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 $5,000, while keeping the purchases below $1,000. Which system of inequalities represents this scenario?

x2 – 2y > 5000
2x + 5y < 1000

x2 – 2y > 5000
2x + 5y ≤ 1000

x2 – 2y ≥ 5000
2x + 5y < 1000

x2 – 2y ≤ 5000
2x + 5y ≤ 1000

The distance from a to the line passing through b and c is 7/5.

To find the distance from a point to a line, you can use the cross product and the dot product.

First, find the vector pointing from a to b and the vector pointing from b to c:

u = b - a = (3, -5, 0) - (0, 3, -5) = (3, -8, 5)

v = c - b = (3, 0, -5) - (3, -5, 0) = (0, 5, -5)

Next, find the cross product of these two vectors, which gives a vector orthogonal to the plane defined by the line:

n = u x v = (-40, 0, 40)

Finally, find the dot product of n and a - b, which gives the magnitude of the projection of a - b onto n:

d = |n . (a - b)| / |n| = |(-40, 0, 40) . (-3, -8, -5)| / |(-40, 0, 40)| = 57 / √(40^2 + 40^2) = 57 / √1600 = 57 / 40 = 7/5

Therefore, the distance from a to the line passing through b and c is 7/5.

To learn more about vectors,

Visit; brainly.com/question/29740341

#SPJ4

1 gallon equal to  3.785411784 liter.

The gallon is a unit of volume in imperial units and United States customary units. Three different versions are in current use:

The imperial gallon (imp gal), defined as 4.54609 litres, which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand and some Caribbean countries.

The US gallon (US gal), defined as 3.785411784 L, (231 cubic inches) which is used in the US and some latin American and Caribbean countries.

The US dry gallon ("usdrygal"), defined as 1/8 US bushel (exactly 4.4.0388377086 L)

By using the above formula to convert US gallons to litres.

Solution: Inserting the value of a gallon in the above formula we will get:

Litre =1×3.785411784 =3.785411784

Hence 1 gallons are equal to 3.785411784 liter.

To learn more about gallon refers to:

brainly.com/question/1106482

#SPJ4

Linear combination of u and v is c1u + c2v where c1,c2 are scalars, eg. (1, -12), (2.5, -7), (6.5, -4.5).

What is vector ?

Vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.

A linear combination of vectors u and v is a vector of the form c1u + c2v, where c1 and c2 are scalars. There are infinitely many possible linear combinations of u and v, here are three examples:

c1u + c2v = (1) (3, -2) + (2) (-1, -5) = (3 + -2, -2 - 10) = (1, -12)

c1u + c2v = (0.5) (3, -2) + (-1) (-1, -5) = (1.5 + 1, -2 - 5) = (2.5, -7)

c1u + c2v = (2) (3, -2) + (-0.5) (-1, -5) = (6 + 0.5, -2 - 2.5) = (6.5, -4.5)

that these are just three examples, there are many more possible linear combinations of u and v.

Linear combination of u and v is c1u + c2v where c1,c2 are scalars, eg. (1, -12), (2.5, -7), (6.5, -4.5).

To learn more about vector visit : brainly.com/question/29740341

#SPJ4

When a plane is inclined at a 45-degree angle and intersects a cylinder's base along its diameter with radius "r," it results in the division of the cylinder into two identical right circular cones.

Imagine a cylinder with a radius "r."

The plane passes through the cylinder's base, creating a line that bisects the circular base into two equal halves.

This intersection between the inclined plane and the cylinder forms a cross-section that resembles an isosceles right triangle.

By symmetrically splitting the cylinder along its central axis, the inclined plane generates two congruent right circular cones, each with a 45-degree angle at its apex. The curved line formed by the intersection represents the boundary between the two cone halves.

Learn more about cylinder here:

https://brainly.com/question/30419673

#SPJ12

Answer:

Below

Step-by-step explanation:

Slope-intercept form of a line  is   y = mx + b     m is slope    b is intercept

so it is just   y = -3/4 x -4

Answer:

If the pet store had 1/9 of a bag of cat food, and they want to divide it equally between 4 cats, then each cat would get 1/9 of the bag divided by 4.

So, each cat would get:

1/9 ÷ 4 = 1/9 * 1/4 = 1/36

So, each cat would get 1/36 of the bag of cat food.

Answer: X=3

Step-by-step explanation: Since it’s a vertical line the Y value is 0 making the line x=3 bc it’s on the 3 for the x-axis

The width of the farm in the drawing is 2 centimeters.

The formula used to calculate the width of the farm in the drawing is: the actual width of the goat pen divided by the scale of the drawing. In this case, 8 meters divided by 4 meters (1 centimeter = 4 meters) is equal to 2 centimeters. So, the width of the farm in the drawing is 2 centimeters.

To calculate the width of the farm in the drawing, we must first understand the scale of the drawing. The scale of the drawing is 1 centimeter = 4 meters. This means that for every 1 centimeter in the drawing, it represents 4 meters in the actual farm.

Next, we must determine the actual width of the goat pen. In this case, it is 8 meters.

Finally, we can calculate the width of the farm in the drawing by dividing the actual width of the goat pen (8 meters) by the scale of the drawing (1 centimeter = 4 meters). 8 meters divided by 4 meters is equal to 2 centimeters. So, the width of the farm in the drawing is 2 centimeters.

Learn more about actual width here:

https://brainly.com/question/12559864

#SPJ4

Answer:

B) 4 - 3r

Step-by-step explanation:

B.  4 - 3r is the mathematical expression.

The value of N equals to -9.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

n+9/9=0

Now,

n+9/9=0

n+9=0

n=-9

Therefore, the answer of this algebra will be -9.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ1

The slope of this line is m = 1.

An equation of this line is y = x.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (1, 1), an equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

Substituting the parameters, we have the following:

y - y₁ = m(x - x₁)

y - 1 = 1(x - 1)

y = x - 1 + 1

y = x

Read more on slope here: brainly.com/question/3493733

#SPJ1

Answer:

PQ=17.088

Step-by-step explanation:

If M is the midpoint of PQ, then PM is half the length of PQ. So we cna find our answer by first finding PM.

Imagine a right angle triangle with PM as its hypotenuse. Since P(x,y)=(5,-15), and M(x,y)=(13,-18), we know that the length of the vertical side of this triangle is the difference between P and M's y (vertical) coordinates, and the length of the horizontal side of this triangle is the difference between P and M's x (horizontal) coordinates. This means the vertical side is equal to -15-(-18)=3 and the horizontal side is equal to 13-5=8. Since we know the lengths of the other two sides and PM is the hypotenuse, we can use pythagorus to find the length of PM:

PM = [tex]\sqrt{3^{2} +8^{2} } =\sqrt{9 +64 }=\sqrt{73} =[/tex]8.544

Since PM is half PQ, PQ=2(8.544)=17.088

7000 is the 3 period moving average forecast for week 6.

Using a moving average, a data set's general trend may be determined. The sales volume from the company's historical data is the data set used in operations management. For predicting recent trends, this method is quite helpful. Simply said, it is the average across a range of times.

The most basic method for predicting is a simple moving average (SMA). The data from the previous 'n' periods are added up, and the sum is divided by 'n' to create a simple moving average. So the projection for the following period is based on the moving average value.

3-period weighted moving forecast for week 6:

= (Demand for Period 3 + Demand for Period 4 + Demand for Period 5) / 3 = (8000 + 7000 + 6000) / 3

= 7000

3-period weighted moving forecast for week 6 = 7000

To know more about average forecast refer to:

https://brainly.com/question/24156398

#SPJ4

The complete question is as follows:

Answer:

i agree good job mate I'm not zooded while doing homework

Step-by-step explanation:

I didn't clear a then another then two more

6.56168 feet  and inches is around two metres.

To learn more about feet refer to:

https://brainly.com/question/26726050

#SPJ4

Step-by-step explanation:

12/10.1

16.85/13

21.61/15

The best way, in my opinion, is to divide each price by it's respective inches. Doing that you will see the cost per inch. the cheapest one is the best deal.

[tex]small = \frac{12}{10.1} = 1.19[/tex]

[tex]medium = \frac{16.85}{13} = 1.30[/tex]

[tex]large = \frac{21.61}{15} = 1.44[/tex]

Seeing these 3, the cheapest was $1.19, making the small pizza the best deal because you get the best price per inch

The system of equations have one solution.

Two or more expressions with an Equal sign is called as Equation.

The system of equations

10x - 8y = -1...(1)

3x + 5y = -17..(2)

Multiply equation 1 with 3 and equation 2 with 10

30x-24y=-3..(3)

30x+50y=-170...(4)

Subtract equation 4 from equation 3

30x-24y-30x-50y=-3+170

-74y=167

Divide both sides by 74

y=2.25

Now plug in y value in equation 1

10x-8(2.25)=-1

10x-18=-1

10x=17

Divide both sides by 10

x=17/10

Hence, the system of equations have one solution.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

C. - 8

Step-by-step explanation:

substitute - 4 for x value

-4 + (2×-4) - (-4)

= -4 + (-8) + 4

= -12 +4

= -8

According to the information, it can be inferred that the balance after 3 months is that we have made interest payments for $107.6 of interest and $264.39.

To calculate the payment balance for the car loan we must take into account the following information:

According to the above, we must find how much the interest is equal to:

So, we must divide the result in the 12 months of the year

and later multiply it by the three months that are being asked.

Additionally, we must calculate how much the installment payment would be.

So we would pay 371.79 for the 3 months.

Learn more about interests in: https://brainly.com/question/29480777

#SPJ1

Answer:

12: A = 40 and C = 32

13: A = 45 , C=72 and D=72

Step-by-step explanation:

Angles inscribed by the same arc are equal.

Answer:

[tex]\text{In terms of Gazebos, the perimeter of Gazebo A = \textbf{46 m}}[/tex]

Step-by-step explanation:

Since the two pentagons are similar the ratio of each side of the smaller pentagon to the corresponding side of the larger pentagon is the same

We are given that in pentagon ABCDE, side AB = 10 and the corresponding side FG of pentagon FGHJK = 15

[tex]\text{Therefore } \\\\\dfrac{\overline {AB}}{\overline{FG}} =\dfrac{10}{15} = \dfrac{2}{3}$ \textrm(divide numerator and denominator by 5)}\\[/tex]

The ratios of all the other sides of ABCDE to the corresponding sides of FGHJK must also be [tex]\displaystyle {\dfrac{2}{3}}[/tex]

Therefore it follows that the perimeter of ABCDE = 2/3 x perimeter of FGHJK

Perimeter of FGHJK = sum of sides  [tex]= 15 + 9 + 12 + 15 + 18 = 69 \;m[/tex]

[tex]\textrm{Perimeter of ABCDE } = \dfrac{2}{3} \cdot 69 = 2 \cdot 23 = 46\text{ m}\\\\[/tex]

[tex]\text{In terms of Gazebos, the perimeter of Gazebo A = \textbf{46 m}}[/tex]

Answer:

central angle

Step-by-step explanation:

an angle with a vertex on the center of a circle and slides that are radii of that circle is called a central angle

Central angle has a vertex on the center of the circle and sides that are radii of that circle .

What does central angle mean?

A right angle, which has sides that are the radii of the circle, and a vertex that is at the center of the circle Given that it intercepts an arc with a length equal to the circle's radius, a central angle has radian measure [Math Processing Error].

Where can I find the center angle?

The angle that the arc at the center of a circle occupies is known as the central angle. The arms of the angle are created by the radius vectors. The formula for calculating a central angle is: Central Angle = Arc length(AB) / Radius(OA) = (s 360°) / 2r, where s denotes the length of the arc and r denotes the radius of the circle.

Learn more about central angle

brainly.com/question/15698342

#SPJ4

Answer: 3/4 * 1/2 = 3/8 = 0.375

hope this helpes

[tex] = \frac{3}{4} \times 8 \frac{1}{2} \\ [/tex]

[tex] = \frac{3}{4} \times \frac{8 \times 2 + 1}{2} \\ [/tex]

[tex] = \frac{3}{4} \times \frac{17}{2} \\ [/tex]

[tex] = \frac{51}{8} \\ [/tex]

(2t)^-6 = 1/(2t)^6 is expression of only positive exponents.

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

the given expression is, (2t)^-6.

Now,

To simplify this using only positive exponents we are going to use the rule for negative exponents: b^(-n) = 1/b^n .

Notice that in this case :

b= 2t

so, we get,

(2t)^-6 = 1/(2t)^6

Hence, (2t)^-6 = 1/(2t)^6 is expression of only positive exponents.

To learn more on exponent number click:

brainly.com/question/19467739

#SPJ1

The scale of figure A to Figure B is given by 9 : 5 and option C is the correct answer.

Shapes in various dimensions can be scaled using the Scale Factor. In geometry, we study many geometrical forms that exist in both two- and three-dimensions. The scale factor is a way to compare figures with similar appearances but differing scales or measurements. Consider two circles that resemble one another but may have different radii.

The scaling factor indicates how much a figure has increased or decreased from its initial value.

The scale of figure A to Figure B is given by:

Scale factor = Segment of figure A / segment of figure B

SF = 36 / 20

SF = 9 / 5

Hence, the scale of figure A to Figure B is given by 9 : 5 and option C is the correct answer.

Learn more about scale factor here:

https://brainly.com/question/29262154

#SPJ1

The linear regression equation for estimating tip amount is y = 0.174x + 1.971, where x is the total bill amount and y is the estimated tip amount.

Learn more about linear regression equation: https://brainly.com/question/25987747

#SPJ4

Percent error in the measurement is 8.3 % ( round to one decimal )

Percent of error show how big the error between measurement and actual value in comparison of actual value, and shown in percentage.

Simple formula to find percent of error is :

% error  = | (T - E) / T | x 100%

Where :

T is actual value

E is estimated / measured value

From the question, we know following information :

1. Measured Value = 13 inches

   --> E = 13 inches

2. Actual value = 1 foot. We know that 1 foot equal to 12 inches

   --> T = 12 inches

% error = | (T - E) / T | x 100%

            = | (12-13)/12 | x 100%

            = | -1/12 | x 100%

            = | -0.083 | x 100%

            = 0.083 x 100%

            = 8.3 %

Hence percent error of the measurement is 8.3%

Learn more about percent error of measurement here

https://brainly.com/question/1626245

#SPJ4

Answer: 9.2%

Step-by-step explanation: did the test and got it correct, hope this helps

18 pounds of candy costing $1.05 and 12 pounds of candy costing $1.35 are needed to be mixed to get a 30 pounds of mixture costing $1.17

An equation is an expression showing the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on depending on the degree.

Let x represent the amount of candy costing $1.05, y represent the candy costing $1.35.

The mixture is worth $1.17 a pound and is about 30 pounds. Hence:

1.05x + 1.35x = 1.17(30)    (1)

Also:

x + y = 30    (2)

From both equations:

x = 18, y = 12

18 pounds and 12 pounds of candy are needed to be mixed

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Step-by-step explanation:

up/down shifts are easy. they just indicate a constant change to the calculated y-values (result values) of f(x).

a shift up is therefore just adding a constant to f(x).

a shift down is just subtracting a constant from f(x).

in our case that would be f(x) + 3 = x³ + 3.

left/right shifts are more difficult to understand.

a shift to the left means that the same y-/result values happen as for f(x) also for g(x), just a bit "earlier" (to the left) on the x-axis.

a shift to the right means via the same principle the y-values for f(x) happen unchanged but "later" (to the right on the x-axis) for g(x).

so, 5 units to the left means that g(x) has the same y-value as f(x+5). f(x+5) happens 5 units earlier (at x).

and so, the full g(x) is

g(x) = f(x+5) + 3 = (x+5)³ + 3 =

= (x² + 10x + 25)(x + 5) + 3 =

= x³ + 5x² + 10x² + 50x + 25x + 125 + 3 =

= x³ + 15x² + 75x + 128

The radius of the circle with the same vertex is 6 and the height of the triangle is 10.39 and the area of the triangle is 62.34.

Since the arc divides the triangle into two regions of equal area, it follows that half of the circle's area is equal to the area of the triangle. The area of a triangle with sides 12 and 12√3 and a 60-degree angle can be found using the formula for the area of a triangle, which is 0.5bh.

The height of the triangle can be found using trigonometry, as the sine of 60 degrees is 0.8660. Thus, the height of the triangle is 10.39 and the area of the triangle is 62.34.

Since half of the circle's area is equal to the area of the triangle, the radius of the circle can be found by taking the square root of the area of the triangle and dividing it by pi. Thus, the radius of the circle is 6.

For more questions like Circle click the link below:

https://brainly.com/question/29142813

#SPJ4

A triangle has a 60-degree angle, and the two adjacent ide are 12 and 12 roots 3. Find the radius of a circle with the same vertex a center, if the arc inside the triangle divides it into two regions of equal area