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allochka39001 [22]
3 years ago
14

on a string of red and blue lights the red light light blink every 3 seconds and thhe blue lights blink every 5 seconds how many

times will they at the same time in one minute
Mathematics
2 answers:
Furkat [3]3 years ago
8 0
4 times. at 15,30,45, and 60 seconds
serious [3.7K]3 years ago
4 0

Answer:

the answer is four times

Step-by-step explanation:

at 15 seconds

at 30 seconds

at 45 seconds

at 60 seconds

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Please help with math question
ELEN [110]

Answer:

y = 4x² -3x +5

Step-by-step explanation:

It can be helpful to plot the points on a graph. The curve through them opens upward, so you know <em>the first two answer choices are incorrect</em>.

<em>Looking at the location of the vertex</em>

The points (-1, 12) and (2, 15) have nearly the same y-value, so the vertex of the parabola will be nearly halfway between those points, at about ...

... x = (-1 +2)/2 = 1/2

Because the point at (2, 15) has a slightly higher y-value, you know it is farther from the vertex, so the vertex will be at an x-value that is less than 1/2.

For quadratic ...

... y = ax² +bx +c

the vertex is found at

... x = -b/(2a)

For the 3rd choice, this is x = -(-4)/(2·3) = 2/3. This is higher than 1/2, so we can eliminate this choice, too.

Only the 4th choice remains. (It passes the vertex location test: x = -(-3)/(2·4) = 3/8 < 1/2.)

_____

There are some other ways to solve this problem, too.

  1. try the given points in the given equations. The +5 as a constant of all of them tell you that all will work for x=0. Both of choices 3 and 4 work for x=-1, so we have to try x=2. Choice 3: 3·2² -4·2 +5 = 9, not 15. Choice 4: 4·2² -3·2 +5 = 15. So Choice 4 is the answer.
  2. write equations for a, b and solve them. a(-1)² +b(-1) +5=12; a(2)² +b(2)+5=15. or a-b=7, 2a+b=5 in standard form. Adding these gives 3a=12, so a=4 and Choice 4 is the answer.
  3. use a graphing calculator to write the quadratic regression formula from the three points. This result is shown in the attachment. The (a, b, c) = (4, -3, 5) correspond to Choice 4.

7 0
3 years ago
What is the height of the triangle? A) 17 units B) 34units C) 51units D) 68units <br><br> Help??
drek231 [11]

Answer:

51 units

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

short leg : long leg : hypotenuse = 1 : sqrt(3) : 2

The reason this is relevant here is that in your case, you start with an equilateral triangle, FGH. An equilateral triangle is also equiangular, so all angles are congruent and measure 60 deg.

m<F = m<FGH = m<H = 60 deg

When the height GR is drawn, <FGH is bisected creating two 30-60-90 degree triangles, FGR and HGR.

The altitude GR also bisects side HF, so

HR = FR = (1/2)HF = 17*sqrt(3)

In 30-60-90 degree triangle FRG, the short leg is FR; the long leg is GR; the hypotenuse is FG.

Now we use the ratio of the lengths of the sides of a 30-60-90 degree triangle.

short leg : long leg : hypotenuse = 1 : sqrt(3) : 2

We use only the short leg and long leg parts of the ratios.

17*sqrt(3) : GR = 1 : sqrt(3)

GR * 1 = 17 * sqrt(3) * sqrt(3)

GR = 17 * 3

GR = 51

8 0
3 years ago
The gravitational force, F, on a rocket at a distance, from the center of the earth is given by F = k / (r^2), where k = 10 ^3 n
makvit [3.9K]
F = k / (r^2)
dF/dt = -2k / (r^3) dr/dt

When r = 10^4 km and dr/dt = 0.2 km/sec
dF/dt = -2(10)^3 (0.2) / ((10^4)^3) = -400 / 10^7 = -0.00004 N/s

The gravitational force is changing at the rate of -0.00004 N/s
3 0
3 years ago
Alina bought an ice cream cone for $3. her 4 ounce scope of ice cream is melting at rate of 0.5<br>​
tangare [24]

Answer:

y=4-0.5x

Step-by-step explanation:

Step one:

given data

Alina bought an ice cream cone for $3

the weight of the ice cream is 4 ounce

the rate of melting is 0.5 ounce per minute

let the number of minutes taken for the ice cream to melt be x

and the weight after x minutes be y

Step two:

Hence the expression for the situation after x minutes is

y=4-0.5x

6 0
3 years ago
Let n be a positive integer and define [n] to be the set of the first n positive integers. That is, [n] = {1, 2, 3, . . . , n}.
yaroslaw [1]

Answer: There are 2^{n-1} ways of doing this

Hi!

To solve this problem we can think in term of binary numbers. Let's start with an example:

n=5,  A = {1, 2 ,3},  B = {4,5}

We can think of A as 11100, number 1 meaning "this element is in A" and number 0 meaning "this element is not in A"

And we can think of B as 00011.

Thinking like this, the empty set is 00000, and [n] =11111 (this is the case A=empty set, B=[n])

This representation is a 5 digit binary number. There are 2^5 of these numbers. Each one of this is a possible selection of A and B. But there are repetitions: 11100 is the same selection as 00011. So we have to divide by two. The total number of ways of selecting A and B is the 2^{5-1} = 2^4.

This can be easily generalized to n bits.

6 0
3 years ago
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