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3 years ago

What is the inverse of the function f(x) = 2x – 10?

1 answer:

6 0

Steps to finding the inverse:
1. Replace f(x) with y.
2. Swap x and y.
3. Solve the equation for y.

f(x) = 2x - 10
1. y = 2x - 10
2. x = 2y - 10
3. Add 10 to both sides
x + 10 = 2y
Divide both sides by 2
(x + 10)/2 = y
y = (x + 10)/2
f^-1(x) = (x + 10)/2

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The graph shows the distance traveled by two runners over several minutes,

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Runner B is going slower.

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Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a2 + b2 = c2, which in this iso

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Complete Question

Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a² + b² = c², which in this isosceles triangle becomes a² + a² = c². By combining like terms, 2a² = c². Which final step will prove that the length of the hypotenuse, c, is StartRoot 2 EndRoot times the length of each leg?

a) substitute values for a and c into the original pythagorean theorem equation.

b) divide both sides of the equation by two, then determine the principal square root of both sides of the equation.

c) determine the principal square root of both sides of the equation.

d) divide both sides of the equation by 2.

Answer:

c) determine the principal square root of both sides of the equation.

Step-by-step explanation:

Pythagoras Theorem for a right angled triangles states that:

a²+ b²= c²

But for an Isosceles Triangle, where two sides of the triangle are equal, we have:

a²+ a² = c²

By combining like terms

2a² = c²

We square root both sides of the equation.

√2a² = √c

√2a² = c

The final step will prove that the length of the hypotenuse, c, is StartRoot 2 EndRoot times the length of each leg = √2a² = c is Option c.

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3 years ago

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What is the area of a semicircle with a diameter of 10 cm?

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Answer:

Step-by-step explanation:

area of semi circle = π r² / 2

where r = 10/2 = 5 cm

area = π (5)² / 2

= 39.27 cm²

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3 years ago

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Solve the system by elimination <br> 2x+6y= -12 <br> 5x-5y= -10

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First thing you should do is reduce coefficients.

1st equation has all multiples of '2'. Divide by 2
---> x +3y = -6

2nd equation has multiples of 5. Divide by 5.
---> x - y = 2

Now elimination part is easier.
Eliminate 'x' variable by subtracting 2nd equation from 1st.

x + 3y = -6
-(x - y = 2)
----------------------
4y = -8

Solve for 'y'
4y = -8

y = (-8)/4 = -2

Substitute value for 'y' back into 2nd equation:
x - (-2) = 2
x + 2 = 2
x = 0

Solution to system is:
x=0, y =-2

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4 years ago

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Planes Q and R are parallel. Lines a and b are shown on planes Q and R, respectively. Planes Q and R are parallel. Plane Q conta

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Answer:

They are skew lines.

Step-by-step explanation:

Which statement is true about lines a and b?

They are parallel lines.

They are perpendicular lines.

They are skew lines.

They will intersect.

As they both are in different directions they are skew lines .

Skew lines are not parallel neither they .They are also not co planar i.e they lie in different planes.

We have two plane Q and R . We have two line a and b on the different planes Q and R. Both planes are parallel but the lines a and b are in different directions. Therefore they are skew lines . They do not intersect and are also not parallel neither co planar.

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