates, that is
A'(1, - 1 ) → A''(1 + 4, - 1 + 1 ) → A''(5, 0 )
B'(4, - 1 ) → B''(4 + 4, - 1 + 1 ) → B''(8, 0 )
C'(4, - 3 ) → C''(4 + 4, - 3 + 1 ) → C''(8, - 2 )
D'(1, - 6 ) → D''(1 + 4, - 6 + 1 ) → D''(5, - 5 )
These are the correct coordinates for the diagram A''B''C''D''
Hence the composition of transformations is correct