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Umnica [9.8K]
2 years ago
8

Find A ∩ B A = {2, 3, 4, 5, 6} B = {3, 6, 9, 12, 15}

Mathematics
2 answers:
kakasveta [241]2 years ago
7 0
\bf A = \{2, \boxed{3}, 4, 5, \boxed{6}\} \qquad  B = \{\boxed{3}, \boxed{6}, 9, 12, 15\}
\\ \quad \\
A\cap B\impliedby \textit{values that intersect or are common to both}
Aliun [14]2 years ago
3 0
It's asking common members so the answer must be {3,6}
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Please help, thank you :)​
Step2247 [10]

Answer:

If you gave out 4 cookie to a people you would have 5 cookies leftover, but if you gave out 12 cookie to a people you would need 11 more cookies.

3 0
2 years ago
The slope of the line passing through the points (0, 3) and (5, 7) is
icang [17]
Slope formula: Change in y over change in x

Change in y: +4
Change in x: +5

Slope: 4/5

Hope this helps :)
Please give brainliest
7 0
3 years ago
How is this solved using trig identities (sum/difference)?
GenaCL600 [577]
FIRST PART
We need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative

Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached

Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13

cos α = side adjacent to the angle / hypotenuse
cos α = -5/13

Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

cos \beta = -\frac{1}{2}  \sqrt{3}

tan \beta= \frac{1}{3}  \sqrt{3}

SECOND PART
Solve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β
sin( \alpha + \beta )=(- \frac{12}{13} )( -\frac{1}{2}  \sqrt{3})+( -\frac{5}{13} )( -\frac{1}{2} )
sin( \alpha + \beta )=(\frac{12}{26}\sqrt{3})+( \frac{5}{26} )
sin( \alpha + \beta )=(\frac{5+12\sqrt{3}}{26})

Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β
cos( \alpha + \beta )=(- \frac{5}{13} )( -\frac{1}{2} \sqrt{3})+( -\frac{12}{13} )( -\frac{1}{2} )
cos( \alpha + \beta )=(\frac{5}{26} \sqrt{3})+( \frac{12}{26} )
cos( \alpha + \beta )=(\frac{5\sqrt{3}+12}{26} )

Find tan (α - β)
tan( \alpha - \beta )= \frac{ tan \alpha-tan \beta }{1+tan \alpha  tan \beta }
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5}{12}) ( \frac{1}{2} \sqrt{3})}

Simplify the denominator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3}   }{1+(\frac{5\sqrt{3}}{24})}
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{1}{2} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the numerator
tan( \alpha - \beta )= \frac{ \frac{5}{12} - \frac{6}{12} \sqrt{3} }{ \frac{24+5\sqrt{3}}{24} }
tan( \alpha - \beta )= \frac{ \frac{5-6\sqrt{3}}{12} }{ \frac{24+5\sqrt{3}}{24} }

Simplify the fraction
tan( \alpha - \beta )= (\frac{5-6\sqrt{3}}{12} })({ \frac{24}{24+5\sqrt{3}})
tan( \alpha - \beta )= \frac{10-12\sqrt{3} }{ 24+5\sqrt{3}}

7 0
2 years ago
(b) Eric removed 72 fish from his pond over a period of 9 days. He removed the same number of
Amanda [17]

Answer:

-8

Step-by-step explanation:

72 ÷ 9 = 8

The fish are being taken out, so negative.

I hope this helps!

pls ❤ and mark brainliest pls!

8 0
2 years ago
Which expression is equal to p + (q + r)?
Verdich [7]
The answer is letter B.
5 0
3 years ago
Read 2 more answers
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