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3 years ago

When graphing a linear inequality, what does a dashed boundary line indicate?

Mathematics

1 answer:

VLD [36.1K]3 years ago

8 0

The dashed boundary line means that the solutions are not on the boundary line. It is used for < and >

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Find the value of x PLEASE HELP MEE

Lynna [10]

Answer:

no idea- I would say the answer is 4 but i don't know if the triangles are similar or not

Step-by-step explanation:

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3 years ago

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A food packet is dropped from a helicopter and is modeled by the function f(x) = −15x2 + 6000. The graph below shows the height

melisa1 [442]

General Idea:

Domain of a function means the values of x which will give a DEFINED output for the function.

Applying the concept:

Given that the x represent the time in seconds, f(x) represent the height of food packet.

Time cannot be a negative value, so

$x\geq 0$

The height of the food packet cannot be a negative value, so

$f(x)\geq 0$

We need to replace $-15x^2+6000$ for f(x) in the above inequality to find the domain.

$-15x^2+6000\geq 0 \; \; [Divide \; by\; -15\; on\; both\; sides]\\ \\ \frac{-15x^2}{-15} +\frac{6000}{-15} \leq \frac{0}{-15} \\ \\ x^2-400\leq 0\;[Factoring\;on\;left\;side]\\ \\ (x+200)(x-200)\leq 0$

The possible solutions of the above inequality are given by the intervals $(-\infty , -2], [-2,2], [2,\infty )$ . We need to pick test point from each possible solution interval and check whether that test point make the inequality $(x+200)(x-200)\leq 0$ true. Only the test point from the solution interval [-200, 200] make the inequality true.

The values of x which will make the above inequality TRUE is $-200\leq x\leq 200$

But we already know x should be positive, because time cannot be negative.

Conclusion:

Domain of the given function is $0\leq x\leq 200$

4 0

3 years ago

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2(4x - 12) + 3x = 6x + 1 help!! ahh

Anuta_ua [19.1K]

2(4x - 12) + 3x = 6x + 1

Distribute.

8x - 24 + 3x = 6x + 1

Combine like terms.

11x - 24 = 6x + 1

5x = 25

x = 5

8 0

3 years ago

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I can't figure out how to find the proper area of a prism, can anyone help?

andrey2020 [161]

Answer:

Search Results

Featured snippet from the web

A right prism is made up of two identical, parallel bases on the ends, and the faces are perpendicular to the bases. The formula for finding surface area is 2B + hP (where B is the area of one of the bases, h is the prism's height and P is the perimeter of the base)

Step-by-step explanation:

hope this helps

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3 years ago

Two forces with magnitudes of 150 and 75 pounds act on an object at angles of 30° and 150°, respectively. Find the direction and

Anastaziya [24]

The problem is modelled in the first picture shown below

To work out the resultant vector, we modelled the vectors 150N and 75N as triangle AOB is shown in the second picture with AB as the resultant vector.

We use the cosine rule to work out the length AB
$AB^{2}= 75^{2}+ 150^{2}-(2*75*150*cos(60))$
$AB^{2} =28125-11250$
$AB^{2}=16875$
$AB= \sqrt{16875} =130$ (nearest whole number)

The third picture shows the full diagram of the vectors

To work out the direction of the resultant vector, we use the sin rule to find the size of angle A and angle B

Angle A
$\frac{130}{sin(60)}= \frac{75}{sin(A)}$
$130sin(A)=75sin(60)$
$sin(A)= \frac{75sin(60)}{130}$
$sin(A)=0.4996300406$
$A= sin^{-1}(0.4996300406)$
$A=30$ (rounded to nearest whole number)

Angle B
$B=180-60-30=90$

Direction is 60° toward negative x-axis

Answer: Magnitude 130N and direction 60° toward negative x-axis

3 0

3 years ago