The equation for a projectile's height versus time is h(t)=-16t^2+Vt+h. A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 130 feet per second. Which equation correctly models the ball's height as a function of time?

Answer:

13946

Step-by-step explanation:

The equivalent expression for the given expression is 12m-15.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 3(4m-5).

Using distributive property A(B+C)=AB+AC, we get

3×4m-3×5

= 12m-15

Therefore, the equivalent expression for the given expression is 12m-15.

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Answer:

40 cm or 2/5 of a meter.

Step-by-step explanation:

A short-sighted person, at a positive diopter, will take an estimation of about 2.5 and make it the denominator by 1 as the numerator to find out the distance (in meters) that they can see clearly.

We can find the value of f, given the value for P:

P = +2.50

f = 1 / p = 1 / 2.50

(changing the units, it will be)  ---> 100 / 2.50 which is equal to 40 cm.

Therefore, 40 cm which is 2/5 of a meter is the distance a person with glasses +2.5d can see clearly.

Answer:

So the answer is 24 cubic units

Step-by-step explanation:

l=4 units,

w=2 units,

h=3 units and

V=4×2×3=24 cubic units.

Not sure what the answer is but this guy didnt attach the dang picture so here.

The median number of pretzels is 54.

The lower and upper quartiles are represented by the left and right sides of the box in a box and whisker plot. The box encompasses the interquartile interval, which contains 50% of the data. The median is the vertical line that divides the box in half. On the box plot, the mean is sometimes shown by a dot or a cross.

From the given box plot we can have the following information:

Minimum = 45

Lower Quartile = 47

Median= 54

Upper Quartile= 61

Maximum = 68

Thus, the Required median is 54.

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Look at the picture.

[tex]y=-\dfrac{1}{2}x\\\\for\ x=0\to y=-\dfrac{1}{2}\cdot0=0\to(0;\ 0)\\\\for\ x=2\to y=-\dfrac{1}{2}\cdot2=-1\to(2;\ -1)\\\\\\y=\dfrac{1}{2}x+1\\\\for\ x=-2\to y=\dfrac{1}{2}\cdot(-2)+1=-1+1=0\to(-2;\ 0)\\\\for\ x=0\to y=\dfrac{1}{2}\cdot0+1=1\to(0;\ 1)[/tex]

Answer: Every points on orange area.

Answer: is c on edge (5,-2) , (3,1) ,(4,2)

The radian measure of a 150° angle is (5/6) π rad, found by multiplying 150° by the conversion factor π/180.

To find the radian measure of a 150° angle, we use the relationship between degrees and radians. Recall that a full circle in degrees is 360° and in radians is 2π rad. Therefore, we can say that 360° equals 2π radians. To convert degrees to radians, we multiply the degree measure by the fraction π/180.

For a 150° angle, the calculation would be:
150° multiplied by the conversion factor π/180
150° * (π/180) = (150/180) * π = (5/6) * π rad

Thus, the radian measure of a 150° angle is (5/6) π rad.

Final answer:

Since Zekia has 6 cups of fruit juice to divide among 8 friends, with 2 not drinking, there will be no juice leftover because each of the 6 drinking friends will receive 1 cup each.

Explanation:

Zekia has 6 cups of fruit juice that she wants to divide equally among her 8 friends, but 2 friends don't drink any. Initially, we would divide 6 cups by 8 to find out how much each friend gets. However, since 2 friends aren't drinking, only 6 friends will be actually consuming the juice.

First, let's calculate the amount of juice each of the 6 friends would receive:

Total juice = 6 cups

Number of friends drinking = 8 - 2 = 6

Juice per friend = Total juice ÷ Number of friends drinking = 6 cups ÷ 6 = 1 cup

So, each of the 6 friends will get 1 cup of juice. Since all 6 cups of juice are consumed, there is no juice leftover.

The cost for a member and a nonmember of a rock-climbing gym will be the same at 30 visits.

To find the total number of visits when the cost for a member and a nonmember will be the same, we need to set up an equation based on the problem statement, which we can then solve.

For the member, the cost is the $360 yearly fee plus $4 per visit (for equipment rental) - so if 'x' represents the number of visits, the total cost for a member would be $360 + 4x.

For a nonmember, the cost is $10 per visit (for gym use) plus $6 per visit (for equipment rental) - so the total cost for a nonmember is $16x.

So, to find the number of visits 'x' where both costs are equal, we need to solve this equation: $360 + 4x = $16x.

Solving the equation gives us $360 = 12x, which simplifies to x = 30.

So, the cost for a member and a nonmember would be the same at 30 visits.

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Answer:

28.27

Step-by-step explanation:

gl on test

To calculate the total taxi fare in Austin, first calculate the initial fee for the first 1/15 mile and then the cost for each additional 1/15 mile. For 5.8 miles, the total cost amounts to $23.25, comprising a $1.75 initial fare and $21.50 for the subsequent distance.

Let's break down the cost of a taxi ride based on the given pricing structure. To find the total cost of a taxi ride for a given distance, we need to calculate the cost for the first 1/5 mile and the additional cost for the remaining distance.

The initial cost for the first 1/5 mile is given as $1.75.

We know the total distance is 5.8 miles. Since the first 1/5 mile is included in the initial cost, the distance to be charged in increments of 1/5 mile is:

[tex]\[ 5.8 - \frac{1}{5} = 5.8 - 0.2 = 5.6 \, \text{miles} \][/tex]

To find the number of 1/5 mile increments in 5.6 miles, divide by 0.2:

[tex]\[ \frac{5.6}{0.2} = 28 \][/tex]

Thus, there are 28 additional 1/5 mile increments.

Each additional 1/5 mile increment costs $0.25. Thus, the total cost for the additional distance is:

[tex]\[ 28 \times 0.25 = 7.00 \][/tex]

The total cost is the initial cost plus the cost for the additional distance:

[tex]\[ 1.75 + 7.00 = 8.75 \][/tex]

Thus, the total cost to take a taxi from the hotel to the airport, given a distance of 5.8 miles, is $8.75.

Answer:

The required trigonometric form is [tex]4(\cos(60)-i\sin(60))[/tex]

Step-by-step explanation:

Given : Complex number [tex]-2+2\sqrt{3}i[/tex]

To find : Express the complex number in trigonometric form?

Solution :

The complex number [tex]a+ib[/tex] trigonometric form is [tex]r(\cos\theta+i\sin\theta)[/tex]                      

Where, [tex]r=\sqrt{a^2+b^2}[/tex]

and [tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]

On comparing with given complex number  [tex]-2+2\sqrt{3}i[/tex]

a=-2 and [tex]b=2\sqrt{3}[/tex]

Substitute the value,

[tex]r=\sqrt{a^2+b^2}[/tex]

[tex]r=\sqrt{(-2)^2+(2\sqrt{3})^2}[/tex]

[tex]r=\sqrt{4+12}[/tex]

[tex]r=\sqrt{16}[/tex]

[tex]r=4[/tex]

[tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]

[tex]\theta=\tan^{-1}(\frac{2\sqrt3}{-2})[/tex]

[tex]\theta=\tan^{-1}(-sqrt3)[/tex]

[tex]\theta=\tan^{-1}(\tan(-60))[/tex]

[tex]\theta=-60[/tex]

Substituting all values in the formula,

[tex]r(\cos\theta+i\sin\theta)[/tex]

[tex]4(\cos(-60)+i\sin(-60))[/tex]

[tex]4(\cos(60)-i\sin(60))[/tex]

Therefore, The required trigonometric form is [tex]4(\cos(60)-i\sin(60))[/tex]