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2 years ago

Write an absolute value inequality for the graph below. Use x for your variable.

Mathematics

1 answer:

Gnoma [55]2 years ago

7 0

Answer:

|x| ≥ 7

Step-by-step explanation:

Taking the absolute value means that any value of x will always be positive, meaning that the absolute value of -7 or less would be 7 or greater, which satisfies the inequality above and line graph.

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a boy is standing on a pole of height 14.7m throws a stone upwards. it moves in a vertical line slightly away from the pole and

fomenos

Answer:

The time taken for the upward motion is 1 second. The same time is taken for the downward motion

It reaches a maximum height of 4.9 meters.

Step-by-step explanation:

The equation of motion is:

$x(t) = -4.9t^{2} + 9.8t$

Since the term which multiplies t squared is negative, the graph is concave down, that is, x increases until the vertex, where it reaches it's maximum height, then it decreases.

Vertex of a quadratic equation:

Quadratic equation in the format $x(t) = at^{2} + bt + c$

The vertex is the point $(t_{v}, x(t_{v}))$ , in which

$t_{v} = -\frac{b}{2a}$

In this question:

$x(t) = -4.9t^{2} + 9.8t$

So $a = -4.9, b = 9.8$

Vertex:

$t_{v} = -\frac{9.8}{2*(-4.9)} = 1$

The time taken for the upward motion is 1 second.

$x(t_{v}) = x(1) = 9.8*1 - 4.9*(1)^{2} = 4.9$

It reaches a maximum height of 4.9 meters.

Downward motion:

From the vertex to the ground.

The ground is t when x = 0. So

$-4.9t^{2} + 9.8t = 0$

$4.9t^{2} - 9.8t = 0$

$4.9t(t - 2) = 0$

$4.9t = 0$

$t = 0$

$t - 2 = 0$

$t = 2$

It reaches the ground when t = 2 seconds.

The downward motion started at the vertex, when t = 1.

So the duration of the downward motion is 2 - 1 = 1 second.

5 0

2 years ago

Seventy cards are numbered 1 through 70 , one number per card. One card is randomly selected from the deck. What is the probabil

Vanyuwa [196]

Answer:

$Probability = \frac{2}{35}$

Step-by-step explanation:

Given

$Total = 70$

First, we need to list the multiples of 5

$M_5 = \{5,10,15,20,25,30,35,40,45,50,55,60,65,70\}$

Then, multiples of 3 $M_3 = \{3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69\}$

Next, is to list out the common elements in both

$M_3\ n\ M_5 = \{15,30,45,60\}$

$n(M_3\ n\ M_5) = 4$

The required probability is then calculated as thus:

$Probability = \frac{n(M_3\ n\ M_5)}{Total}$

$Probability = \frac{4}{70}$

$Probability = \frac{2}{35}$

7 0

3 years ago

Find X, AB, BC, and AC if B is the midpoint of AC

Mkey [24]

Answer:

x=6, AB=61, BC=61, AC=122

Step-by-step explanation:

$AB=BC \\ \\ 10x+1=8x+13 \\ \\ 2x=12 \\ \\ x=6 \\ \\ AB=BC=61 \\ \\ AC=122$

4 0

1 year ago

Using the given points and line, determine the slope of the line. (-3, 0) and (2, 7)

Nuetrik [128]

Slope for (x₁, y₁) and (x₂, y₂): (-3, 0) and (2, 7)

Slope: (y₂ -y₁) / (x₂ -x₁)

Slope: ( 7 - 0) / (2 - -3) = 7/(2 + 3)

<span>Slope = 7/5
</span>

4 0

2 years ago

Find a vector 3 units long in the opposite direction from v = 〈3, 1,-4).

lutik1710 [3]

Unit vector along the direction v = <3,1,-4> is :

$\hat{v} = \dfrac{3i + j -4k}{\sqrt{3^2 + 1^2 + 4^2}}\\\\\hat{v} = \dfrac{3i + j -4k}{5.1}$

So, unit vector opposing the $\hat{v}$ is :

$\hat{v'} = -\hat{v}\\\\\hat{v'} = -( \dfrac{3i + j -4k}{5.1})\\\\\hat{v'} = \dfrac{-3i - j +4k}{5.1}$

so, vector of magnitude 3 units in opposite direction from v is :

$\vec{V} = 3\hat{v'}\\\\\vec{V} = \dfrac{3}{5.1}( -3i -j+4k)$

Hence, this is the required solution.

5 0

3 years ago

Write an absolute value inequality for the graph below. Use x for your variable. ​

Write an absolute value inequality for the graph below. Use x for your variable.