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3 years ago

Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k.

Mathematics

1 answer:

Rasek [7]3 years ago

6 0

Answer: -3.

Step-by-step explanation:

We are given that : $g(x)=kf(x)$ (1)

It means that f(x) and g(x) are proportional.

[Equation of direct variation: y=kx , where k= proportionality constant.]

From the given graph ,

At x= -3 , f(x)=1 and g(x) =-3

Put value of x=-3 in (1) , we get

$g(-3)=kf(-3)$

$\Rightarrow\ -3=k(1)$ [∵ f(x)=1 and g(x) =-3]

$\Rightarrow\ -3=k$

i.e. The value of k = -3

Hence, the correct answer is -3.

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What is the square root of 348

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4 0

4 years ago

30 POINTS AVAILABLE

kherson [118]

Answer:

$\large\boxed{(x-2)^2+(y-1)^2=34}$

Step-by-step explanation:

The equation of a circle in standard form:

$(x-h)^2+(y-k)^2=r^2$

(h, k) - center

r - radius

We have the endpoints of the diameter: (-1, 6) and (5, -4).

Midpoint of diameter is a center of a circle.

The formula of a midpoint:

$\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)$

Substitute:

$h=\dfrac{-1+5}{2}=\dfrac{4}{2}=2\\\\k=\dfrac{6+(-4)}{2}=\dfrac{2}{2}=1$

The center is in (2, 1).

The radius length is equal to the distance between the center of the circle and the endpoint of the diameter.

The formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the coordinates of the points (2, 1) and (5, -4):

$r=\sqrt{(5-2)^2+(-4-1)^2}=\sqrt{3^2+(-5)^2}=\sqrt{9+25}=\sqrt{34}$

Finally we have:

$(x-2)^2+(y-1)^2=(\sqrt{34})^2$

3 0

3 years ago

Find the value of 2cosx+1=0;0 less than x less than 360°

ohaa [14]

Answer:

120°; 240°

Step-by-step explanation:

Let's first solve for $cosx$ : $2cosx=-1 \rightarrow cosx=-\frac12$ At this point it's just a matter of drawing a circle, and mark where the angle is(please excuse my paint skills, but free hand drawing would be even worse). Red line, is $-\frac12$ on the cosines, and both the green and blue lines are valid solutions. The green line is a quarter of a circle, plus 30°, or 120°. The blue one is 3/4 of a circle, minus 30 degrees, or 240°.