The feasible solution is the best solution possible for a mathematical model.
a. true
b. false

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.The ratio of dogs to  in the shelter is 10 to 8. If there are 20 cats, then 25 dogs are in the shelter.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

The ratio of dogs to cats in the shelter is 10 to 8. i.e 10/8

If there are 20 cats then we need to find number of dogs.

Let the number of dogs be x when there are 20 cats.

10/8=x/20

Apply cross Multiplication.

200=8x

Divide both sides by 8.

x=25.

Therefore there are 25 dogs in the shelter if the number of cats are 20.

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The product of the two linear functions f(x) = x − 3 and g(x) = −2x + 4 is -2x² + 10x - 12

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the linear functions f(x) = x − 3 and g(x) = −2x + 4, hence:

(f.g)(x) is the product of the two functions:

(f . g)(x) = (x - 3)(-2x + 4)

(f . g)(x) = -2x² + 6x + 4x - 12 = -2x² + 10x - 12

The product of the two linear functions f(x) = x − 3 and g(x) = −2x + 4 is -2x² + 10x - 12

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The range of values for the radius of the explosion circle is found to be 500-600 ft.

A circle is a shape founded by all locus in a plane at a fixed distance from its centre.

Now, according to the stated question;

Evaluate the circumference by the formula;

Formula: 2πr

Radius = 800 feet

Substitute the value in the formula;

C = 2πr

C = 2π800

C = 5026.54825 feet

Therefore, radius of the explosion circle will range from 500 to 600 feet.

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Margo works 23 hour per week to earn approximately $300 per week .

It is given that Margo earns $13.50 per hour .

Using unitary method , we get

To get his weekly financial gain, we have a tendency to multiply his hourly wage by the quantity of hours he worked.

Pay = hourly rate × variety of hours worked

300 = 13.50 × number of hours worked

number of hours worked = 300 /13.50

                                           = 22.22

On rounding off , we get the hour = 23 hours

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Answer:

well done...I hope it's helpful

The algebraic expression in simplest terms is 200 · x² - 79 · x + 14 = 0.

In this problem we have a sum of products of binomials as algebraic expression and we must reduce to its simplest terms by using algebra properties, that is, using these properties until a polynomial is found:

(- 10 · x + 2) + (- 9 · x + 8) · (- 10 · x + 2) + (- 9 · x + 8) · (- 10 · x + 2) + (- 9 · x + 8)

(- 10 · x + 2) + 2 · (- 9 · x + 8) · (- 10 · x + 2) + (- 9 · x + 8)

(- 10 · x + 2) · [1 + 2 · (- 10 · x + 2)] + (- 9 · x + 8)

(- 10 · x + 2) · (1 - 20 · x + 4) + (- 9 · x + 8)

(- 10 · x + 2) · (3 - 20 · x) + (- 9 · x + 8)

3 · (- 10 · x + 2)  + (- 20 · x) · (- 10 · x + 2) + (- 9 · x + 8)

- 30 · x + 6 + 200 · x² - 40 · x - 9 · x + 8

200 · x² - 79 · x + 14

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No, If y² varies directly with x², it does not that mean y must vary directly with x

Let's say y² =  16 and x² =  4

Now if y²  =  16

Then y = 4 or -4  and same for x = 2 or -2

As the square root can be either negative or positive, if y² varies directly with x², it does not that mean y must vary directly with x .

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

The next 50 phones are working? ---> 88.3%

The next 100 phones are working? ---> 93.6%

The next 500 phones are working? ---> 98.6%

Step-by-step explanation:

I hope this helps

The distance between line k and point F(-4,0) is 3.6 units

The correct answer is an option (G) 3.6 units

We know that for a line l: ax + by + c = 0 and a point P(x1, y1), the distance between the line line 'l' and a point P is:

[tex]d=\frac{|ax_1+by_1+c|}{\sqrt{a^{2} +b^{2} } }[/tex]

In this question we have been given a line k contains points at (4,1) and (-5,-5).

Also, we have been given a point F(-4, 0)

We need to find the distance between line k and point F(-4,0).

First we find the equation of line k.

[tex]\frac{y-1}{-5-1} =\frac{x-4}{-5-4} \\\\\frac{y-1}{-6} =\frac{x-4}{-9} \\\\-9y+9=-6x+24\\\\6x-9y+9-24=0\\\\6x-9y-15=0[/tex]

So, the equation of line k is 6x - 9y - 15 = 0

Now we find the distance between line k and point F(-4, 0).

Using above formula the distance between line k and point F(-4,0) would be,

[tex]d=\frac{|6(-4) - 9(0) - 15|}{\sqrt{6^{2} +(-9)^{2} } } \\\\d=\frac{|-24-0-15|}{\sqrt{36+81} }\\\\ d=\frac{|-39|}{\sqrt{117} } \\\\d=\frac{39}{10.82}\\\\ d=3.6[/tex]

Therefore, the distance between line k and point F(-4,0) is 3.6 units

The correct answer is an option (G) 3.6 units

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The slope-intercept form is y = 3/2x - 6 for line perpendicular to y = (2/3)x - 1 through (0,6)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

In an equation, perpendicular lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that y = (2/3)x - 1

Here 2/3 is the slope and 1 is the y-intercept

To find a perpendicular line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = 3/2, x₁ = 0 and y₁ = 6

y - 6 = 3/2(x - 0)

y - 6 = 3/2x - 0

y = 3/2x - 6

We have the slope-intercept form y = 3/2x - 6 of a line  perpendicular to y = (2/3)x - 1 through (0,6)

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Answer:

x=1

Step-by-step explanation:

Ok, this is a two step equation, so the first step you will do is get the regular numbers (-4 and -3) on one side of the equation, like this:

3/2x-4=1/2x-3

       +4        +4

3/2x=1/2x+1

Next, you need to get the variables on one side of the equation, so you will minus 1/2x like this.

3/2x=1/2x+1

-1/2x -1/2x

2/2x=1

Simplify

x=1

Answer:

x = 1

Step-by-step explanation:

[tex]\frac{3}{2} x-4 = \frac{1}{2} x-3[/tex]

[tex]x - 4 = -3[/tex]

x = 1

Answer:

84.7

Step-by-step explanation:

first you multiply 3.85 x 25 =96.25 then you need to determin the percent of 12 which is 11.55 the lasly you subtract 96.25-11.55=84.7      btw 84.7 for bannas is a scam for real

Answer:

what

Step-by-step explanation:

Using the midpoint concept, the location of the point directly between the two airplanes is (-500, 1000, 2600).

The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.

For this problem, the coordinates are given as follows:

Hence the coordinates of the midpoint are given as follows:

The location is (-500, 1000, 2600).

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Length of AC is 54 units.

The midpoint of a line is a point that bisects the line into equal parts. It is equidistant from both end points of the line.

As B is the midpoint of AC,

AB = BC

∴ 4x - 5 = 11 + 2x

∴ 4x - 2x = 11 + 5

∴ 2x = 16

∴ x = 8.

Now, AC = AB + BC

∴ AC = 4x - 5 + 11 + 2x

Substituting the value of x,

∴ AC = 4(8) - 5 + 11 + 2(8)

∴ AC = 54 units

Thus, the length of AC is 54 units.

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The formula for nth term of the given sequence is [tex]T_{n+1} = T_{n} - 8[/tex].

According to the given question.

We have a sequence, 21,13,5,-3, .......

Since, the first term of the given sequence is 21.

The second term of the given sequence is 13.

Here we can see that, each term is less than 8 to the previous term. It means the common ratio of the given sequece is -8 and it is an arithmetic sequence.

Therefore, the formula for nth term of the given sequence is given by

[tex]T_{n+1} = T_{n} - 8[/tex]

Where, n is the number of term.

Hence,  the formula for nth term of the given sequence is [tex]T_{n+1} = T_{n} - 8[/tex].

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Answer:

47002 :)

is how you write 47 thousand +2

Answer:

3760/4000(2 tons=4000pounds)

$0.94 is the answer

So, from the question statement, we can conclude that the y and x axes are directly proportional. In order to  show it in the equation form, we can write,

Y=kx (directly proportional)

y=k x

The values that are given in the question are

y = 15

and,

x = 10

Now we will put these individual values in the above relation equation of x and y,

y=k x

15=10k

k=15/10

k=1.5

So, we found the unknown factor by putting the values of the available terms. Now in order to find the new value of y, when the new values of x are given and is,

x=22

We will simply modify the relation equation,

y=k x

By putting the known terms in the above equation,

x=22, k=1.5

y=1.5 * 22

y = 33.

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    The numbers that are given:

-0.5-0.25-0.125- . . . . . .

 They are part of an infinite series

 A series is the summation of a set of numbers or sequences.

      A sequence is an order of elements that are governed by a pattern, that is, it has variations between each element that remain constant and allow us to determine values before or after the known elements.

 A sequence maintains an order, and this numerical order can be finite or infinite, in the given case we have the following list:

-0.5-0.25-0.125- . . . . . .

If we analyze the variation between each term we have the form:

(-1/2ⁿ)

(-1/2ⁿ)

  In this series we have the initial value of the same, but we do not know the final value, although we know its behavior, we can say that this series has no end, it is an infinite serie.

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 The vertex, focus and directrix of the parabola y = x²/4 are:

  The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

  The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

  In this case we have an expression given by:

x = y²/16

   We must find the canonical equation:

(y - 0)² = 16 (x - 0)

has the form

(y - k)² = 4p(x - h)

  This means that the vertex of this parabola is

v = (h, k)

v = (0,0)

  To know the focus we must know the value of "p".

f = (0 + 4, 0)

f = (4, 0)

d = y = 0 - 4

d = y = -4

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Answer:

13/15

Step-by-step explanation:

If we give all of these fractions a common denominator, this problem will be much easier. We see that a common denominator can be 15.

We can take 1/3 and multiply both the numerator and denominator by 5, getting 5/15. 7/15 already has a denominator of 15. Now if we multiply the numerator and denominator by 3, we get 9/15. Then we have 11/15.

Now the pattern is 5/15, 7/15, 9/15, 11/15. The numerator increases by 2 each time, so the next fraction should be 13/15.

Answer:

11 people

Step-by-step explanation:

14-8+5

6+5

11

According to the Centers for Disease Control and Prevention (CDC), the average shower lasts 8 minutes. If you like to linger in the shower for longer than 15 minutes, you might want to rethink your hygiene routine.

According to board-certified dermatologist Dr. Edidiong Kaminska, MD, the recommended maximum shower time is about 5 to 10 minutes. This is enough time to cleanse and hydrate the skin without overdoing it. “Our skin needs water, just like our bodies, but if we over- or under-do it, then it may have consequences,” she adds.

And if you have dry skin or eczema, Dr. Anna Guanche, MD, FAAD, says shorter, lukewarm showers are recommended. Moreover, the Baylor College of Medicine says it’s especially important to avoid hot showers in the wintery months since the heat can damage the surface of the skin, which can lead to inflammation and increase symptoms of eczema.

Side effects of long showers

While a long, hot shower might seem like the best way to pamper your body, over-showering may dehydrate the skin. “The purpose of showering is to hydrate and cleanse the skin, but warm or hot showering for prolonged periods strips away natural oils of the skin and opens up our pores and allows moisture to escape,” Kaminska says.

To keep moisture in, she usually recommends applying a body moisturizer after showering to the skin since it allows the water (hydration) to stay in the skin and not escape.

Answer: Slope: 3/2

Step-by-step explanation:

Coordinates: (1, -3), (3, 0)

Slope formula: m=(y2-y1)/(x2-x1)

m=(0-(-3))/(3-1)

m=(0+3)/2

m=3/2 ==> Slope: 3/2

For 10 animals do Jose and Nancy charge the same amount.

For, the given question;

Let there be 'x' number of animals.

Jose charges $15 plus $2 per animal.

15 + 2x

And, Nancy charges $5 plus $3 per animal.

5 + 3x

Then,

For the same amount, equate both equations.

15 + 2x = 5 + 3x

On solving;

x = 10

Thus, for 10 animals, their total charge will be equal.

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Answer:

3rd option

Step-by-step explanation:

using the sine and cosine ratios for the 60° angle in the right triangle and the exact values.

cos60° = [tex]\frac{1}{2}[/tex] and sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{12}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = 12 ( divide both sides by 2 )

x = 6

and

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{12}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2y = 12[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

y = 6[tex]\sqrt{3}[/tex]

Answer:

C

Step-by-step explanation:

[tex]Answer:\ f^{-1}(x)=\sqrt[3]{x} -4[/tex]

Step-by-step explanation:

[tex]f(x)=(x+4)^3[/tex]

Extract the cube root from both parts of the equations:

[tex]\sqrt[3]{f(x)} =x+4\\\sqrt[3]{f(x)}-4=x+4-4\\ \sqrt[3]{f(x)} -4=x[/tex]

Redefine the variables:

[tex]f^{-1}(x)=\sqrt[3]{x} -4[/tex]

Answer:

3. Line q

4. Point B and Point A

5. Line DC or Line CD

6. Plane G

7. Line n, Line q, Line AB, Line BA, Line BE, Line EB

8. Line N, and Line Q

Step-by-step explanation: