After t seconds the displacement, s(t), of a particle moving rightwards along the x-axis is given (in feet) by

s(t) = 4t^2-5t+3

By determining the average velocity
successively over the time intervals
[1, 1.1], [1, 1.01],

what is a plausible estimate for the instantaneous velocity, v(1), of
the particle at time t = 1.

ANSWER CHOICES:

1. v(1) = 3 ft/sec
2. v(1) = 1 ft/sec
3. v(1) = 4 ft/sec
4. v(1) = 5 ft/sec
5. v(1) = 2 ft/sec

Answer:

x=60

Step-by-step explanation:

1. Add all the 12's on the right side together = 48

2. then you add the 12 on the left side to the right side to make it = 60

3. X=60!

HOPE THIS HELPS

Answer:

x = 60

Step-by-step explanation:

12+12+12+12=12*4=48 48+12=60=x

the reason I added another 12 is because it said x minus 12

The calculated value of x at g(x) = 2 is x = 2.5

from the question, we have the following parameters that can be used in our computation:

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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Answer: 15.6

Step-by-step explanation: maths

3x-y=15

Solve for y:

3x-y=15

subtract 3x from both sides of the equation:

3x-y-3x =15-3x

-y = 15-3x

multiply each side by -1

-y(-1) = (15-3x)-1

y= -15+3x

Rearranging:

y= 3x-15

Answer: A

Step-by-step explanation:

\(-\frac{4}{x}+1=0\\\\1=\frac{4}{x}\\\\x=4\)

Answer:

2 (4+x)

Step-by-step explanation:

4 + x     is  the sum of four and a number 'x'   now multiply by 2

2  ( 4+ x)

To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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Answer: The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Step-by-step explanation: irst, we calculate the amount of discount that is applied to the original price:

30% of $1199 = 0.3 x 1199 = $359.70

So, the discounted price is:

$1199 - $359.70 = $839.30

Next, we apply the additional 10% off coupon to this discounted price:

10% of $839.30 = 0.1 x $839.30 = $83.93

The final price after the coupon is applied is:

$839.30 - $83.93 = $755.37

Finally, we calculate the sales tax on this final price:

7% of $755.37 = 0.07 x $755.37 = $52.88

The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

The number of groups of 3/4 in 11/4 is 3 2/3

Divide 11/4 by 3/4

= 11/4 ÷ 3/4

multiply by the reciprocal of 3/4

= 11/4 × 4/3

= (11 × 4) / (4 × 3)

= 44/12

= 3 8/12

= 3 2/3

Therefore, number of groups of 3/4 in 11/4 is 3 2/3

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Answer:

C)

Step-by-step explanation:

The line is in the form of y = ax + b, which (a) part is just the slope, so the slope is 3/4.

Answer:

3/4

Step-by-step explanation:

Y=mx+b

Answer:

11 $

Step-by-step explanation:

substitute 12 into t

making (0.5 × 12) + 5 = 6 + 5 = 11 $

The length of the third side is 14.4 units.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We find the third side of a triangle by using Pythagoras theorem.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

8²+12²=x²

64+144=x²

208=x²

Take square root on both sides

x=14.4

Hence, the length of the third side is 14.4 units.

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Answer:

Step-by-step explanation:

Quadratic means squared equation so

the first one is your answer.

y= 4x²

Answer:

23m

Step-by-step explanation:

The inverse g(x) of the given relation f(x) be g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4))

An inverse function will have its input and output reversed. Set the function equal to y to use algebra to identify the function's inverse (if one exists). Swap x and y after that, and then get y in terms of x.

In essence, an inverse function reverses the effects of the original function. If f(x) instructs you to multiply by 2 and then add 1, the opposite f(x) will instruct you to take 1 away and then divide by 2. If you want to see this graphically, the function f(x) and its inverse will be reflections of the line y = x.

A function's inverse is a function that reverses the effects of another function. If x=g whenever y=f(x), then a function g is the inverse of a function f. (y). In other words, applying f and then g is equivalent to not acting at all. This can be expressed as g(f(x))=x when f and g are combined.

Therefore, the correct answer is option d) g(x) = {(3, 8), (1, 4), (-1, 0), (-3, -4)).

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Answer:

It's the last one.

Step-by-step explanation:

Edge 2020.

The tank is filled up at a total rate of 10 gal/min, and currently contains 500 gal of solution. It can hold up to 1000 gal, so it will take time t to fill it up completely:

500 gal = (10 gal/min) t

t = (500 gal) / (10 gal/min)

t = 50 min

In that time,

(8 gal/min) (50 min) = 400 gal of cola

and

(2 gal/min) (50 min) = 100 gal of cherry syrup

are added to the tank, so that when it's full, the tank contains 850 gal of cola and 150 gal of syrup.

So 150 gal of the total 1000 gal of solution is cherry syrup, or (150 gal)/(1000 gal) = 15/100 = 15% of the mixture.

Answer:

#23 is x+27°=27

2x-17°=-17

#24 is x+23°=23

x+54°=54

#25 is x+79°=79

2x-37°=-37

#26 is 3x+71°=71

5x+37°=37

Step-by-step explanation:

how you ask because when it is like x+55° and 6x+88° that means its going to be a positive number.

but when it is like 5x-78° that means its going to be a negative number.

remember this +=positive and -=negative

hope this helped you out!

The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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A graph of the image of the figure after a reflection across the x-axis is shown below.

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

By applying a reflection over or across the x-axis to triangle GLQ, we have;

(x, y)                →      (x, -y)

G (3, 4)             →      (3, -(4)) = G' (3, -4)

L (1, 2)                →     (1, -(2)) = L' (1, -2).

Q (4, -1)              →      (4, -(-1)) = Q' (4, 1)

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Answer:

1

Step-by-step explanation:

There are no two Real numbers that add up to -2 and multiply to 10.

The numbers that add up to -2 and multiply to 10, we can use algebraic methods. Let's denote the two numbers as x and y. Based on the given conditions, we can set up two equations:

Equation 1: x + y = -2

Equation 2: x * y = 10

To solve this system of equations, we can use substitution or elimination methods. Let's solve it using the substitution method:

1. Solve Equation 1 for x:

  x = -2 - y

2. Substitute the value of x in Equation 2:

  (-2 - y) * y = 10

3. Simplify the equation:

  -2y - y^2 = 10

4. Rearrange the equation to standard form:

  y^2 + 2y + 10 = 0

5. Since the equation is a quadratic equation, we can apply the quadratic formula:

  y = (-b ± √(b^2 - 4ac)) / (2a)

  In this case, a = 1, b = 2, and c = 10.

6. Calculate the discriminant: b^2 - 4ac:

  2^2 - 4(1)(10) = 4 - 40 = -36

7. Since the discriminant is negative, the quadratic equation does not have real solutions. Therefore, there are no real numbers that satisfy both conditions of adding up to -2 and multiplying to 10.

In conclusion, there are no two real numbers that add up to -2 and multiply to 10.

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Answer:

\(\mathrm{Domain\:of\:}\:4\sqrt{t}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:t\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}\)

The graph is also attached below.

Step-by-step explanation:

Given the expression

\(f\left(t\right)=\sqrt{t}\:+3\sqrt{t}\)

We know that the domain of a function is the set of inputs or argument values for which the function is real and defined.

We know that we can not have a negative value of 't' inside the radicals because if we put any negative number inside the radical expression, it would make the function undefined.

In other words,  the value of t ≥ 0.

Therefore, the function domain is:

\(\mathrm{Domain\:of\:}\:4\sqrt{t}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:t\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}\)

The graph is also attached below.

Answer: 3

Step-by-step explanation:

Answer:

Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose 57 dollars on each policy sold.

Explanation:

If a person lives to the age of 70, they will earn $765. So, there is a 97% chance to earn $765. On the other hand, if a person dies before age of 70, they will lose $26635 because

$27,400 - $765 = 26,635

Then, there is a 3% chance to lose $26635.

Now, we can find the expected value, multiplyion each option by its probability, so:

E = $765(0.97) - (26635)(0.03)

E = $742.05 - $799.05

E = - $57

Since the sign is negative they can expect to lose money, so the answer is:

Avicenna can expect to lose money from offering these policies. In the long run, they should expect to lose 57 dollars on each policy sold.

The number of souvenirs you can  buy if each one costs 450 Jamaican dollars is; 13

We are given;

Amount you have while on vacation in Jamaica = 40 US Dollars

Now, we are told that one souvenir costs 450 Jamaican dollars.

It should be noted that the money you have is in US Dollars and as such since the souvenir is purchased with Jamaican dollars, you will need to convert the money to Jamaican dollars to purchase the souvenirs.

We are given the conversion rate as;

1 U.S. dollar = 154.8 Jamaican dollars

Thus, your amount in Jamaican dollars is;

(40 * 154.8)/1 = 6192 Jamaican Dollars

Thus;

Number of souvenirs you can buy = 6192/450 = 13.76

Approximately 13.

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A)

In order to check this sentence, we need to convert the value from foot to yard.

Knowing that 1 yard is equal 3 feet, we have that:

So Debbie's affirmation is incorrect, therefore we disagree.

B)

First we need to calculate the area of the table cloth.

Converting the length to foot, we have:

Now, calculating the area (which is the product of the length and the width), we have:

If each square foot is $0.25, we just need to multiply the area by the cost of one square foot in order to find the cost of the fabric for the table cloth:

So the cost is $30.

Answer:

Mercury, Venus, Earth, Mars, and Uranus

Step-by-step explanation:

Calculate the escape velocity for each planet, using the equation v = √(2gR).

\(\left[\begin{array}{cccc}Planet&R(m)&g(m/s^{2})&v(m/s)\\Mercury&2.43\times10^{6}&3.61&4190\\Venus&6.07\times10^{6}&8.83&10400\\Earth&6.37\times10^{6}&9.80&11200\\Mars&3.38\times10^{6}&3.75&5030\\Jupiter&6.98\times10^{7}&26.0&60200\\Saturn&5.82\times10^{7}&11.2&36100\\Uranus&2.35\times10^{7}&10.5&22200\\Neptune&2.27\times10^{7}&13.3&24600\end{array}\right]\)

The rocket's maximum velocity is double the Earth's escape velocity, or 22,400 m/s.  So the planets the rocket can escape from are Mercury, Venus, Earth, Mars, and Uranus.

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