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alisha [4.7K]
2 years ago
13

There are between 24 to 40 children in a class

Mathematics
1 answer:
r-ruslan [8.4K]2 years ago
8 0

Answer:

33

Step-by-step explanation:

4 + 7 = 11

No. of students has to be a multiple of 11

Between 24 and 40, the only multiple of 11 is 33

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Answer:

The average rate of change is 4.

Step-by-step explanation:

It is 4 because when you do the formula to find the rate of change it comes out to be 4.

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3 years ago
These triangles are similar. find Y and X
CaHeK987 [17]

It these triangles are similar, then the sides of the triangles are in proportion:

\dfrac{y}{10}=\dfrac{y+4}{15}      <em>cross multiply</em>

15y=10(y+4)    <em>use distributive property</em>

15y=10y+40       <em>subtract 10y from both sides</em>

5y=40           <em>divide both sides by 5</em>

\boxed{y=8}


\dfrac{x}{4}=\dfrac{6}{8}            <em>cross multiply</em>

8x=(4)(6)

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3 0
3 years ago
Find the vector projection of B onto A if A = 5i + 11j – 2k,B = 4i + 7k​
valkas [14]

Answer:

\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\

Step-by-step explanation:

Given A = 5i + 11j – 2k and B = 4i + 7k​, the vector projection of B unto a is expressed as proj_ab = \dfrac{b.a}{||a||^2} * a

b.a = (5i + 11j – 2k)*( 4i + 0j + 7k)

note that i.i = j.j = k.k  =1

b.a = 5(4)+11(0)-2(7)

b.a = 20-14

b.a = 6

||a|| = √5²+11²+(-2)²

||a|| = √25+121+4

||a|| = √130

square both sides

||a||² = (√130)

||a||²  = 130

proj_ab = \dfrac{6}{130} * (5i+11j-2k)\\\\proj_ab = \frac{30}{130} i+\frac{11}{130} j-\frac{12}{130} k\\\\proj_ab = \frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\\\

<em>Hence the projection of b unto a is expressed as </em>\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\<em></em>

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3 years ago
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