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2 years ago

Are the set of all square numbers under 50 and the set of all triangular numbers that are less than 50 disjoint?

Mathematics

1 answer:

Alina [70]2 years ago

7 0

Answer:

No, the two sets are not disjoint.

Step-by-step explanation:

Set of triangular numbers to 50: 1, 3, 6, 10, 15, 21, 28, 36, 45

Set of square numbers to 50: 1, 4, 9, 16, 25, 36, 49

They have 1 and 36 in common, so they are not disjoint, or in other words, they have some of the same numbers.

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Nuts.com sells raw almonds for $10 per pound and roasted pistachios for $12 per pound. Christopher spends $70, before taxes and

sp2606 [1]

Christopher purchased 2.8 pounds of almonds and 3.5 pounds to roasted pistachios.

Step-by-step explanation:

Cost of almonds per pound = $10

Cost of roasted pistachios = $12

Total amount spent = $70

Weight of nuts = 6.3

Let,

Weight of almonds = x

Weight of roasted pistachios = y

According to given statement;

x+y=6.3 Eqn 1

10x+12y=70 Eqn 2

Multiplying Eqn 1 by 10

$10(x+y=6.3)\\10+10y=63\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2;

$(10x+12y)-(10x+10y)=70-63\\10x+12y-10x-10y=7\\2y=7$

Dividing both sides by 2

$\frac{2y}{2}=\frac{7}{2}\\y=3.5$

Putting y=3.5 in Eqn 1

$x+3.5=6.3\\x=6.3-3.5\\x=2.8$

Christopher purchased 2.8 pounds of almonds and 3.5 pounds to roasted pistachios.

Keywords: linear equations, elimination method

Learn more about elimination method at:

#LearnwithBrainly

8 0

2 years ago

Answer this A(n)=12(n-1)5

just olya [345]

Distribute:

(12n-12)5

60n-60 = A(n)

You can't really find what n is I don't think, because you have 2 unknown variables n and A(n).

6 0

2 years ago

Write an equation of the line that has a slope of 3 and contains the point (2,5) in point-slope for

enot [183]

The equation would be y=3x-1

Point Slope Formula:

y - y1 = m(x - x1)

y - 5 = 3(x-2)
y - 5 = 3x - 6
+ 5 + 5
--------------------
y = 3x - 1

8 0

2 years ago

Read 2 more answers

Calculate the average rate of change for the given graph from x = -2 to x = 0

Ludmilka [50]

Answer: x goes from 0 to 2, y changes from 0 to -2

Step-by-step explanation:

7 0

2 years ago

Answer plzzzz<br> What are the set of all natural numbers greater than or equal to 5?

nlexa [21]

5,6,7,8,9,10 probably

8 0

2 years ago