Mathematics, 12.07.2021 16:40, qwerty8364

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answered: Zaynt

Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

Step-by-step explanation:

The general form of the straight line equation is, y = m·x + c

Where;

m = The slope

c = The y-intercept

The parent function is, f(x) = x

The slope of the parent function, m₁ = 1

The y-intercept of the parent function, c₁ = 0

The x-intercept of the parent function = 0

The equation of the given function g(x) is derived as follows;

Two points on the line g(x) are (-2, 5) and (1, -4)

The slope of g(x), m₂ = (-4 - 5)/(1 - (-2)) = -3

The equation of g(x) is therefore;

y - 5 = -3 × (x - (-2)) = -3·x - 6

∴ y = -3·x - 6 + 5 = -3·x - 1

y = -3·x - 1

The slope of the given function, m₂ = -3

The y-intercept of the given function, c₂ = -1

The x-intercept of the function = -1

We have that a reflection of (x, y) across the y-axis gives (-x, y)

Therefore, the function g(x) is a reflection of f(x) across the y-axis

The slope of g(x) = -3 × The slope of f(x), therefore, g(x) is obtained by a vertical stretch of of f(x) by a factor of 3

The y-intercept of g(x) is lower than the y-intercept of g(x) by -1, therefore, f(x) is shifted down vertically by 1 unit to obtain g(x)

Therefore, the sequence of transformation that can be used to obtain g(x) from the parent function f(x) are;

Reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

answered: Guest

answer: it is d

step-by-step explanation:

answered: Guest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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