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balu736 [363]
3 years ago
10

Gym class of 30 boys and 45 girls is divided into groups each group has the same number of students each group has only boys or

girls which is the greatest possible group sizes if every student participates
Mathematics
1 answer:
Alexus [3.1K]3 years ago
7 0
The greatest number of groups is 15. This is because 15 is a common multiple of 30 and 45
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X + 1 > 3 how many solutions are there?
vagabundo [1.1K]

Answer:

its infinite

Step-by-step explanation:

Given equation is 2x+1=x−3

That is 2x−x=−3−1

⇒x=−4

Thus there is only one point on the number line that satisfies the equation  x=−4, but on cartesian plane i.e. X-Y plane , there are infinite number of solutions as x=−4, and y can have any real value.

7 0
3 years ago
Consider an object moving along a line with the given velocity v. Assume t is time measured in seconds and velocities have units
Yakvenalex [24]

Answer:

a) positive direction: t < 2s & t>6s   ; negative direction: 2s < t < 6s

b) 7 m

c) 71 m

Step-by-step explanation:

Given:

v(t) = 3t^2 -24t +36   [0 , 7]

Find:

a) The value of time when particle is moving in positive direction:

The change in direction of the particle can be determined by v(t) > 0

Hence,

                                    0 < 3t^2 -24t +36

                                    0 < t^2 - 8t + 12

                                    0 < (t - 2)*(t - 6)

                                    t < 2s  , t  > 6s  

The particle travels in positive direction in the interval t < 2s and t > 6s , While it travels in negative direction when 2s < t < 6s.

b) The displacement ds over the given interval [ 0 , 7 ]

                                  ds = integral (v(t)).dt

                                  ds = t^3 -12t^2 +36t

                                  ds = 7^3 -12*7^2 +36*7

                                  ds = 7 m

c) Total distance traveled in the interval:

                                 Total distance= ds(0-2) + ds(2-6) + ds(6-7)

                                 D = 2*(2^3 -12*2^2 +36*2) - 2*(6^3 -12*6^2 +36*6) + 7

                                 D = 2*32 - 2*0 + 7

                                 D = 71 m          

     

6 0
3 years ago
The sum of the digits of a two-digit number is 8. The difference between the number and the reversed number is 10 more than the
Vesna [10]

Answer:

The number is 62

Step-by-step explanation:

Let the digits of the number be T and U;

A 2 digit number is represented as: 10T + U

So,

T + U = 8

10T + U - (10U + T) = 10 + 10U + T

Required

Find the digit

Make U the subject in the first equation

U = 8 - T

Substitute 8 - T for U in the second

10T + U - (10U + T) = 10 + 10U + T

10T + 8 - T - (10*(8-T) + T) = 10 + 10(8 - T) + T

10T + 8 - T - (80-10T + T) = 10 + 80 - 10T+ T

10T + 8 - T -80+10T - T = 10 + 80 - 10T+ T

Collect Like Terms

10T + 10T - T- T + 8  -80 = 10 + 80 - 10T+ T

18T -72 = 90 - 9T

9T + 18T  = 90 + 72

27T  = 162

T = 162/27

T = 6

Recall that:

U = 8 - T

U = 8 - 6

U = 2

<em>Hence, the number is 62</em>

5 0
3 years ago
2. Vectors u and v are given by: u=5i-4j+ pk v=2i+tj-3k (a) Express p in terms of t when u and v are perpendicular. ​
Sindrei [870]

If u and v are perpendicular, then their dot product is zero:

\vec u \cdot \vec v = (5\,\vec\imath-4\,\vec\jmath+p\,\vec k) \cdot (2\,\vec\imath+t\,\vec\jmath - 3\,\vec k) = 10 - 4t - 3p = 0

Solve for p :

10 - 4t - 3p = 0

3p = 10 - 4t

\boxed{p = \dfrac{10-4t}3}

6 0
2 years ago
On a coordinate plane, kite w x y z has points (1, 1), (3, 4), (5, 1), (3, negative 3). kite wxyz is graphed on a coordinate pla
brilliants [131]

The area of the kite will be C. 14 square units.

<h3>How to calculate the area?</h3>

From the information given, on coordinate plane, kite w x y z has points (1, 1), (3, 4), (5, 1),

The area of the kite will be;

= 2(1/2 × 7 × 2)

= 2 ×7

= 14 units²

Therefore, the area of the kite will be 14 square units.

In conclusion, the correct option is C.

Learn more about area on:

brainly.com/question/25292087

#SPJ4

5 0
3 years ago
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