Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function.

The solution for the inequality 3(x + 2) > x is given by:

B. {x | x > -3}.

An inequality is solved similarly to an equality, in which we isolate the desired variable.

The biggest difference is the fact that the solution for the inequality won't be a single value like the solution for the equality, it will be a range containing infinity real values.

For this problem, the inequality is given as follows:

3(x + 2) > x.

Applying the distributive property, we have that:

3x + 6 > x.

Now we move x to the left side and 6 to the right side, both with inverse signals, hence:

3x - x > -6.

2x > -6

x > -6/2

x > -3.

Hence the correct option for the inequality in this problem is given by option B.

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From the given information, we know that the mean and standard deviation are, respectively,

From the 68-95-99 rule, we know that approximately 95% falls between 2 standard deviation of the mean, that is,

and

From equation (A), we have

then

Now, from equation (B), we get

Therefore, the answer for part a is: Approximately 95% of the students have commute between 10.6 and 27.4 miles

In this case, we need to find the z score value for 6.4 miles and 31.6 miles and then obtain the corresponding probabilty from the z-table.

For 6.4 miles, the z score is

and for 31.6 miles, the z score is

Now, we need to find the corresponding probability between z=-3 and z=3, which is 0.9973

Therefore, the answer for part b is: Approximately. 0.9973 of the students have commute distances between 6.4 miles and 31.6 miles

ANSWER

EXPLANATION

addox has $100.

He plans to spend $20 each time he goes to the movies.

To find out how many times he can go to the movies,

1. Remember

Means

Therefore,

2. Remember that we have to solve what's inside the parenthesis first. Therefore,

If each of the 4 sloping side ahs length 10 cm

This implies they have length 40 cm altogether

To find the base length, simply subract the 40 cm from the total length of 68cm

68 - 40 = 28

each base length = 28/4 = 7cm

Area of the square base is = l x l = 7 x 7 = 49 cm²

The chain rule tells us how to find derivative of a composite function., The following set of equations: R = ln(u² + v² + w²) with u = x + 2y, v = 2x-y, w = 2xy​ ƏR/Əx= 9/7 and ƏR/Əy = 9/7.

The Chain Rule is a mathematical method to differentiate a composition of the functions. From this composition of the functions, we can discern the functions' derivatives and their relationships.

In other words, the derivative of composite function = derivative of the outside function × derivative of the inside function.

The Chain Rule gives:

ƏR/Əx= ƏR/Əu × Əu/Əx + ƏR/Əv × Əv/Əx + ƏR/Əw × Əw/Əx

= [tex]\frac{2u}{u^{2}+v^{2}+w^{2} } *1 + \frac{2v}{u^{2}+v^{2}+w^{2} } *2+ \frac{2w}{u^{2}+ v^{2}+w^{2} } *2y[/tex]

When from given information we have, x = y = 1, we have u = 3, v = 1, and w = 2, so

ƏR/Əx = 6/14 × 1+ 2/14 ×2+ 4/14×2 = 18/17 = 9/7

ƏR/Əy= ƏR/Əu × Əu/Əy + ƏR/Əv × Əv/Əy + ƏR/Əw × Əw/Əy

= [tex]\frac{2u}{u^{2}+v^{2}+w^{2} } *2 + \frac{2v}{u^{2}+v^{2}+w^{2} } *(-1)+ \frac{2w}{u^{2}+ v^{2}+w^{2} } *2x[/tex]

When from given information we have, x = y = 1, we have u = 3, v = 1, and w = 2, so

ƏR/Əy = 6/14 × 2 + 2/14 × (-1) + 1/14 × 2= 18/14 = 9/7

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Solution

For this case the unitary circle is given by:

this unitary circle is important for the trigonometric identities

Can be used also to solve inequalities

Can be used also in physics applications and in linear algebra

Answer:

Explanation:

iven the function:

The density of the gasoline is 690 grams per litre.

The mass of the jerrycan when fully filled is 16.3 kg

He fills a 20 litre jerrycan with gasoline.

A volume  of gasoline of 1 litre has a mass of 690 grams and the empty jerrycan weighs 2.5 kg.

Therefore, the density of the gasoline can be calculated as follows:

density = mass / volume

Hence,

mass of the gasoline = 690 grams

volume of the gasoline = 1 litres

density of the gasoline = 690 / 1

density of the gasoline = 690 grams per litre.

The weight of the jerrycan when filled with gas can be calculated as follows:

1 litre of gas = 690 grams

20 litres gas = 13800 grams

Hence,

1000 grams  = 1kg

13800 grams = 13.8 kg

Therefore,

weight of the jerry can when filled with gas = 13.8 + 2.5 = 16.3 kg

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Answer: sqrt{3} over 2, this also equivalent to 0.866025

He should have divided both sides by -10.

____________________________________________

Slope-Intercept Form - Solution and Explanation

____________________________________________

Hello! So...

We are given the following to convert:

Convert into Slope-Intercept Form

(-2, 5), slope = -4

____________________________

1. Compute the line equation y = mx + b for slope. In this case, our slope (m) equals -4, and passes through (-2, 5).

____________________________

2. Determine the y-intercept. In this case, b = -3.

____________________________

3. Now, construct the line equation (y = mx + b), where m = -4 and b = -3. Then, you will have your converted solution in Slope-Intercept Form.

Slope-Intercept Form:

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

___________________________________________

Hope this helps! If not, feel free to comment on the matter and I will see what else I can do to assist your further. However, if this does help, lmk! Thanks and good luck!

The length of the shadow of fence will be equal to 6 feet.

Proportionality may be defined as the term which can be used to describe or denote a relationship between two entities which are always in the same ratio. For example, the number of bananas is proportional to the number of trees with the proportionality being average number of bananas per number of trees. Here, we are given the height of house = 16 feet and length of its shadow = 24 feet and also the height of fence = 4 feet. Since, both house and fence lie in the same area they both are proportional. Let the length of shadow be x. Since, they are proportional

16/24 = 4/x

2/3 = 4/x

=> x = 12/2

=> x = 6 feet.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases} \\\\\\ A=3000\left(1+\frac{0.06}{12}\right)^{12\cdot 20} \implies A=3000(1.005)^{240}\implies A \approx 9930.61[/tex]

Answer:

1 and 403    13 and 31   13 and 31

Step-by-step explanation:

Answer:

they all are correct asu know first expression is multiple by other one so u can check

The element would remain 515 grams after 17 years.

Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.

Given Data

the initial mass of a sample of Element X is 610 grams

Element X is a radioactive isotope such that every 70 years, its mass decreases by half.

Since the half-life, or the number of years after which an isotope decays to half its original level, is stated to be 70 years.

k = [tex]\frac{2}{70}[/tex]

k= 0.0099

Equation-

N = 610e⁻⁰°⁰⁰⁹⁹ˣ

x = time

time = 17

N = 610 e⁻⁰°⁰⁰⁹⁹⁽¹⁷⁾

N = 610(0.845)

N = 515.49

The element would remain 515 grams after 17 years.

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Solution

From the given graph

The zeros of the given graph are

Converting the zeros to roots gives

The factorized form of the equation of the given graph is

Hence, the answer is option B

The length of JK is 42.

JL is a line and K is the mid-point of that line.

   J____________.___________L

                              K

From this we get:

JK = KL

JL = JK + KL

JL= 2JK = 2KL

Here it is given that,

JK = 6x and JL = 13x - 7

JL = 2JK

13x - 7 = 2× 6x

13x - 7 = 12x

x = 7

We have to find the length of JK

JK = 6x

    =6× 7

    = 42

Therefore the length of JK is 42.

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Answer:

It's 5.31

Explanation:

Using a linear function, the constraints for the values of x and of y, respectively, are given as follows:

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

In the context of this problem, we have that:

Thus the linear function that models the depth of the submarine after x seconds is given by:

f(x) = -50 - 10.5x.

This rate is for 5 seconds, hence the constraint for x is 0 ≤ x ≤ 5, and the minimum depth attained by the submarine is:

f(5) = -50 - 10.5(5) = -102.5 ft.

Hence the constraint for y is given as follows:

-102.5 ≤ y ≤ -50.

The complete problem is given by the image at the end of the answer.

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we have the equations

equate both equations

First iteration

For x=1

For x=2

For x=1.5

the answer must be less than 1.5 and greater than 1

so

Verify each option

A ----> 13/8=1.625 -----> is not a solution

B ----> 23/16=1.4375 ---> could be an approximate solution

C ---> 25/16=1.5625 ----> is not a solution

D ---> 7/4=1.75 ----> is not a solution

therefore

Solution

For this case we know that the distance covered by the plane is 1350 mi and the velocity 400 mph

We also know that the distance is given by:

D= vt

Let D= Distance travelled by the car and airplane

Vp= Vc+ 400 (Velocity of the plane)

1350 = (Vc +400)*t

150 = Vc * t

We can solve for t and we got:

t= 150/Vc

Replacing in the first equation we got:

1350= (Vc+400)* (150/Vc)

Solving for Vc we got:

1350= 150 + 60000/Vc

1200 = 60000/Vc

Vc= 60000/1200= 50 mph

Then the velocity of the car is Vc= 50mph and for the plane

Vp= 50+ 400= 450 mph

The maximum height reached by the ball in discuss as described is; 96 while the time spent by the ball in the air is; 0 seconds.

It follows from the task content that the maximum height of the ball in the air is to be determined and so.is the time spent by the ball in the air.

Therefore, since the correct form of the function given is;

h(t) = -16t² + 96

By expressing the function above in vertex form; it follows that we have;

h(t) = -16 (t - 0)² + 96.

This vertex form function above therefore translates to the fact that the point, (0, 96) represents the vertex of the balls motion curve.

Ultimately, the maximum height reached by the ball is; 96 and the time it takes to reach this height is; 0 seconds.

PS; The scenario above in real life situation would translate to dropping a ball from the top.

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Answer:

  y = 1/2cos(x/2 -5π/4) -1

Step-by-step explanation:

You want the equation of the shifted and scaled cosine function shown in the graph.

A point on a function f(x) will be translated (right, up) = (h, k) by the transformation ...

  g(x) = f(x -h) +k

A function will be vertically expanded by a factor of p and horizontally expanded by a factor of q by the transformation ...

  g(x) = p·f(x/q)

The graph shows a cosine function with a peak-to-peak amplitude of 1, which is 1/2 the parent function's amplitude, so p=1/2.

The period is (9π/2 -π/2) = 4π, which is twice the period of the parent cosine function, so q=2.

The first peak of the graphed waveform is at x=5π/2, and the midline of the graphed waveform is y=-1, so we have (h, k) = (5π/2, -1).

Putting these transformations together, we find the equation of the graph to be ...

  y = 1/2cos((x - 5π/2)/2) -1 . . . . . . scaling applied before translation

  y = 1/2cos(x/2 -5π/4) -1

Answer:

see explanation

Step-by-step explanation:

(a)

the angles shown are alternate interior angles and are congruent

(c)

since they are congruent , then

- 1 + 8x = 7x + 11 ( subtract 7x from both sides )

- 1 + x = 11 ( add 1 to both sides )

x = 12

(d)

then

7x + 11 = 7(12) + 11 = 84 + 11 = 95

- 1 + 8x = - 1 + 8(12) = - 1 + 96 = 95

Answer: y = 2x² + 2x - 60

Step-by-step explanation:

        We will write this in factored form since we are given the roots and leading coefficient. This will be written in the form y = c(x - a)(x - b) where c is the coefficient and a & b are the roots.

        y = c(x - a)(x - b)

        y = 2(x + 6)(x - 5)

        Now, we will distribute so we end up with the standard quadratic equation form.

        y = 2(x + 6)(x - 5)

        y = 2x² + 2x - 60

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Answer:

(-7,6)

Step-by-step explanation:

Midpoints

x = (x1 + x2)/2

y = (y1 + y2)/2

-6 = (-5 + x2)/2

x2 - 5 = -12

x2 = -7

2 = (-2 + y2)/2

y2 - 2 = 4

y2 = 6

ANSWER:

STEP-BY-STEP EXPLANATION:

We have that the given expression is the following:

The other expression is the following:

We simplify in each case:

This means that the expressions are equal

The dimensions of the given right triangle would be 5.66 inches and 11.31 inches.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Let the legs of the triangle be x and y

Using the Pythagorean theorem:

c² = a²+b²

So the hypotenuse will be:

x² + y² = 8²

x² + y² = 64

x² = 64 - y²

So the area of the triangle is:

A = 1/2bh

A = 1/2xy

⇒16 = 1/2xy

32 = xy

x = 32/y

x² = 1024/y²

Substitute the above value in x² = 64 - y² and solving for y we get:

1024/y² = 64 - y²

1024 = 64y²- y⁴

This can be written as:

y⁴ - 64y² + 1024 = 0

Thus y = 4√2 = 5.66

x = 64/(4√2)= 16/√2 = 8√2 = 11.31

Therefore, the dimensions of the given right triangle would be 5.66 inches and 11.31 inches.

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