3 What is the range of the function shown
in the graph?

Explanation

To answer the question, we have to understand the different parts of an algebraic expression

An expression containing variables, numbers, and operation symbols is called an algebraic expression. is an example of an algebraic expression. Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.

We are given the algebraic expression:

For the given question

The difference means the result of subtracting one number from another or How much one number differs from another, so we have

Then

The coefficient is is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial, so we have

Also

A quotient is a number resulting from the division of one number by another, so we have

Finally,

A product is the result of multiplication or an expression that identifies factors to be multiplied.

Thus, we have

A sale price for the bicycles that would allow this company to achieve a profit of $189,800 is: B. $230.

In order to determine the sale price for the bicycles that would make it possible for this company to achieve a profit of $189,800, we would simply evaluate the profit function by substituting the value of the profit as follows:

P(x) = −2x² + 920x + 84,000

189,800 = −2x² + 920x + 84,000

Re-arranging the profit function by collecting like terms, we have:

2x² + 920x + 189,800 - 84, 000 = 0

2x² - 920x + 105,800 = 0

Dividing both sides by 2, we have:

x² - 460x + 52,900 = 0

Next, we would solve the quadratic equation by using factorization method:

x² - 230x  -230x + 52,900 = 0

x(x - 230) + 230(x - 230) = 0

(x - 230)(x + 230) = 0

x = 230 or -230

Since the price cannot be negative, the required sale price for this company is equal to $230.

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Complete Question:

A bicycle company has designed and built a new model of sports bicycle. They have determined that the profit for the sale of the bicycles can be modeled by the function P(x) = −2x² + 920x + 84,000, where x is the price of each bicycle. Which of the following is a sale price for the bicycles that will allow the company to achieve a profit of $189,800?

A. $210

B. $230

C. $250

D. $270

Answer:

it should be the variable divided by 1. For example, x/2.

Answer:
[tex]k - a + h[/tex]

Step-by-step explanation:

Hope this helps you! :))

Answer:

It means that you are done.

Step-by-step explanation:

When you are trying to find factors of a number or an algebraic expression, you must keep on factoring until you have all PRIME factors. PRIME factors cannot be further factored. So that means you are done factoring.

example: (a number)

6

factors: 2 and 3

2 and 3 are prime they can't be factored anymore so you have completely factored 6.

example: 20

factors: 4 and 5

5 is prime but 4 is not, so you can factor it more.

4 is 2×2

So 20 factored is 2×2×5

Or algebra example:

Factor x^4 - 81

factors: x^2 - 9 and x^2 + 9

x^2 + 9 cannot be factored more (prime) but x^2-9 can. Its x-3 and x+3.

The profuct of the given expression (x-2)³ is (x³ - 6x² + 12x - 8).

So, (x-2)³:

Do, the product as follows:

Perfect cube root formula: (a - b)³ = a³ - 3a²b + 3ab² -b³

Simplify:

Therefore, the profuct of the given expression (x-2)³ is (x³ - 6x² + 12x - 8).

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The height of the box is decreasing at a rate of 2/45 cm/sec.

The volume of a box remains constant at 1100m³ but the area of the base is increasing at a rate of 10 m²/sec.

Since the base of the box is a square, let the sides of the box be a, a, and h. The area of the base can be written as,

A = a²

Differentiate the above equation with respect to t.

dA/dt = 2a(da/dt)

Substitute 10 for dA/dt and 15 for a, to find the rate of change of side of base.

10 = 2(15)(da/dt)

da/dt = 1/3

The volume of the box can be written as,

V = (a)(a)(h) = a²h

Differentiate the above equation with respect to t.

0 = 2a(da/dt) + a² (dh/dt)

dh/dt = -2/a (da/dt)

Substitute 15 for a and 1/3 for da/dt in the above equation, to find the rate of change of height of the box.

dh/dt = -2/15 (1/3)

         = -2/45

Thus, the height of the box is decreasing at a rate of 2/45 cm/sec.

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Answer:0.0008994

Step-by-step explanation:

[tex]=-10x^4-4x^3+6x^2[/tex]

The length and the width of the rectangle are 14 and 15 meters, respectively

From the question, the statement is given as

Length and width are consecutive integers

Where

Area = 210 square feet

Represent the dimensions with x and y

Where Length = x and Width = y

And also, we have

y = x + 1

The area of a rectangle is

Area = Length x width

Mathematically, this can be represented as

Area = x * y

So, we have

x * y = 210

Substitute y = x + 1 in x * y = 210

x * (x + 1) = 210

Express 210 as 14 * 15

x * (x + 1) = 14 * 15

This means that

x = 14

Substitute x = 14 in y = x + 1

y = 14 + 1

Evaluate

y = 15

So, we have

x = 14 and y = 15

Hence, the length and the width are 14 and 15 meters

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The length of the wall for the ladder reach will be 3.4 meter.

What is mean by Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The foot of a ladder is 1.5 m from a vertical wall.

And, The ladder makes an angle of 68° with the horizontal.

Now,

By the figure,

The length of BC = 1.5 m

The measure of ∠ACB = 68°

So, Find the length of AC as;

cos 68° = 1.5 / AC

AC = 1.5 / 0.44

AC = 3.4 m

Therefore,

The length of the wall for the ladder reach will be 3.4 meter.

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Answer: No.

Step-by-step explanation:

    To test this ordered pair, we plug it back into the equation given as (x, y), and then simplify to solve. If we end up with an equal equation, the answer is yes. If not, the answer is no.

y = 1/2x - 3

(1) = 1/2(-8) - 3

1 = -4 - 3

1 ≠ -7

           This ordered pair is not a solution.

The opposite for each number is: ( -8, 8), (-1,1), (-17,17), (31,-31) and (11,-11).

Thus, you can conclude that the opposite number of a positive number is a negative number. And the opposite number of a negative number is a positive number.

The question gives the follow numbers

1. -8 8

2. -1 -11

3. -17 17

4. 31 -31

5. 11 1

The opposite for:

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4.

The volume of a cube equals its side cubed. Since the side of the cube is 12ft long, then its volume is given by:

Then, the volume of the cube, is:

5.

The volume of the prism equals the product of each of its dimensions. Then:

Then, the volume of the rectangular prism, is:

Hello

To expand this, we will multiply the value outside the bracket with the one inside the bracket.

The answer to this question is -8x +17

value outside the bracket with the one inside the bracket.

Answer:

The rule is. the nth term  aₙ is given by

aₙ = n² + 1

Step-by-step explanation:

The following is the summary of n, aₙ

n            aₙ      In terms of n

1             2        1² + 1

2            5        2² + 1

3            10       3² + 1

4            17        4² + 1

5            26       5² + 1

6            37       6² + 1

So the nth term is given by
n² + 1

Explanation

we have a secant and a tangent

To solve the question, we will apply the intersecting secant and tangent theorem

So, for the question

we have

Therefore, the value of PB is 12

3/706 is 0.00424929178, but if you mean 706/3, then the answer is 235 and 1/3. Hope this helps! :)

Answer:

b= -1, -6

Step-by-step explanation:

divide by common factor

then use x=- b+- sqrt b^2-4ac/2a

separate the equations and solve them

The number of permutations possible to seat the 3 pairs of siblings in a way that one may not sit right next to their sibling and no child may sit directly in front of his or her sibling is 96.

A permutation cannot be formed with siblings in the same row.

As a result, each row should have siblings from various families.

Any of the six youngsters can take the first seat.

After deducting the kid who currently occupies the first seat and their sibling, the second seat can be filled by any of the four children.

permutation = 6 × 4

permutation = 6 × 4 × 2

Now, for the third row, there are only 3 children left to be seated.

Only 2 out of the remaining three can be seated in the first position.

Hence, the remaining possibility is 2.

permutation = 6 × 4 × 2 × 2

Similarly, the third row can only be filled with one possibility remaining of the 6 since it is not allowed to seat siblings right up front.

permutation = 6 × 4 × 2 × 2 × 1 × 1 = 96

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Given data:

Total packs 3x3 sticky notes: 24 packs

Cost of 24 packs: 28.99

Number of sticky notes in a pack: 100

With the information above, we can proceed to find the answers to the questions

Part A: What is the price for each pack?

Since 24 packs cost 28.99

Then 1 pack will cost =

Hence, a pack will cost $1.21

Part B: How much is every single sticky note?

Since each pack cost 1.21, and each pack has 100 sticky notes, then

each sticky note will cost

=> every single sticky note will cost $0.012

Possible answers to the expression 2x - 15 are given as follows:

An expression is solved isolating the variable of which we want to find the value.

In this problem, the expression is given as follows:

2x - 15 = c.

In which c is a constant that is not given in the incomplete problem here, hence we will attribute values to it.

With c = -35, we have that the solution is found as follows:

2x - 15 = -35

2x = -20 (-35 + 15)

x = -20/2

x = -10.

Now, if c = 3, the solution is calculated as follows:

2x - 15 = 3

2x = 18

x = 18/2

x = 9.

In your problem, a value for c(the right-handed side of the equality) will be given, and you will solve it applying the same procedure I applied in the answer here.

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Answer:

Rewrite using the commutative property of multiplication.

2

(

2

x

0

y

2

)

−

3

y

x

3

Anything raised to

0

is

1

.

2

(

2

⋅

1

y

2

)

−

3

y

x

3

Multiply

2

by

1

.

2

(

2

y

2

)

−

3

y

x

3

Rewrite the expression using the negative exponent rule

b

−

n

=

1

b

n

.

2

1

(

2

y

2

)

3

y

x

3

Simplify the denominator.

Tap for more steps...

2

1

8

y

6

y

x

3

Simplify terms.

x

3

4

y

5

3 equations that can be used to solve the given scenario are:

So, equations that can be used to solve the following scenario are:

Then,

Therefore, 3 equations can be used to solve the given scenario are:

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Answer: 6

Step-by-step explanation:

m = -4 / 2 = -2 / 1 = -2

To determine the percet of shoppers that use coupons, the manager interviews every shopper thay enters the greeting aisle and records wether they use or not coupons.

Since he does not take any measures, nor divide the shopers into groups or, for example, interviews one every k number of shoppers, the sampling method he used is the most simple and common one, named

"Simple random sample" or "random sample"

Answer:

a.) Let x be Kim's sister's age.  Kim's age would therefore be 2x.

b.) 2x + x = 36

c.) 2x + x = 36  

          3x = 36

             x = 12

d.) So Kim's sister (x) is 12.

e.) Since Kim's age is 2x, Kim is 24.

Step-by-step explanation:

See above.

The distance between Ashely’s house and the public library is of 7.8 miles.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between these two points is given by the following rule:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the Cartesian plane, with the hypotenuse representing the distance between them.

In the context of this problem, the coordinates of her house and of the library are given as follows:

Hence the distance is calculated as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]D = \sqrt{(10 - 4)^2+(7 - 2)^2}[/tex]

D = sqrt(61)

D = 7.8 miles, as each unit on the plane represents one mile.

The problem states that each unit on the plane represents one mile and the image gives their position on the plane.

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you didn't attach the figure....