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2 years ago

What is the solution to the system of equations?

1 answer:

3 0

simplify third eqn -2x+5y+2x=4
5y=4
y=4/5

substitute back to 1st n 2nd eqn n solve for x n z
-4x-4-z=18 and -2x-4-2z=12
simplify -4x-z=22 and -2x-2z=16
-4x-(-x-8)=22
-3x+8=22
x=-14/3
z=-10/3
y=4/5

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Working alone, it takes Kristin 11 hours to harvest a field. Kayla can harvest the same field in 16 hours. Find how long it woul

viktelen [127]

Answer:

(11 hrs + 16 hrs)/2 = 13.5 hrs

13.5 hrs /2 = 6.75 hrs

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2 years ago

A line passes through the points (7, -5) and (3, 1). Determine the slope of the line.

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2 years ago

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2 years ago

Which of the following have the property that a(x)=a−1(x)? I. y=x II. y=1/x III.y=x^2 IV. y=x^3 A. I and II, only B. IV, only C.

valentina_108 [34]

Answer:

Correct answer:

A. I and II

Step-by-step explanation:

First of all, let us have a look at the steps of finding inverse of a function.

1. Replace y with x and x with y.

2. Solve for y.

3. Replace y with $f^{-1}(x)$

Given that:

$I.\ y=x \\II.\ y=\dfrac{1}x \\III.\ y=x^2 \\IV.\ y=x^3$

Now, let us find inverse of each option one by one.

I. y = x, a(x) = x

Replacing y with and x with y:

x = y

x = $a^{-1}(x)$ = $a(x)$ Hence, I is true.

II. $y =\dfrac{1}{x}$

Replacing y with and x with y:

$x =\dfrac{1}{y}$

$x=\dfrac{1}{a^{-1}(x)}$

$\Rightarrow a^{-1}(x) = \dfrac{1}{x}$

$a^{-1}(x)$ = $a(x)$ Hence, II is true.

III. $y =x^{2}$

Replacing y with and x with y:

$x =y^{2}\\\Rightarrow y = \sqrt x\\\Rightarrow a^{-1}(x) = \sqrt{x} \ne a(x)$

Hence, III is not true.

IV. $y =x^{3}$

Replacing y with and x with y:

$x =y^{3}\\\Rightarrow y = \sqrt[3] x\\\Rightarrow a^{-1}(x) = \sqrt[3]{x} \ne a(x)$

Hence, IV is not true.

Correct answer:

A. I and II

4 0

3 years ago

1 Point The circle below is centered at (-3, 2) and has a radius of 3. What is its equation?

arlik [135]

Answer:

(x + 3)^2 + (y - 2)^2 = 9

Step-by-step explanation:

Equation for a circle: (x – h)^2 + (y – k)^2 = r^2

Step 1: Determine what h, k, and r are

h is the x value of the point: -3

k is the y value of the point: 2

r is the radius of the circle: 3

Step 2: Plug in and solve

(x – h)^2 + (y – k)^2 = r^2

(x – (-3))^2 + (y – (2))^2 = (3)^2

(x + 3)^2 + (y - 2)^2 = 9

Answer: (x + 3)^2 + (y - 2)^2 = 9

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3 years ago