I need help i don't get this

The function in the context of this problem is modeled as follows:

t(r) = 12/(6 + r)

In which the input and output of the function are given, respectively, by:

Then the numeric value at t = 3 represents the time in hours it takes for the boat to cross the river when the velocity of the river is of 3 kilometers per hour.

The vertical asymptote of a function are the values of the input for which the function is not defined.

A fraction is not defined at the zeros of the denominator, hence:

t + 6 = 0

t = -6 is the vertical asymptote of the function.

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The expression that uses the greatest common factor and distributive property to write the given expression, 18 + 24, is 6(3 + 4)

From the question, we are to determine the expression that uses the greatest common factor and the distributive property to write the given expression.

The given expression is

18 + 24

First, we will determine the greatest common factor of 18 and 24

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

Thus,

The greatest common factor is 2 × 3 = 6

Now, we will write the expression using the greatest common factor and the distributive property

18 + 24

6(3 + 4)

Hence, the expression is 6(3 + 4)

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Answer:

-12x + 2

Step-by-step explanation:

-6+8 = 2

-3x - 9x = -12x

-12x + 2

Answer:

Step-by-step explanation:

-12x+14 i believe

The trigonometric expression cos 3x / (sin x · cos x) is equivalent by trigonometric formulas to the trigonometric expression csc x · cos 2x - sec x · sin 2x. (Correct choice: A)

In this problem we find the definition of a trigonometric expression, whose equivalent expression must be found by using algebra properties and trigonometric formulas. First, write the trigonometric function:

cos 3x / (sin x · cos x)

Second, use trigonometric formulas:

cos (x + 2x) / (sin x · cos x)

(cos x · cos 2x - sin x · sin 2x) / (sin x · cos x)

cos 2x / sin x - sin 2x / cos x

csc x · cos 2x - sec x · sin 2x

The equivalent trigonometric expression is csc x · cos 2x - sec x · sin 2x.

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Answer:

The length will be 13 feet.

Step-by-step explanation:

Let the width be represented by w.

Based on the information given, the length will be:

= (2 × w) - 3

= 2w - 3

Therefore, the perimeter will be:

2(w) + 2(2w - 3) = 42

2w + 4w - 6 = 42

6w = 42 + 6

6w = 48

w = 48/6

w = 8

Therefore, the length will be:

L = 2w - 3

L = 2(8) - 3

L = 16 - 3

L = 13 feet

The length is 13 feet.

Answer:

The length will be 13 feet.

Step-by-step explanation:

Let the width be represented by w.

Based on the information given, the length will be:

= (2 × w) - 3

= 2w - 3

Therefore, the perimeter will be:

2(w) + 2(2w - 3) = 42

2w + 4w - 6 = 42

6w = 42 + 6

6w = 48

w = 48/6

w = 8

Therefore, the length will be:

L = 2w - 3

L = 2(8) - 3

L = 16 - 3

L = 13 feet

The length is 13 feet.

The value of the function g(f(2)) is 29 and 2.f(g(x)) is (x - 1)(2x - 2).

When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Given, f(x) = 4x² - 1. and g(x) = 2x - 1.

Now, g(f(2)) is the output of f(2) is the input of g(x).

∴ f(2) = 4(2)² - 1.

f(2) = 15.

Now, g(f(2)) = 2(15) - 1.

g(f(2)) = 29.

Also given,

f(x) = x² and g(x) = x - 1.

Now, 2.f(g(x)).

2.f(g(x)) = 2.f(x- 1).

2.f(g(x)) = 2(x - 1)².

2.f(g(x)) = 2(x² - 2x + 1).

2.f(g(x)) = 2x² - 4x + 2.

2.f(g(x)) = 2x² - 2x - 2x + 2.

2.f(g(x)) = 2x(x - 1) - 2(x - 1).

2.f(g(x)) = (x - 1)(2x - 2).

There is no restriction to the domain of this quadratic function.

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1) 16.7% probability of rolling 10+.

2) 50% probability an odd number is rolled.

3) 7 is the most likely total result.

These are all the possible outcomes:

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

There are 36 possible outcomes

1) what is the probability of rolling 10+?

There are 6 possible outcomes in which 10+ is rolled:

(4,6), (5,5),(5,6), (6,4), (6,5),(6,6).

So there is a 6/36 = 0.167 = 16.7% probability of rolling 10+.

2) what is the probability of rolling an odd number?

There are 18 possible outcomes in which an odd number is rolled.

So there is a 18/36 = 0.5 = 50% probability an odd number is rolled.

3) what is the total that is most likely to result?

There are 6 outcomes in which 7 is rolled.

So 7 is the most likely total result.

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The pair of lines given are parallel to each other.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have the following pair of lines -

y = 5x + 12

y = 5x - 1.3

Since the slope of lines are same, both of these lines are parallel to each other.

Therefore, the pair of lines given are parallel to each other.

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Answer:

102

Step-by-step explanation:

First, divide 7.30 by 73 to find how much 1 text message costs. We get 0.1. Next, divide 10.20 by 0.1, which gives us the final answer of 102.

Answer:

99 text messages

Step-by-step explanation:

        $7.50 = 73

           ÷73    ÷73

         ---------------------

amount to  =   $0.102739726

send one text

0.102739726x = $10.20

÷0.102739726    ÷0.102739726

-------------------------------------------------

x ≈ 99.28

I hope this helps!

The perimeter of the new enlarged garden whose side length lengthened by factor of 8 is equal to 576ft.

As given in the question,

Shape of the garden is right triangle

Let 'x' , 'y' , and 'z' represents the three sides of the triangle shape garden.

Perimeter of the garden = 72 ft

⇒ x + y + z = 72 ft  __(1)

Now, length of the each sides of the new garden is lengthened by factor of 8.

Sides of the new garden are '8x' , '8y' , and '8z'

Perimeter of the new garden = 8x + 8y + 8z

⇒ Perimeter of the new garden = 8 ( x + y + z )

⇒ Perimeter of the new garden = 8 (72)

⇒ Perimeter of the new garden =  576 ft

Therefore, perimeter of the new garden is equal to 576ft.

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According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

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The three points which correctly represents a solution to the given inequality are;

It follows from the task content that the points which are solutions to the given inequality bare to be determined.

Since the given inequality as in the task content is; y > 4 x - 3.

By evaluating the inequality at one x-value of x = 1.

We have ;

y > 4 ( 1 ) - 3

y > 4 - 3

y > 1.

Therefore, the possible values of y which are greater than 1 are; 2, 3, and 4.

On this note, it is correct to conclude that the points which are solutions to the given inequality are; ( 1, 2 ), ( 1, 3 ) and ( 1, 4 ).

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Answer:

-3x, where x is the number of yards lost on the first play.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\tt 6(x-2)(x-3) + 4(x-2)(x - 5)[/tex]

When, x = -3

----------------------------------------------

To find the value of 6(x-2)(x-3) + 4(x-2)(x - 5), we need to substitute x with -3.

[tex]\tt 6\left(-3-2\right)\left(-3-3\right)+4\left(-3-2\right)\left(-3-5\right)[/tex]

[tex]\tt (6)(-5)(-3-3)+4(-3-2)(-3-5)[/tex]

[tex]\tt -30\left(-6\right)+4\left(-3-2\right)\left(-3-5\right)[/tex]

[tex]\tt -30\left(-6\right)+4\left(-5\right)\left(-3-5\right)[/tex]

[tex]\sf -30\left(-6\right)+4\left(-5\right)\left(-8\right)[/tex]

[tex]\tt 180+4\left(-5\right)\left(-8\right)[/tex]

[tex]\tt 180-\left(-160\right)[/tex]

[tex]\tt 180-\left(-160\right)[/tex]

[tex]\tt =340[/tex]

Therefore, the value of 6(x-2)(x-3) + 4(x-2)(x - 5) is 340!

____________________

Hope this helps!

Have a great day!

Answer: 122 12/46 OR 122 R 12 OR 1252.69565

Step-by-step explanation:

The probability that exactly one of the next four calls results in a reservation being made is 40.75%

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

A random call to their reservation phone line results in a reservation being made is 0.31

Now, we find

Exactly one call gets resevervation = 4 * (1-0.31)3(0.31)

= 0.4075 = 40.75%

Now we can simulate an experiment by using random numbers from 0 to 100,000 as probability values between 0 and 31,000 are p to reservation otherwise they don't.

Hence, the probability that exactly one of the next four calls results in a reservation being made is 40.75%

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The football field is longer than soccer field.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

We have a soccer field that is 105 meters long and a football field is 120 yards long.

In one yard, we have -

1 yard = 0.9144 meters

Then, in 120 yards, we will have -

120 x 0.9144 = 109.728 meters

Now, 109.728 meters > 105 meters.

Therefore, the football field is longer than soccer field.

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Factors over the complex numbers for the given expression y⁴ + 14y² + 49 is equal to [ ( y + i√7) (y - i√7 ) ]² .

As given in the question,

Given expression is :

y⁴ + 14y² + 49

Simplify the given expression to get the factors of it , we get ,

y⁴ + 14y² + 49

= y⁴ + 2 ( 7 )y² + ( 7 )²

= ( y² + 7 )²

Now convert the factors into complex numbers ,

= [ y² - (-1)(√7)²]²

We know that ( -1 ) = i²

= [ y² - ( i√7)² ]²

= [ ( y - i√7 )( y + i√7) ]²

Therefore, the complex numbers factors of the given expression is equal to [ ( y - i√7 )( y + i√7) ]².

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Answer:

p=8

Step-by-step explanation:

[tex]2(p+1)=18\\\frac{2(p+1)}{2}=\frac{18}{2}\\p+1=9\\p+1-1=9-1\\p=8[/tex]

Answer:P=8

Step-by-step explanation:

I TOOK THE TEST

Solution to the inequality on the number line is y < 4 and y > −4.

What is inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

When resolving an inequality, you can do one of the following:

• Add the same amount to each side;

• Subtract the same amount from each side;

• Multiply or divide each side by the same positive amount.

You must flip the inequality symbol if you multiply or divide each side by a negative number.

Let's solve your inequality step-by-step.

|y| < 4

Solve Absolute Value.

|y| < 4

We know y < 4 and y > −4

y < 4  (Condition 1)

y > −4  (Condition 2)

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Answer:

y^2

Step-by-step explanation:

a^m/a^n = a^(m - n)

y^5/y^3 = y^2

The reduced form of the fraction would be 2.8/2.

What is a fraction?

A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction describes the number of parts of a specific size, such as one-half, eight-fifths, or three-quarters.

Given that a/b is a fraction and when it is divided by 100 it will result in 0.014.

So we can write,

            [tex]\frac{\frac{a}{b} }{100}=0.014\\\\ \frac{a}{b}=0.014*100\\\\\frac{a}{b}=1.4\\[/tex]

Now 1.4 can be written as

       a/b = 2.8/2

Hence, the reduced form of the fraction would be 2.8/2.

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The number of runs up and runs down for the preceding data is 5.

Runs up refers to the number of observations that are higher than the number of observations before them.

Runs down refers to the number of observations that are lower than the number of observations before them.

As 2nd observation is higher than 1st observation, 4th observation is higher than 3rd observation and 6th observation is also higher than 5th observation so 2nd, 4th,6th observation should be included in runs up.

Therefore,

Runs up = 2nd + 4th + 6th observations

             = 3

As 3rd observation is lower than 2nd observation,5th observation is also lower than 4th observation so 3rd,5th observation should be included in the runs down

Therefore,

Runs down= 3rd +5th observations

                 =2

Therefore,

Runs up + Runs down  =3+2

                                        =5

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The perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.

Given that, the breadth of a rectangle =5 units and the length of a rectangle =(x-2) units.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Here, perimeter =2(x-2+5)

= 2(x+3)

= 2x+6 units

Area of a rectangle =length × width

= (x-2) × 5

= 5x-10 square units

Therefore, the perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.

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South direction was she facing.

What does the word "direction" mean?

Direction can refer to the way something moves, the way you must go to get somewhere, the way something is beginning to take shape, or the direction you are facing.

                                  When you turn right rather than left, that is an illustration of direction.

Which forms of direction are there?

There are only four genuine directions north, south, east, and west. Northeast, Southeast, Southwest, and Northwest are the directions on the compass that are located midway between these cardinal points.            

                                                 These transitional locations are referred to as intermediate directions. Maps and globes only display east-west and north-south lines.

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The value of angle Z= 39°, line XY= 21.9 and line XZ= 34.7

A right-angled triangle is a type of triangle which as one of it's sides equal to 90°. Since angle Y is 90°, then ∆ABC is a right-angled triangle

angle Z = 180-(90+51)

angle Z= 180- 141= 39°

using trigonometry ratio

tan51 = 27/XY

XY= 27/tan51

XY= 27/1.2

XY= 21.9

using Pythagoras theorem

XZ²= 21.9²+27²

XZ²= 1208.6

XZ= √1208.6

XZ= 34.7

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The number of stores in each level of the shopping mall are 56 stores.

An equation is an expression that can be used to show the relationship between variables and numbers. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let x represent the number of stores on each level.

A shopping mall has 226 stores on 4 levels. If there are same number of stores in each level:

(4 × x) = 226

4x = 226

Divide

x = 226 / 4

x = 56.5

There are about 56 stores per level.

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The correct options are: The length of side RS equals the length of side WX and The measure of angle R equals the measure of angle W.

A geometry translation is an isometric transformation, meaning that the original figure and the image are congruent.

Given that, WXY is the image of RST after a translation 3 units up.

As we know in translation, both figures are congruent so, we have,

WX = RS

XY = ST

WY = RT

And

∠ R = ∠ W

∠ S = ∠ X

∠ T = ∠ Y

Hence, The correct options are: The length of side RS equals the length of side WX and The measure of angle R equals the measure of angle W.

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Answer:

272 bison

Step-by-step explanation:

y(5)=240[tex](1+0.025)^{5}[/tex]

y(5) = 271. 5 bison ≈272 bison