All categories

3 years ago

Which point is a solution to y ≤ 3x- 4? O A. (0,4) O B. (-2, 0) OC. (0, 0) OD. (3,1)

Mathematics

2 answers:

Andrew [12]3 years ago

8 0

I’d say the answer is D. (3,1)

Nina [5.8K]3 years ago

4 0

Answer:

(D). (3, 1)

Step-by-step explanation:

y ≤ 3x - 4

(A). (0, 4)

4 ≤ 3(0) - 4

4 ≤ - 4 (False statement)

(B). (-2, 0)

0 ≤ 3(- 2) - 4

0 ≤ - 10 (False statement)

(C). (0, 0)

0 ≤ 3(0) - 4

0 ≤ - 4 (False statement)

(D). (3, 1)

1 ≤ 3(3) - 4

1 ≤ 5 (True statement) 

You might be interested in

All of the following are equivalent, except _____.

puteri [66]

Everything except 11x2

3 0

3 years ago

Read 2 more answers

Three listening stations located at (3300, 0), (3300, 1100), and (-3300, 0) monitor an explosion. The last two stations detect t

erastovalidia [21]

Answer:

The coordinates of the explosion is (3300, -2750)

Step-by-step explanation:

I have plot the points and attached to thus answer for easy understanding.

Now, from the question, since station A is the first to hear the explosion, we'll make it the foci of the parabola in the graph I attached and it will be horizontal since the distance between station C and A is much more than that between station B and A. Thus, the reason why station C will have to be the other foci with the hyperbola centred at the origin.

Now, sound travels at a speed of 1100 ft/s and station B is located 1100 ft from station A. Thus, the explosion would likely have occurred at a point on the line x = 3300ft . Since station A is 3300ft from centre C = 3300,hence C² = 3300² = 10,890,000. Since it takes 4 seconds longer for the sound to reach station C than A, the sound has traveled 4(1100)= 4400 ft.

Thus, 4400 = d1 = d2 = 2a

So,2a = 4400 and so, a =2200

a² = 2200² = 4,840,000 where d1 is the distance from station C to the explosion and d2 is the distance from station A to the explosion. To find b², let's use the equation ;

c² = a² + b² and so; b² = c² - a² = 10,890,000 - 4,840,000 = 6,050,000

Equation of hyperbola is given as;

(x²/a²) - (y²/b²) = 1

Plugging in the values of a² and b², we obtain ;

(x²/4,840,000) - (y²/6,050,000) = 1

Since we have deduced that the explosion must occur on the line x= 3300, we'll put in 3300 for x to obtain ;

(3300²/4,840,000) - (y²/6,050,000) = 1

2.25 - 1 = (y²/6,050,000)

y² = (1.25 x 6,050,000)

y² = 7562500

y = √7562500

y = ± 2750

Due to the fact that the explosion will occur at a point further from station B than from station A, the explosion will take place in quadrant 4. Thus, we will take the negative value of y which is - 2750.

So explosion will occur at the coordinate (3300, -2750)

7 0

3 years ago

Thank you!!!!!!!!!!!!!!!

OverLord2011 [107]

Answer:

Binomial distribution requires all of the following to be satisfied:

1. size of experiment (N=27) is known.

2. each trial of experiment is Bernoulli trial (i.e. either fail or pass)

3. probability (p=0.14) remains constant through trials.

4. trials are independent, and random.

Binomial distribution can be used as a close approximation, with the usual assumption that a sample of 27 in thousands of stock is representative of the population., and is given by the probability of x successes (defective).

P(x)=C(N,x)*p^x*(1-p)^(n-x)

where N=27, p=0.14, and C(N,x) is the number of combinations of x items out of N.

So we need the probability of at most one defective, which is

P(0)+P(1)

= C(27,0)*0.14^0*(0.86)^(27) + C(27,1)*0.14^1*(0.86^26)

=1*1*0.0170 + 27*0.14*0.0198

=0.0170+0.0749

=0.0919

4 0

3 years ago

Match these similar triangles proof

AlekseyPX

Answer:

Step-by-step explanation:

Ok. They are trying to reconstruct the smaller looking triangle in the bigger triangle using angle A as the common angle.

The first statement is always the given.

Second they constructed line segment XY into the bigger triangle so that XY is parallel to BC.

Third, from the construction of the parallel lines we can now find corresponding angles that are congruent. This would be the use of F.

Since we have all three angles in triangle AXY and triangle ABC, then the construction of the smaller triangle we made inside the bigger triangle is similar to the bigger triangle. So we have the triangles are similar. You could say E or D here in my opinion. This is choice D.

Fifth the creation of those fractions of sides being equal comes from us knowing the corresponding sides of similar triangles are proportional. This is choice H.

Things looked cut off for the sixth thing so I can't fully read it, but it is possible a substitution has occured.

The seventh thing is a congruence statement which can be proven by a congruence postulate. The only one listed is SAS. So that is G.

The last thing, since the triangle construction is congruent to the smaller triangle then we know the smaller triangle is also similar to the bigger triangle since the bigger one is also similar to the construction we made. I really think E and D is interchangeable. Choice E goes here.

7 0

3 years ago

1.64*10^0/2.0*10^2 in scientific notation

jarptica [38.1K]

1.64*10^0/2.0*10^2 in scientific notation

 $1.64 * 10^0 : 2.0 * 10^2= (1.64:2.0) * 10^0:10^2= 0.82 * 10 ^{0-2} = \\ \\ 0.82 * 10 ^{-2} =0.82 * \frac{1}{10^2} =0.82 * \frac{1}{100} =0.0082= \boxed{ 8.2 * 10^{-3} }$

5 0

3 years ago