The value of a company’s stock is represented by the expression x2 – 2y and the company’s purchases are modeled by 2x + 5y. The company’s goal is to maintain a stock value of at least $6,000, while keeping the purchases below $2,000. Which system of inequalities represents this scenario?

A.) x2 – 2y ≥ 6000
2x + 5y < 2000

b.) x2 – 2y > 6000
2x + 5y < 2000

C.) x2 – 2y > 6000
2x + 5y ≤ 2000

D.) x2 – 2y ≤ 6000
2x + 5y ≤ 2000

Answer:

15 2/3

Step-by-step explanation:

[tex]5\frac{2}{3} + 2 \frac{2}{3} = 8[/tex]

[tex]8 + 2 \frac{2}{3} + 5[/tex]

[tex]10 \frac{2}{3} + 5 = 15 \frac{2}{3} [/tex]

[tex]15 \frac{2}{3} [/tex]

Answer:

15 2/3

Step-by-step explanation:

Answer:

a) x = 9.

b) y = 61.

Step-by-step explanation:

As the 2  weighing scales balance:

4 + 4x = 31 + x

3x = 31 - 4 = 27

x = 9.

Also 4 + 4x + x + 31  = y + 2x + 1

Substituting  for x:

4 + 4(9) + 9 + 31 = y + 2(9) + 1

80 = y + 19

y = 80 - 19 = 61.

Answer:

x = 9

y = 61

Step-by-step explanation:

The main scales are balanced.

The left side of the main scales comprises another scale, which is also balanced.

From this and the values given, we can construct two equations.

Equation 1

Balancing the scales on the left of the main scales:

⇒ 4 + 4x = 31 + x

Solving this for x:

⇒ 4 + 4x - 4 = 31 + x - 4

⇒ 4x = 27 + x

⇒ 4x - x = 27 + x - x

⇒ 3x = 27

⇒ 3x ÷ 3 = 27 ÷ 3

⇒ x = 9

Equation 2

Balancing the main scales:

4 + 4x + 31 + x = y + 1 + 2x

Rearranging to make y the subject:

⇒ 5x + 35 = y + 1 + 2x

⇒ 5x + 35 - 1 = y + 1 + 2x - 1

⇒ 5x + 34 = y + 2x

⇒ 5x + 34 - 2x = y + 2x - 2x

⇒ 3x + 34 = y

Substituting the found value of x (from Equation 1) and solving for y:

⇒ y = 3(9) + 34

⇒ y = 27 + 34

⇒ y = 61

Therefore:

Answer:

200 ft per min.

Step-by-step explanation:

So this is asking if so and so can walk 3000 ft in 15 min, how many ft can they walk in 1 min.

So just divide the 3000 and 15 by 15.

So 200 over 1.

Step-by-step explanation:

when given similar terms sometimes its easier to work the problem out before sinplifying

Answer:  x2 + y2. − 4x + 5y − 8=0.

Step-by-step explanation:

Answer:

[tex]\dfrac{dy}{dx}=\dfrac{1}{2y}[/tex]

Step-by-step explanation:

Given equation:

[tex]y^2=x[/tex]

Differentiate:

[tex]\implies y^2\:\dfrac{d}{dx}=x\:\dfrac{d}{dx}[/tex]

[tex]\implies 2y\:\dfrac{dy}{dx}=1[/tex]

[tex]\implies \dfrac{dy}{dx}=\dfrac{1}{2y}[/tex]

The Mean Absolute Deviation for the following data: 6, 1, 3, 8, 5, 11, 1, 5 is 2.5

The mean absolute deviation of a dataset is the average distance between each data point and the mean.

mean absolute deviation = [tex]\frac{summation|x-mean|}{n}[/tex]

where

Therefore, let's calculate the mean first.

Arrange the data in ascending order.

1, 1, 3, 5, 5, 6, 8, 11

mean = 1 + 1 + 3 + 5 + 5 + 6 + 8 + 11 / 8 = 40 / 8 = 5

Therefore, let's calculate the distance between each dat point and mean.

|1 - 5| + |1-5| + |3-5| + |5-5| + |5-5| + |6-5| + |8-5| + |11-5|

4 + 4 + 2 + 0 + 0 + 1 + 3 + 6 = 20

Hence,

mean absolute deviation = 20 / 8 = 2.5

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The cost in dollars of making x items is given by the function C(x) = 10x + 900. The fixed cost is 900 dollars. C(25 ) = $1150. The Range is 250.

The function is a type of relation, or rule, that maps one input to specific single output.

The cost in dollars of making x items is given by the function

C(x) = 10x + 900

a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item.

The fixed cost

C(0) = 10(0) + 900

       = 0 + 900

       = $900

b. What is the cost of making 25 items?

C(25) = 10(25) + 900

       = 250 + 900

       = $1150

Therefore, C(25 ) = $1150

c. Suppose the maximum cost allowed is $1900. What are the domain and range of the cost function, C(x)?

The domain is the set of values for which the given function is defined.

Range = Maximum value of the data set - Minimum value of the dataset

Range = C(25 ) - C(0)

           = 1150 - 900

           = 250

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Answer:

x = 12°

Welcome to concept of Inscribed Angle theorem

In the diagram shown above, the inscribed angle m∠SUT intercepts the diameter ST.

Then,

m∠SUT = 90°

In Δ SUT,

m∠S + m∠U + m∠T = 180°

Substitute.

m∠S + 90° + 43° = 180°

m∠S + 133° = 180°

Subtract 133° from each side.

m∠S = 47°

m∠UST = 47°

By Inscribed Angle Theorem,

m∠arc UT = 2 ⋅ m∠UST

Substitute.

(9x - 14)° = 2 ⋅ 47°

(9x - 14)° = 94°

9x - 14 = 94

Add 14 to each side.

9x = 108

Divide each side by 9

x = 12

Hence, we get as x = 12°

Answer:

[tex]4+x=22[/tex]

Step-by-step explanation:

Hope this helps

Step-by-step explanation:

Here...

2 × 2 × 2 × 3 × 3 × 5 = 360..

hence the LCM is 360...

[tex]..[/tex]

( There is also another method to solve this but I choose this one cause this one is easy to understand....)

Answer:

center = (-2, 6)

radius = 6

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

(where (a, b) is the center and r is the radius)

Therefore, we need to rewrite the given equation into the standard form of an equation of a circle.

Given equation:

[tex]x^2+y^2+4x-12y+4=0[/tex]

Collect like terms and subtract 4 from both sides:

[tex]\implies x^2+4x+y^2-12y=-4[/tex]

Complete the square for both variables by adding the square of half of the coefficient of [tex]x[/tex] and [tex]y[/tex] to both sides:

[tex]\implies x^2+4x+\left(\dfrac{4}{2}\right)^2+y^2-12y+\left(\dfrac{-12}{2}\right)^2=-4+\left(\dfrac{4}{2}\right)^2+\left(\dfrac{-12}{2}\right)^2[/tex]

[tex]\implies x^2+4x+4+y^2-12y+36=-4+4+36[/tex]

Factor both variables:

[tex]\implies (x+2)^2+(y-6)^2=36[/tex]

Therefore:

The equivalent expression of the given expression (3x⁴ + 17x³ − x) and (− 2x⁴ − 5x) will be (x⁴ + 17x³ − 6x).

The equivalent is the functions that are in different forms but are equal to the same value.

The expression is given below.

(3x⁴ + 17x³ − x) + (− 2x⁴ − 5x)

Then the equivalent expression of the given expression will be

3x⁴ + 17x³ − x − 2x⁴ − 5x

x⁴ + 17x³ − 6x

The equivalent expression of the given expression (3x⁴ + 17x³ − x) and (− 2x⁴ − 5x) will be (x⁴ + 17x³ − 6x).

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Based on the information in the table, it can be inferred that the values with two dots are 28 1/2 and 25 1/2.

A dot plot is a type of graph that is characterized by representing the frequency of an event by means of points on a line that has the values.

According to the information in the table, it can be inferred that two values have a frequency of 2, these values are:

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Answer:

Rent

Step-by-step explanation:

When someone wants to buy something for a specific time without keeping it permanently, they rent it. Like a hotel, you rent a hotel for a certain number of nights, you do not stay there forever. When you buy something, you keep it forever, like buying a toy, it's your's and no one can rightfully take it from you. To lease something is to let someone rent the item you are leasing, so when they pay rent, you get paid.

give brainliest.

Answer:

You pay 67.5 for the shoes.

Step-by-step explanation:

10% of 75 is 7.5.

75 - 7.5 = 67.5

Please Mark Brainliest!

Answer:

Here ya go! Hope it helps

[tex]18*(7*(-3))=18*7+18*(-3)\\18*-21=126 - 54\\-378 \neq 72[/tex]

LHS [tex]\neq[/tex] RHS

Answer :

To verify an equation, we need to see if the LHS = RHS.

Equation [tex]\downarrow[/tex]

[tex]18\times(7\times(-3))=18\times7+18\times(-3)[/tex]

Let's solve the left hand side (LHS) first.

[tex]18\times(7\times(-3))\\= 18 \times (-21)\\=\underline{ -378}[/tex]

Now, let's solve the right hand side (RHS).

[tex]18\times7+18\times(-3)\\= 126 - 54\\=\underline {72}[/tex]

But,

[tex]\boxed{-378 \neq 72}[/tex]

We can see that the LHS doesn't match or isn't equal to the RHS.

Hence, we can say that LHS [tex]\neq[/tex] RHS & the  equation is NOT true.

[tex]\rule{150pt}{2pt}[/tex]

Answer:

-5(y - 3)/-2

Step-by-step explanation:

y² - 9/-2y × -5y/y + 3

Multiply Rewrite

Simplify the expression

(y - 3)×(y + 3)/2 × 5/y + 3

Simplify the expression

y - 3/2 × 5

Calculate

5(y - 3)/2

HOPE THIS HELPS :)

Answer:

[tex]\huge\boxed{\dfrac{-5(y-3)}{-2}}[/tex]

Step-by-step explanation:

[tex]\dfrac{y^2-9}{-2y}\cdot\dfrac{-5y}{y+3}=\dfrac{y^2-3^2}{-2y}\cdot\dfrac{-5y}{y+3}[/tex]

use: a² - b² = (a - b)(a + b)

[tex]=\dfrac{(y-3)(y+3)}{-2y}\cdot\dfrac{-5y}{y+3}[/tex]

simplify fractions

(y + 3) and y

[tex]=\dfrac{y-3}{-2}\cdot\dfrac{-5}{1}=\dfrac{-5(y-3)}{-2\cdot1}=\dfrac{-5(y-3)}{-2}[/tex]

Answer:

[tex]y=2(x-2.5)^2-1.5[/tex]

Step-by-step explanation:

[tex]y=2x^2-10x+11[/tex]

Factor highest common numerical factor of the first two terms:

[tex]y=2(x^2-5x)+11[/tex]

Add [tex](\frac{-5}{2})^2[/tex] inside the parentheses and subtract [tex]2(\frac{-5}{2})^2[/tex]:

[tex]y=2(x^2-5x+6.25)+11-12.5[/tex]

[tex]y=2(x^2-5x+6.25)-1.5[/tex]

Factor parentheses:

[tex]y=2(x-2.5)^2-1.5[/tex]

Compare to vertex form of parabola

Vertex at (2.5,-1.5)

Answer:

Pls refer

Step-by-step explanation:

I hope you understand

Feel free to ask any doubts

The new matrix that is formed by the 3A + B is given below. Then the value of x is 102.

[tex]\begin{bmatrix} w & z \\y & z \\\end{bmatrix} = \begin{bmatrix} 46 & 102 \\15 & -2 \\\end{bmatrix}[/tex]

A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The [tex]a_{ij }[/tex] element in a matrix, such as M, refers to the i-th row and j-th column element.

The matrices are given below.

[tex]\rm A = \begin{bmatrix}9 & 27 \\0 & 6 \\\end{bmatrix}\\\\\\B = \begin{bmatrix}19 & 21 \\15 & -20\\\end{bmatrix}[/tex]

Then the new matrix is given as 3A + B. Then we have

[tex]\rm 3A + B =\begin{bmatrix} w & z \\y & z \\\end{bmatrix}\\\\\\3A + B =3 \times \begin{bmatrix}9 & 27 \\0 & 6 \\\end{bmatrix} + \begin{bmatrix}19 & 21 \\15 & -20\\\end{bmatrix}\\\\\\3A + B = \begin{bmatrix}27& 81\\0 & 18\\\end{bmatrix} + \begin{bmatrix}19 & 21 \\15 & -20\\\end{bmatrix}\\\\\\3A + B = \begin{bmatrix} 46 & 102 \\15 & -2 \\\end{bmatrix}[/tex]

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base= 10 ft

height= 12 ft

the surface area of the given pyramid.

[tex]s.a = {a}^{2} + 2a \sqrt{ \frac{ {a}^{2} }{4} + {h}^{2} } [/tex]

[tex]s.a = {10}^{2} + 2 \times 10 \times \sqrt{ \frac{ {10}^{2} }{4} { \times 12}^{2} } [/tex]

[tex]s.a = 360 \: {ft}^{2} [/tex]

therefore, the surface area of the given pyramid is 360 square feets.

answer= option D

Answer+Step-by-step explanation:

[tex]\frac{1}{5} \left( 4m+20\right) =\frac{4}{5}m + \frac{20}{5} = \frac{4}{5}m + 4[/tex]

[tex]9\left( \frac{5}{4} y-\frac{1}{3} \right) =\frac{9\times5}{9} y-\frac{9}{3} = 5y - 3[/tex]

Answer:

[tex]\left( x-2\right)^{2} +\left( y-6\right)^{2} =12[/tex]

Step-by-step explanation:

Formula ………………………………………………………………………

The equation of a circle with center (a , b) and radius r is :

[tex]\left( x-a\right)^{2} +\left( y-b\right)^{2} =r^{2}[/tex]

===================

Now ,let’s apply what we have learnt:

The equation of the circle with center (a , b) = (2 , 6) and radius r = 2√3 is :

[tex]\left( x-2\right)^{2} +\left( y-6\right)^{2} =\left( 2\sqrt{3} \right)^{2}[/tex]

[tex]\Longleftrightarrow \left( x-2\right)^{2} +\left( y-6\right)^{2} =12[/tex]

[tex]\text{Note :} \left( 2\sqrt{3} \right)^{2} =2^{2}\times \sqrt{3}^{2} =4\times3=12[/tex]

Answer:

448 cm³

Step-by-step explanation:

Finding volume :

Answer: 448 cm³

Step-by-step explanation:

    Volume of a triangle prism can be found with;

V = [tex]\frac{1}{2}[/tex] * W * L * H

V = [tex]\frac{1}{2}[/tex] * W * L * H

V = [tex]\frac{1}{2}[/tex] * 8 cm * 14 cm * 8 cm

V = [tex]\frac{1}{2}[/tex] * 8 cm * 14 cm * 8 cm

V = 448 cm³

     The triangle prism has an area of 448 cm³

Answer:

(2,0)

Step-by-step explanation:

Answer:

Number graph ranging from negative three to three on the x axis and negative one to six on the y axis. A line is drawn on the graph that passes through the points (negative three, zero) and (zero, six).

Step-by-step explanation:

Simplified y-4 = 2(x + 1) ⇒ y = 2x + 6

Graphed function on desmos graphing calculator

Matched the through points of option #4, (-3, 0) and (0 ,6) to the graph.

Answer: D. "Number graph ranging from negative three to three on the x axis and negative two to four on the y axis. A line is drawn on the graph that passes through the points (negative one, zero) and (zero, four)."

Step-by-step explanation:

We know that our graph passes through two given sets of points, therefore we can plug in those points to find the correct answer.

Let's test it with choice A. It gives us the points (0,-6) and (3,0). We can plug these into the equation to see if it is true. y-4 = 2(x+1) becomes
-6-4 = 2(3+1), or -10 = 8 which is not true, so we can eliminate it.

Choice B gives us (0,-4) and (1,0) -4-4 = 2(0+1) or -8 = 2, this one is wrong.

Choice C gives us (-1,0), so 0-4 = 2(-1+1) or -4 = 0, this one is also wrong.

Choice D gives us (-3,0) so 0-4 = 2(-3+1) or -4 = -4. This is the only option which has a correct solution, and therefore it is your answer.

Answer:

(5-i)

(5-4i)

(-12i^2+2i+2)

(6i^2-2i)