What is the domain of the following function

Answer:

f(5) = -5

Step-by-step explanation:

To find the value of f(5), find the value of y when x = 5.

To find the value of y from a given value of x, find the position of x on the x-axis, then trace vertically until you meet the line.

Once you meet the line, trace horizontally to the y-axis to find the corresponding value of y.

Therefore, the value of f(5) is -5.

See attachment.

Answer:

Step-by-step explanation:

Given the graph of the function f(x).

In order to find the value of f for any value of x on the graph, find the point x on the x-axis, then add a vertical line from this point to the graph. The y-coordinate of the intersection is the value of the function at given x-coordinate.

We are asked to find the value of f(5).

This is f(5) = - 5 as per above explanation.

See the attached for better understanding.

After applying the distributive property, Ezra's expression was 8y + 16.

After he used the commutative property, his expression was 16 + 8y.

When using the distributive property, we are able to expand an expression with a bracket by multiplying the things in the bracket with the things outside:

8( y + 2)  becomes:

= (8 x y) + (8 x 2)

= 8y + 16

The commutative property on the other hand, means that when adding, the position of the number does not matter. For instance, a + b = b + a

When the commutative property is applied therefore, we get:
8y + 16 = 16 + 8y

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The option that is a a linear equation is B. 4x - 2 = 20.

An equation is the statement that illustrates that the variables given. 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

This is illustrated as 4x - 2 = 20

4x = 20 + 2

4x = 22

x = 22/4 = 5.5

This illustrates an equation.

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Answer:

x + 3 = 18

Step-by-step explanation:

original number of kids: x

additional kids: 3

new total number of kids: x + 3

actual total number of kids: 18

Equation: x + 3 = 18

The true statement about the sentence 'sample of gas is enclosed in a container of fixed volume' are:

When a sample of gas is been enclosed in a container of fixed volume then then if the container temperature is been reduced then the kinetic energy of the gas will reduce.

Therefore the first and the third option are correct.

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After solving the value of x in the equation is x [tex]=[/tex] -9  .

In the question ,

it is given that ,

the equation is 1/4(8x+12)  =  -15

Applying the associative property of multiplication ,

we get ,

8x/4 + 12/4 = -15

cancelling out the common factor 2 from numerator and denominator ,

we get ,

2x + 3 = -15

Subtracting the number 3 from both sides of the equation ,

we get ,

2x = -15 - 3

2x = -18

Dividing both sides of the equation above by the number 2 ,

we get ,

x = -18/2

x = -9

Therefore , After solving the value of x in the equation is x [tex]=[/tex] -9  .

The given question is incomplete , the complete question is

Solve the given equation for x ?

1/4(8x+12)= -15  

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Answer:

mary=x

andrew=8

jim=2*8=16

together=4*mary

total=8+16=24

24/4=x

x=6

Step-by-step explanation:

Answer:

9x3

Step-by-step explanation:

x+9

/4

9x=8

x=2

+2=4

x=1+4234

[tex]{ \green{ \sf{G = \sqrt{ ab}}}}[/tex]

[tex]{ \green{ \sf{G = \sqrt{ (ab³)(a³b)}}}}[/tex]

[tex]{ \green{ \sf{G = \sqrt{ a⁴b⁴}}}}[/tex]

[tex]{ \red{ \boxed{ \pink{ \sf{G = \sqrt{ a².b²}}}}}}[/tex]

Answer:a. 24

b. 14

Step-by-step explanation:

a. 3ab=

3*a*b=

3*4*2=

12*2=24

b. a+5b=

a+5*b=

4+5*2=

4+10=14

Answer: a) 24

              b) 14

Step-by-step explanation:

step1: We have to substitute the numbers.

step2: Then finish the answer.

a) 3ab = 3 x 4 x 2 = 24

b) a+5b = 4 + 5 x 2 = 4 + 10 = 14

Answer:

15 minutes

Step-by-step explanation:

The 3/4 of an hour is,

→ 60 × (3/4)

→ 180/4 = 45

Now required time spend on rope is,

→ 45 × (1/3)

→ 45/3 = 15 minutes

Hence, he had spend 15 minutes.

Answer:

8.50x + 6.00y < 60 and y > 3.

Please consider the complete question.

Amy's restaurant has a budget of at most $60 to spend this month on gourmet coffee. All international blends cost $8.50 per package and all house blends cost $6.00 per package. She would like to purchase some global combinations and at least 3 boxes of the house blends. Write a system of linear inequalities that describes this situation.

Let x represent the number of international blends and y represent the number of house blends.

The cost of x international blends would be and the cost of y house blends would be.

Since Amy's restaurant has a budget of at most $60 to spend this month on gourmet coffee, so the cost of x international blends and y house blends should be less than or equal to 60.

We can represent this information in an inequality as:

Since Amelia wants to purchase at least 3 packages of the house blends, so y should be greater than or equal to 3. We can represent this information in an inequality as:

Therefore, our required system of inequalities would be 8.50x + 6.00y < 60 and y > 3.

Step-by-step explanation:

T-test paired two samples for means should be used .

What does test score mean?

here the samples are dependent, the score of one twins is compared with the score of any another from the same pair .

Hence, T-test paired two samples for means should be used

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The equation's graph is a straight line: y= 3/4x - 1/2.

acc to our question-

There are an endless number of solutions to a linear equation with two variables, and we can obtain each one as a pair of numbers.

Draw the two-variable linear equation's graph by plotting these values on a coordinate plane.

Using the slope and y-intercept is the simplest approach to graph something in slope-intercept form because that information is already available.

Follow all of the instructions listed below to plot the equation's graph.

Step 1: When x = 0, the y-intercept is 0, and y would then equal -1/2. (0, -1/2) are the points.

Step 2: Since the slope is 3/4 rise over run, go three up (rise) and four across (run).

Step 3: The slope of the line is upward since the slope in the  equation, not negative.

Step4; There are two points, draw a line connecting the two points.

hence,The equation's graph is a straight line: y= 3/4x - 1/2.

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Answer:

9 i think

Step-by-step explanation:

The probability that Rupert picked 2 green balls is 1/21.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. It's value ranges from 0 to 1.  

Main Body:

total balls = 7  , green balls =2

1st try:  

probability of getting green ball = 2/7

As there is no replacement so now,

total balls = 6  , green balls = 1

2nd try:  

probability of getting green ball = 1/6

total probability = (2/7)*(1/6)

                          = 1/21

Hence the answer is 1/21.

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A model for representing the relationship between the number of key chains and the number of feet of cotton cord is: 8x - 3y = 0.

Since Lucia creates braided key chains from out cotton cord and can create 3 braided key chains per each 8 feet of cotton cord she does have, the following equations must be performed via cross multiplication to symbolize the relationship between both the feet of cotton cord as well as the number of key chains but also obtain the number of cotton cord Lucia requires to achieve 5 key chains:

8 cotton cords = 3 key chains

Let the total length in feet of cotton cords be x.

And the total number of key chain made be y.

Then, the linear equation formed as;

8x = 3 y

8x - 3y = 0

Thus, a model for representing the relationship between the number of key chains and the number of feet of cotton cord is: 8x - 3y = 0.

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Answer:

(- 25, 5 )

Step-by-step explanation:

- 3x - 6y = 45 → (1)

- 5y = x → (2)

substitute x = - 5y into (1)

- 3(- 5y) - 6y = 45

15y - 6y = 45

9y = 45 ( divide both sides by 9 )

y = 5

substitute y = 5 into (2)

- 5(5) = x , then

x = - 25

solution is (- 25, 5 )

1. The length of RS is 5.

2. The length of JK is 6.

3. The length of RT is 4.

4. The perimeter of triangle JKL is 24.

What do you mean by right angle triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

According to data in the diagram of the given question:

We have :

The ΔJKL, ΔRKS and ΔRTS are right-angle triangle.

The length of RK=3 and KS=4

We are using pythagoras theorem for determine the length of RS,

(RK)²+(KS)²=(RS)²

(3)²+(4)²=(RS)²

9+16=(RS)²

25=(RS)²

(5)²=(RS)²

RS=5

∴ The the length of RS is 5.

Now, we need to find the length of JK,

JK=2(RK)=2(3)=6

JK=6       [Because RK is midpoint of the side JK]

We have given value of KS=4 and the side KS is the opposite side of RT,

So, that's why the value of RT=4.

Now, we will find the perimeter of ΔJKL,

JK=6, KL=8 and we need to find the side JL,

(JK)²+(RL)²=(JL)²

(6)²+(8)²= (JL)²

36+64=(JL)²

100=(JL)²

(10)²=(JL)²

JL=10

The perimeter of the triangle ΔJKL,

Perimeter=6+8+10=24

Therefore, the perimeter of the triangle is 24.

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The function (g∘f)(x) expressed as a polynomial in standard form is  9x² - 36x + 40

A function can be defined as an equation, a rule or a law that shows or rather explain the relationship between two variables in an equation.

The variables are known as;

We have the function given;

To determine the composite function (g ∘f)(x), we have to substitute the value of x as fx) in the function g(x), we have;

(g∘f)(x) = (- 3x + 5)² + 2( -3x + 5) + 5

expand the bracket

(g∘f)(x) = 9x² - 15x - 15x + 25 - 6x + 10 + 5

Now, collect like terms, we get;

(g∘f)(x) = 9x² - 15x - 15x - 6x + 25 + 10 + 5

Add or subtract the like terms, we get;

(g∘f)(x) = 9x² - 36x + 40

The polynomial is written as;  9x² - 36x + 40

Hence, the value is  9x² - 36x + 40

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Answer:

87c

Step-by-step explanation:

Nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.

What is the pigeon-hole approach?
According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m. For instance, if one possesses three gloves but none of them are ambidextrous or reversible, then there must be at least two right-handed gloves or at least two left-handed gloves since there are three items but only two categories of handedness. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.

The standard 52 deck has 4 suits of 13 cards each, thus as per n pigeons need to be extracted from p = 4 pigeon-holes; as per established literature above.
∴ [(n - 1) / p] + 1 = 3 ⇒ [(n - 1) / 4] + 1 = 3 ⇒ n - 1 = 8 ⇒ n = 8 + 1 ⇒ n = 9
Therefore, nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.

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The probability 11.1% of domestic airfares within the United States are $250 or less.

The formula for the z score is -

z = (x - μ)/σ

In which,

Substitute the value in formula.

P(x ≤ 250) = (250 - 385)/100

P(x ≤ 250) = -1.22

Select the p value from negative z score table;

P(x ≤ 250) = 0.111

P(x ≤ 250) = 11.1%

Thus, 11.1% of domestic flights within the United States are $250 or less.

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Answer:

8 feet

Step-by-step explanation:

there's 12 inches in 1 foot so 12 x 8 = 96

Answer:

g(10) = -12

Step-by-step explanation:

Mean Value Theorem

If f is continuous on [a, b] and differentiable on (a, b), then there is a number c  such that a < c < b and:

[tex]f'(c)=\dfrac{f(b)-f(a)}{b-a}[/tex]

We are told that the function g(x) is continuous on the closed interval [8, 10] and differentiable on the open interval (8, 10).

Therefore:

Given:

As 8 < 8.5 < 10 then c = 8.5:

[tex]\begin{aligned} \implies g'(8.5)=\dfrac{g(10)-g(8)}{10-8}&=-9\\\\\dfrac{g(10)-6}{2}&=-9\\\\g(10)-6&=-18\\\\g(10)&=-12\end{aligned}[/tex]

Answer:

Step-by-step explanation:

Isabella,  do you know how to do the "elementary row operations"?

Also, when did they begin teaching  linear algebra in H.S.  :DDD  nice work getting there.

Gauss Jordan, just mean get your matrix in RREF  (Reduced Row Echelon Form)

I suggest using Matlab to do this.  it's got the  "RREF(x)  function to do this exact thing.  

Your teacher probably wants you to do this by hand.  thou, huh.  :/  

here is my Matlab code and the answer

clc

close all

clear

format compact

A=[3 -4 2;0 -1 7]

mymatx=rref(A)

A =

    3    -4     2

    0    -1     7

mymatx =

   1.0000         0   -8.6667

        0    1.0000   -7.0000

Yes, maybe it's totally cheating, but it seems fair nowadays to use technology that is commonly available.    :)

So answer A) looks right

Yes, you are safe to land, If the landing angle at an airport is 4° and you are two miles out and ½ mile high.

The final approach, also known as the final leg or final approach leg, is the last leg of an aircraft's approach to landing in aviation. During this leg, the aircraft is aligned with the runway and descending for a landing. In aircraft radio lingo, it is frequently abbreviated to "final".

Given,

If the landing angle at an airport is 4° and you are two miles out and ½ mile high,

Yes, you are safe to land.

A normal airport landing pattern calls for aircraft to turn from the base leg to the final within 0.5 to 2 miles of the airport when visual meteorological conditions (VMC) are present. A "straight-in" final approach, when all other legs are skipped, is frequently employed for instrument approaches as well as VFR approaches onto controlled airfields. At American non-towered airports, straight-in approaches are discouraged.

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For the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.

As given in the question,

Given four congruent parallelograms

Shaded area of the parallelogram is 192cm²

As four parallelograms are congruent

Let the area of each parallelogram is A

4A = 192

⇒A = 48cm²

For two parallelogram base length = 24cm

Base length of each parallelogram = 12cm

Area of parallelogram = base × height

48 = 12 × height

⇒ height = 4cm

Value of x = 2 times of height

                = 2 (4)

                = 8cm

Therefore, for the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.

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The equivalent ratios table is:

Toss     Dollars  

5             2

30           12

45           18

See the diagram in the attachment that shows the plotted points.

Equivalent ratios are ratios that have the same value when they are compared together.

For example, 4/6 = 2/3, therefore, the equivalent ratios are 2:3 and 4:6.

Create an equation that models equivalent ratios that can be used to complete the table if:

x = toss

y = dollars

Therefore, given that 30 toss equals $12,

Constant of proportionality, k = y/x = 12/30

k = 2/5.

Plug in the value of k into y = kx:

y = 2/5x.

Therefore:

2 dollars (y = 2), will give:

2 = 2/5(x)

x = 10/2

x = 5 toss

45 tosses (x = 45) will need:

y = 2/5(45)

y = 18 dollars

The equivalent ratios table would be:

Toss | Dollars  

5           2

30        12

45         18

The graph below shows the points, (5, 2), (30, 12), and (45, 18), where y = dollars, and x = toss.

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