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1 year ago

The inverse of G(x) is a function. • A. True • B. False

Mathematics

1 answer:

Julli [10]1 year ago

5 0

Answer: False

Step-by-step explanation:

G(x) is not a one-to-one function (since it fails the horizontal line test). Therefore, it doesn't have an inverse.

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◆ Quadratic Equations ◆ Please help !

Mila [183]

I'm sure there's an easier way of solving it than the way I did, but I'm not sure what it could be. Never dealt with a problem like this before.

Anyway, I just plugged in and tested. Chose random values for a, b, c, and d, which follow the rule 0 < a < b < c < d:

a = 1
b = 2
c = 3
d = 4

$\sf ax^2+(1-a(b+c))x+abc-d)$

$\sf 1x^2+(1-1(2+3))x+(1)(2)(3)-(4))$

Simplify into standard form:

$\sf x^2+(1-1(5))x+6-4$

$\sf x^2+(1-5)x+2$

$\sf x^2-4x+2$

Use the quadratic formula to solve:

$\sf x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

For functions in the form of $\sf ax^2+bx+c$ . So in this case:

a = 1
b = -4
c = 2

Plug them in:

$\sf x=\dfrac{4\pm\sqrt{(-4)^2-4(1)(2)}}{2(1)}$

Solve for 'x':

$\sf x=\dfrac{4\pm\sqrt{16-8}}{2}$

$\sf x=\dfrac{4\pm\sqrt{8}}{2}$

$\sf x\approx\dfrac{4\pm 2.83}{2}$

$\sf x\approx 0.59,3.41$

So the answer would be A.

3 0

3 years ago

U'LL GET BRAINLIEST IF U ANSWER FIRST

Tanzania [10]

Answer:

$\boxed{\bold{a+2b}}$

Explanation:

Simplify expression to find its equivalent

Expand $\bold{2\left(a+2b\right): \ 2a+4b}$

= $\bold{2a+4b-a-2b}$

Simplify $\bold{2a+4b-a-2b: \ a+2b}$

= $\bold{a+2b}$

Mordancy.

6 0

3 years ago

The outer and inner triangles are both equilateral and the circle touches all three sides of the outer triangle. If the area of

Brrunno [24]

Answer:

The area of outer Δ = 40 cm²

Step-by-step explanation:

∵ Area of the small triangle = 10 cm²

If we join the center of the circle with the 3 vertices of the inner Δ

These 3 segments are the radii of the circle

Now the inner triangle has 3 isosceles Δ their sides are r , r and s1 with vertex angle 120° ⇒ (360° ÷ 3 = 120°)

Where r is the radius of the circle and s1 is the side of the inner triangle

By using cosine rule

(s1)² = r² + r² - 2r²cos120 = r² + r² - 2r² (-0.5) = r² + r² + r² = 3r²

∴ s1 = r√3

∵ The radius of the circle ⊥ to the side of the outer Δ because the side of the outer Δ is a tangent to the circle

If we join a vertex of the outer Δ with the center of the circle

We will have a right angle triangle of two legs r and half s2 with angle 60° (120° ÷ 2 )between them ⇒ s2 is the side of outer Δ

∴ tan 60° = 1/2 (s2) ÷ r ⇒ √3 = 1/2 (s2) ÷ r = (s2)/2r

∴ s2 = 2r√3

∴ s2 : s1 = 2r√3 ÷ r√3 = 2 : 1

∴ The side of the outer Δ is double the side of the inner Δ

By using similarity ratio

A2/A1 = (s2/s1)² ⇒ A2 and A1 are the areas of outer and inner triangles

∴ A2 : A1 = (2/1)² = 4/1

∴ A2 = 4 A1

∴ A2 = 4 × 10 = 40 cm²

5 0

3 years ago

What the simplified form of x- 1 +4+7x-3

Nuetrik [128]

Collect like terms (x + 7x) + (-1 + 4 - 3)

Simplify

Answer: 8x

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3 years ago

Radon went to America on holiday . She took 750 USD Dollars with her to spend

Alex777 [14]

Answer:

Step-by-step explanation:

4 0

1 year ago