Write the rationalized expression of:

Answer:

1st option

Step-by-step explanation:

let y = f(x) and rearrange making x the subject , that is

y = [tex]\frac{1}{9}[/tex] x - 2 ( add 2 to both sides )

y + 2 = [tex]\frac{1}{9}[/tex] x ( multiply both sides by 9 to clear the fraction )

9(y + 2) = x

9y + 18 = x

change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then

[tex]f^{-1}[/tex] (x) = 9x + 18

Answer: A

Step-by-step explanation:

GOT IT RIGHT ON EDG TEST

Answer:

can you rephrase it? how many pounds are there?

Step-by-step explanation:

The quotient of the synthetic division problem is "f(x) = -2x² + 9x + 5" (Option C).

When a polynomial division is executed using the shorthand method, using a linear factor, one is  said to have executed a Synthetic Division.

The synthetic division translates to

- 2 15 -22 -15

3 | -6 27 15

-2 9 5 0

Citing the coefficient of the quotient of the first three numbers:

- 2, 9, 5. The last number is given as the remainder.

Hence the remainder is zero.

Given that the coefficient of the quotient are three, the interpretation is that the polynomial greatest degree is 2.

Thus,

f(x) = -2x² + 9x + 5

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Answer:

its A

Step-by-step explanation:

Its a because its A =)

The number of balloons needed to fill the classroom are  46240 balloons (approx)

Concept: Fermi process is the technique that helps to formulate an answer to a problem based on a series of logical assumptions.

No. of balloons = Volume of rectangular prism/ Volume of each sphere (balloon)

Given: The classroom is a rectangular prism with a length of 38 ft, a width of 52 ft, and a height of 12 ft, and the balloons are spheres with a radius of 0.35 ft.

No. of balloons = Volume of rectangular prism/ Volume of each sphere (balloon)

No. of Balloons = 38*52*12/3.14*0.35*0.35*(4/3)

No. of Balloons = 23712/0.5128 = 46240 balloons (approx)

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The equations;

A linear equation is one in which there is only one solution. In a linear solution, the highest power of x is 1.

If we look at the equations listed, we will discover that they are all linear equations, as such;

Will all have exactly 1 solution.

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The value of the composite function (h•f)(0) is -2/3

The functions are given as:

f(z)=(1/3)

h(z) = z+4/z-2

Start by calculating f(0) and h(0)

f(0) = 1/3

h(0) = (0+4)/(0-2)

h(0) = -2

The composite function is then calculated as:

(h•f)(0) = h(0) * f(0)

This gives

(h•f)(0) = -2 * 1/3

Evaluate

(h•f)(0) = -2/3

Hence, the value of the composite function (h•f)(0) is -2/3

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(x+4) is a factor of this trinomial given , Option A is the right answer.

A factor is a number o expression that completely divides the number or the expression and the remainder is equal to zero.

The given trinomial is

x² +12x+32

x² + 8x +4x +32

x(x+8)+4 (x+8)

(x+8)(x+4)

From the given option Option A (x+4) is the right answer.

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The value of a is 72.74.

Probability is the study of likeliness of an event to happen.

It is given that

The mean [tex]\rm \mu[/tex] of the distribution is 70

Standard deviation [tex]\rm \sigma[/tex]  is 2

p( x<a) = 0.9147

a = ?

From Z table

For p ( p < 0.9147) , z = 1.37

[tex]\rm Z = \dfrac { X - \mu}{ \sigma}[/tex]

[tex]\rm \rm 1.37 = \dfrac { a - 70}{ 2}[/tex]

a = 70+ 2*1.37

a = 72.74

Therefore the value of a is 72.74.

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The value of the angle R in the right triangle PQR is sin⁻¹ 6 / 8

The situation forms a right angle triangle.

The angle R can be found as follows:

using trigonometric ratios,

sin R = opposite / hypotenuse

Therefore,

opposite sides = 6

hypotenuse = 8

sin R = 6 / 8

R = sin⁻¹ 6 / 8

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The numbers should be 2, 2, 5, 9 and 12.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.

Let us take numbers 2, 2, 5, 9 and 12.

mean = 30/5

mean= 6

range = 10.

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Answer:

A line traveling to the left with an open dot on x=1.

Explanation:

The inequality x < 1 basically means "less than 1." On number lines, the further left you go, the smaller the number becomes, and the further right you go, the larger the number becomes. So we know that because it's less or smaller than 1, then the line will be to the left. On the other hand, the inequality does not have a line under it to indicate a "less than or equal to 1," just "less than." Therefore, the dot is open. If there were a line under the inequality, then it would indicate "less than or equal to 1" and the dot would be closed.

Function y=3/x, y= 2/x+4, and xy=-3 shows an inverse variation option (b), (e), and (f) are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we know, when x is not equal to zero and k is a nonzero real number constant, the equation of the form xy = k describes the nonlinear function known as inverse variation.

a) y=6x

The above function is a linear function

b) y=3/x

or

xy = 3

The above function shows an inverse variation.

c) y=1/3x

or

y = (1/3)x

The above function is a linear function

d) y= -.07x

The above function is a linear function

e) y= 2/x+4

or

y = (2+4x)/x

xy = 2 + 4x

The above function shows an inverse variation.

f) xy=-3

The above function shows an inverse variation.

Thus, function y=3/x, y= 2/x+4, and xy=-3 shows an inverse variation option (b), (e), and (f) are correct.

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Answer:

4/9 of the students chose summer.

Step-by-step explanation:

Think about it this way. There are 9 students being asked what their favorite season is. 1 chose spring, 3 chose summer. Add those together, and you have 4 people that chose either spring or summer. That number goes on top of the fraction. The total amount of people that were asked goes on the bottom, which is 9.

Answer:

B = an event that in the second turn it will land on Lose a Turn. Based from the given wheel, there are 24 equal parts with three $500 and one Lose a Turn. Thus, the probability of landing on $500 then lose a turn is 1921 .

this is possible IF thewheele consists of 24 parts

The chance of landing on $500 and then Lose A Turn will be 1/192. Then the correct option is C.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

The diagram is given below.

The total number of the events will be

Total events = 24

Then the chance of landing on $500 will be

The number of favorable events will be

Favorable events = 3

⇒ 3/24

⇒ 1/8

Then the chance of the Lose A Turn will be

Favorable event = 1

⇒ 1/24

The chance of landing on $500 and then Lose A Turn will be

P = (1/24)(1/8)

P = 1/192

The chance of landing on $500 and then Lose A Turn will be 1/192.

Then the correct option is C.

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Answer:

wait lang yong tppp heheehhehe

Answer:

b is the awancer yw

Step-by-step explanation:

Answer:

the answer is A K= -2.5

Step-by-step explanation:

i did the problem

The simple interest is $24.75.

The simple interest that is paid on an amount of money is a function of the amount deposited, time and interest rate.

Simple interest = amount deposited x time x interest rate

$375 x 0.022 x 3 = $24.75

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Answer:

x = 9

y = 61

Step-by-step explanation:

let me know if you want an explanation!

Step-by-step explanation:

4a.

the circumference of a circle is

2×pi×r

we know, r = 6 cm.

so the whole circumference is

2×pi×6 = 12×pi = 37.69911184... cm

4b.

the arc BC is the part of the full circumference that corresponds to 120° out of the 360° of a full circle.

the arc BC is then

12×pi × 120/360 = 12×p × 1/3 = 4×pi = 12.56637061... cm

the perimeter of the shaded area (pie slice) is the arc BC plus 2 radius lengths (from the arc points to the center of the circle)

12.56637061... + 2×6 = 12.56637061... + 12 =

= 24.56637061... cm

4c.

the area of a circle is

pi×r²

in our case

pi×6² = 36pi = 113.0973355... cm²

the area of the shaded area (pie slice) is the 120° part of the full 360° circle area :

36pi × 120/360 = 36pi × 1/3 = 12pi = 37.69911184... cm²

Answer:

b = 0 and b = 4

Step-by-step explanation:

[tex]\frac{5}{3b^3-2b^2-5}[/tex] = [tex]\frac{2}{b^3-2}[/tex] ( cross- multiply )

2(3b³ - 2b² - 5) = 5(b³ - 2) ← distribute parenthesis on both sides

6b³ - 4b² - 10 = 5b³ - 10 ( subtract 5b³ from both sides )

b³ - 4b² - 10 = - 10 ( add 10 to both sides )

b³ - 4b² = 0 ← factor out b² from each term on the left side

b²(b - 4) = 0

equate each factor to zero and solve for b

b² = 0 ⇒ b = 0

b - 4 = 0 ⇒ b = 4

Answer:

(i) x-intercepts: (2, 0), (6, 0)

(ii) vertex : (4, -4)

Explanation:

y = x² - 8x + 12

To find x intercepts, [set y = 0]

x-intercepts: (2, 0), (6, 0)

To find vertex:

x = -b/2a

  = -(-8)/2(1)

  = 4

y = x² - 8x + 12

  = 4² - 8(4) + 12

  = -4

Vertex : (4, -4)

Solve the equation for y=0

X inetercepts (2,0) and (6,0)

Vertex :-

x coordinate

Y coordinate

Verted at (4,-4)

Answer:

One number, let's call it x, is 6 more than twice the other number, let's say this number is y.

x= 2y+6

x+y=21

We're left with a system of equations.

If we substitute the first equation in the second we find the value of y.

(2y+6)+y=21

3y+6=21

3y=15

y=5

Now that we have found the value of y, we can take that value and substitute it in the second equation (since it's easier) to find the value of x.

x+ (5)=21

x=16

Now to check if our answers are correct, we plug in both values into any equation and see if they equate.

x+y=21

(16)+(5)=21

21=21

Our solution is correct!

Answer:

The ordered pair which makes both the inequalities true is = (–2, 2)

Step-by-step explanation:

inequalities are the relationships between two expressions which are not equal to one another.

Inequalities are represented by the following relations:

an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

so, the option B(-2,2) satisfies  the inequalities expressions given in the question

therefore we can conclude that (-2,2) is the ordered pair which ,makes both the given inequalities true.

so the correct answer is (-2,2)

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The correct value of the given function at x = 5 is y =3.

An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.

Here, the given equation :

         y = x - 2

put x = 5 in the given equation, we get

        y = 5 - 2

        y = 3

Thus, the correct value of the given function at x = 5 is y =3.

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Subtraction is a mathematical operation that reflects the removal of things from a collection. Supplier B would cost $625 more than supplier A. Thus, the correct option is A.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The cost of 500 bushels from supplier A will be,

Cost = ($5.25 × 500) + ($3 × 500)

        = $4,125

The cost 500 bushes from supplier B will be,

Cost = $1,500 + ($6.250×500)

        = $4,750

Now, the difference between the two suppliers' costs for 500 bushels will be,

Difference = $4,625 - $4,125 = $500

Hence, Supplier B would cost $625 more than supplier A. Thus, the correct option is A.

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Answer:

Exact Form:

x=3/8e^2

Decimal Form:

x=0.05075073…

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The quadratic inequality represented by the graph is:

y ≤ 2x² - 8x + 3

First, we can see that the shaded region is below the parabola, and the line of the parabola is solid, which means that the points on the parabola are solutions, then the inequality is:

y ≤ quadratic equation.

Now we need to get the quadratic equation.

Now, if you look at the y-intercept, you can see that it happens at y = 3. Then the constant term of the quadratic equation is 3.

The only one that has that (and the  ≤  symbol)  y-intercept is the first option:

y ≤ 2x² - 8x + 3

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