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3 years ago

Drag each number to show whether or not it is a solution to the inequality shown.

Mathematics

1 answer:

Pani-rosa [81]3 years ago

5 0

Answer:

The numbers that work are: -15, 5, 3.5, and 4 3/4

Step-by-step explanation:

Subtract 5 from both sides of the equation. Which will give you 15≥3x. Then you divide both sides by 3 which will give you 5≥x.

20≥5+3x

15≥ 3x

5 ≥ x

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If a simple harmonic motion is described by x = 3 cos(πt), starting from t = 0 s, what is the first occurrence of a value of t f

poizon [28]

Answer:

The first occurence of t for which x = 0 is t = 0.5.

Step-by-step explanation:

The harmonic motion is described by the following equation.

$x(t) = 3\cos{\pi t}$

What is the first occurrence of a value of t for which x = 0?

This is t when $x(t) = 0$ . So

$x(t) = 3\cos{\pi t}$

$3\cos{\pi t} = 0$

$\cos{\pi t} = \frac{0}{3}$

$\cos{\pi t} = 0$

The inverse of the cosine is the arcosine. So we apply the arcosine function to both sides of the equality.

$\arccos{\cos{\pi t}} = \arccos{0}$

$\pi t = \frac{\pi}{2}$

$t = \frac{\pi}{2 \pi}$

$t = \frac{1}{2}$

$t = 0.5$

The first occurence of t for which x = 0 is t = 0.5.

3 0

3 years ago

It takes 8 hours for 4 men to paint a room.

eimsori [14]

Answer:

16 men would be needed to paint the room in 2 hours

Step-by-step explanation:

We can use proportion to solve the problem given, but first we need to determine whether it is a direct or indirect proportion.

If the number of men are increase, the time taken to do the work will decrease, If the number of men are decrease, the time taken to do the work will increase. Therefore, this is an indirect proportion.

We are going to arrange the data inversely.

Let x be the number of men needed to paint the room in two hours

8 hours = 2 hours

x = 4 men

Cross-multiply

2×x = 8×4

2x = 32

Divide both-side of the equation by 2

2x/2 = 32/2

x = 16 men

16 men would be needed to paint the room in 2 hours

7 0

4 years ago

The distance between the paralled lines 3x + 4y +15 = 0 and 3x + 4y -10 = 0 is equal to: pls help ASAP

Delvig [45]

Answer:

5 units

Step-by-step explanation:

Please see attached pictures for the full solution.

(This distance is the perpendicular distance between the 2 parallel lines, which is the shortest distance between them.)

6 0

3 years ago

Rewrite 2x2x2 using an exponent.

Nastasia [14]

Answer:

2³

Step-by-step explanation:

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6 0

3 years ago

A) Describe the congruence shortcut (postulate/theorem) that could be used to prove that ΔABC≅ΔDEF

bixtya [17]

Answer:

A. By the Side-Side-Side (SSS) Congruence Theorem, ΔABC ≅ ΔDEF.

B. $\overline{AB} \cong \overline{DE}$

$\overline{BC} \cong \overline{EF}$

$\overline{AC} \cong \overline{DF}$

Step-by-step explanation:

a. From the diagram given, it shows that all three sides of ∆ABC are congruent to all the three corresponding sides of ∆DEF.

Therefore, by the Side-Side-Side (SSS) Congruence Theorem, ΔABC ≅ ΔDEF.

b. The sides that are congruent in the ∆s given that applies to the SSS Congruence Theorem are:

$\overline{AB} \cong \overline{DE}$

$\overline{BC} \cong \overline{EF}$

$\overline{AC} \cong \overline{DF}$

6 0

3 years ago