Consider the composite function g (f (x)) = x startroot 6 endroot. if f(x) = 3x2, g (x) = StartRoot 2 x EndRoot.
What is squareroot?
In mathematics, the square root is a factor that, when multiplied by itself, equals the original integer. For instance, the square roots of 9 are both 3 and -3. The Babylonians had efficient techniques for calculating square roots as early as the second millennium bc.Example of a square root-
The radical symbol for the number's root is shown here. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number. For instance, the square of 3 is 9, the square root of 9 is 9, and 32 also equals 9.Learn more about square root
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PLEASE SOLVE ITS FOR A TEST
Answer:
[tex]3\sqrt{3}[/tex]
Step-by-step explanation:
Claire has $300 in an account. She decides she is going to take out half of what's left in
there at the end of each month.
Recursive:
Explicit:
The recursive function is Tn = 1/2T(n - 1) where T1 = 300
How to determine the recursive and the explicit functions?Recursive function
Here, we have
She decides she is going to take out half of what's left in there at the end of each month.
This means that
Tn = 1/2T(n - 1)
Hence, the recursive function is Tn = 1/2T(n - 1) where T1 = 300
Explicit function
Here, we have
Initial, T1 = 300
Rate, r = 1/2
The explicit function is represented as
Tn = T1 * r^(n-1)
So, we have
Tn = 300 * (1/2)^(n-1)
Hence, the explicit function is Tn = 300 * (1/2)^(n-1)
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Solve each question for the variable.
7. p+12,982= 25,000 (1 point)
Op = 12,010
Op=12,018
Op = 12,028
Solve each question for the variable.
8. 912+e=1,201 (1 point)
Oe=389
Oe=299
Oe=289
Solve each question for the variable.
3. 918.2 + v= 1,920.8 (1 point)
Ov=1,000.6
Ov=1,002.6
Ov= 1,001.6
You have 80 fluid ounces of lemonade and you need to put them into containers that hold 1 pint. How many containers will you need?
When you have 80 fluid ounces of lemonade and you need to put them into containers that hold 1 pint, the number of containers will be 5.
How to compute the value?Note that the conversion ounce to pint is to divide the value by 16.
Therefore, 80 fluid ounces to pint will be:
= 80/16
= 5
Therefore, the value is 5 pints.
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What is the gradient of the graph shown?
Give your answer in its simplest form.
Answer:
1/3
Step-by-step explanation:
Gradient or slope can be found using the point-slope formula:
[tex]y-y_{1} =m(x-x_{1} )[/tex]
We can rearrange the equation to find slope (m) like so:
[tex]m=\frac{y-y_{1} }{x-x_{1} }[/tex]
To use this formula we need to find two well-defined points and use their coordinates.
Let's use (0,2) and (3,3) because they are clear points on the graph.
(0,2) will represent [tex]x[/tex] and [tex]y[/tex] in the equation respectively, and (3,3) our other point will represent [tex]x_{1}[/tex] and [tex]y_{1}[/tex].
Now we just need to plug the numbers into the equation:
[tex]m=\frac{2-3}{0-3} \\\\m=\frac{-1}{-3} \\m=\frac{1}{3}[/tex]
The gradient of the graph is 1/3.
Hope this helped!
The length of a rectangle is 3 cm longer than its width.
If the perimeter of the rectangle is 58 cm, find its length and width.
The length and width of the given rectangle is 16cm and 13cm.
What is a rectangle?A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. It can also be defined as an equiangular quadrilateral because all of its angles are equal; or a parallelogram with a right angle. A square is a rectangle with four equal-length sides.Formula of perimeter of a rectangle: 2(l+b)
Let, width be 'x' then length will automatically be 'x+3'.
Now, put the values in the formula:
P = 2(l+b)58 = 2(x+3+x)58 = 2(2x + 3)58 = 4x + 64x = 58 - 64x = 52x = 52/4x = 13So, width is 13cm then length is (13+3) that is 16cm.
Therefore, the length and width of the given rectangle is 16cm and 13cm.
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b) Find the value of 2a2 + 5b2 when a = -6 and b = 2
Answer: -4 because 2(-6)2 = -24 and 5(2)2 = 20 so -24 + 20 is -4.
Answer:-4
Step-by-step explanation:
2(-6)2
2 x -6 x 2=-24
5 x 2 x 2=20
-24+20=-4
What is the ratio of protonated/deprotonated acetic acid at ph 1.8, 5.8, and 10.8?
The ratio of protonated/deprotonated acetic acid at the given pH is:
pH 1.8: 1000:1, pH 5.8: 1:10, pH 10.8: 1:1000000What is acetic acid?Acetic acid, also known as ethanoic acid, is a colorless liquid with a strong, vinegar-like odor. It is referred to as glacial acetic acid when it is pure (100% acetic acid). Acetic acid is a byproduct of fermentation that gives vinegar its distinctive aroma. Vinegar contains approximately 4-6% acetic acid in water. More concentrated solutions are available in laboratories, and glacial acetic acid is pure acetic acid containing only traces of water. Human Reactions: Acetic acid, in vapor form, is a severe irritant to the eyes, mucous membranes, upper respiratory tract, and skin. When acetic acid solutions of 80% or higher come into contact with the skin or eyes, they can be corrosive, causing severe burns to any exposed tissue.The protonated/deprotonated acetic acid pH 1.8, 5.8, and 10.8 ratios are 1000:1, 1:10, and 1:1000000, respectively.Therefore, the ratio of protonated/deprotonated acetic acid at the given pH is:
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Dyani began solving the equation g = x-1/k for x by using the addition property of equality. explain dyani's error. then describe how to solve for x
Given equation g = x-1/k in terms of x would be x = 1 + gk
for given question,
we have been given an equation g = x-1/k
Dyani began solving the equation g = x-1/k for x by using the addition property of equality.
We solve given equation for x.
⇒ g = x-1/k ..........(Given)
⇒ gk = (x - 1/k)k .........(Multiply both the sides by k)
⇒ gk = x - 1
⇒ gk + 1 = x - 1 + 1 .........(Add 1 to each side)
⇒ gk + 1 = x
⇒ x = 1 + gk
Therefore, given equation g = x-1/k in terms of x would be x = 1 + gk
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The difference between two positive numbers is 2 and the difference between their squares is 40. Work out the two numbers.
Figure ABCD is a kite. What is the length of line segment AD? 8 units O 14 units 22 units 36 units
Length of line segment AD = 22 units .
Given : ABCD is a kite
AB and BC are congruent
AD and CD are congruent
AB = 14 units
CD = 22 units
To find : length of line segment AD
When 2 sides of a triangle are congruent , they are equal in measure ie. their magnitude is equal .
Since , AB and BC are congruent
⇒ AB = BC = 14 units
Similarly , CD = AD = 22 units
Therefore , length of line segment AD = 22 units .
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Answer: c on edge
Step-by-step explanation:
.chris p. bacon worked 44 hours last week and gets double time pay for overtime. his regular pay is $14 per hour. how much was his paycheck for the week?
The total paycheck for the week is of $672 as Chris bacon work for 44 hours last week, regular pay $14 per hour and double time pay for overtime.
As given,
Regular pay per hour = $14
Overtime work payment= 2 × ($14)
Total hours work done last week = 44hours
Let regular timing be 8 hours per day 5 days a week
Total regular working hours = 8 × 5
= 40 hours
Over time = 44-40
= 4 hours
Payment check = (40 × 14)+ (4 × 28)
= $672
Therefore, The total paycheck for the week is of $672 as Chris bacon work for 44 hours last week.
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HELP ME DO THESE PROBLEMS PLS THANK YOU
Answer:
6. 7
7. 32
8. -17
9. -24
10. 6 ft
Step-by-step explanation:
6: 2(3) +1
6+1=7
7: 16-4(-4)
16+16=32
8: 12(-2)+7
-24+7=-17
9: -9-3(5)
-9-15=-24
10: 24-3(6)
24-18=6
How much of a(n) 70% orange juice drink must be mixed with 18 gallons of a 30% orange juice drink to obtain a mixture
that is 50% orange juice?
Answer:
18 gallons
Step-by-step explanation:
Start with x gallons of 70% juice and 18 gallons of 30% juice.
Result: x + 18 gallons of 50% juice
0.7x + 0.3 × 18 = (x + 18)(0.5)
0.7x + 5.4 = 0.5x + 9
0.2x = 3.6
x = 18
Answer: 18 gallons
Given the functions f and g, EXPLAIN why you canNOT find f * g.
f = {(-1, 7), (1, 3), (3, 4), (6, 8), (7, 0)}
g = {(0, 10), (2, "-6)," (4, 7), (8, "-1)}
You cannot find f * g because the functions have different domains
How to explain why you cannot find f * g?The functions are given as:
f = {(-1, 7), (1, 3), (3, 4), (6, 8), (7, 0)}
g = {(0, 10), (2, "-6)," (4, 7), (8, "-1)}
In the above function definitions. we have
Domain of f(x): -1, 1, 3, 6, 7
Domain of g(x): 0, 2, 4, 8
See that both functions have different domains
This means that you cannot find f * g because the functions have different domains
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Antwan determines the distance between the points –7 and 2 on a number line. Maggie determines the difference between the numbers –7 and 2. How are Antwan’s and Maggie’s solutions related?
Maggie’s solution is the absolute value of Antwan’s solution.
Antwan’s solution is the absolute value of Maggie’s solution.
Both solutions are greater than either of the two numbers in the problem.
Both solutions are less than either of the two numbers in the problem.
Antawan's solution is the absolute value of Maggie's solution is the solution related to Antawan's and Maggie's solution.
Given
Antawan determines the distance between two points as 9.
Maggie finds the difference between two numbers ₋ 7 ₋ 2 = ₋9
Hence we notice that Antawan's solution is the absolute value to the Maggie's solution.
The non-negative value of x, regardless of its sign, is the absolute value (or modulus) | x | of a real number x. For instance, 5 has an absolute value of 5 and so does 5, which likewise has an absolute value of 5. One way to conceptualize a number's absolute value is as its separation from zero on the real number line.
hence option 2 is right.
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Flying to Houston with a tailwind a plane averaged 107 mph. On the return trip the plane only averaged 85 mph while flying back into the same wind. Find the speed of the plane in still air and the speed of the wind
The wind speed and plane speed is 11 and 96 mph.
It is required to find the speed of the plane in still air and the speed of the wind.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Let plane speed be "p".
Let wind speed be "w".
According to given question we have,
p + w = 107 mph
p - w = 85 mph
By the method of elimination we get,
2p = 192
p = 96 mph
The plane speed is 96 mph.
Solve for "w":
p + w = 107
96 + w = 107
w = 11 mph
The wind speed is 11 mph.
Therefore, the wind speed and plane speed is 11 and 96 mph.
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3(8-3)+2(4-1)
9(6-2)-11(5-2)
the solution for it ..
solving the bracket is important
5) If the sun is out, then it is daytime.
Converse:
Inverse:
Contrapositive:
the 3 statements are:
The converse statement is: If it is daytime, then the sun is out.
The inverse statement is: if the sun is not out, then is not daytime.
The contrapositive statement is: if it is not daytime, then the sun is not out.
How to find the converse, inverse, and contrapositive statements?
If we have two propositions P and Q, then we have a conditional statement:
If P then Q.
The converse statement is: if Q then P
The inverse statement is: if Not P, then Not Q.
The contrapositive statement is: if Not Q, then Not P.
The conditional statement is:
"If the sun is out, then it is daytime"
So we have:
P = the sun is out.
Q = it is daytime.
Then the 3 statements are:
The converse statement is: If it is daytime, then the sun is out.
The inverse statement is: if the sun is not out, then is not daytime.
The contrapositive statement is: if it is not daytime, then the sun is not out.
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The perimeter of the quadrilateral below is 119 units. Find the length of side AB.
Answer:
Step-by-step explanation:
Pls help me w thissssss
In this problem, we need to use multiplication and subtraction method to solve it.
_________________________________
x(y) means to multiply x with y
_________________________________
Note that {a = 7} and {b = 6}
First, we need to multiply 4 with {a = 7}, we get:
4(7) = 28
Then, we need to subtract {b = 6} from 28, we get:
28 – 6 = 22
Finally, this simplifies as:
4(7) – 6 = 22
Hope this helps :)
Which graph represents the function h (x) = -√x+2?
Answer:
Step-by-step explanation:
See the attached file below it will help to understand this problem and it will improve your grade and score.
Un automóvil recorre 1122.4 km con 80 litros de gasolina ¿cuántos kilómetros recorre con 16 litros de gasolina?
The automobile covers 224.48 km.
This problem can be solved by using the unitary method.
In this method we calculate the value for a unit quantity and then multiply it with the desired number for which we want to calculate.
Here it is given that a automobile covers 1122.4 km with 80 liters.
For 1 liter of gasoline distance covered = [tex]\frac{1122.4}{80}[/tex]
= 14.03 km
So, for 16 liters of gasoline distance covered will be = 16× 14.03
= 224.48 km
Therefore the automobile covers 224.48 km for 16 liters of gasoline.
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1/5 raised to the power minus 1
Simplification form of 1/5 raised to the power minus 1 is 5.
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
If a fraction's top and bottom share only one additional common factor, it is said to be in its simplest form. In other words, the top and bottom cannot be divided further and remain full numbers. Simplest form is also referred to as "lowest words."
The reduced form of a fraction is another name for its most basic form. For instance, the simplest representation of a fraction with a common component of 1 is 34 The simplest form, however, is not 2/4 because 12 is a further simplification of 2/4 that can be written.
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The 10th term of arithmetic sequence is three and common difference is three find the third term
Answer:
-18
Step-by-step explanation:
From 3 to 10th term is 7 d's ( d = common difference)
3 - 7d = third term
3 - 7(3) = -18
If 14 people are to be divided into 4 committees of respective sizes 2, 3, 4, and 5, how many divisions are possible?
The final answer is 24,024
In the given statement is :
If 14 people are to be divided into 4 committees of respective sizes 2, 3, 4, and 5
To find the how many divisions are possible
Let us understand the:
What do you mean by Permutation?
A Permutation is an act of arranging the objects or number in order.
Formula of Permutation :
The formula for Permutations is : n P r = n! / (n - r)!
n p r = n! /(n-r)!
14 P 4 = 14 ! / (14-4)!
= 14 × 13 × 12 × 11 x 10! / 10!
= 14 × 13 × 12 × 11
= 24,024
Hence, The answer is 254,024
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The formula for potential energy is p=mgh, where p is potential energy, m is mass , g is gravity and h is height . Which expression can be used to represent g
Answer:
The formula for potential energy depends on the force acting on the two objects. For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m / s2 at the surface of the earth) and h is the height in meters.
Step-by-step explanation:
Write 863.141 in expanded form.
Use the SOLVE Strategy to solve the problem below.
Wendy has taken two tests with scores of 77 and 80. To get an 82 average, what must her grade be on the third test?
Write and solve an equation to find her third test score. Show your work to explain how you determined her test score.
Rubric :
S - Underline the Question. ( 1 Point )
Answered Question, What is the Problem is asking me to find? ( 2 Points )
O- All Math facts are identified. ( 2 Points )
Unnecessary facts are eliminated. ( 2 Points)
All Necessary Facts are listed: ( 1 Point)
L- Use of correct operations . ( 2 Points )
Representation of the unknown. ( 2 Points)
Explained in a logical and sequential order. ( 2 Points)
V- Make estimation . ( 2 Points )
Number sentence matches plan for L. ( 2 Points)
Computation is correct . ( 2 Points )
E- Answer written in complete sentence. ( 1 Point )
Sentence Matches S. ( 1 Point )
Answer is correct . ( 1 Point )
Estimate was reasonable for the answer. ( 1 Point )
Answer: wendy should pick S
Step-by-step explanation:
Find EFgiven E(-7, -2) and F(11, 3)
According to the given statement;
EF=18.682.
What is Distance Formula?
The distance between two points is the length of the line joining the two points. If the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.
Distance formula used to find the distance measure between two lines, the sum of the lengths of all the sides of a polygon, perimeter of polygons on a coordinate plane, the area of polygons and many more.
According to the given value;
(-7, - 2) ; x1 = - 7 ; y1 = - 2
F = (11, 3) ; x2 = 11 ; y2 = 3
EF = √((x2 - x1)² + (y2 - y1)²)
EF = √((11 - -7)² + (3 - -2)²)
EF = √((11 + 7)² + (3 + 2)²)
EF = √(18² + 5²)
EF = √324 + 25
EF = √349
EF = 18.6815
EF = 18.682 units (3 decimal places )
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