In the xy-plane, line n passes through point (0,0) and has a slope of 4. If line n also passes through point (3,a), what is the value of a?

Given:

To find the time interval when the height is about more than 4000 feet:

Let us substitute,

Using the quadratic formula,

Here, a= -16, b=600, and c= -3775

So, the interval is,

Their total dinner bill including sales tax rate is 8% and  18% tip will be  $156.43 by using the concept of percentages and addition.

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.

A sales tax is a fee that is paid to the government when certain goods and services are sold. Typically, laws permit the seller to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing body.

Here,

$122.75 dollars to be paid without tax and tip,

=8% of $122.75

=$9.82.

=122.75+9.82

=$132.57

=18% of 132.57

=$23.86

=132.57+23.86

=$156.43

Using the addition and percentages concepts, they can calculate their total dinner bill, which is $156.43 after adding the 8% sales tax and 18% gratuity.

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These are the conditions of the continuity in a function:

First, the value of x must have an image.

Second, the lateral limits must be equal:

Finally, the value of the limit must be equal to the image of x. This means that:

In this case, we must find a value of k that can make the two lateral limits equal in x =3:

We can solve these two limits easily by replacing the x with the value of 3

Finally, we can see that the answer is k=2.

We will ave the following:

*First: We will determine the sum of all internal angles of the polygon:

*Second: Now, that we know that the sum of all internal angles will be 540°, the following is true:

Now, we solve for alpha [The angle]:

So, the measure of the angle at the bottom is 90°.

The solution to the composite function is as follows;

The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).

If we are given two functions, it is possible to create or generate a “new” function by composing one into the other.

Composite functions are when the output of one function is used as the input of another.

In other words, a composite function is generally a function that is written inside another function.

Therefore,

f(x) = x² + 5

g(x) = 3x

Hence, the composite function can be solved as follows:

(f + g)(x) = f(x) + g(x)  = x² + 5 + 3x = x² + 3x + 5

(f - g)(x) = f(x) - g(x)  = x² + 5 - 3x = x² - 3x + 5

(f. g)(x) = f(x) . g(x) = (x² + 5)(3x) = 3x³ + 15x

(f / g)(x) = f(x) / g(x) = x² + 5 / 3x

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We have that the volume of sphere is

and the volume of a cube is

so if s=r=3. The volume of the sphere is greater.

If they have the same volume, we get that

when s=r=2 we have that

so the volume of the sphere is greater

Consider drawing a card at random from a standard deck of cards,

Part A: Determine the probability that the card is a spade, given that it is black,

Part B: Determine the probability that the card is red, given that it is a heart,

Part C: Determine the probability that the card is an ace, given that it is black.

Part D: Determine the probability that the card is a queen given that it is a face card,

we have 52 cards

A standard 52-card deck comprises 13 ranks in each of the four French suits: clubs (♣), diamonds (♦), hearts (♥) and spades (♠)

so

Part A: Determine the probability that the card is a spade, given that it is black,

If the card is black, that means the possible outcomes are 26 cards

so

P=13/26

Part B: Determine the probability that the card is red, given that it is a heart,

if the card is a heart, that means, the possible outcomes are 13

so

P=13/13

because all the cards that are heart are red

Part C: Determine the probability that the card is an ace, given that it is black.

if the card is black the possible outcomes are 26

therefore

P=2/26

Part D: Determine the probability that the card is a queen given that it is a face card

we have the following:

Solve the given equation for x as shown below

We notice the following:

Then, possible solutions of the inequality are all real numbers greater or equal than 81. From the given set of solution, those numbers that fullfill that requirement are:

For each game, Drew spends 10.75 minutes, this means in total Drew spends

this product gives

then, in the fifth challenge Drew spends 53.75 minutes

The slope of a line, m, comes in the equation as the coefficient of x.

In the given equation, m= -5/4. Two perpendicular lines have slopes that are the negative reciprocals of each other.

So, the slope of the perpendicular line will be +4/5.

Between the given options, letter c will be:

4x-5y=15

-5y=15-4x (divided by -5)

y=4/5x-3

Letter C

We are asked to determien the slope of the line between 10 and 13 minutes. Since this is a horizontal line, it's slope is 0.

We have the following:

Martin's graph is good and correct, although it is not totally straight, but the relationship that it keeps is totally proportional.

On the other hand, Isabelle's graph, although it is totally straight, is wrong, because she must start from 3, which is the rental value of the shoes, and her graph starts at 0, therefore it is wrong, despite of which shows a proportional relationship.

Therefore the correct answer is Martin's graph.

Answer:

Step-by-step explanation:

Answer:

Slope = 4

Step-by-step explanation:

The slope of a line can be calculated using the following formula:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

From the question can put the points as:

(2, -5) as (x1, y1)

and

(4, 3) as (x2, y2)

Therefore, we can put in the values into the formula to solve for the slope.

[tex] \frac{3 - ( - 5)}{4 - 2} \\ = \frac{3 + 5}{2} \\ = \frac{8}{2} \\ = 4[/tex]

Answer:

[tex]y-9=-\dfrac{8}{3}(x-7)[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]

Define the given points:

Substitute the defined points into the slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{1-9}{10-7}=-\dfrac{8}{3}[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and one of the points into the point-slope formula:

[tex]\implies y-9=-\dfrac{8}{3}(x-7)[/tex]

You have the following expression:

(5x + 7) - (x + 2)

in order to simplify the previous expression, eliminate parenthesis and take into account that if a parenthesis is preceeded by a minus sign, when you elminate th eparenthesis the sign inside change to the opposite, just as follow:

(5x + 7) - (x + 2) =

5x + 7 - x - 2 =

5x - x + 7 - 2 =

4x + 5

Hence, the simplified expression is 4x + 5

Answer: a is 51

Step-by-step explanation:

Hope this help.

Answer:

a==51

Step-by-step explanation:

15=a/3-2

a/3-2+2=15+2

a/3=17

a=17*3

a=51

The required least number of trips that Dylan would have made across the river is 62.

Given that,
Dylan’s boat can carry 40 people across a river. Last month, 2504 people rode on Dylan’s boat. What is the least number of trips that Dylan could have made across that river is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Total people road  = 2504
Maximum people can road at single trip = 40
Least number of trip = 2504 / 40
Least number of trip = 62

Thus, the required least number of trips that Dylan would have made across the river is 62.

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A  person weigh on the Mercury if they weigh 135 pounds on Earth is  43.94 pounds.

Weight of person on Earth = 145pounds

145 = mg

Weight of person on Mercury = 47.2pounds

47.2 = ma

145/47.2 = mg/ma

145/47.2 = g/a

a = 47.2g/145      .....1.

If weight of person on earth = 135pounds

135 = mg

  m = 135/g        .......2.

Then, Weight of person on Mercury = ma

using the above values of a and m we we get

= (135/g)x (47.2g/145 )

= 135 x 47.2 / 145

= 43.94 pounds

A  person weigh on the Mercury if they weigh 135 pounds on Earth is  43.94 pounds.

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Solution

We have the following expression:

Here we have 3 terms:

Variable terms:

Constant term

The function operation ( f - g )( x ) in the functions f(x) = x² + 1 and g(x) = 5 - x is x² + x - 4.

A function is simply a relationship that maps one input to one output. Each x-value can only have one y-value.

Given the data in the question;

To find ( f - g )( x ), replace the function designators in ( f - g ) with the actual functions.

( f - g )( x ) = f( x ) - g( x )

( f - g )( x ) = ( x² + 1 ) - ( 5 - x )

Remove the parenthesis using distributive property

( f - g )( x ) = ( x² + 1 ) - ( 5 - x )

( f - g )( x ) = x² + 1 - 5 + x

Collect and add like terms

( f - g )( x ) = x² + x + 1 - 5

( f - g )( x ) = x² + x - 4

Therefore, the function operation ( f - g )( x ) is x² + x - 4.

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The required function would be (f – g)(x) = x² + x - 4.

A mathematical expression that defines the connection between two variables is considered a function.

The given functions following as

f(x) = x² + 1 and g(x) = 5 - x

We have to determine the function (f – g)(x).

(f – g)(x)  = f(x) - g(x)

Substitute the values of functions f(x) = x² + 1 and g(x) = 5 - x in the function (f - g).

(f – g)(x) = (x² + 1) - (5 - x)

Open the parenthesis and apply the arithmetic operation,

(f – g)(x)  = x² + 1 - 5 + x

Rearrange the terms likewise and combine them,

(f – g)(x) = x² + x + 1 - 5

Apply the subtraction operation to get

(f – g)(x) = x² + x - 4

Therefore, the required function would be (f – g)(x) = x² + x - 4.

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Given

$152,000

52% assessment rate

$48 per $1,000

Procedure

First, let's calculate the assessment rate.

Now let's calculate the taxes

Property taxes are equal to $3,793.92.

We have a point (4,-9) it moves to (9,-14)

(4+x = 9, -9+y= -14)

x = 9-4

x = 5

y = -14 +9

y = -5

We are moving to the right 5 and down 5

We want to move the point (-9,-8) exactly the same way

(-9+5, -8-5)

(-4, -13)

(-4, -13)

The values for the dimensions of the open box are L = (30 - x)inches, W = (30 - x)inches, and H = (x)inches.

A cube is 3- dimensional shape with 6 equal sides, 6 faces, and 6 vertices. Each face of a cube is a square. In there dimension, the cube's sides are; the L = length, W = width, and H = height.

From question, squares of equal sides x are cut out of each corner of the metal sheet, hence the dimension for the height of the box is equal to x.

So; H = (x) inches,

L = (30 - x)inches, and

W = (30 - x)inches.

Therefore, the dimensions of the box that can maximize the volume of the metal sheet of 30inches by 30inches are L = (30 - x)inches, W = (30 - x)inches, and H = (x)inches.

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TW = 6

WV = 2

UV = 25

XV = ?

XV/UV = WV/TV

XV/25 = 2 /(6 + 2)

XV = 2(25)/7

XV = 50/7

XV = 7.1428

Rounded to the nearest hundredth

XV = 7.14

sin C = 3/5

Given:

CB = 32

AC = 40

AB = 24

To find:

sin C

To determine sinC, we will apply the sine ratio:

We have a phone service fee which can be divided in:

- A fixed fee of $19 per month.

- A variable fee of $0.04 per minute, so that the cost for m minutes is 0.04*m.

We can add the two fees to express the total cost in function of the minutes as:

For a month where the cost is C(m) = 70.28, we can calculate the minutes as:

Answer: if she pays at least $70.28, she has talked at least m = 1282 minutes per month.

the variables are

where

a -----> is the number of adults

b-------> is the number of children.

answer is option B