A small toy rocket is launched from a 48-foot pad. The height (h, in feet) of the rocket t seconds after
taking off is given by the formula h = - 3t2 +0t + 48. How long will it take the rocket to hit the
ground?
t =

The ordered pairs that is a solution to the linear inequality y > 3x + 2 is

(2, 9)

The inequality is as follows;

y > 3x + 2

Therefore, let's try option 1

(-1, -5)

-5 > 3(-1) + 2

-5 > -3 + 2

-5 > - 1 (This is false)

(–2, –7)

-7 > 3(-2) + 2

-7 > -6 + 2

-7 > -4 (This is false)

(2, 8)

8 > 3(2) + 2

8 > 6 + 2

8 > 8 (false)

(2, 9)

9 > 3(2) + 2

9 > 8 (This true)

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Answer:

8by + 2ax - 4bx - 4ay

Step-by-step explanation:

I assume you mean expand so:

(a - 2b)(3x - 5y) + (2b - a)(x - y)

3ax - 5ay - 6bx + 10by + 2bx - 2by - ax + ay

Now collect like terms:

2ax - 4ay - 4bx + 8by

This is your answer but in a better order:

8by + 2ax - 4bx - 4ay

Answer:

0.375 second and 3.5 second

Step-by-step explanation:

The position can be modeled by a quadratic function [tex]\displaystyle{h=-16t^2+62t+6}[/tex]. We are tasked to find the time when a ball reaches a height of 27 feet. Therefore, let h = 27:

[tex]\displaystyle{27=-16t^2+62t+6}[/tex]

Solve for t:

[tex]\displaystyle{27-6=-16t^2+62t}\\\\\displaystyle{21=-16t^2+62t}\\\\\displaystyle{16t^2-62t+21=0}[/tex]

Since the equation is quite complicated and more time-consuming to solve, i'll skip the factoring or quadratic part:

[tex]\displaystyle{t=0.375, 3.5}[/tex]

After done solving the equation, you'll get t = 0.375 and 3.5 seconds. These solutions are valid since both are positive values and time can only be positive.

Hence, it'll take 0.375 and 3.5 seconds for a ball to reach 27 feet.

The probability of all three events happening when the dies are rolled is; 0.0083

A) On the first die, it has 6 sides and 3 must come out, that is, 1 event out of 6 possible, therefore the probability is: 1/6

B) On the second die, it has 20 sides and if 19 or 20 can come out, that is 2 events out of 20 possible, so the probability is: 2/20 = 1/10

C) On the third die, which is 12 sides, an odd number can come out. The odd numbers would be 1, 3, 5, 7, 9, 11; i.e, 6 events out of 12 possible numbers.

Thus, the probability would be: 6/12 = 1/2

The final probability would be;

(1/6) * (1/10) * (1/2) = 0.0083

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Using the law of cosines, it is found that the approximate length of side a is 3.99 units.

The law of cosines states that we can find the side c of a triangle as follows:

[tex]c^2 = a^2 + b^2 - 2ab\cos{C}[/tex]

in which:

In the context of this problem, we have that side a is opposite to the angle of 53º, hence:

[tex]a^2 = b^2 + c^2 - 2bc\cos{53^\circ}[/tex]

We are given that:

Then:

[tex]a^2 = 34 - 30\cos{53^\circ}[/tex]

a² = 15.95

[tex]a = \sqrt{15.95}[/tex]

a = 3.99.

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Al aplicar operaciones de aritmética básica, tenemos que la mitad de 980 es igual a 490.

En esta pregunta tenemos un número par de tres dígitos que termina en cero. De acuerdo con la teoría numérica, un número de base 10 de más de un dígito que tenga un número par relacionado con números impares como último dígito, tendrá un número impar si es dividido por 2.

Ahora bien, si tenemos un número par con más de un dígito que termina en cero, entonces tendrá un número par que termina en 0 si es dividido por 2.

Si dividimos 980 por 2, entonces tenemos 490 como resultado:

980/2 = 98/2 × 10 = 49 × 10 = 490

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hi,

the function is given with it's canonic form.  

canonic form is  :  f(x) = a ( x-α)² + β

α  and β are the value of the coordonnates of the vertex.

so here we  have : ƒ(x) = 2(x−1)² +3

with α = 1  and β = 3

so vertex is  V (1;3)

So yes, answer is   A.

Hence, the missing internal angle is [tex]15[/tex].

What is the angle?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays.

Angles are also formed by the intersection of two planes. These are called dihedral angles.

Here given that,

[tex]Q = 87 + 40Q = 127X + 127 + 38 = 180X = 180 - 127 - 38X = 15[/tex]

Hence, the missing internal angle is [tex]15[/tex].

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The point that the graphs of f and g have in common are (1,0)

The given functions are:

f(x) = log₂x

and

g(x) = log₁₀x

We know that logarithm of 1 is always zero.

This means that irrespective of the base, the y-values of both functions will be equal to 0 at x=1

Therefore the point the graphs of f and g have in common is (1,0).

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Answer:

Its (1,0)

and the second one is A. F

Step-by-step explanation:

Answer:

Angle D & Angle E

Step-by-step explanation:

Angle C & Angle F are ALTERNATE EXTERIOR angles.

Angle B & Angle E are CONSECUTIVE angles.

Angle D & Angle G are CORRESPONDING angles.

Step-by-step explanation:

If a stock's price falls all the way to zero, shareholders end up with worthless holdings. Once a stock falls below a certain threshold, stock exchanges will delist those shares.strong earning result in the stock price moving up and vice versa.

in the question you asked,the situation that will make stock price move from -$2.85 to zero means the stock, bond, or commodity market, or an index representing them, currently trades higher than it did at some specific point in the past.

The inequality which shows all possible values of m is; m < 9.

It follows from the task content that the variable in discuss, m is described as less than 9.

On this note, the most appropriate inequality to represent the set of all possible values of m is; m < 9.

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Answer:

-2

Step-by-step explanation:

When x = 1, 3x² + 2x - 7 = -2.

The area of the desktop is 12. 5 feet square

The formula for area of a rectangle;

Area = length × width

Length = 2. 5 feet

Width = 5 feet

Area = 2. 5 × 5

Area = 12. 5 feet square

Thus, the area of the desktop is 12. 5 feet square

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Answer:

Cinthia studied 2/3 of her time on Tuesday

The five-number summary is: 41, 56, 65, 67, 69.

The box plot that represents the data is: option B.

Correct statement for the shape of the distribution is: B. the distribution is skewed to the left.

The five-number summary is a five data value that describes the distribution of a data set, which include: lower and upper quartiles, minimum and maximum values, and the median of the data.

The five-number summary is used to construct a box plot.

Given the data, 65, 56, 67, 68, 66, 66, 67, 69, 48, 57, 59, 68, 59, 41, 44, the five-number summary for the data is:

This means that the box plot that will represent this data will have a box that ranges between 56 and 67, and the data at both whiskers will be 41 and 69, while the data at the point where the vertical line divides the box would be 65.

Thus, the box plot that represents the data is: option B.

The median is closer to the right of the third quartile/upper quartile, therefore: B. the distribution is skewed to the left.

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Answer:

5) y = 1x + 2

6) y = -0.5x + 6

Explanation:

5)

Given points are (-3, -1), (2, 4)

[tex]\sf slope \:formula: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here, find slope:

[tex]\rightarrow \sf slope \ (a) = \dfrac{4-(-1)}{2-(-3)} = \dfrac{5}{5} = 1[/tex]

Find Equation:

y = ax + q

Here found that a = 1, take (x, y) = (-3, -1)

[tex]\sf -1 = 1(-3) + q[/tex]

[tex]\sf q - 3 = -1[/tex]

[tex]\sf q = -1 + 3[/tex]

[tex]\sf q = 2[/tex]

So, in total equation:

y = 1x + 2

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

6)

Given points are (-2, 7), (2, 5)

[tex]\sf slope \:formula: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here, find slope:

[tex]\rightarrow \sf slope \ (a) = \dfrac{5-7}{2-(-2)} = -0.5[/tex]

Find Equation:

y = ax + q

Here found that a = -0.5, (x, y) = (-2, 7)

[tex]\sf 7 = -0.5(-2) + q[/tex]

[tex]\sf 7 = 1 + q[/tex]

[tex]\sf q = 7-1[/tex]

[tex]\sf q = 6[/tex]

So, in total equation:

y = -0.5x + 6

Answer:

The equation of the line that is perpendicular to y = 1/6 is: B. x = -8.

Perpendicular lines have slope values that equals -1 when multiplied together, that is, they are negative reciprocals.

Given the equation, y = 1/6, the slope is 0. This means it is a vertical line, therefore, the line that is perpendicular to it would automatically be a vertical line with an undefined slope which passes through (,8, -2).

The line therefore, would intercept the x-axis at -8. The equation would be: x = -8.

Equation of the perpendicular line is therefore: B. x = -8.

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The expression that we need to get is:

[tex]N = \frac{(23)*(10.4) + (10.5)*(7.2)}{200}[/tex]

So the correct option is the second one.

We know that 1 gallon is enough to cover 200 ft².

We have two rectangular areas, one of:

23 feet by 10.4 feet, and other of 10.5 feet by 7.2 feet.

Then the total area is:

A = (23 ft)*(10.4 ft) + (10.5ft)*(7.2 ft)

The number of gallons needed is given by the quotient between the area that we want to cover, and the area that covers one gallon, so the expression is:

[tex]N = \frac{(23ft)*(10.4ft) + (10.5ft)*(7.2ft)}{200ft^2} \\\\N = \frac{(23)*(10.4) + (10.5)*(7.2)}{200}[/tex]

So the corerect option is the second one.

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In accordance with the function velocity, the car will have a complete stop after 6 seconds.

Herein we have a function of the velocity of a car (v), in feet per second, in terms of time (t), in seconds. The car stops for t > 0 and v = 0, then we have the following expression:

0.5 · t² - 10.5 · t + 45 = 0

t² - 21 · t + 90 = 0

By the quadratic formula we get the following two roots: t₁ = 15, t₂ = 6. The stopping time is the least root of the quadratic equation, that is, the car will have a complete stop after 6 seconds.

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This problem is about pension fund management. It is to be noted that the best Feasible Capital Allocation Line (CAL) is: 0.3162.

A graph's capital allocation line depicts all conceivable combinations of risky and risk-free assets, allowing investors to estimate future returns depending on risk.

It is to be noted that the optimal risky portfolio's stock percentage is determined by:

Weight of Stock = ((Return on Stock - Risk Free Rate) * Variance of bond) - ((Return on Bond - Risk Free Rate) * Co-Variance of bond & Stock)/ ((Return on Stock - Risk Free Rate) * Variance of bond + (Return on Bond - Risk Free Rate) * Variance of Stock - ((Return on Bond - Risk Free Rate + Return on Stock - Risk Free Rate + ) * Co-Variance of bond & Stock)

→ The weight of stock

= ((15% - 5.5%) * 529) - ((9% - 5.5%) * 110.40)/ ((15% - 5.5%) * 529) + (9% - 5.5%) * 1,024 - ((15% - 5.5% + 9% - 5.5%) * 110.40)

= [(50.255) * (3.864) /(50.255) + (46.08) - (14.352)]

Weight of Stock = 0.646628

Weight of  Bonds = 1 - 0.646628

Weight of  Bonds= 0.353372

Expected return of portfolio = 0.646628 * 15% + 0.353372 * 9%

= 12.88%

Standard Deviation of Portfolio (SDP)= (0.6466282² * 1,024 + 0.3533722² * 529 + 2 * 0.646628* 0.353372* 110.40)⁰·⁵

SDP = (544.67)⁰·⁵

SDP = 23.34%

Hence,

Best feasible CAL = (12.88% - 5.5%)/ 23.34%

Best feasible CAL = 0.3162

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Full Question

See the attached spread sheet for additional information related to the questions.

Answer: [tex]\frac{9g}{4y}[/tex]

Step-by-step explanation:

[tex]\frac{6g}{2} \times \frac{3}{4y}=\frac{18g}{8y}=\frac{9g}{4y}[/tex]

Answer:

A = 228 tickets

Step-by-step explanation:

We need to set up a system of equation to find the number of adult tickets sold, where A represents the adult tickets and S represents the student tickets.

Because the number of adult and student tickets together equals 506, we have A + S = 506.

Because there are 56 more student tickets than adult tickets we have A + 56 = S

And the way the system is already set up allows us to use substitution.

Thus, we have:

[tex]A + S=506\\A+56 = S\\\\A+A+56 =506\\2A+56=506\\2A=456\\\\A=228\\228+56=S\\278=S[/tex]

The number of student tickets was not necessary to find in this problem, but I found anyway just in case you wanted check the work or wanted to prove the validity of the values.

Answer:

Step-by-step explanation:

∫(cos(1/x)/x² dx

[tex]put~\frac{1}{x} =t\\diff.\\\frac{-1}{x^2} dx=dt\\\int(- cos~t~)dt=-sin~t+c\\=-sin (\frac{1}{x} )+c[/tex]

Answer: 23,5%

Step-by-step explanation:

[tex]23\frac{1}{2} %[/tex]% = [tex]\frac{47}{200}[/tex] = 0,235 = 23,5%

Answer:

the answer is congruent making d midpoint

Answer:

Line A

Step-by-step explanation:

Hello!

Given that the x-values is the time in minutes, and the y-axis is the number of dishes stacked, for every minute, the line should go up by 7.

This means, that the value of y when x is 1 should be 7. The line that follows this rule is Line A. For every minute, 7 dishes are stacked.

The answer is Line A.