How can I evaluate P = 3n+2r+t -1 when n=3, r=2, and t=5?

The system of inequalities that best matches the graph is Option C

Step-by-step explanation:

To find the system of inequalities, we simply need to find the equation of each line.

Thus, let's find the inequality that is represented by each line.

Red Line:

First, let’s determine the slope. To do so, we can use the slope formula:

m = (y₂-y₁) / (x₂-x₁)

We can use any two points that's on the Red Line. Using (3, -2) and (6, -4) and substituting them into the slope formula yields:

m = (-4+2) / (6-3)    = -2/3

Therefore, the slope of the red line is 2.

To write the equation of the red line, we can use the slope-intercept form:

y = mx + c

Notice that our y-intercept of our red line is (0, 3). Therefore, b = 3 and we already determined that m = -2/3:

y = ((-2/3)x) + (-3)

y   = (-2/3)x -3

Now, we need to determine our sign. Notice that the shaded region is below the red line. Therefore, y is less than our equation.

And since our line is shaded, our sign will be less than or equal to. Therefore:

y ≤ (-2/3)x - 3

Blue line:

Again, let’s first find the slope. We can use the two points (3,0) and (0, -3). Hence:

m = (-3-0) / (3-0)  = -3/3  = -1

So, the slope is -1.

We can now use the slope-intercept form. Notice that our y-intercept is (0, 0). Thus, we will substitute -1 for m and 0 for b. This yields:

y = -1x + 0

y = -x

Finally, we will determine our sign. Since the shaded region is above the blue line, our y is lesser than our equation. Therefore, our equation is:

y < -x

Thus, all together, our inequalities are:

y ≤ (-2/3)x - 3

y < -x

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Answer:

c = 11.46 yd

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ c² = (8.1)² + (8.1)²

→ c² = 65.61 + 65.61

→ c² = 131.22

→ c = √131.22

→ [ c = 11.46 yd ]

Hence, value of c is 11.46 yd.

The triangle does not exist, as the property, the sum of two sides of a triangle is greater than the third side length of the triangle does not hold true.

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric forms is represented by the symbol △ and consists of three connected vertices. Triangles may be categorized into a number of different varieties according to their sides and angles.

It is a triangle's property that the sum of any two sides of a triangle is greater than the third side.

Here sides given are 3 m, 5 m, 9 m.

Let us add the sides length 3 m and 5 m

3 m + 5 m = 8 m

Compare this with the third-side length of the triangle

8 m < 9 m

So, the property does not hold true.

So, the triangle does not exist.

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The value of the algebraic expression 2/5g + 3h - 6 if evaluated when g = 10 and h = 6 is 16.

2/5g + 3h - 6

When g = 10 and h = 6

2/5g + 3h - 6

2/5(10) + 3(6) - 6

20/5 + 18 - 6

4 + 18 - 6

16

In conclusion, the value of the expression 2/5g + 3h - 6 when evaluated is given by 16

Complete question:

Evaluate 2/5g + 2h - 6 start fraction, 2, divided by, 5, end fraction, g, plus, 3, h, minus, 6 when g=10 g, equals, 10 and h=6 h, equals, 6

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Answer:

10

Step-by-step explanation:

(2w + 4) - (2w - 6)

2w + 4 - 2w + 6

2w - 2w + 4 + 6

10

I hope this helps!

432 ways are there to paint each of the integers 2, 3,..., 9 either red, green, or blue so that each number has a different color from each of its proper divisors.

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It claims that if there are n ways to do something and m ways to do something else after that, then there are n m n*m methods to do both of these acts.

Here,

(1) All prime number can take any of three colors, except one of 2 or 3 as both are connected via 6..

so 2, 5, 7 can have 3 ways each - 3*3*3 = 27 ways

(2) Let us take the multiples of 2..

4 can take any of the remaining 2 colors, while 8 would take the remaining colour. As like 4, 6 can also take any of 2 colors other than the colour of integer 2.

Thus 2*2*1=4

3 is restricted because of 6, so it cannot have the same color as 6 and therefore 3 can have any of the remaining 2 colors.

We could also have taken 3 colors for 6, and then 2 and 3 would have 2 colors each and overall 2*2*3.. We are still getting the same

Only integer left is 9, so it will take any of the 2 colors other than that of 3, so 2 ways..

Total 2*2=4

Combined way of  integers = 27∗4∗4=432 ways

There are 432 different methods to paint the numerals 2, 3,..., 9 red, green, or blue so that each number has a different hue from each of its suitable divisors.

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Answer:

Step-by-step explanation:

     I am going to transform this equation into slope-intercept form, as it is usually easier to graph it that way.

  Given:

-8 + x = 4y - 16

  Add 16 to both sides of the equation:

-8 + x + 16 = 4y

  Divide both sides of the equation by 4:

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

  Reflexive property and combine like terms:

y = [tex]\frac{1}{4}[/tex]x + 2

  Now, we will graph. The 2 is our y-intercept and the  [tex]\frac{1}{4}[/tex] is our slope, graphed as "rise over run." This means we will rise one unit up and run four units right.

      See attached.

The expression that is equivalent is y(x + 2) and xy + 2y and x(x + y + 2) and  x² + xy + 2x

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Now, let's check if the expression are equivalent by simplifying it.

y(x + 2) and xy + 2y

xy + 2y and xy + 2y

Therefore, the expressions are equivalent.

x(x + y + 2) and  x² + xy + 2x

x² + xy + 2x and x² + xy + 2x

They are equivalent expression.

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A 12-ounce can of beer contains the same amount of alcohol as a five-ounce glass of wine.

In a five-ounce glass of wine, the percentage of alcohol is 12%, which is the same in the 12-ounce can or bottle of beer, and 1.5 ounces of 86-proof liquor. Although a person under the influence of alcohol will have impaired judgment and therefore must avoid driving, doesn't matter what kind of alcoholic beverage they drink. Digestion of alcohol doesn't take place as soon as you drink it, it is absorbed in your bloodstream which reaches the brain and thus creates impaired judgment.

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The equation that could be used to solve for the time t in hours that she drove before her stop is 80t + 100(8/3 - t) = 250.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let t = time she drove before her stop

If the total trip time is 3 hours including the stop, which took 20 minutes, then the time she drove after the stop is 3 - t - 1/3 or 8/3 - t.

If altogether she drove a distance of 250 km, then the sum of the products of the rate of speed and time each drive is equal to 250.

(80 km/h)(t) + (100 km/h)(8/3 - t) = 250

Simplify the equation.

80t + 100(8/3 - t) = 250

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Answer:

to find the max number of guests:

25x-400 = 50

25x = 50 + 400

25x + 450

then divide

x = 450/25

x = 18

to find the min number of guests:

25x = 400 - 50

25x = 350

then divide

x = 350/25

x = 14

Minimum number of tables reserved:

is dividing the max/7 per table

x = 18/7

x = 3

Step-by-step explanation:

Answer:717 calories

Step-by-step explanation:

first you need to find what one ounce would be:

430/12=35.83...

then you multiply the answer by 20

35.83*20=716.6...=717

The equivalent fraction for 2/3 and 8/11 is 22/33 and 24/33.

What is least common denominator?

The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.

Given fractions are

2/3 and 8/11

L.C.M of 3 and 11 is 33.

We get,

2/3 ×11/11 = 22/33

and

8/11×3/3 = 24/33

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Answer:

1200

Step-by-step explanation:

1,500-300=1200

8.08 percent of babies are born prematurely .

We have following information,

lengths of pregnancy of humans are Normally distributed.

mean of distribution ( μ ) = 268 days

standard deviations of distribution = 15 days

We shall find out the pecent of babies are born. prematurely.

Using the Normal distribution formula ,

Z = ( X - μ ) /σ

where X---> sample mean

μ --> poplution mean

putting the possble values of variables we get,

if a baby born three weaks early then he is considered as premature.

X = 21 , μ = 268 , r =

Z = ( 21-268)/ 15 = - 247/15 = - 16.4

Now, p-value corresponding to Z-value= -16.4 is

8.08..

thus for z= -16.4 , p-value will be 8.08 .. So, 8.08 percent of babies are born prematurely.

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The circumference of the circle to the nearest hundredth is 21.98 inches.

The circumference of a circle is the measure of the boundary or the length of the complete arc of a circle.

The circumference of a circle is the perimeter of the circle. It's the wholes boundary of the circle.

The circumference of the circle can be found as follows:

circumference of a circle = 2πr

where

Therefore,

diameter of the circle = 7 inches

radius of the circle = 7 / 2 = 3.5 inches

Hence,

circumference of a circle = 2 × 3.14 × 3.5

circumference of a circle = 21.98 inches

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Answer:

[tex] - 8(9 - ( - 33 - 15) \div 12[/tex]

[tex] - 8(9 - ( - 48) \div 12[/tex]

[tex] - 8(9 + 4)[/tex]

[tex] - 8(13)[/tex]

[tex] - 104[/tex]

Answer:

-104

Step-by-step explanation:

Divide 108 by 12

Calculate -3 × 11 - 15 which is 48

Remove the parentheses

Divide 48 by 12 which is 4

9 + 4 is 13

-8 × 13 = -104

The expected value of the sum of these events will be 2 / 3.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that the expected value for getting heads, on 30 coin tosses, is 15. The expected value for rolling a 1, after 30 die rolls is 5.

The probability of the sum will be calculated as,

P = ( 15 / 30 ) + ( 5 / 30 )

P =  ( 20 / 30 )

P = 2 / 3

Therefore, the expected value of the sum of these events will be 2 / 3.

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The transformation from the graph of [tex]f[/tex] to the graph of [tex]r[/tex] is 4.

The given functions are f(x)=-1/4 x-2 and r(x)=4f(x).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here,

r(x)=4f(x)

So, r(x)=4(-1/4 x-2)

⇒ r(x)=-x-2

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Vertical: stretch

The graph of the functions is given below.

Therefore, the transformation from the graph of [tex]f[/tex] to the graph of [tex]r[/tex] is 4.

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Answer: $9.76

Step-by-step explanation: If you multiply f, the order of fries (5) by the cost of it ($1.08) you would get $5.40 & if you multiply d, the order of drinks (4) by the cost of it ($1.09) you would get $4.36. If you add up both the total numbers, you would get a final answer of $9.76.

Answer:

$9.76

Step-by-step explanation:

1.08f + 1.09d= Total

1.08(5)+1.09(4)= Total

5.40+4.36= Total

The equation of the line is y = -3/4x + 10, the graph of the equation has been plotted

The slope of the line = -3/4

The slope of the line the change in y coordinate with respect to the change in x coordinate of the function

The line is passing through the point (0,10)

The point slope form is

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute the values in the equation

y-10 = -3/4(x-0)

y - 10 = -3/4x

y = -3/4x + 10

The equation of the line in slope intercept form is

y = -3/4x + 10

Plot the graph using the slope intercept form

Hence, the equation of the line is y = -3/4x + 10, the graph of the equation has been plotted

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From the properties of a right triangle is found that the missing length x= [tex]5\sqrt{3}[/tex].

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos  (x) and tan  (x) .

The sum of the internal angles of a right triangle also is equal to 180°.

The question gives a figure which is compound for two right triangles.

For each triangle is informed two angles, then:

       45+90+ x = 180

       135 + x =180

        x=180-135

        x=45°

       60+90+ y = 180

       150+ y =180

        y=180-150

        y=30°

Thus, the angles for the given triangle are:

From the trigonometric ratio sinФ, you can find the hypotenuse the triangle 2. See below.

[tex]sin \theta =\frac{opposite\ leg }{hypotenuse} \\ \\ sin 45 =\frac{hypotenuse \ triangle 2 }{hypotenuse \ triangle 1} \\ \\ \frac{\sqrt{2} }{2}=\frac{hypotenuse \ triangle 2 }{10\sqrt{2} }\\ \\ 2*hypotenuse \ triangle 2 = 10*2\\ \\ hypotenuse \ triangle 2 = \frac{10*2}{2} \\ \\ hypotenuse \ triangle 2 =10[/tex]

If the hypotenuse of triangle 2 is 10, you can apply again the trigonometric ratio sinФ for finding x

[tex]sin \theta =\frac{opposite\ leg }{hypotenuse} \\ \\ sin 60=\frac{x }{hypotenuse \ triangle 2} \\ \\ \frac{\sqrt{3} }{2}=\frac{x }{10}\\ \\2x=10 \sqrt3\\ \\ x=5\sqrt3[/tex]

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Answer:

Step-by-step explanation:

Answer: C. (2, 1)

Step-by-step explanation:

The numbers labeled are

(-5, -8)

(-2, 1)

(4, 0)

(2, 9)

Find coordinates by looking at each line. (x, y)

The x-axis is the horizontal line in the middle.

The y-axis is the vertical line going across.

The x-axis always goes first when plotting down coordinates, and y goes second.

So, the one NOT labeled is C (2, 1)

The answer is 6 groups of 0.7 tenths is 4.2. in the decimal form.

What is Decimals?

Decimals are a form of a number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

6 groups of ____ tenths is 4.2

4.2 ÷ 6 = 0.7

Hence,  6 groups of 0.7 tenths is 4.2

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The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

a)

The given condition makes a right-angle triangle as shown below,

The tan function,

tanθ = 6/25

θ = 14.50°

b)

When a player is 5 feet closer means (20 feet far)

tanθ = 6/20

θ = 16.70°

c)

As the player gets closer the angle becomes more and more.

Hence "The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases".

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The surface area of the rectangular prism is 172cm^2

Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross sections. The faces of the prism are parallelograms or rectangles.

The surface area of prism is 2A+ pH

where A is the base area

P is the perimeter of the base

and h is the height

for a rectangular prism, the base area is 2×8=16cm^2

perimeter of a rectangle= 2(l+b)

= 2(8+2)

= 20cm

surface area =( 2× 16) + 20× 7

= 32+ 140

= 172cm^2

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