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dsp73
2 years ago
7

Graph the lines by finding the points of intersection with the axes (intercepts):

Mathematics
1 answer:
saul85 [17]2 years ago
3 0

The equation is in slope-intercept form, so you can read the equation to find the y-intercept is (0, -1).

Since the slope is -1/2, the graph goes <em>up</em> 1 unit for each 2 units to the <em>left</em>. The x-axis is up 1 unit from the y-intercept, so the x-intercept is 2 units to the left of x=0, at (-2, 0).

The graph is the line that goes through the points (0, -1) and (-2, 0).

_____

If you like, you can put the equation into intercept form, which shows you both the x- and y-intercepts at once. That form is ...

... x/a + y/b = 1

where <em>a</em> and <em>b</em> are the x- and y-intercepts.

If we add 1-y to the given equation, we have ...

... 1 = (-1/2)x - y

... 1 = x/(-2) + y/(-1) . . . . intercept form

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3 years ago
If h(x)=(fog)(x) and h(x) = sqrt x+5, find g(x) if f(x) = sqrtx+2
Katen [24]

Answer: The value of g(x) is x+3.

Step-by-step explanation:

Since we have given that

h(x)=f\circ g(x)

Here,

h(x)=\sqrt{x+5}\\\\and\\\\f(x)=\sqrt{x+2}

We need to find the value of g(x):

f(x)=\sqrt{x+2}\\\\f(g(x))=\sqrt{g(x)+2}\\\\h(x)=\sqrt{g(x)+2}\\\\\sqrt{x+5}=\sqrt{g(x)+2}\\\\x+5=g(x)+2\\\\g(x)=x+5-2=x+3

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3 0
3 years ago
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
3 years ago
Solve for x by completing square x^2-18x=65
Nastasia [14]

Answer:

See Image below:)

Step-by-step explanation:

You can use the app photo math, you just take a picture of the question and it shows you the steps.

7 0
2 years ago
What is 3.06 rounded to the nearest whole number
Gnom [1K]
3.06 rounded to the nearest whole number is 3.
.06 is much closer to 0 than it is to 1, so round down.
3.06 rounded down is 3, so that is your answer.
4 0
3 years ago
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