Answer:105 boys
Step-by-step explanation :for every group of 7 students (3+4) there are 3 boys and 4 girls. And how many groups do we have? We have:
245/7= 35 We have 35 groups, and we just said that each group has 3 boys and 4 girls:
35*3= 105 boys
35*4= 140 girls
Total: 245 students
Let's say Diana is "x" years old today.
in 3 years, she's going to be " x + 3 " years old.
33 years ago, she was " x - 33 " old.
how much is 4 times that anyway? well 4(x-33), that's 4 times as 33 years ago her age.
now, we know in 3 years, x+3, she'll be "<span>4 times as old as she was 33 years ago", 4(x-33), therefore, those amounts are equal then,
</span>
![\bf \stackrel{\textit{3 years from now}}{x+3}~~=~~\stackrel{\textit{4 times as old as she was 33 years ago}}{4(x-33)} \\\\\\ x+3=4x-132\implies 135=3x\implies \cfrac{135}{3}=x\implies 45=x](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7B3%20years%20from%20now%7D%7D%7Bx%2B3%7D~~%3D~~%5Cstackrel%7B%5Ctextit%7B4%20times%20as%20old%20as%20she%20was%2033%20years%20ago%7D%7D%7B4%28x-33%29%7D%0A%5C%5C%5C%5C%5C%5C%0Ax%2B3%3D4x-132%5Cimplies%20135%3D3x%5Cimplies%20%5Ccfrac%7B135%7D%7B3%7D%3Dx%5Cimplies%2045%3Dx)
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why is it most logical to use "x" for her age today?
well, because 3 years from now is just x + 3
and
33 years ago is x - 33, 4 times that is 4( x - 33 ).
works very well as a point of reference.</span>
What we know:
Circle A has a center at (2,0) and a radius of 8
Circle A' has a center at (-1,5) and a radius of 3
What we need to find:
we need to find the transformation from the center point of A to A' and the scale factor
Circle A can be mapped to Circle A'
center point translation (x,y)⇒[(x+a),(y+b)]⇒(x-3, y+5)
2+a=-1 0+b=5
-2+2+a=-1-2 b=5
a=-3
scale factor is 3/8
8x=3
8/8x=3/8
x=3/8
<span>A)(x, y) → (x - 3, y + 5); scale factor 3/8 </span>
Answer: Triangle A is ACUTE, Triangle B is OBTUSE, Triangle C is RIGHT, Triangle D is ACUTE.
Step-by-step explanation:
- Acute triangles are less than 90 degrees
- Obtuse triangles are greater than 90 degrees
- Right triangles are equal to 90 degrees
I really hoped this helped, have an amazing day/night!
I think it’s A)-0.15 if it’s incorrect I’m sorry!!