Answer:
- One proportion to solve is 8/18 = x/8
- Exact answer as a fraction: x = 32/9
- Approximate answer in decimal form: x = 3.556
In reality, the 5's go on forever, but we have to round off somewhere.
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Explanation:
Break up the triangles as your teacher recommends. See the diagram below as to what I mean.
The smaller triangle has A = 8 as the horizontal side, and B = x as the vertical side
The larger triangle has C = 10+8 = 18 as the horizontal aside, and D = 8 as the vertical side.
We can form the proportion A/C = B/D.
A/C connects the horizontal sides (small/large) while B/D has the vertical sides tied together. The order of division is the same small over large. You could do large over small, but make sure you keep both sides consistent.
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Let's solve for x
A/C = B/D
8/18 = x/8
8*8 = 18*x .... cross multiply
64 = 18x
18x = 64
x = 64/18 .... divide both sides by 18
x = 32/9 exactly in fraction form
x = 3.556 approximately in decimal form
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Another proportion you can solve is A/B = C/D and you should get the same x value. It's the same as A/C = B/D because the B and C swap places. There are many other approaches you could take using different proportions.
Answer:
A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.
B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.
Step-by-step explanation:
f(x) = 12x^2 + 5x - 2.
Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).
To find the roots of f(x), set f(x) = 0. Therefore:
12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:
12x^2 + 8x - 3x - 2 = 0.
4x(3x + 2) -1(3x+2) = 0.
(4x-1)(3x+2) = 0.
4x-1 = 0 or 3x+2 = 0.
x = 1/4 or x = -2/3.
It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!
Answer:
C. sqrt((-3-6)² + (4+2)²)
Step-by-step explanation:
as we are using Pythagoras and asking for the distance as a side length (actually the Hypotenuse, the side opposite of the 90 degree angle) in a right-angled triangle, only an expression of a square root of a sum of squares can be right.
so, A and B are automatically out without even further analysis.
for the distance between 2 points on a coordination grid we build the mentioned right-angled triangle with the difference in x-direction as one side (e.g. "a"), the difference in y-direction as a second side (e.g. "b").
and the direct distance is then the Hypotenuse "c".
you remember Pythagoras :
c² = a² + b²
and therefore
c = sqrt(a² + b²)
in our example "a" is the difference between the 2 x-values.
a = (-3 - 6)
and "b" is the difference between the 2 y-values.
b = (4 - -2) = (4 + 2)
since we have to square them for the formula, the direction of what is subtracted from what is irrelevant, as the square of a negative value is also positive.
c = sqrt((-3 - 6)² + (4 + 2)²)
and that is answer option C
Answer:
132
Step-by-step explanation:
TPR = 180
UPT = 48
180-48=132
The correct answer is: [B]: " IV, II, I, III " .
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