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3 years ago

13

Mrs. Smythe needs 54 buttons to make costumes for the school play. Buttons come on cards of 9 buttons each. How many cards of bu

ttons should Mrs. Smythe buy?
9
45
7
6

1 answer:

V125BC [204]3 years ago

6 0

54 buttons ÷ 9 button cards = 6

She should buy 6 cards of buttons.

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HELPPPPP!!!!!!!!!!!!!!!!!!!

8090 [49]

A trinomial is a polynomial with three terms. It can be determined if it is a difference of two squares when you factor it.

The resulting factor of a trinomial that is a difference of two squares is: a²<span> – b</span>²<span> = (a + b)(a – b) or (a – b)(a + b)</span>

You will notice that the middle term is missing. This means that the middle term zeroes out as a result of having the same number of different signs (+ and -)

5 0

4 years ago

Let f(x) = 1/x^2 (a) Use the definition of the derivatve to find f'(x). (b) Find the equation of the tangent line at x=2

Verdich [7]

Answer:

(a) $f'(x)=-\frac{2}{x^3}$

(b) $y=-0.25x+0.75$

Step-by-step explanation:

The given function is

$f(x)=\frac{1}{x^2}$ .... (1)

According to the first principle of the derivative,

$f'(x)=lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{x^2-(x+h)^2}{x^2(x+h)^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{x^2-x^2-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-h(2x+h)}{hx^2(x+h)^2}$

Cancel out common factors.

$f'(x)=lim_{h\rightarrow 0}\frac{-(2x+h)}{x^2(x+h)^2}$

By applying limit, we get

$f'(x)=\frac{-(2x+0)}{x^2(x+0)^2}$

$f'(x)=\frac{-2x)}{x^4}$

$f'(x)=\frac{-2)}{x^3}$ .... (2)

Therefore $f'(x)=-\frac{2}{x^3}$ .

(b)

Put x=2, to find the y-coordinate of point of tangency.

$f(x)=\frac{1}{2^2}=\frac{1}{4}=0.25$

The coordinates of point of tangency are (2,0.25).

The slope of tangent at x=2 is

$m=(\frac{dy}{dx})_{x=2}=f'(x)_{x=2}$

Substitute x=2 in equation 2.

$f'(2)=\frac{-2}{(2)^3}=\frac{-2}{8}=\frac{-1}{4}=-0.25$

The slope of the tangent line at x=2 is -0.25.

The slope of tangent is -0.25 and the tangent passes through the point (2,0.25).

Using point slope form the equation of tangent is

$y-y_1=m(x-x_1)$

$y-0.25=-0.25(x-2)$

$y-0.25=-0.25x+0.5$

$y=-0.25x+0.5+0.25$

$y=-0.25x+0.75$

Therefore the equation of the tangent line at x=2 is y=-0.25x+0.75.

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3 years ago

Find the distance between the two points.(-7,4/19) and (7,4/9)

Dafna1 [17]

Answer:

<h2>d=(14,0)</h2>

Step-by-step explanation:

<h2>√(7-(-7))^+(4/19-4/19)^</h2><h2>√(7+7)^+(0)^</h2><h2>√(14)^+0</h2><h2>= 14</h2>

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3 years ago

Evaluate 5x – 2y + (7x – y) for x = 7 and y = –2. 90 –18 –45 63

seropon [69]

The value of the expression 5x – 2y + (7x – y) when x = 7 and y = -2 is 90

<h3>How to evaluate the expression?</h3>

The expression is given as:

5x – 2y + (7x – y)

Substitute x = 7 and y = –2 in the above expression

5 * 7 - 2 * -2 + (7 * 7 + 2)

Evaluate the expression

90

Hence, the value of the expression 5x – 2y + (7x – y) when x = 7 and y = -2 is 90

Read more about expressions at:

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2 years ago

The answer too this??? And how to solve

julia-pushkina [17]

alright then, 12x + 17 = 66! we started with 17 and there is twelve months with x amount of inches grown plus the already 17 that equals the total 66

so it is 12x + 17 = 66

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2 years ago

Read 2 more answers