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Alex Ar [27]
3 years ago
8

Is f(x)=x^2-2x+3 a quadratic function

Mathematics
2 answers:
Sav [38]3 years ago
6 0

Answer:

yes

Step-by-step explanation:

A quadratic function has the general form

fx) = ax² + bx + c ( a ≠ 0 )

f(x) = x² - 2x + 3 ← is in this form and is a quadratic function

Over [174]3 years ago
5 0
You learned this you should know
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Find the exact value of cos(sin^-1(-5/13))
son4ous [18]

bearing in mind that the hypotenuse is never negative, since it's just a distance unit, so if an angle has a sine ratio of -(5/13) the negative must be the numerator, namely -5/13.

\bf cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{then we can say that}~\hfill }{sin^{-1}\left( -\cfrac{5}{13} \right)\implies \theta }\qquad \qquad \stackrel{\textit{therefore then}~\hfill }{sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}}\impliedby \textit{let's find the \underline{adjacent}}

\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12=a \\\\[-0.35em] ~\dotfill\\\\ cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right]\implies cos(\theta )=\cfrac{\stackrel{adjacent}{\pm 12}}{13}

le's bear in mind that the sine is negative on both the III and IV Quadrants, so both angles are feasible for this sine and therefore, for the III Quadrant we'd have a negative cosine, and for the IV Quadrant we'd have a positive cosine.

8 0
2 years ago
What is 32767/32768 as a reduced fraction?
Anit [1.1K]
32,767/32,768 is in lowest terms and can't be reduced.
8 0
3 years ago
Given P(A)=0.5P(A)=0.5, P(B)=0.71P(B)=0.71 and P(A\cap B)=0.415P(A∩B)=0.415, find the value of P(A|B)P(A∣B), rounding to the nea
Marysya12 [62]

Answer:

0.585

Step-by-step explanation:

P(A|B) = P(A∩B) / P(B)

P(A|B) = 0.415 / 0.71

P(A|B) = 0.585

8 0
3 years ago
Triangle EFG is dilated by a scale factor of 3 centered at (0, 1) to create triangle E'F'G'. Which statement is true about the d
lesya [120]

Answer:

segment EH and segment E prime H prime both pass through the center of dilation.  

Step-by-step explanation:

Center of dilation is point (0.1), same as H. Both, E(0,5) and H(0,1) are placed over y-axis, then E' and H' are also located at y-axis.

After dilation, H' is placed at (0,1) because it coincides with the center of dilation

Distance between E and center of dilation is 4 units, then E' should be at 4*3=12 units from the center of dilation and over y-axis. Therefore, E' is placed at (0, 13)

So, segment E'H' goes from (0,1) to (0,13), and pass through the center of dilation, like segment EH.

4 0
3 years ago
Jane and sali cycled along the same 63 km route.
Alina [70]

Answer:

<em>Sali's speed was 18.75 km/h.</em>

Step-by-step explanation:

Jane took 3.5 hours to cycle the 63 km.

As,  Speed= \frac{Distance}{Time} , so the speed of Jane will be:  \frac{63}{3.5} km/h = 18 km/h

Suppose, the speed of Sali is  x km/h

Sali caught up with Jane when they had both cycled 30 km.

So, <u>the time required for Jane to cycle 30 km</u> = \frac{30}{18}=\frac{5}{3} hours and <u>the time required for Sali to cycle 30 km</u>  =\frac{30}{x} hours

Given that, Sali started to cycle 4 minutes or (\frac{4}{60}) or (\frac{1}{15}) hours after Jane started to cycle. So, the equation will be.......

\frac{5}{3}-\frac{30}{x}= \frac{1}{15}\\ \\ \frac{30}{x}= \frac{5}{3}-\frac{1}{15}\\ \\ \frac{30}{x}= \frac{24}{15}\\ \\ 24x=450\\ \\ x= \frac{450}{24}= 18.75

Thus, the speed of Sali was 18.75 km/h.

8 0
2 years ago
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