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mars1129 [50]
3 years ago
6

What property of equality is 43n = -43

Mathematics
2 answers:
VashaNatasha [74]3 years ago
6 0

Answer:

Division

Step-by-step explanation:

43n = - 43 (divide both sides by 43)

43/43 = -43/43

= -1

Mumz [18]3 years ago
3 0

Answer:

n=-1

Step-by-step explanation:

43/-43=-1

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Function k is a linear function with a slope of 1/2 that passes through the point (4,2). What equation represents Function K?
Novay_Z [31]

Answer:

A. y = 1/2 x.

Step-by-step explanation:

Use the point-slope form of a linear (straight line) function:

y - y1 = m(x - x1)

m = 1/2, x1 = 4 and y1 = 2, so:

y - 2 = 1/2(x - 4)

y = 1/2x - 2 + 2

y = 1/2 x (answer)

8 0
3 years ago
Which statement describes the inverse of m(x) = x2 – 17x?
stealth61 [152]

Answer:

The correct option is;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

Step-by-step explanation:

The given information is that m(x) = x² - 17·x

The above equation can be written in the form;

y = x² - 17·x

Therefore;

0 = x² - 17·x - y

From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;

x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}

By comparison to the equation,0 = x² - 17·x - y, we have;

a = 1, b = -17, and c = -y

Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;

x = \dfrac{-(-17)\pm \sqrt{(-17)^{2}-4\times (1) \times (-y)}}{2\times (1)} = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}

Which can be simplified as follows;

x =  \dfrac{17\pm \sqrt{289+4\cdot y}}{2}= \dfrac{17}{2} \pm \dfrac{1}{2}  \times \sqrt{289+4\cdot y}} = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +\dfrac{4\cdot y}{4} }}

And further simplified as follows;

x = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +y }} = \dfrac{17}{2} \pm \sqrt{y + \dfrac{289}{4} }}

Interchanging x and y in the function of the inverse, m⁻¹(x), we have;

m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}

We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;

m'(x) = 2·x - 17 = 0

x = 17/2

Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;

m''(x) = 2 > 0, therefore, the point is a minimum point on the graph

Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;

The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }} to increase m⁻¹(x) above the minimum.

8 0
3 years ago
What is the width of a rectangle that has an area of 10 ft.² and a length of 24 inches give your answer in feet
VladimirAG [237]

Answer:

Width = 5 ft

Step-by-step explanation:

A=wl

10 = wl

24 inches = 2 ft

10 = w*2

10/2=w*2/2\\5=w

5 0
3 years ago
Math help pls, will reward lol, thanks
Ahat [919]

Answer:

see explanation

Step-by-step explanation:

Given f(x) then f(x - 2) represents a horizontal translation of f(x) shifted 2 units to the right, thus

The marked points on f(x) → f(x - 2) are

(0, 0 ) → (2, 0 )

(2, 4 ) → (4, 4 )

(3, 9 ) → (5, 9 )

8 0
3 years ago
I’ll give someone brainliest if they answer this
Dimas [21]

Answer:

2. The answer should be the last one.

3. The answer should be the first three.

Step-by-step explanation:

<u>Question 2</u>

KE = (1/2)mv²

2KE = mv²

v² = 2KE/m

v = ±√(2KE/m)

Therefore the answer should be the last one.

<u>Question 3</u>

b^(1/2) * b^(5/2)

Remember that the <u><em>product rule</em></u> states that b^x * b^y = b^(x+y)

So this means b^(1/2) * b^(5/2) = b^(1/2+5/2) = b^(6/2) = b^3

Also remember that the <u><em>power rule</em></u> states that √b = b^(1/2)

so this means b^(6/2) can also be written as (√b)^6

Therefore the answer should be the first three.

<em>If you want to double check all of your answers, just replace b with a number (for example, 2), and plug all of the choices into the calculator. Just </em><u><em>make sure</em></u><em> you are </em><u><em>very careful</em></u><em> when typing into the calculator.</em>

3 0
3 years ago
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