What is the domain of f(x)=[1/2]*

Answer:

  28 toys

Step-by-step explanation:

Ben has 50 toys, of which 15 are new, 9 are favorites, and 2 are new and favorites. You want to know the number that are neither new nor favorite.

The number of new toys includes (new and favorite) and (new and not favorite). That is ...

  15 = 2 + new and not favorite

So ...

  new and not favorite = 15 -2 = 13

Likewise, the number of favorite toys includes (new and favorite) and (not new and favorite). That is ...

  9 = 2 + not new and favorite

  not new and favorite = 9 -2 = 7

The total of 50 toys includes ...

  total = (new and favorite) + (new and not favorite) + (not new and favorite) + (not new and not favorite)

  50 = 2 + 13 + 7 + (not new and not favorite)

Then the number of (not new and not favorite) is ...

  not new and not favorite = 50 -2 -13 -7 = 28

These are the toys that Ben gives away.

Ben gives away 28 toys.

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Answer:

D.

Step-by-step explanation:

4/5 ÷ 3 = 4/5 * 1/3

This is 1/3 of 4/5.

The dimensions of the rectangle are 40 and 18 units respectively

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given here: The length of a rectangle is 4 feet more than twice the width.

Then let the width be x then length is equal to 2x+4 and therefore the perimeter is 2(2x+4+x)=116

                       3x+4      = 58

                             3x    = 54

                               x     = 18

Hence, the dimensions of the rectangle are 40 and 18 units respectively.

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Answer: Let's say,

y = the amount of money Perry will owe his brother after n months.

x = the principal (the initial amount borrowed) = 150

r = the interest rate per month = 7/100 = 0.07

n = number of months.

We know that Interest on a loan is calculated by multiplying the principal by the interest rate.

Therefore, the interest for n months is (0.07*x)*n

So to find the total amount Perry will owe his brother after n months, we need to add the interest to the principal amount.

y = x + interest

y = x + (r*x)n

y = x(1 + rn)

Therefore, the rule in the "y =..." form that will give the amount of money, y, Perry will owe his brother after n months, assuming that he doesn't make any payments is:

y = 150(1 + 0.07*n)

It's worth noting that this formula can be used to calculate the amount he will owe after any number of months by changing the value of n, and It's assuming he doesn't make any payments, meaning if he makes any payments, the total amount he will owe will change.

Step-by-step explanation:

Answer:

The table with (-3, 2), (0, 2), etc.

Every input has exactly one output.

Hope this helps :)

The domain of the function F(x) = 3 [tex]\sqrt{x-2}[/tex] is {x : x ≥ 2 and x is a real number}.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given function is,

F(x) = 3 [tex]\sqrt{x-2}[/tex]

Domain of this function is all the values of x for which the function is defined.

The expression [tex]\sqrt{x-2}[/tex] is defined only when the value of x - 2 is positive.

x - 2 > 0 ⇒ x > 2

So the function will be defined for all x > 2.

Hence the domain of the function is the set of all x such that x > 2.

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The area of the parallelogram is 72 square units. Option B

The formula for calculating the area of a parallelogram is expressed as;

A = bh

Given that;

From the information given, we have that;

Now, substitute the values

x + y = 8 + 4

add the values

x + y = base = 12 units

h = 6 units

Now, substitute the values into the formula, we get;

Area, A = 12(6)

multiply the values

Area, A = 72 square units

Hence, the value is 72 square units

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Answer:

Q = 3.667

Step-by-step explanation:

Answer:

Area= 46,000

Permiter= 4,600

Step-by-step explanation:

The formula to find the area of a rectangle is Length(L) times Width(W).

So 2,000(L) times 23 (W)= 46,000.

The formula for perimeter is 2(l+w).

So you're going to go 2,000 + 23 = 2,300 times 2 which equals 4,600.

Hope that helped, have a great day!!

Answer:

49200 rs. so the cost of flooring =246*200=49200 rs

Step-by-step explanation:

we measure the area of veranda by taking width in addition of length and breadth- house area

it means

area of veranda =outer rectangle-inner rectangle

⇒area= (20+3+3)*(15+3+3)-20*15

⇒area=26*21-300

⇒area= 546-300

⇒area=246 m²

Hence , the cost of flooring =246*200=49200 rs.

Therefore , the solution of he given problem of linear equation comes out to be x = 5.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

Here,

Given : 2x-4=6

To prove x =5

Thus,

We have to find the value of x

[tex]= > 2x =10\\= > x =10/2\\= > x =5[/tex]

Therefore , the solution of he given problem of linear equation comes out to be x = 5.

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Answer: Yes.

Step-by-step explanation: They are in 1:4::1:4

Hope this helps

Answer:

Step-by-step explanation:

Are The Numbers 16,64,18 and 72 In Proportion​?

16 : 64 = 18 : 72

0.25 = 0.25

or

1/4 = 1/4

so your answer is yes

Answer:

yes

Step-by-step explanation:

51 to nearest ten is 50

37 to nearest ten is 40

50 * 40 = 2000

and it's an estimate so yes

The function f(g) is 8/(8+9x) and the function g(f) is -8x/(x-9).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=x/(x-9) and g(x)= -8/x.

1) f(g)

Here, f(-8/x)= -8/x ÷ (-8/x -9)

= -8/x ÷ (-8-9x)/x

= -8/x × x/(-8-9x)

= 8/(8+9x)

2) g(f)

Now, -8/x/(x-9)

-8x/(x-9)

3) f(f)

Here, f(f) = x/(x-9) ÷ (x/(x-9) -9)

= x/(x-9) ÷ ((x-9x+81)/(x-9))

= x/(x-9) × (x-9)/(-8x+81)

= x/(-8x+81)

4) g(g)

Now, -8/(-8/x)

= 64/x

Therefore, the function f(g) is 8/(8+9x).

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Answer:

x+x+10=90 being Right angle triangle.

2x=90-10

2x=80

x =40

then x+10= 40 + 10

= 50

Answer:

To find the principal, P we can use the same formula, A=P(1+rn)nt. We have the balance of the account, A, after 6 years, $1,780.80. The interest rate, r, is 6.8% (or 0.68 as a decimal) and is compounded annually, so n=1. The time, t, is 6, since we know he opened his account 6 years ago. Plug in the known values into the formula and solve for the missing variable, P.

Step-by-step explanation:

1,780.80 = P (1+0.0681 divided 1^(6)

1,780.80= 1.484P

1,200=P         the principal amount Lex used to open his account 6 years ago

The trigonometric ratios for the angle x in the triangle are given as follows:

The three trigonometric ratios are defined as follows:

In the right triangle in this problem, we have that d represents the hypotenuse, while the sides relative to angle x are given as follows:

These sides are used along with the definitions of each ratio to give the three trigonometric ratios of angle x.

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The number of atoms that are there in 400 grams of hydrogen will be 2.408 × 10^26.

Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.

In this case, there are 6.02 × 10^23 atoms in 1 gram of hydrogen.

The number of atoms that are there in 400 grams of hydrogen will be:

= 6.02 × 10^23 × 400

= 2408 × 10^23

= 2.408 × 10^3 × 10^23

= 2.408 × 10^26

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If the total length of the journey is 146 km and he maintain the same  speed, the longer time he will be using for driving  will be 65m.

The  total length of my journey is 146 km.

Then the remain of the journry to reach 146 km = 146- 48 = 98

Then the if the same speed is maintained the estimate of  longer time he will be using for driving  will be calculated as :

(32 * 98)/48

Then get the productor quotient = 196/3 = 65 minutes

Therefore, option E is correct.

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MISSING OPTIONS:

A. 32

B.40

C. 52

D. 60

E.65

Answer:

Step-by-step explanation:

This is a right triangle that has two equal sides - so it is also isosceles.

It can be solved using Pythagoren Theorem.

a²  +  b²  =  c²

In this case a = b

so:  

6²  +  6²  = c²

36 +  36 =  c²

72  =  c²

[tex]\sqrt{72[/tex]  =  [tex]\sqrt{c^{2} }[/tex]

8.49 = c

round to 8.5

This is the length of the flap.

Using the provided quadratic expression and factorizing it, The answer is  x = ± √6.4 or x = ± 2.51 and  x = 1 or x = -2.5 .

An equation is a statement of equality between two expressions. It typically includes numbers and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is a statement that the value of the expression 2x + 3 is equal to the value of 7. Equations can also include variables, which represent unknown values that can be solved for.

Roots of an equation are the values of the variable that make the equation true. For example, the roots of the equation x^2 + 2x - 3 = 0 are -1 and 3, because (-1)^2 + 2(-1) - 3 = 0 and 3^2 + 2(3) - 3 = 0. In general, finding the roots of an equation can be a difficult task and may require the use of mathematical techniques such as factoring, graphing, or numerical methods. Roots are also known as solutions or zeroes of an equation. They can be found by setting the equation equal to zero and solving for the variable.

(4+5x²-36) = 0 or (2x²+9x-5) = 0

Solving the first factor:

4+5x²-36 = 0

5x²-32 = 0

5x² = 32

x² = 6.4

x = ± √6.4

x = ± 2.51 or -2.51

Solving the second factor:

2x²+9x-5 = 0

x²+4.5x-2.5 = 0

(x-1)(x+2.5) = 0

x = 1 or x = -2.5

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Answer:

It means that if the system of equations has an infinite number of solution, then the system is said to be consistent.

Candles should burn one hour for every 1 inch in diameter of the actual candle size. For example, a candle that is 2 inches across should burn for 2 hours.

At what rate does then candle burn, in inches per hour?

Smaller candles with smaller wicks will burn at a rate of 7 to 9 hours per 28 g of wax used. Larger candles with larger wicks consume wax at a faster rate. The larger wicks can be expected to yield 5 to 7 hours per 28 g of wax used.

Estimate the total number of burns by dividing the total wax weight used in the candle (not the weight of the candle with container) by the amount of wax used from burning the candle. Finally, multiply the estimated total burns by the burn time hours. This will provide an estimate of the candle's burn time.

The two main factors for burning candles is wick size and type of wax. Wider or thicker wicks will burn much faster than thin ones, and the material the wick is made with can also make an impact. Different types of candle wax burn at different temperatures.

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Answer:

320 pushups

Step-by-step explanation:

16/6= 8/3

8/3*120=32

x = 3/4 is the correct solution of the given expression.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

The expression Lin tried to solve
8(x-3)+7=2x(4-17)

Simplifying the expression,
8x - 24 = 2x(-13)
8x - 24 = -26x
8x+26x = 24
32x = 24
x = 24/32
x = 3/4

Thus, x = 3/4 is the correct solution of the given expression.

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Answer:

Error is in line 3

Error description: Root of 4 is 2 not 4

Correct answer should be 9*√5 (12*√5 - 3*√5)

Therefore ,We can see that in equation 1 plunk yields the most lorgs at 30. So the plunk coin is the most valuable.

A mathematical statement known as an equation is created by joining two expressions using the equivalent sign. For instance, 5x - 5 = 25 is an equation. We can find that the variable x has a value of 6  by resolving this equation.

Here,

we need to convert everything to the same unit in order to establish a legitimate comparison when comparing units like inches, feet, and yards. Therefore, we would have to convert everything, for example, to inches. For these five coins, the same concept holds true. Either lorgs, sinds, plunks, harps, or dalts must be used for everything (pick one of those five).

It's equivalent to attempting to change a dollar amount into cents (for example, $1.37 becomes 137 cents). The alternative is to think about it as 1 dollar = 100 cents, 1 quarter = 25 cents, 1 dime = 10 cents, and so on.

The procedures in the various parts below are designed to convert all coinage to lorgs, which will serve as our base unit. Trial and error led me to the conclusion that the lorg coin had the lowest worth, thus I'm striving to obtain everything in lorgs.

The four equations provided are

4 lorgs to a sind

5 dalts x 2 plunks

2 harps from 5 sinds.

3 harps equal 1 plunk.

In that order, I'll refer to them as equations (1) through (4).

One sind equals four logs (1)

5 sinds = 20 lorgs; add 5 to both sides.

2 harps = 20 lorgs; in the equation, swap out "5 sinds" with "2 harps" (3)

1 harp = 10 lorgs; multiply both sides by 2, then write this as an equation (5)

Equation: 1 plunk = 30 lorgs (6)

Each of those equations enables us to determine the lorg value of the coins sind, dalt, harp, and plunk.

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The complete question is : " A nation has five types of coins: sinds, dalts, lorgs, harps, and plunks.1 sind = 4 lorgs ,2 plunks = 5 dalts ,5 sinds = 2 harps , 1 plunk = 3 harps Which coin is the most valuable? a) sindb) daltc) harpd) plunk"

Answer:

(-6, -2) x=-6, y=-2

Step-by-step explanation:

3x + 5(x+4) = -28

3x + 5x+20=-28

8x+20=-28

8x=-48

x=-6

Y=-6+4

y=-2

Answer:

The cost of a single pack would be $2.45.

Step-by-step explanation:

If a 5 pack costs 12.25 then to find the cost of 1 packet we need to divide.

We would divide by 5.

$12.25/5=$2.45

The equation of line that passes through (-2,-1) and is perpendicular to f(x) = (-1/5)x + 1 is f(x) = 5x + 9.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the graph

f(x) = (-1/5)x + 1

Using the slope intercept, slope m is -1/5

The equation of a perpendicular line to f(x) = (-1/5)x + 1 must have a slope that is the negative reciprocal of the graph.

Slope of perpendicular line = -1 / (-1/5)

Slope of perpendicular line = 5

Plug the slope m = 5 and point (-2,-1) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - (-1) ) = 5( x - (-2) )

( y + 1 ) = 5( x + 2 )

y + 1 = 5x + 10

y = 5x + 10 - 1

y = 5x + 9

f(x) = 5x + 9

Therefore, the equation of the perpendicular line is f(x) = 5x + 9.

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