What is the equation of the line that is parallel to the line y = -1/3x + 4 and passes through the point (6, 5)?

The maximum height is; 180 ft and the Total time in the air is 12 seconds

We are given the equation that represents the height of the rocket as;

d = 60t - 5t²

Taking the derivative of the formula gives us;

d' = 60 - 10t.  

-10t represents the acceleration.  The 60 represents the initial velocity.

Set 60 - 10t = 0 and solve for t to get;

t = 60/10 = 6seconds.  

That's when the maximum height occurs. Plug that value of t into the original quadratic equation to get the maximum height.

d(6) = 60t - 5t²

d(6) = 60(6) - 5(6²)

d(6) = 180

So,  maximum height is about 180 ft.  

Thus, total time in air = 2 * 6 = 12 seconds

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Answer:

Step-by-step explanation:

the expected profit should be 2 dollars a drink

Answer:

C. 35.1

Step-by-step explanation:

First get the length of AC by using the Pythagorean Theorem, that ends up being about 11.18. Then you need to get the radius of the circle so you divide 11.18 by 2 and get 5.59. Then plug 5.59 for r into 2(pi)(r). 2(pi)(5.59) = 5.123

Answer:

Answer B is correct

Step-by-step explanation:

First, let us find the diameter (AC) of the circle using the Phythogerem theorem.

AC² = AB² + BC²

AC² = 2² + 11²

AC² = 4 + 121

AC² = 125

AC = √ 125

AC = 5√5

And now let us find the circumference of the circle.

C = π × d

C = π × 5√5

C = 5√5π in

Answer: [tex]-8x^2 -40x-50[/tex]

Step-by-step explanation:

[tex]h(g(f(x))\\\\=h(g(2x+5))\\\\=h((2x+5)^2)\\\\=h(4x^2 +20x+25)\\\\=-2(4x^2 +20x+25)\\\\=-8x^2 -40x-50[/tex]

The value of the composite function h(g(f(x))) = -8x² - 40x - 50.

We have,

To find the composition h(g(f(x))), we need to substitute the function g(f(x)) into h(x) and simplify.

Given:

f(x) = 2x + 5

g(x) = x²

h(x) = -2x

First, we find g(f(x)) by substituting f(x) into g(x):

g(f(x)) = g(2x + 5) = (2x + 5)² = (2x + 5)(2x + 5) = 4x² + 20x + 25

Now, we substitute g(f(x)) into h(x):

h(g(f(x))) = h(4x² + 20x + 25) = -2(4x² + 20x + 25) = -8x² - 40x - 50

Therefore,

The value of the composite function h(g(f(x))) = -8x² - 40x - 50.

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Answer:

Below in bold.

Step-by-step explanation:

Standard form:

-12x⁴ - 6x² + 3.

Leading Coefficient:

-12.

Answer: 19

Step-by-step explanation:

Multiplying both sides of the equation by [tex]-3[/tex] gives that [tex]x=19[/tex].

Answer: try 35

Step-by-step explanation:

Answer:

These ratios are not equivalent as Marcia is 2 per friend while Jen is 3 per friend

Step-by-step explanation:

Marcia made 10 bracelets for 5 friends where each friend will be getting 2 bracelets with a 1:2 ratio

Jen made 12 bracelets for 4 friends where each friend will be getting 3 bracelets with a 1:3 ratio

Answers

The ratio x:y:z is 10:5:3  

Ali got 20,000

===================================================

Explanation:

Let

Those amounts add to 36,000

x+y+z = 36,000

We're told that x = 2y, so let's replace x with 2y in the equation above to get these steps

x+y+z = 36,000

2y+y+z = 36,000

3y+z = 36,000

We're also told that 3y = 5z, so we can replace that previously mentioned 3y with 5z to end up with one variable, in which we can solve for like shown below.

3y+z = 36,000

5z+z = 36,000

6z = 36,000

z = (36,000)/6

z = 6,000

This tells us that Chris got 6,000

Use this to find y

3y = 5z

3y = 5*6,000

3y = 30,000

y = (30,000)/3

y = 10,000

Ben received 10,000

Lastly, determine x.

x = 2y

x = 2*10,000

x = 20,000 which is the amount Ali got.

The ratio x:y:z turns into 20,000:10,000:6,000 which fully simplifies to 10:5:3 after dividing all three parts by the GCF 2000. It might be tempting to try to reduce the 10:5 portion into 2:1, but we cannot divide by 5 since it's not a factor of that 3 at the end.

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

Check:

Ali + Ben + Chris = 20,000 + 10,000 + 6,000 = 36,000

which helps confirm the answer.

Proficiency in statistics is an important skill for a data analyst because it is needed in  identifying patterns and correlations in data.

Data analysis can be regarded as the  process of collecting as well as modeling, and analyzing data so as to be able to extract insights that support decision-making.

Some Types of Data Analysis are:

It should be noted that Proficiency in statistics is an important skill for a data analyst because it is needed in  identifying patterns and correlations in data.

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The value of x for the given equation is 0.632 and -0.632.

According to the statement

We have given that the equation and we have to a find the value of the x.

So, The given quadratic equation are:

Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power solve for x in the quadratic equation

The given terms are

[tex]6x^2 + 4(x^2 - 1) = 0[/tex]

Solving the equation the the outcome equation is

[tex]6x^2 + 4x^2 - 4 = 0\\10x^2 - 4 = 0\\10x^2 = 4\\x^2 = 4/10[/tex]

The value of x is 0.632 and -0.632.

So, The value of x for the given equation is 0.632 and -0.632.

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Answer:

89.19

Step-by-step explanation:

           8 9  .  1     9

         79,56 . 00, 00

8    |  64

      |  1556

169 |  1521

      |      3500

1781 |      1781

              1719

17829|        6200

The value of 'a' closest to hundredths is 41.41

A triangle could also be  a polygon with three sides and three angles. The three sides for a triangle DEF shown above, written symbolically as △DEF, are line segments DE, EF, and DF

If three sides of a triangle are adequate to three sides of another triangle, then the triangles are congruent. (2) If three angles of a triangle are respectively  adequate to three angles of another triangle, then the 2 triangles are congruent.

Since this is often a right triangle, we'll  use trig functions:

cos theta = adjacent / hypotenuse;

cos a=FD/DE;

cos a=45/60.

Taking the inverse of each side:

cos-1(cos a) =cos-1(3/4);

a=41.40962211.

After Rounding to the closest hundredth:

The value of a is 41.41.

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Answer:

-1/3

Step-by-step explanation:

1:make y the subject.

2:slope of line is the coefficient of x

the value of b is = 10.

The equation of a hyperbola is x^2/24^2 - y^2/ (10)^2= 1.

The geometric characteristics of a hyperbola or the equations for which it is the solution set characterize it as a particular kind of smooth curve that lies in a plane. Mirror reflections of each other that resemble two infinite bows make up a hyperbola's two connected components or branches.

The general formula for hyperbola = (x - h)²/a²- (y - k)²/(b)² = 1

x²/24 - y²/(b)² = 1

(x - 0)²/24 - (y -0)²/(b)² = 1

a=24,h=0 and k=0

Now equation of the directrix

x=a²/c...(1)

and we know x=576/26...(2)

Therefore from 1 and 2 we get

24²/c=576/26.

isolate the c so we get,

C=26

C= center of focii

c = √(a² + b³)

c² = a² + b²

b = c² - a²

b = 10

So we get the value of b is 10.

Therefore the equation of a hyperbola is x²/24² - y²/ (10)² =  1.

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Answer: Choice D

Reason:

Add up the arc measures, then divide by 2

x = (32 + 54)/2

x = 86/2

x= 43 degrees

The valid prediction for the mean of the population possible using these samples is C. Yes, the variation of the sample means is small

It should be noted that a sample mean is an average of a set of data . Also, the sample mean can be used to calculate the standard deviation, central tendency, and the variance of a data set.

The sample mean can be applied to a variety of uses, including calculating population averages.

Here, the sample variance is a measure of the degree to which the numbers in a list are spread out. Here, the numbers given are close to each other.

If the numbers in a list are all close to the expected values, the variance will be small and if they are far away, the variance will be large.

Therefore, the correct option is C.

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Answer:

C: Yes, the variation of the sample means is small.

Step-by-step explanation:

Correct answer on edge

The average view of the dress code is that this dress is not good

For Rashad's sample to be a random sample gotten from the population, the following must be considered.

To do this, we simply create a bar graph.

The response would go into the x-axis, while the number of people would go into the y-axis

See attachment for bar graph

The average view of the dress code is that this dress is not good

It is considered the average view of the dress code because it is the opinion with the most frequency

The number of students that do not like the dress as:

210 + 206 + 770 = 1186

Their percentage is

Percentage = 1186/(210 + 206 + 770 + 358)

Percentage = 77%

This means that

Yes, the dress will change

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Answer:

23

Step-by-step explanation:

The question gives the first equation:

0.05N + 0.10D = 2.20

It can be rewritten as:

0.05$ times the number of nickels plus 0.10$ times the number of dimes is equivalent to $2.20.

Notice that 0.05$ or 5 cents is equivalent to one nickel and 0.10$ or 10 cents is equivalent to one dime.

The question asks for N+D. We know that N stands for the number of nickels Daniel has and D stands for the number of dimes Daniel has. We also know that Daniel only has dimes and nickels in his pocket. Therefore N+D most be equivalent to the total number of coins, which is given in the question to be equal to 23 coins.

Therefore...

N+D = 23

The composition of transformation that maps ABCD to EHGF is "(x, y) → (x', -y') → (x' + 6, y' + 3)".

The basic transformation rules are:

The given quadrilateral ABCD has vertices,

A(-5, 2), B(-3, 4), C(-2, 4), and D(-1, 2)

The transformed quadrilateral EHGF has vertices,

E(1, 1), H(3, -1), G(4, -1), and F(5, 1)

In the map ABCD to EHGF, the transformations that took place are:

1) Reflection over x-axis

2) Translation by (x + a, y + b)

Step 1: Reflection over x-axis; (x, y) → (x, -y)

A(-5, 2) → A'(-5, (-2)) = A'(-5, -2)

B(-3, 4) → B'(-3, (-4)) = B'(-3, -4)

C(-2, 4) → C'(-2, (-4)) = C'(-2, -4)

D(-1, 2) → D'(-1, (-2)) = D'(-1, -2)

So, the reflected quadrilateral is A'B'C'D'

Step 2: Translation by (x, y) → (x + a, y + b);

The reflected quadrilateral A'B'C'D' is now translated by

A'B'C'D' → EHGF

So, (for A'(-5, -2) and E(1, 1))

x + a = 1

⇒ -5 + a = 1

⇒ a = 1 + 5

∴ a = 6

and

y + b = 1

⇒ -2 + b = 1

⇒ b = 1 + 2

∴ b = 3

Thus, the translation is (x + 6, y + 3).

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Answer:

522.1

Step-by-step explanation:

Calculated based on 2 given angles and 1 given side.

Side b = 204

Angle ∠A = 90°

Angle ∠B = 23°

Angle ∠C = 180-90-23 = 67°

a = b·sin(A)/sin(B) = 522.09815

The true statement relating to a property of the function y =sin x is that the maximum and minimum values of the function are 1 and -1 respectively. Option B

The following are the properties of the sin trigonometric ratio of the function;

From the above listed deductions, we can see that the true statement about the function y = sin x is that the range which is always known as the maximum and minimum values of the function are 1 and - 1 respectively.

Thus, the true statement relating to a property of the function y =sin x is that the maximum and minimum values of the function are 1 and -1 respectively. Option B

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Answer:

  y = -5/3x   or   5x +3y = 0

Step-by-step explanation:

To write the equation of a line through the origin, we need only find its slope. It is parallel to the line through the given points, so will have the same slope.

The slope of a line through points (x1, y1) and (x2, y2) is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For the given points, the slope is ...

  m = (5 -0)/(-6 -(-3)) = 5/(-3) = -5/3

The line trough the origin has a y-intercept of zero, so its equation will be ...

  y = mx

For the slope we found, the desired equation is ...

  y = -5/3x

If we multiply by 3 and add 5x, we have ...

  3y = -5x

  5x +3y = 0 . . . . . . standard form equation of the line

IfIf a free kick is given in a soccer game where the player taking the kick is 14 yards from the left post. How far is the kicker from the right post, to the nearest yard is: A. 23 yards.

Using sine theorem

Let Left triangle=3/sinx=14/sin∝

Let Right triangle=5/sinx=y/sin(180°-∝°)

Let Sin∝°=sin(180°-∝°)  sinx=sinx

Let y represent how far is the kicker

Hence:

3/5=14/y

y=5×14/3

y=70/3

y=23.3333

y=23 yards (Approximately)

Therefore If a free kick is given in a soccer game where the player taking the kick is 14 yards from the left post. How far is the kicker from the right post, to the nearest yard is: A. 23 yards.

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Sophie will pay money equivalent to $ 100 for 15 m at the same store.

The term "money" in mathematics refers to a form of payment, such as bills, coins, and demand deposits, that is used to purchase goods and services. Money is used to pay for the worth or price of an item or service.

A country's monetary system is referred to as its currency.

In the case of Gareth,

Money paid for 9 m of climbing = $ 60

Money paid per m of climbing = $ 60/9

Thus, money paid by Sophie for 15 m of climbing = 15 * 60/9

                                                                                    = $ 100

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Slope can be found between two points using the formula [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].

If we substitute in your points (which is x and which is y does not matter as long as it is consistent), we will get

[tex]\frac{(4-1)}{(2-0)}[/tex].

Simplifying this further, your slope will be

[tex]\frac{3}{2}[/tex].

hope this helps!

Answer:

m∠DBC = 51°

Step-by-step explanation:

Circle Theorem vocabulary

Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of the intercepted arc.

Therefore:

[tex]\sf \implies \angle DBC=\dfrac{1}{2}\:\overset{\frown}{BC}[/tex]

[tex]\sf \implies \angle DBC=\dfrac{1}{2}\:(102^{\circ})[/tex]

[tex]\sf \implies \angle DBC=51^{\circ}[/tex]

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[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

To determine ∠DBC, we will apply the theorem relating the inscribed angle to the intercepted arc:

[tex]\longrightarrow \sf{Intercepted \: arc= (inscribe \: angle)}[/tex]

[tex]\longrightarrow \sf{Intercept \: arc= 102^\circ}[/tex]

[tex]\longrightarrow \sf{Inscribed \: angle= \angle DBC }[/tex]

[tex]\longrightarrow \sf{102=2( \angle DBC)}[/tex]

[tex]\longrightarrow \sf{\angle DBC= \dfrac{102}{2} }[/tex]

▪ [tex]\longrightarrow \sf{\angle DBC = 51^\circ}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\boxed{\bf{\large m \: \angle DBC= 51^\circ}}[/tex]

Answer:

20 L volume and 12.5 cm depth.

Step-by-step explanation:

See attached image.

❄ Hi there,

let us first figure out what we need to do to find x in this equation.

Since x is

we will

In other words we'll do just the opposite.

[tex]\sf{3x=2}\\\sf{x=\dfrac{2}{3}}[/tex]

That's it!

❄