The sum of two consecutive integers is sixty-five. Find the smaller of the two numbers.
1 answer:
Answer:
32
Step-by-step explanation:
We can write an algebraic equation to solve this situation: , where x = first integer (small number) and x + 1 = the following integer.
Step 1: Combine like terms.
Step 2: Subtract 1 from both sides.
Step 3: Divide both sides by 2.
Therefore, the smaller number is 32 while the larger number is 33.
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Answer:
see below
Step-by-step explanation:
f(x) = −16x^2 + 24x + 16
Set equal to zero to find the x intercepts
0 = −16x^2 + 24x + 16
Factor out -8
0 = -8(2x^2 -3x-2)
Factor
0 = -8(2x +1) (x-2)
Using the zero product property
2x+1 =0 x-2 =0
x = -1/2 x=2
The x intercepts are -1/2 ,2
Since the coefficient of x^2 is negative the graph will open down and the vertex will be a maximum
The x value of the maximum is 1/2 way between the zeros
(-1/2+2) /2 = 1.5/2 =.75
To find the y value substitute into the function
f(.75) = -8(2x +1) (x-2)
=-8(2*.75+1) (.75-2)
= -8(2.5)(-1.25)
=25
The vertex is at (.75, 25)
We have the zeros, and the vertex. We know the graph is symmetrical about the vertex
Answer:
-3, 7 = x
Step-by-step explanation:
3|x – 2| + 2 = 17
- 2 - 2
________________
3|x - 2| = 15
_______ ___
3 3
|x - 2| = 5
+ 2 + 2 + 2 + 2
_______________ ____________
x = -3 x = 7
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Answer:
C. 8
Step-by-step explanation:
I almost thought this was going to be Pythagorean Theorem, but no.
Use Cosine Law:
cos θ =
θ = cos−1(0.6)
θ = 53.130...
Now use the SOHCAHTOA ratio for sine () to find x now that you have one angle:
sin θ =
x = 10sinθ (θ isn't needed to be written out as it is shown in the equation above)
x = 8