Answers + Explanation:
1. x + 7 =10
if you know some number + 7 is 10, you know that number must be 3.
so, x = 3
the other way you can solve this would be:
x + 7 = 10
subtract 7 from both sides of the equation
x + 7 - 7 = 10 - 7
x = 3
2. Use the same strategy:
x - 8 = -5
add 8 to both sides of the equation
x - 8 + 8 = -5 + 8
x = 3
3. x + 3 = 6
subtract 3 from both sides of the equation
x + 3 - 3 = 6 - 3
x = 3
4. x + 6 = 3
subtract 6 from both sides of the equation
x + 6 - 6 = 3 - 6
x = -3
Answer:
(C) 2√15
Step-by-step explanation:
Recognize that all the triangles are right triangles, so are similar to each other. In these similar triangles, the ratio of the short side to the long side is the same for all.
... CB/CA = CT/CB
... CB² = CA·CT = 10·6 = 60 . . . . . . . . . . multiply by CA·CB; substitute values
... CB = √60 = 2√15 . . . . . . . take the square root; simplify
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<em>Comment on this solution</em>
The altitude to the hypotenuse of a right triangle (CB in this case) divides the hypotenuse into lengths such that the altitude is their geometric mean. That is ...
... CB = √(AC·CT) . . . . as above
This is true for any right triangle — another fact of geometry to put in your list of geometry facts.
Answer: 150 boys
Step-by-step explanation:
Let the number of boys be x
Since there were 200 more girls than boys, the number of girls will be: = x + 200
Since the ratio of boys to girls was 3:7, this can be solved further below:
3/7 = x/x+200
Cross multiply
(7 × x) = 3(x + 200)
7x = 3x + 600
7x - 3x = 600
4x = 600
x = 600/4
x = 150
The number of boys enrolled is 150
Number of Girls will be:
= X + 200
= 150 + 200
= 350
Check: Number of boys / Number of girls
= 150/350
= 3/7
= 3:7
Answer:
the distance between the two points is √130.
Step-by-step explanation:
a^2 + b^2 = c^2
a^2 = 9^2 = 81
b^2 = 7^2 = 49
c^2 = 81 + 49 = 130
c = √130
