Determine the range of f(x) equals |X |+3

The radius of the cylindrical bucket is 11 inches.

Now, According to the question:

We have the given data is :

A cylindrical bucket that is 30 inches tall

A cylindrical 11,400 cubic inches of water.

We have to find the radius of bucket's.

Height (h) = 30 inches tall

Volume of cylinder is 11,400

We know that the:

Volume of cylinder is = [tex]\pi r^2h[/tex]

Plug all the values in the formula.

[tex]\pi =3.14[/tex]

11,400 = 3.14[tex](r)^2[/tex]× 30

11,400 = 94.2[tex](r)^2[/tex]

[tex](r)^2[/tex] = 11400/94.2

r = [tex]\sqrt{121.00}[/tex]

r = 11

Hence, The radius of the cylindrical bucket is 11 inches.

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Answer: it is table "a"

explanation:

as the equation is y= 2x + 5 you should substitute each of the x values from -2 to 4 in order to get the y value which will help you decide which table should be used by Cindy to graph the equation.

now, this is how you should substitute the values into the equation and simplify it so that you get the "y" value.

the first x value given is -2 therefore:

you put -2 in the equation instead of putting x, this will allow you to find the y value which you can compare with the choices given.

y= 2x+5 (this is the equation)

y= 2(-2)+5 (here I have replaced the x with -2)

y= -4+5 (you should multiply 2 and -2)

y= 1 (therefore the answer is 1)

you should further continue this way and get the y values which will help you decide which is the correct table to be used. Now you already know that table "a" is the answer.

Answer:

The answer is table A

Step-by-step explanation:

Given:

Form the table of values from x = -2 to x = 4

Hence,

Therefore, the table that can be used for the graph of the equation is;

Table A

Since varies directly with y, the value of y when x= 10 is equal to -80/3.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = -8/3

When the value x = 10, the value of y can be calculated as follows;

y = kx

y = -8/3 × 10

y = -80/3

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The original price of the ski jacket is $184.

What is price?

The sum of money paid or the amount of compensation offered by one party to another in exchange for goods or services is known as a price. The cost of production can take on different names depending on the circumstance. If the item is a "good" in a commercial transaction, the cost of the item will probably be referred to as its "price".

Given:

Paula bought a ski jacket on sale for $8 less than half its original price.

She paid $84 for the jacket.

We have to find the original price of the ski jacket.

Let

The original price = x

The amount she bought it = x/2 - 8

She paid $84 for the jacket

Therefore,

84 = x/2 - 8

Add 8 on both sides,

84 + 8 = x/2 - 8 + 8

92 = x/2

x = 184

Hence, the original price of the ski jacket is $184.

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The area of the parallelogram would be 216.6 ft².

Given is a parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet.

The area of the || gm is -

A = 1/2 x b x h

A = 1/2 x 22.5 x 19.25

A = 216.6 ft²

Therefore, the area of the parallelogram would be 216.6 ft².

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The figures that will fill the boxes correctly to solve the above division question would be

box 1 = 238

box 1 = 238box 2= 800

box 1 = 238box 2= 800box 3 = 120

box 1 = 238box 2= 800box 3 = 120box 4 = 32

Division is defined as the one of the major arithmetic operation used in the field of mathematics that helps to share a data set amount other values.

The type of division method that is being represented above is the long division method which has its divisor written outside the right parenthesis or the left sidebar, while the dividend is placed within, and the quotient is written above the overbar on top of the dividend.

Thus, when 952 is divided by four using the long division method, the resulting value would be = 238.

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If the cost for first 200 words is $50 and anything over200 words will be an additional $0.05 per word , then the piecewise function is [tex]C(x) = \begin{array}{cc} \{ & \begin{array}{cc} 50 & 0\leq x\leq 200 \\ 50+(x-200)\times0.05 & x > 200 \end{array}\end{array}[/tex].

For posting the advertisement in local newspaper , there are two criteria ,

if the advertisement is for 200 words then the cost will be $50 ;

let the number of words be x ;

So , the domain for this in the piecewise function will be [tex]0\leq x\leq 200[/tex]  ;

and if there are more than 200 words , then the additional cost is $0.05 per word ,

that means , the domain will be [tex]x > 200[/tex] ;

also given that , we have used 84 words in the advertisement ,

84 lies in this [tex]0\leq x\leq 200[/tex] , So ,the cost will be $50 .

The Piecewise Function can be represented as : [tex]C(x) = \begin{array}{cc} \{ & \begin{array}{cc} 50 & 0\leq x\leq 200 \\ 50+(x-200)\times0.05 & x > 200 \end{array}\end{array}[/tex].

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Answer:

Give more points

Step-by-step explanation:

Answer:

[tex]HD=5.5[/tex]

Step-by-step explanation:

[tex]4(HD)=22 \implies HD=5.5[/tex]

Answer: 53

Step-by-step explanation:

x = 180 - 90 - 37

  = 180 - 127

  = 53

a. Yes, the columns of matrix a are linearly independent if the equation ax = 0 has the trivial solution.

This means that the only solution to the equation is x = 0, which implies that the vectors in the matrix are not linear combinations of each other.

b. No, if s is a linearly dependent set, then each vector is not necessarily a linear combination of the other vectors in s. A linear combination is a combination of two or more vectors where each vector is multiplied by a scalar and then added together.

A linearly dependent set means that one of the vectors can be expressed as a linear combination of the other vectors, but not necessarily all of them.c. No, the columns of any 4 5 matrix are not necessarily linearly dependent.

Linear dependence is determined by the rank of the matrix. If the rank of the matrix is equal to the number of columns, then the columns of the matrix are linearly independent.

However, if the rank of the matrix is less than the number of columns, then the columns of the matrix are linearly dependent.

d. Yes, if x and y are linearly independent, then any linear combination of x and y must equal to zero. This means that the coefficients of x and y must be equal to zero in order for the linear combination to equal zero.

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Complete question:

Determine if the columns of the matrix form a linearly independent set. Justify your answer. Choose the correct answer below. A. The columns of the matrix do form a linearly independent set because the set contains more vectors than there are entries in each vector. B. The columns of the matrix do form a linearly independent set because there are more entries in each vector than there are vectors in the set. C. The columns of the matrix do not form a linearly independent set because the set contains more vectors than there are entries in each vector. D. The columns of the matrix do not form a linearly independent set because there are more entries in each vector than there are vectors in the set.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

√81 = 9

-√144  = -44

√4/25 = 2/25

√0.36 = 0

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Answer: The answer Is conic

Step-by-step explanation:

For A, I got 81 cards. I'm pretty sure that's correct.

For B , there can be 1 attribute that is different and the other 3 can be the same, there can be 2 that are different and 2 can be the same, there can be 3 that are different and 1 is the same, or all 4 attributes are different.

If 1 is different and the other 3 are the same, there are [tex]$\binom{4}{1}[/tex]= 4$ sets.

If there are 2 different and 2 are the same, there are[tex]$\binom{4}{2}[/tex]= 6$ sets.

If there are 3 different and 1 is the same, there are [tex]$\binom{4}{2}[/tex] = 4$ sets.

But I don't know how many sets there are if all 4 are different.

To get my final answer for b, I would add all the sets up.

(b) There are 108/3 = 36 unique sets.

(c) For the first card, there are 3 ways to choose the number.  For the second, there 2 choices, and then there is only 1 choice.  So there are 3*2*1 = 6 ways that the numbers can be chosen.  Doing this for the other attributes, we get 6*6*24*6 ways.  But the order of cards doesn't matter in a set, so we divide by 3!: 6*6*24*6/3! = 864.  So there are 864 sets for part (c).

(d) The cards can have the same number, color, shape, or shading.  If all the colors are the same, then there are 6*24*6/3! = 144 sets.  If all the numbers are the same, then there are 144 sets.  We get the same number for shape and shading, so there are 4*144 = 576 sets for part (d).

(e) We need to choose two of the attributes.  There are C(4,2) = 6 ways of choosing two attributes.  For each of these two attributes, there are 3 options.  For the other two attributes, there are 3 ways of assigning the choices, so there are 6*3*3*3*3 = 486 sets for part (e)

(f) First we choose which attributes are the same.  There are C(4,3) = 4 ways of choosing which attributes are the same.  There are then 3*3*4 = 36 ways to assign which is which for each of these three attributes, and there are 4 ways to assign the choices for the fourth attribute, so there are 4*36*4 = 576 sets for part (f).

As for c, d, e, and f, I'm pretty sure I can just refer to b.

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Answer:

70.3

Step-by-step explanation:

7 tenths = 70

Answer:

Option #4 7.3

Step-by-step explanation:

First you multiply 7 by 10 the denominator. (7x10)=70

Second add 3 to the sum. (70+3)= 73

Third divide 73 by 10. (73/10)=7.3

This makes the answer 7.3.

-Hope this helped

Here, y = 0 is the equation of the x-axis.

Also, y = 5 is the equation of a line parallel to the x-axis.

⇒ y = 0 and y = 5 are parallel to each other

Since the equations are parallel, then they have no solution.

Hence, the pair of equations y = 0 and y = 5 has no solution.

A linear equation in two variables is an equation of the form ax + by + c = 0 where a, b, c ∈ R, a, and b ≠ 0. When we consider a system of linear equations, we can find the number of solutions by comparing the coefficients of the variables of the equations. Also, we can find the number of solutions by the graphical method.

Consider the pair of linear equations in two variables x and y.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here a1, b1, c1, a2, b2, c2 are all real numbers.

Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0

1. If (a1/a2) ≠ (b1/b2), then there will be a unique solution. If we plot the graph, the lines will intersect. This type of equation is called a consistent pair of linear equations.

2. If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions. The lines will coincide. This type of equation is called a dependent pair of linear equations in two variables

3. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. If we plot the graph, the lines will be parallel. This type of equation is called an inconsistent pair of linear equations.

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Answer:

$0.40

Step-by-step explanation:

10 lbs  ÷ 10 = 1 lb

---------   =    ---------

$4.00 ÷ 10  = $0.40

Answer:

5⁻³

Step-by-step explanation:

There are 8 adults. This is because 1 adult is needed for every 8 students, so 8 multiplied by 8 is 64, which is the number of students. Therefore, 8 adults are needed.

If the quadratic expression with integer coefficients is factorable over the integers then its discriminant is a perfect square.

The term quadratic expression is defined as an expression with the variable with the highest power of 2.

Here we have to identify the way to know that  if a quadratic equation is factored.

As per the definition here we know that if it is a positive perfect square the equation can be factored fairly easily.

Where as here we have also know that not every quadratic equation can be solved by factoring or by extraction of roots.

And if the quadratic expression that is written as the product of a constant times two linear factors then it is said to be in factored form.

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The cost of 4 dance lessons will be $52.

Given is that the cost for 7 dance lessons is $82 and the cost for 11 lessons is $122.

The given coordinate points are -

(7, 82) and (11, 122)

We can write the equation as -

y = mx + c

Now -

m = (122 - 82)/(11 - 7)

m = 40/4

m = 10

The equation will now become -

y = 10x + c

For the point (7, 82), we can write -

82 = 10 x 7 + c

c = 82 - 70

c = 12

So, the equation representing the cost to the total number of dance lessons is -

y = 10x + 12

For {x} = 4, we can write -

y = 40 + 12

y = 52

Therefore, the cost of 4 dance lessons will be $52.

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Answer: If the slopes are the same but the y-intercepts are different, the system has no solution. If the slopes are different, the system has one solution. If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.

The trapezoid's area if its height is 8 is 156.

Trapezoid area is the area of a four-sided flat shape with two sides that are parallel. It is a type of quadrilateral with two non-parallel sides. To calculate the area of a trapezoid, you need to multiply the sum of the lengths of the two parallel sides by the height of the trapezoid and then divide by two. The formula for trapezoid area is A = (a + b) * h / 2, where a and b are the lengths of the two parallel sides and h is the height of the trapezoid.

The area of a trapezoid is calculated by multiplying the height by the average of the two bases. Therefore, the area of the trapezoid in question is 8 multiplied by the average of 12 and 27, which is 19.5. The final answer is then 156.

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The slopes for the given pairs are:

If a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is given by:

a = (y₂ - y₁)/(x₂ - x₁)

Using the first pair of points (9, 10) and (7, 2) the slope is:

s = (2 - 10)/(9 - 7)

s = -8/2 = -4

For the second pair:

(5, -6) and (2, 3)

Here the slope is:

s = (3 + 6)/(2 - 5)

s = 9/3 = -3

The last pair of points is (4,7) and (6, 2) the slope is:

s = (2 - 7)/(6 - 4)

s = -5/2

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There are three types of systems of linear equations in two variables: Consistent System,Inconsistent System,Dependent System.

A linear system is a mathematical model of a system of linear equations, in which the variables and constants have a linear relationship. This type of system is widely used in engineering, physics, economics, and other areas of study. Linear systems are often used to find solutions to problems in areas such as optimization or forecasting. They are also used in many machine learning algorithms. Linear systems are characterized by their linearity and they are usually solved using linear algebra techniques.

1. Consistent System: A consistent system of linear equations in two variables has at least one solution. This means that there is at least one set of values for the two variables that will make all equations true.

2. Inconsistent System: An inconsistent system of linear equations in two variables has no solution. This means that there is no set of values for the two variables that will make all equations true.

3. Dependent System: A dependent system of linear equations in two variables has an infinite number of solutions. This means that there is more than one set of values for the two variables that will make all equations true.

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The given equation has 161700 distinct solution.

If a sum of non-negative integers whose values is pre-defined say m is equal to a fixed value say n such that:x1+x2+x3+...+xm=n then the total combination of m non negative integers x1,x2,...xm in mathematical form can be written as: n+m−1Cm−1.

The above problem can also be written as:

x1+x2+x3+x4=100x1≥1x2≥2x3≥0x4≥0

Here x3 and x4 are non-negative integers and there is a restriction on x1 and x2.

Removing the restriction on x1 and x2  as:100 - 1 - 2 = 97

The number of distinct solution that the equation x1+x2+x3+x4=100 has is equivalent to the non-negative solution. of x1+x2+x3+x4=97 and is given by:

97+4−1C4−1=100C3=161700

Hence, the number of distinct solution that the equation x1+x2+x3+x4=100 has is 161700.

The solutions of equations basically depends on the power of variables present on it .

The solutions of equations also show that the how much the power of variables Is present that times it cuts the axis .

For example

1.if x+2=0 then x=—2 that means it has one solution and it also means it cut the x -axis one time .

2.if x^2–4=0 then x have two values that is x=+2,x=—2 it also means it cut the x-axis two times

Similar for power is 3 then it have three solution.

And so on for if power is n then it have solutions .

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Number of miles in 8,400 feet are 1.6 miles.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, there are 5,280 feet in 1 mile.

Let the number of miles in 8,400 feet be x.

So, 5280/1 = 8400/x

5280x=8400

x= 8400/5280

x= 1.6 miles

Therefore, number of miles in 8,400 feet are 1.6 miles.

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The balloon's radius is expanding at a rate of 0.035 cm/s.

Let R & V stand for the provided spherical balloon's radius (in cm) and volume (in cm3), respectively.

So, using the data above, we can derive the following relation:

V = (4/3)*π*(R^3) …… (1a)

When we differentiate (1a) with regard to time (t), we obtain either

dV/dt = (4*π*R^2)*(dR/dt)

or dR/dt = (dV/dt)/(4*π*R^2) … … (1b)

(1b) Using the information provided, we can deduce that

dR/dt = 100/[4*π*(30/2)^2] = 1/(9*π) = 0.035 (cm/s)

Thus, it is clear from above that the balloon's radius is expanding at a rate of 0.035 cm/s.

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The question is incomplete, the full question

Air is pumped into a spherical balloon so that its volume increases at a rate of 100 cm^3/sec. How fast is the radius of the balloon increasing when the diameter is 50 cm?

To solve for the factored form of an equation, you can use a variety of methods, such as grouping, factoring by grouping, factoring by inspection, factoring by using the difference of squares, sum of cubes, or difference of cubes.

Grouping: This method involves grouping the like terms in the equation and factoring out the greatest common factor from each group.

Factoring by grouping: This method involves grouping the terms in the equation and factoring out the common factor that is shared by each group.

Factoring by inspection: This method involves looking at the equation and identifying any common factors that can be factored out of the equation.

Factoring by using the difference of squares, sum of cubes, or difference of cubes.

Factoring by using the quadratic formula.

Once you have factored the equation, you can set each factor equal to zero and solve for the variable.

For example, let's consider the equation x^2 + 5x + 6 = 0. Using the factoring by inspection method, we can see that (x + 2)(x + 3) = 0, so either x + 2 = 0 or x + 3 = 0. Solving for x, we find that x = -2 and x = -3 are the solutions to the equation.

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