Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Check all that apply.

True

6 x 3 = 18 square feet. which is the surface area of the room.

so john will have 2 square feet to spare

The statement is false. The domain of the composite function (f◦g)(x) is not always the same as the domain of g(x). It includes only the values of x for which both g(x) and f(g(x)) are defined.

The statement is False. The domain of the composite function (f◦g)(x) is not always the same as the domain of g(x). In a composite function (f◦g)(x), the domain includes only the values of x for which both g(x) and f(g(x)) are defined.

For example, if g(x) = sqrt(x) and f(x) = 1/x, the domain of g(x) would be all real numbers x ≥ 0, but the domain of the composite function (f◦g)(x) = 1/sqrt(x) would be x > 0, because 1/sqrt(x) isn't defined for x = 0.

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To find the safe load of a 10-foot long beam, first calculate the constant of proportionality k using the safe load and length of the known beam, and then multiply k by the new length. The safe load for a beam of length 10 feet would be 1333.3 pounds.

First, calculate the constant of proportionality k using the information provided: k = 2000 pounds / 15 feet = 133.33 pounds/foot.

Next, find the safe load y for a beam of length 10 feet: y = k * x = 133.33 pounds/foot * 10 feet.

Calculate the result: y = 1333.3 pounds.

Therefore, the safe load for a beam of length 10 feet would be 1333.3 pounds.

The statement is true; a function defined only for a set of discrete numbers, such as whole numbers, is indeed called a discrete function.

The statement that a function defined only for a set of numbers that can be listed, such as the set of whole numbers, is called a discrete function is true. A discrete function is, in fact, characterized by a domain that consists of distinct and separate elements. For example, the number of phone calls you receive on each day is a representation of discrete data because the counts can only be whole numbers, demonstrating the nature of a discrete function. This is opposed to continuous functions, which have a domain that may include all real numbers, allowing for an infinite number of values between any two different numbers.

Additionally, the concept of a function is that it relates each element of its domain to a single and unique value in its range. If the domain is composed of discrete elements like whole numbers, then the function that relates these elements to values is considered a discrete function.

Keep in mind that a characteristic function or membership function can also be considered a discrete function since it maps elements to specific values, often representing the presence (1) or absence (0) within a set.

1. 2 and 7 are equal

2. angle 1 = 68 degrees

3. 1st answer

Answer:

40%

Step-by-step explanation:

The total cost of the boat after six years is $6,616.44.

To find the total cost of the boat after six years, we need to calculate the interest paid on the loan over that period of time.

The loan amount is $9,640 with an interest rate of 9.4% per year.

Since the loan is for six years, we multiply the loan amount by the interest rate and the number of years: $9,640 × 0.094 × 6 = $5,441.44.

Adding the down payment of $1,175 to the interest paid on the loan, we get the total cost of the boat after six years: $5,441.44 + $1,175 = $6,616.44.

Final answer:

The ratio of cups of rice to cups of water in the recipe is 2 to 3, which can also be written as 2/3.

Explanation:

The question asks us to find the ratio of cups of rice to cups of water. The recipe provided uses 2 cups of rice and 3 cups of water. To find this ratio, we simply compare the number of cups of rice to the number of cups of water and write it as a fraction or a division problem.

In this case, the ratio is:

2 cups of rice : 3 cups of water

Which we can also write as 2/3 or say that for every 2 cups of rice, there are 3 cups of water.

Answer:  The required solution is   x = -2,  2.

Step-by-step explanation:  We are given to solve the following quadratic equation by square root method :

[tex]x^2-14=-10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

In square root method, we take the square of the unknown variable on one side and the constant term on the other side. Then, we take the square roots on both sides.

From equation (i), we have

[tex]x^2-14=-10\\\\\Rightarrow x^2=-10+14\\\\\Rightarrow x^2=4\\\\\Rightarrow x=\pm\sqrt{4}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightrarow x=-2,2.[/tex]

Thus, the required solution is   x = -2,  2.

I did this question already. The answer is 2

1. any number times2 then subtracted by the same number can't = 0 , so it is Null Set

2. 2^2 = 4 +12 = 16, 8*2 = 16, answer is 2

Final answer:

To express the ratio of 7 meters to 250 centimeters in its lowest terms, convert both to the same unit and simplify. 7 meters is 700 centimeters, leading to an initial ratio of 700:250, which simplifies to a final ratio of 14:5.

Explanation:

To state 7m to 250cm as a ratio in its lowest terms, we need to convert them to the same unit. One meter is equivalent to 100 centimeters, so 7 meters is the same as 700 centimeters.

Now we can write the ratio as 700 cm : 250 cm, which can be simplified by dividing both terms by 250 cm (the greatest common divisor of both numbers).

The simplified ratio is 700÷ 250 : 250÷ 250, which simplifies to 7 : 2.5. Since we want the ratio in its lowest terms with whole numbers, we can multiply both terms by 2 to eliminate the decimal, resulting in a final ratio of 14 : 5.

Answer: Answer is 1

Step-by-step explanation:

edge

The answer is:  [C]:  " f(x) = 0.7(5)ˣ " .

_________________________________________________________

 Explanation:

_________________________________________________________

From all the answer choices given; 

Answer choice:  [C]:  "  f(x) = 0.7 (5)ˣ " ;  is the answer choice with a "positive number"; {which is then multiplied by: [ a "positive whole number" or a "positive number greater than "1"; that is raised to a "positive variable"] .

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How I solved this:  Further Explanation:

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A positive number multiplied by a {"number less than 1; raised to "x"] would result in increasingly lower values as "x" increases. Same with "raised to "negative x" {refer to "Answer choice [D]" }.

Answer:

The answer is:  [C]:   f(x) = 0.7(5)ˣ

Step-by-step explanation:

Answer:

answer is 180 degrees

Step-by-step explanation:

180 degrees has the Ferris wheel rotated

Rotation is the circular movement of an object around an axis of rotation.

Given:

There is ferries wheel when we board on ferris wheel it will be considered as 0 degree.

but when the ferris wheel stop to get more riders on at that time we are vey top.

So, we have covered half of the complete angle i.e., 180 degree

Hence, the ferris wheel cover 180 degrees.

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The correct expression representing the larger number is [tex]\( 2x + 3 \)[/tex]. So option (b) is correct.

To solve this problem, let's represent the smaller number as x and the larger number as y. According to the given conditions:

1. y is 3 more than 2 times ( x ), so ( y = 2x + 3 ).

2. The sum of the two numbers is 27, so ( x + y = 27 ).

Now, let's substitute the value of ( y ) from the first equation into the second equation:

[tex]\[ x + (2x + 3) = 27 \][/tex]

Combine like terms:

[tex]\[ 3x + 3 = 27 \][/tex]

Subtract 3 from both sides:

[tex]\[ 3x = 27 - 3 \][/tex]

[tex]\[ 3x = 24 \][/tex]

Divide both sides by 3:

[tex]\[ x = \frac{24}{3} \][/tex]

[tex]\[ x = 8 \][/tex]

Now, we can find ( y ) by substituting the value of ( x ) into the equation for ( y ):

[tex]\[ y = 2(8) + 3 \][/tex]

[tex]\[ y = 16 + 3 \][/tex]

[tex]\[ y = 19 \][/tex]

So, the smaller number ( x ) is 8, and the larger number ( y ) is 19.

Now, let's check which expression represents the larger number:

1. [tex]\( 3x + 2 = 3(8) + 2 = 24 + 2 = 26 \)[/tex]

2. [tex]\( 2x + 3 = 2(8) + 3 = 16 + 3 = 19 \)[/tex] - This matches the value we found for the larger number.

3. [tex]\( 2(x + 3) = 2(8 + 3) = 2(11) = 22 \)[/tex]

So, the correct expression representing the larger number is [tex]\( 2x + 3 \)[/tex].

The equation y = 7x + 16 represents how long his jog will be after x additional weeks option (B) is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Gordon recently started jogging. Last week he jogged for 16 minutes.

Let x be the number of weeks

and y represents the total number of minutes Gordon walks

From the given data the linear equation can be framed as follows:

y = 7x + 16

Thus, the equation y = 7x + 16 represents how long his jog will be after x additional weeks option (B) is correct.

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Answer:

it's 2.125

Step-by-step explanation:

The required speed of family's paddling speed in still water is 2.125 mi/h.

Given that,
A family is canoeing (with the current). Their speed relative to the banks of the river averages 2.75mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relatives to the riverbank.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
Let the speed of the family on still water be x,
Speed of the current be y
According to the question,
upstream speed,
1.5 = x - y  - - - - - (1)
Downstream speed,
2.75 = x + y - - - - - (1)

Solving equations 1 and 2 givens,
2x = 4.25
x = 2.125 mi / h

Thus, the required speed of the family paddling speed in still water is 2.125 mi/h.

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Answer:

Therefore the roots of equation 1 are 1,3 1/2,-i,+i

Step-by-step explanation:

in this question we have given

[tex]f(x) = 2x^5 - 9x^4 + 12x^3 - 12x^2 + 10x - 3 = 0[/tex].......1

we have to find the roots of this equation

put x=1 in equation 1

[tex]f(1)=2-9+12-12+10-3\\f(1)=0[/tex]

It means x=1 is root  of equation 1

now put x=3 in equation 1

[tex]f(3)=2\times3^5-9\times3^4+12\times3^3-12\times3^2+10\times3-3\\f(3)=0[/tex]

therefore,x=3 is root of equation 1

Now put x=[tex]\frac{1}{2}[/tex] in equation 1

[tex]f(\frac{1}{2})=2\times (\frac{1}{2} )^5-9\times(\frac{1}{2})^4+12\times(\frac{1}{2})^3-12*(\frac{1}{2})^2+10\times \frac{1}{2}-3\\f(\frac{1}{2})=0[/tex]

It means x=[tex]\frac{1}{2}[/tex] is also root of equation 1

therefore equation one can be written as

[tex]f(x)=(x-1)(x-3)(2x-1)(x^2+1)[/tex]

therefore remaining 2 roots can be calculated by solving

[tex]x^2+1=0\\x=\sqrt(-1)\\x=i,-i[/tex]

Therefore the roots of equation 1 are 1,3 1/2,-i,+i