The path of an airplane taking off is modeled by a linear equation. The slope of the
line is 50, and (2, 150) is a point on the line. What is the equation of the line in
slope-intercept
form.

The piecewise definition for the function is

The definition of the function is given as:

f(x) = |3x^3|

Remove the absolute bracket in the above function

So, we have:

f(x) = 3x^3 and f(x) = -3x^3

The domain of the above functions are

x < 0 and x >=0

Next, we plot the graph of the function

See attachment for the graph of the piecewise definition for the function

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From the situation described, we have that:

a) The exponential function is: [tex]y(t) = 500e^{-0.041759389t}[/tex]

b) The rule is: [tex]y(t) = y(0)\left(\frac{358}{500}\right)^{\frac{t}{8}}[/tex]

c) The half-life of the element is of 16.599 days.

The exponential function for the substance's amount after t days is given by:

[tex]y(t) = y(0)e^{-kt}[/tex]

For this problem, we have that:

y(0) = 500, y(8) = 358.

Hence we can solve for k as follows:

[tex]y(t) = y(0)e^{-kt}[/tex]

[tex]358 = 500e^{-8k}[/tex]

[tex]e^{-8k} = \frac{358}{500}[/tex]

[tex]\ln{e^{-8k}} = \ln{0.716}[/tex]

-8k = ln(0.716)

k = -ln(0.716)/8

k = 0.041759389.

Hence:

[tex]y(t) = 500e^{-0.041759389t}[/tex]

For item b, 358/500 of the substance is the amount remaining each period of 8 days, hence f(t) = t/8 and the rule is given by:

[tex]y(t) = y(0)\left(\frac{358}{500}\right)^{\frac{t}{8}}[/tex]

For item c, using the rule from item a, we have to find t for which y(t) = 0.5y(0), hence:

[tex]y(t) = y(0)e^{-0.041759389t}[/tex]

[tex]0.5y(0) = y(0)e^{-0.041759389t}[/tex]

[tex]e^{-0.041759389t} = 0.5[/tex]

[tex]\ln{e^{-0.041759389t}} = \ln{0.5}[/tex]

-0.041759389t = ln(0.5)

t = -ln(0.5)/0.041759389

t = 16.599.

The half-life of the element is of 16.599 days.

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The probability that it is blue or red is 1

The given parameters are

Marbles = 8

Red = 2

Blue = 6

The probability that the selected marble is blue or red is calculated as

P  = P(Blue) + P(Red)

This gives

P = 6/8 + 2/8

Evaluate the sum

P = 1

Hence, the probability that it is blue or red is 1

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Complete question

A bag with 8 marbles is shown below. 2 marbles are red, and 6 are blue. A marble is chosen from the bag at random. What is the probability that it is blue or red?

Write your answer as a fraction or a whole number.

The x intercept of the defined line is x = -4

The equation of the line is given as

y = 1/2x + 2

At the x intercept of the defined line, the value of y is 0

i.e. y = 0

So, we have

1/2x + 2 = 0

Subtract 2 from both sides of the equation

So, we have

1/2x = -2

Multiply through the equation by 2

So, we have

x = -4

Hence. the x intercept of the defined line is x = -4

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Answer:

$18.59

Step-by-step explanation:

Tax:

15.80 x .045 = .711

Cost after tax:

15.80 +.711  = 16.511

Tip:

16.511 x .15 = 2.47665

Total cost

16.511 + 2.47665 = 18.58665 Rounded to the nearest penny is $18.59

The scientific notation of (4.3 × 10⁻²)(5.12 × 10⁻¹⁰) on simplifying is 2.2016 × 10⁻¹¹ which is option (A).

It is given that  (4.3 × 10⁻²)(5.12 × 10⁻¹⁰) .

On multiplying 4.3 by 5.12 , we get

4.3 × 5.12 = 22.016

Using exponent law for 10⁻² and 10⁻¹⁰ , we get

10⁻² × 10⁻¹⁰ = 10⁻²⁻¹⁰

                   = 10⁻¹²

Hence as a whole it is written as 22.016 × 10⁻¹².

In scientific notation , it is written as 2.2016 × 10⁻¹¹ .

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The coordinates of point B, (x, y) is given by (x, y) = ((a₁ + c₁)/2, (a₂ + c₂)/2)

From the question, we are to determine how to find the coordinates of B

From the given information,

Point B is the midpoint of line AC

If the coordinates of point A are (a₁, a₂) and the coordinates of point C are (c₁, c₂)

Then,

The coordinates of the midpoint (x, y) is given by

(x, y) = ((a₁ + c₁)/2, (a₂ + c₂)/2)

Hence, the coordinates of point B, (x, y) is (x, y) = ((a₁ + c₁)/2, (a₂ + c₂)/2)

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By factoring out the coefficient of variable, -2x+3 can be written as [tex]-2(x-\frac{3}{2})[/tex].

Factoring out means isolating a common factor from an expression. A number or a variable that is multiplied by another variable in the expression forms the coefficient. The factoring out of the coefficient of variable means taking the factor of the coefficient part of the variable term.

Given data is an expression -2x+3.

-2 is the coefficient of variable x. So, factoring out the (-2) from -2x+3:

It can be written as [tex]-2(x-\frac{3}{2} )[/tex]

Hence, -2x+3 can be written  [tex]-2(x-\frac{3}{2})[/tex] by factoring out the coefficient of variable.

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Answer:

247/8

Step-by-step explanation:

Two expressions with an equal sign is equation, The given function is 7x+2y=6, The equation when x is independent variable is x=(6-2y)/7.

Two expressions with an equal sign in between is called as equation.

The given equation is 7x+2y=6.

In the given equation x and y are two variables.

According to the question, to make x as independent variable we have to perform few operation in equation.

7x+2y=6.

Subtract 2y on both sides

7x+2y-2y=6-2y

7x=6-2y

Divide both sides by 7

x=(6-2y)/7.

Therefore the independent variable x is (6-2y)/7.

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The width and height of a newer 90 inch televison whose aspect ratio is 16:9 are 57.6 and 32.4 inches

The given parameters are

Aspect ratio = 16 : 9

Size = 90 inches

The width is calculated as

Width = 16/(16 + 9) * 90

Evaluate

Width = 57.6

This means that

height = 9/(16 + 9) * 90

Evaluate

height = 32.4

Hence, the width and height of a newer 90 inch televison whose aspect ratio is 16:9 are 57.6 and 32.4 inches

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Answer:

[tex]\textsf{23.} \quad c)\;\;y=-2x+7[/tex]

[tex]\textsf{24.} \quad 12[/tex]

[tex]\textsf{25.} \quad -2.33\:\:\sf (2\:d.p.)[/tex]

Step-by-step explanation:

Given equation:

[tex]y=\dfrac{1}{2}x-1[/tex]

If two lines are perpendicular to each other, the slopes are negative reciprocals.  

Therefore, the slope of a line perpendicular to the given equation is -2.

Substitute the found slope and the given point (3, 1) into the point-slope formula to find the equation of the line:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-1=-2(x-3)[/tex]

[tex]\implies y-1=-2x+6[/tex]

[tex]\implies y=-2x+7[/tex]

Define the variables:

Given information:

Create two equations with the given information:

[tex]\begin{cases}x+y=15\\20x+50y=390\end{cases}[/tex]

Solve the first equation for y:

[tex]\implies y=15-x[/tex]

Substitute the found expression for y into the second equation and solve for x:

[tex]\implies 20x+50(15-x)=390[/tex]

[tex]\implies 20x+750-50x=390[/tex]

[tex]\implies -30x+750=390[/tex]

[tex]\implies -30x=-360[/tex]

[tex]\implies x=12[/tex]

Therefore, Kerry received 12 twenty-dollar bills.

Given expression:

[tex]\dfrac{6^2-4^2}{-10+\sqrt{2}}[/tex]

Following the order of operations (PEMDAS), simplify the numerator:

[tex]\implies \dfrac{36-16}{-10+\sqrt{2}}[/tex]

[tex]\implies \dfrac{20}{-10+\sqrt{2}}[/tex]

Calculate the square root:

[tex]\implies \dfrac{20}{-10+1.414213...}[/tex]

Simplify the denominator:

[tex]\implies \dfrac{20}{-8.5857864...}[/tex]

Divide the numerator by the denominator:

[tex]\implies -2.3294313...[/tex]

Therefore:

[tex]\implies \dfrac{6^2-4^2}{-10+\sqrt{2}}=-2.33\:\: \sf (2\:d.p.)[/tex]

at the end the particle is at 3 units from the starting point.

Here we have one-dimensional motion, so the position of the particle is given by scalars.

We know that the particle starts at position 5. If it moves to the left, we subtract the value, if it moves to the right, we add the value.

Here we have the sequence of motions:

Then the final position will be at:

5 - 4 + 8 + 6 - 13 = 2

Then the final position is at 2, and the initial position is at 5, the difference between these is: 5 - 2 = 3

Then, at the end the particle is at 3 units from the starting point.

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The minimum value of the function is = -12

The function g(x) is defined for integers x such that if x is even, g(x) = x/2 and if x is odd, g(x) = x + 5.

given that , g(x)= x^2 - 6x - 12

asked to find minimum value

to get minimum value of g(x) put x=0

on  putting x=0 ,the value of x^2 becomes 0

                           the value of 6x also becomes 0

so the equation g(0) becomes 0-0-12

            g(0)= -12

on putting x=0 we get g(0) as -12 which is its minimum value

we get minimum value for g(x) when x=0

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Answer:

The function's minimum value is -12.

Step-by-step explanation:

Integers x are used to define the function g(x), and it is defined so that if x is even, g(x) = x/2 and if x is odd, g(x) = x + 5.

Considering, g(x)=x2 - 6x - 12

requested to determine the minimal value

Put x=0 to obtain the minimal value of g(x).

When x=0 is entered, the value of x2 is changed to 0.

6x's value is also reduced to 0.

so the equation g(0) becomes 0-0-12

           g(0)= -12

on putting x=0 we get g(0) as -12 which is its minimum value

we get minimum value for g(x) when x=0

Answer:

√-100 = 10 i

Step-by-step explanation:

√-100 = √100 × √-1

The square root of 100 is 10. Furthermore, the square root of negative 1 is an imaginary insignificant number (iota) which can be transliterated as i. That's it. Now, we have our answer to the square root of negative 100.

Answer: 45

Step-by-step explanation:

1. Replace x with 9 in term. Replacing x with 9 turns the term 5x into 5(9).

2. Multiply. 5 times 9 = 45.

This means that if x is equal to nine, then 5x is equal to 45/

Answer: 162000

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

162000

[tex]\displaystyle\\Answer:\ (\frac{6}{125})^4[/tex]

Step-by-step explanation:

[tex]\displaystyle\\(\frac{125}{6} )^{-4}=\\\\(\frac{6}{125})^{-(-4)}= \\\\(\frac{6}{125})^4[/tex]

Answer:

C. $598

Step-by-step explanation:

$33.90 = $34

$24.99 = $25

$539.95 = $539

The expression that represents the relationship between the number of months and the height of the plant will be 3 + 3.1m

It should be noted that from the information, Gabrielle buys a plant that is 3 inches tall and the plant grows at a rate of 3.1 inches per month.

Therefore, the expression to show the relationship will be:

= 3 + (3.1 × m)

= 3 + 3.1m

Therefore, the expression that represents the relationship between the number of months and the height of the plant will be 3 + 3.1m.

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(a) The probability of an infant has a low birth weight is equal to 1540.

(b) Won't  find a probability that the event is not less than 27 and are not independent. So we need to answer that we will have to find a low both by given less than equal to the 27 point.

(c) Probability in less than equal to 36 and 8, given problem the 1 now for the probability the we have found already equal to 0692 point and for the time it will be the sum of the 3 of them.

The length of the gestation 123 under 4, and the first 1 will be small and then the came 3 weeks, and this 1 will be from the 22. The 27 weeks- and this will be the 28 to the 36 weeks- this will be the greater than the 36 weeks and we have the probability for each of them, for the first 1 will be. The 1 will be 59 point. This 1 will be the 855, and this 1 will be the ebon 9 to 82 and the next 1. We will have the call this. The means that the will be the frame is not the lowest weight, so condition will be low, and this 1 will be no more, which makes it easier now and no more no more. It will be, and this will be no more.

It will again now and then no more so from the question here even to win be less than 20, with the probability low weight equal to 1540, the common among 1 minus that equal to 46 point the next 1 for the 2227 point, the probability equal to the 1, is 13, the common 1 equals to 1 minus 0 upon , 131 minus upon 13 ease and the next 1 will on 3791 minus 379 to 621, and the last 1 will be the 1351 minus 35 o 965, and that will be the summary of The question here the question:  find the probability that an infant has a child, so we have the lobed and we want to root the. By going to the first plan, and  this 1 . I got you this 1 and then got you.  got  the last 1 and then got to the low, so we multiply them like a pair and then we add them up. So if we do it, we should get the tiptoe. We keep going like this until the last value will be on 982 time 35, and if we compute it, we will have the 4 times 4 plus 59 times upon a 13 plus 3855 times 379 plus upon 9082 times 35 equal to 0692 point for the question B, won't you find a probability that the event is not less than 27 and are not independent. So we need to answer that we will have to find a low both by given less than equal to the 27 point, so it will be between the both of them here. So we will end up the first and second 1, so we will have. It will be equal to. I will try to find the probability, the al and the less than equal to 27 point. So we'll add up this 1 and this 1 together. So we get  on 5 , 59 and 10 times 13, and if we compare the  54 plus 5910 on a 135127 point and then we want to find a probability of the time with the probability  point probably the end. We have equal to the 1692 we found in the time when the problem is the last time question to 27 will be the sum of the all be the 59, and we can equal to the 59 times 4 equal to the 2152 times 10 to the power. Minus 6 and it's a different form, the 127 point, so the form they are not independent and for of question c 1251 is the probability of the testation will be less than equal to the thirty. Sixth, given that  this 1 by the formula equal probability in less than equal to 36 and 8, given problem the 1 now for the probability the we have found already equal to 0692 point and for the time it will be the sum of the 3 of them here on together, so it will be easy adjacent to her .0692 l minus the last 1 here will be minus 982 times 35 and if we compute it, we go have on in 82 times 35006. So let me compute again. 0.9082100. .035 point.  the son from here, so let me compare again time, 5 or so 59 times upon it: 13 plus 55 times 3  on 982 times upon 35, then this 1 equal to the point 6 p. This will be correct here, 692 point. So this 1 minus 82 times 5692 point and if we compute we can equal to the 0.54071.

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Answer:

Step-by-step explanation:

Point slope form y-y₁ = m(x-x₁)

-9 - (-17) = m(1 - 3)

8 = m(-2)

-4 = m

y= -4x + b

-9 = -4(1) + b

b = -5

y = -4x - 5

Step-by-step explanation:

the sum of fmeasure angle of triangle is 180°

so <A + < B + <C = 180

6x - 24 = 0

x = 4

The required differentiation of  f(x) is f'(x) = 6hx -7h -4h² - f'(x + h)

Given that,
To determine the differentiation f'(x)
f(x+h) - f(x) = -3hx² + 7hx + 4h²x - 5h² - 3h³ is given,

Differentiation is defined as the instantaneous rate of change of a particular quantity with respect to another.

Here,
f(x + h) - f(x) = -3hx² + 7hx + 4h²x - 5h² - 3h³

differentiate with respect to x
d[f(x + h)]/dx    - df(x)/ dx = -3hdx² /dx + 7hdx /dx + 4h²dx/dx - d(5h² + 3h³)/dx
f'(x + h) - f'(x) =  -6hx + 7h + 4h²
f'(x) = 6hx -7h -4h² - f'(x + h)

Thus, required differentiation of  f(x) is f'(x) = 6hx -7h -4h² - f'(x + h).

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Answer:

b

Step-by-step explanation:

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Answer

Number of level 1 engineers is 6 and number of level 2 engineers is 2.

Let a is the number of level 1 engineers working at SpaceX and b is the number of level 2 engineers working at SpaceX.

So, Total Numbers of Engineers at SpaceX is 8.

[tex]a+b=8\\[/tex]

Yearly Salary of a Level 1 Engineer that will get is $56,000. and yearly salary of a Level 2 Engineer that will get is $68,000.

And the amount of salary next year company will only be able to afford $472,000.

So,

[tex]56000a + 68000b = 472000[/tex]

Solving both the equation

[tex]a+ b = 8\\56000a + 68000b = 472000[/tex]

on multiplying first equation -56000 and adding it

[tex]-56000x - 56000y = -448000\\56000x + 68000y = 472000[/tex]

[tex]12000b = 24000\\b = 2\\[/tex]

So, a = 6.

So, Number of level 1 engineers is 6 and number of level 2 engineers is 2.

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Number of level 1 engineers is 6 and number of level 2 engineers is 2.

Let a is the number of level 1 engineers working at SpaceX and b is the number of level 2 engineers working at SpaceX.

SinceTotal Numbers of Engineers at SpaceX is 8.

[tex]a+b=8[/tex]

Yearly Salary of a Level 1 Engineer that will get is $56,000. and yearly salary of a Level 2 Engineer that will get is $68,000.

And the amount of salary next year company will only be able to afford $472,000.

So,

[tex]56000a+68000b=472000[/tex]

Solving both the equation

on multiplying first equation -56000 and adding it

[tex]-56000a-56000b=-448000\\56000a+68000b=472000[/tex]

[tex]12000b = 24000\\b = 2000[/tex]

So, a = 6.

So, Number of level 1 engineers is 6 and number of level 2 engineers is 2.

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The equivalent expression is negative eleven sixths times n minus one twelfth. Option C

Algebraic expressions are expressions that are made up of terms, variables, factors, coefficients, constants.

They are also made up of mathematical operations.

Equivalent expressions are defined as expressions have the exact same solution but may have different arrangement of values.

Given the expression;

[ -3 1/ 3n + 1/ 6 } + { 1 3/ 6n - 3/ 12 }

simply the expression;

- 10/ 3n + 1/ 6 + 9/6n - 3/ 12

collect like terms

-10/ 3n + 9/ 6n + 1/ 6 - 3/ 12

-20n + 9n/6 + 2 - 3  /12

Add like terms

-11n/ 6 - 1/ 12

Thus, the equivalent expression is negative eleven sixths times n minus one twelfth. Option C

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