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2 years ago

G(x)=-2/5x-2 inverse function with steps please

Mathematics

1 answer:

podryga [215]2 years ago

4 0

Answer:

${g}^{ - 1} (x) = - \frac{5}{2} x - 5$

Step-by-step explanation:

We want to find the inverse of

$g(x) = - \frac{2}{5}x - 2$

Let

$y= - \frac{2}{5}x - 2$

We interchange x and y to get:

$x= - \frac{2}{5}y - 2$

We now solve for y to obtain:

$x + 2=-\frac{2}{5}y$

$5x = - 2y - 10$

Add 10 to both sides to get:

$5x + 10 = - 2y$

Divide through by -2

$y = - \frac{5}{2} x - 5$

Therefore

${g}^{ - 1} (x) = - \frac{5}{2} x - 5$

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Find the two square roots of each complex number by creating and solving polynomial equations.

son4ous [18]

Answer:

1) w₁=4 - i w₂= -4 + i

2) w₁= 3 - i w₂= -3 + i

3) w₁= 1 + 2i w₂= - 1 - 2i

4) w₁= 2- 3i w₂= -2 + 3i

5) w₁= 5 - 2i w₂= -5 + 2i

6) w₁= 5 - 3i w₂= -5 + 3i

Step-by-step explanation:

The root of a complex number is given by:

$\sqrt[n]{z}=\sqrt[n]{r}(Cos(\frac{\theta+2k\pi}{n}) + i Sin(\frac{\theta+2k\pi}{n}))$

where:

r: is the module of the complex number

θ: is the angle of the complex number to the positive axis x

n: index of the root

1) z = 15 − 8i ⇒ r=17 θ= -0.4899 rad

w₁= $\sqrt{17}(Cos(\frac{-0.4899}{2}) + i Sin(\frac{-0.4899}{2}))$ =4-i

w₂= $\sqrt{17}(Cos(\frac{-0.4899+2\pi}{2}) + i Sin(\frac{-0.4899+2\pi}{2}))$ =-1+i

2) z = 8 − 6i ⇒ r=10 θ= -0.6435 rad

w₁= $\sqrt{10}(Cos(\frac{ -0.6435}{2}) + i Sin(\frac{ -0.6435}{2}))$ = 3 - i

w₂= $\sqrt{10}(Cos(\frac{ -0.6435+2\pi}{2}) + i Sin(\frac{ -0.6435+2\pi}{2}))$ = -3 + i

3) z = −3 + 4i ⇒ r=5 θ= -0.9316 rad

w₁= $\sqrt{5}(Cos(\frac{-0.9316}{2}) + i Sin(\frac{-0.9316}{2}))$ = 1 + 2i

w₂= $\sqrt{5}(Cos(\frac{-0.9316+2\pi}{2}) + i Sin(\frac{-0.9316+2\pi}{2}))$ = -1 - 2i

4) z = −5 − 12i ⇒ r=13 θ= 0.4426 rad

w₁= $\sqrt{13}(Cos(\frac{0.4426}{2}) + i Sin(\frac{0.4426}{2}))$ = 2- 3i

w₂= $\sqrt{13}(Cos(\frac{0.4426+2\pi}{2}) + i Sin(\frac{0.4426+2\pi}{2}))$ = -2 + 3i

5) z = 21 − 20i ⇒ r=29 θ= -0.8098 rad

w₁= $\sqrt{29}(Cos(\frac{-0.8098}{2}) + i Sin(\frac{-0.8098}{2}))$ = 5 - 2i

w₂= $\sqrt{29}(Cos(\frac{-0.8098+2\pi}{2}) + i Sin(\frac{-0.8098+2\pi}{2}))$ = -5 + 2i

6) z = 16 − 30i ⇒ r=34 θ= -1.0808 rad

w₁= $\sqrt{34}(Cos(\frac{-1.0808}{2}) + i Sin(\frac{-1.0808}{2}))$ = 5 - 3i

w₂= $\sqrt{34}(Cos(\frac{-1.0808+2\pi}{2}) + i Sin(\frac{-1.0808+2\pi}{2}))$ = -5 + 3i

6 0

2 years ago

Peter says that 3/4 of a pizza is always the same as 6/8 of a pizza. Nadia says that while they are equivalent fractions, 3/4 an

allsm [11]

Nadia

6/8 is 3/4 and both is 75% of a pizza but, the eighths of a pizza is a smaller slice of pizza.

4/4 is four slices of pizza
8/8 is eight slices of pizza They are different amounts.

5 0

2 years ago

Read 2 more answers

Which equation describes the circle

deff fn [24]

Answer:

B. (x-5)²+(y+1)² = 49

Step-by-step explanation:

An equation of a circle with center (h, k) and radius r is

$\large \boxed{ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} }$

We have all given information we need. Our h is 5 - Our k is -1 and our radius is 7

Substitute these values in

$\large{ {(x - 5)}^{2} + {(y - ( - 1))}^{2} = {7}^{2} } \\ \large{ {(x - 5)}^{2} + {(y + 1)}^{2} = {7}^{2} } \\ \large{ {(x - 5)}^{2} + {(y + 1)}^{2} = 49 }$