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klemol [59]
3 years ago
10

When Louisa arranges her pennies into a rectangle with two equal rows, three equal rows, four equal rows, or six equal rows, she

has one leftover penny. When she arranges her pennies into a rectangle with five equal rows, she has two leftover pennies. How many pennies could Louisa have? Remember he has between 10 and 40 pennies total.
Mathematics
1 answer:
kodGreya [7K]3 years ago
5 0

Answer:

37

Step-by-step explanation:

The answer must be (a multiple of 2, 3, 4 and 6) + 1, and (a multiple of 5) + 1, because 1 or 2 coins were left over when dividing by 2, 3, 4, 6 or 5.

Let's look at the lowest common multiples of 2, 3, 4, 6:

Prime factorisation:

2 = 2

3 = 3

4 = 2 * 2

6 = 2 * 3

therefore, the lowest common multiple is 2 * 2 * 3 = 12

Let's look at the answers that this would give us (ie multiples of 12):

12 + 1 = 13 <-- this would work, but 11 (ie two less than 13) is not a multiple of 5

12 * 2 + 1 = 25 <-- 23 is not a multiple of 5 either

12 * 3 + 1 = 37 <-- 35 (two less than 37) is a multiple of 5 :)

therefore 37 is our answer since it is one more than a multiple of 12 (ie 36) and two more than a multiple of 5 (ie 35)

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Y=-1/2x +7
yarga [219]

Answer:

B; (2,-4)

Step-by-step explanation:

The general equation of a straight line is;

y = mx + b

where m is the slope and b is the y-intercept

So from the question, when we look at the given equation, its slope is -1/2

mathematically, when two lines are perpendicular, the product of their slopes is -1

thus;

m1 * m2 = -1

m2 * -1/2 = -1

-m2 = -2

m2 = 2

The general equation form is;

y-y1 = m(x-x1)

where (x1,y1) = (4,0)

y-0 = 2(x-4)

y = 2x - 8

So, now we look at the point that will work for this equation

For the line that will work, if we substitute its x-value, we get the y-value

Let us take a look at option B

y = 2(2) -8 = 4-8 = -4

we can see that (2,-4) works

4 0
3 years ago
What is the tangent ratio for ∠A?<br><br><br>6/8<br><br><br>8/6<br><br><br>10/8<br><br><br>8/10
makkiz [27]

Tangent is Opposite over adjacent.


The opposite side of Angle A is 6 and the adjacent side is 8.


The tangent ratio would be 6/8



8 0
3 years ago
Which function is the same as y = 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2? y = 3 sine (2 (x startfraction p
kirza4 [7]

The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

<h3>How to convert sine of an angle to some angle of cosine?</h3>

We can use the fact that:

\sin(\theta) = \cos(\pi/2 - \theta)\\\sin(\theta + \pi/2) = -\cos(\theta)\\\cos(\theta + \pi/2) = \sin(\theta)

to convert the sine to cosine.

<h3>Which trigonometric functions are positive in which quadrant?</h3>
  • In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
  • In second quadrant(π/2 < θ < π), only sin and cosec are positive.
  • In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.
  • In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.

(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)

Here, the given function is:

y= 3\cos(2(x + \pi/2)) - 2

The options are:

  1. y= 3\sin(2(x + \pi/4)) - 2
  2. y= -3\sin(2(x + \pi/4)) - 2
  3. y= 3\cos(2(x + \pi/4)) - 2
  4. y= -3\cos(2(x + \pi/2)) - 2

Checking all the options one by one:

  • Option 1: y= 3\sin(2(x + \pi/4)) - 2

y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2

(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.

  • Option 2: y= -3\sin(2(x + \pi/4)) - 2

This option if would be true, then from option 1 and this option, we'd get:
-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0

which isn't true for all values of x.

Thus, this option is not same as the given function.

  • Option 3: y= 3\cos(2(x + \pi/4)) - 2

The given function is y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2

This option's function simplifies as:

y= 3\cos(2(x + \pi/4)) - 2 = 3\cos(2x + \pi/2) -2 = -3\sin(2x) - 2

Thus, this option isn't true since \sin(2x) \neq \cos(2x) always (they are equal for some values of x but not for all).

  • Option 4: y= -3\cos(2(x + \pi/2)) - 2

The given function simplifies to:y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2

The given option simplifies to:

y= -3\cos(2(x + \pi/2)) - 2 = -3\cos(2x + \pi ) -2\\y = 3\cos(2x) -2

Thus, this function is not same as the given function.

Thus, the function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

Learn more about sine to cosine conversion here:

brainly.com/question/1421592

4 0
2 years ago
Read 2 more answers
In the drawing below , PQ is parallel to ST. Triangle is similar to triangle TSR.
Lapatulllka [165]
SR corresponds to PR
7 0
3 years ago
singh works at a restaurant where he is paid by the hour plus time and a half for his hours over 40. last week he worked four ho
padilas [110]

Answer:

$8.5 per hour

Step-by-step explanation:

Number of overtime hours = 4 hours

Since overtime starts after 40 hours, then the number of hours worked = 40 + 4 = 44 hours

Total amount earned = $391

Let Hourly pay = x

Overtime pay = 1 1/2x = 3/2x

Therefore ;

40x + (4*3/2x) = 391

40x + 6x = 391

46x = 391

x = 391 / 46

x = 8.5

Hourly pay = $8.5 per hour

7 0
3 years ago
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