a rock is thrown from the top of a tall building. the distance, in feet, between the rock and the ground x seconds after it is thrown is given by f(x)=-16x62-4x+382 How long after the rock is thrown does it hit the ground

Using the Law of Sines, we determined that it is possible to form one triangle with the given measurements A=38°, a=432, and b=382. The calculation includes finding angle B and angle C, ensuring all triangle conditions are met.

To determine how many triangles can have the given measurements (A=38°, a=432, b=382), we need to check if these values satisfy the triangle inequalities and if they can form a possible triangle using the Law of Sines.

First, let's use the Law of Sines which states that:

sin(A)/a = sin(B)/b = sin(C)/c

Given:

We can calculate angle B using:

sin(B) = (b × sin(A)) / a

sin(B) = (382 × sin(38°)) / 432 ≈ 0.556

Finding the arc sine of 0.556, we get:

B ≈ 33.8°

Now, we find angle C:

C = 180° - A - B ≈ 180° - 38° - 33.8° = 108.2°

Using the Law of Sines again to find side c:

c = (a × sin(C)) / sin(A)

c = (432 × sin(108.2°)) / sin(38°) ≈ 676.85

Thus, it's possible to form one such triangle with the given conditions.

Answer:  The required measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}[/tex] are [tex]-\dfrac{3\pi}{2}[/tex] and [tex]\dfrac{5\pi}{2}.[/tex]

Step-by-step explanation:  We are given to find measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}.[/tex]

Let x and y represents the positive and negative co-terminal angles respectively.

We know that

the measures of any two co-terminal angles differ from each other by a multiple of [tex]2\pi.[/tex]

So, the values of x and y can be found as follows :

[tex]x=\dfrac{\pi}{2}-2\pi=-\dfrac{3\pi}{4},\\\\\\y=\dfrac{\pi}{2}+2\pi=\dfrac{5\pi}{2}.[/tex]

Thus, the required measures of two angles one positive and negative that are co-terminal with [tex]\dfrac{\pi}{2}[/tex] are [tex]-\dfrac{3\pi}{2}[/tex] and [tex]\dfrac{5\pi}{2}.[/tex]

Final answer:

The positive coterminal angle with π/2 is 5π/2, and the negative coterminal angle is -3π/2; both angles are found by adding and subtracting 2π radians from the original angle.

Explanation:

To find the measures of two angles, one positive and one negative, that are coterminal with π/2, we need to add and subtract 2π (360 degrees) to the original angle since the angles are coterminal when they share the same initial and terminal sides and differ by a full circle (360 degrees) or a multiple thereof. The angle π/2 radians is equivalent to 90 degrees, so adding 2π radians (360 degrees) gives us a positive coterminal angle, and subtracting 2π radians (360 degrees) gives us a negative coterminal angle.

Positive coterminal angle: π/2 + 2π = 5π/2.

Negative coterminal angle: π/2 - 2π = -3π/2.

The graph for these inequalities intersects at point (0,0).

The graph displays the solution to the system of inequalities: 2x + y < 0 and y ≥ -4 - 2x. Here's a breakdown:

First Inequality (2x + y < 0):

This translates to a blue line with a negative slope. Points like (0, -2) and (3, -6) lie on this line.
We shade the region below this line because the inequality specifies "less than." Points there, like (1, -5), satisfy the inequality.
Second Inequality (y ≥ -4 - 2x):

This translates to a green line with a negative slope as well. Points like (0, -4) and (2, -8) lie on the line.
Unlike the first, we shade the region above this line because the inequality specifies "greater than or equal to." Points like (1, -3), above the line, satisfy the inequality.
Combined Solution:

The solution space is the overlap where both inequalities hold true. This is the triangular region shaded in both blue and green. Points within this region, like (1, -5), satisfy both inequalities.
Checking Points:

If unsure about shading, test points outside the shaded region. For example, point (0, 0) lies above both lines, satisfying both inequalities. This confirms the shading is correct.

Answer:

Step-by-step explanation: False.

When using a Venn diagram to determine how many people like either funnel cake or fried Oreos out of a survey of 50, after subtracting the 20-person overlap from each individual preference to avoid double counting, the total number liking either is found to be 35 people.

To determine how many people like either funnel cake or fried Oreos, we need to use the concept of set union from Venn diagrams. First, we draw two overlapping circles, one for people who like funnel cake and another for those who like fried Oreos.

The overlapping area represents people who like both. Given that 30 people like funnel cake and 25 like fried Oreos, with a 20-person overlap liking both, we add the individual preferences and subtract the overlap to avoid double counting.

The representation is:

Number liking funnel cake only: 30 - 20 = 10

Number liking fried Oreos only: 25 - 20 = 5

Number liking both: 20

Adding these, the total number liking either funnel cake or fried Oreos is 10 + 5 + 20 = 35 people.

Answer:

Reducing the length of the loan and increasing the down payment

Step-by-step explanation:

Assuming Francis has the ability to choose the length of his loan and the amount of the down payment.

The method that would help Francis to decrease the total cost of the loan is - reducing the length of the loan and increasing the down payment.

When a person pays more amount in down payment, then he will have to loan out a smaller amount. And he will have to pay less interest. If the loan is short, the interest to be paid will be less. If the loan term is long, the interest also increases. One has to pay interest for the whole tenure of the loan.

So, if someone wants to reduce the loan amount, he must pay more in down payment.

I think its b

Hope this helps

Use the Inscribed Angle theorem to get the measure of AC. The intercepted arc AC is [tex]21^{\circ}[/tex].

Given,

The inscribed angle [tex]\angle ABC[/tex] is [tex]3x-1.5[/tex].

And the Intercepted arc AC is [tex]3x+9[/tex].

We know that, Inscribed Angle Theorem stated that the measure of an inscribed angle is half the measure of the intercepted arc.

So,

[tex]3x-1.5=\frac{1}{2} (3x+9)[/tex]

[tex]2 (3x-1.5)=3x+9[/tex]

[tex]6x-3.0=3x+9[/tex]

[tex]6x-3x=9+3[/tex]

[tex]3x=12\\x=4[/tex]

Since the intercepted arc AC is [tex]3x+9[/tex], putting the value of [tex]x=4[/tex] we get,

intercepted arc AC is [tex]21^{\circ}[/tex].

Hence the intercepted arc AC is [tex]21^{\circ}[/tex].

For more details on the Inscribed Angle theorem follow the link:

https://brainly.com/question/5436956

Answer:

The correct answer is B

Step-by-step explanation:

The solution of the two expressions for x = 20 will be equivalent.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two expressions are 8(12x + 4) and 96x + 32. The expressions will be solved as,

8(12x + 4) = 8[12(20) + 4 ] = 1952

96x + 32 = 96 (20) + 32 = 1952

To know more about an expression follow

https://brainly.com/question/25968875

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what he said hope it helped      

Step-by-step explanation: