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2 years ago

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Simplify the expression 4(2x + 8) using the distributive property.

2 answers:

bazaltina [42]2 years ago

7 0

Simplify the expression <em>4(2x + 8) </em>using the distributive property.

<em>The distributive property tells us how to solve expressions in the form of a(b + c). The distributive property is sometimes called the distributive law of multiplication and division. ... Then we need to remember to multiply first, before doing the addition!</em>

<em></em>

Hence, the information sho above we can now solve the equation

4(2x + 8) without any problem.

4(2x + 8) <u><em>---></em></u> 4 * 2x + 4 * 8 <em><u>---></u></em> 8x + 32

<em>Therefore, your finnal answer is </em>

<em>8x + 32</em>

Goryan [66]2 years ago

6 0

Answer:

$8x + 32$

Step-by-step explanation:

$4(2x+8)$

4 × 2x = 8x

4 × 8 = 32

$8x + 32$

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2 years ago

Find the zeroes of the polynomial function f(x)=x^4-5x^3+11x^2-25x+30.

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Step-by-step explanation:

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2 years ago

Find the point (,) on the curve =8 that is closest to the point (3,0). [To do this, first find the distance function between (,)

ELEN [110]

Question:

Find the point (,) on the curve $y = \sqrt x$ that is closest to the point (3,0).

[To do this, first find the distance function between (,) and (3,0) and minimize it.]

Answer:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

Step-by-step explanation:

$y = \sqrt x$ can be represented as: $(x,y)$

Substitute $\sqrt x$ for $y$

$(x,y) = (x,\sqrt x)$

So, next:

Calculate the distance between $(x,\sqrt x)$ and $(3,0)$

Distance is calculated as:

$d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}$

So:

$d = \sqrt{(x-3)^2 + (\sqrt x - 0)^2}$

$d = \sqrt{(x-3)^2 + (\sqrt x)^2}$

Evaluate all exponents

$d = \sqrt{x^2 - 6x +9 + x}$

Rewrite as:

$d = \sqrt{x^2 + x- 6x +9 }$

$d = \sqrt{x^2 - 5x +9 }$

Differentiate using chain rule:

Let

$u = x^2 - 5x +9$

$\frac{du}{dx} = 2x - 5$

So:

$d = \sqrt u$

$d = u^\frac{1}{2}$

$\frac{dd}{du} = \frac{1}{2}u^{-\frac{1}{2}}$

Chain Rule:

$d' = \frac{du}{dx} * \frac{dd}{du}$

$d' = (2x-5) * \frac{1}{2}u^{-\frac{1}{2}}$

$d' = (2x - 5) * \frac{1}{2u^{\frac{1}{2}}}$

$d' = \frac{2x - 5}{2\sqrt u}$

Substitute: $u = x^2 - 5x +9$

$d' = \frac{2x - 5}{2\sqrt{x^2 - 5x + 9}}$

Next, is to minimize (by equating d' to 0)

$\frac{2x - 5}{2\sqrt{x^2 - 5x + 9}} = 0$

Cross Multiply

$2x - 5 = 0$

Solve for x

$2x =5$

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

Substitute $x = \frac{5}{2}$ in $y = \sqrt x$

$y = \sqrt{\frac{5}{2}}$

Split

$y = \frac{\sqrt 5}{\sqrt 2}$

Rationalize

$y = \frac{\sqrt 5}{\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$y = \frac{\sqrt {10}}{\sqrt 4}$

$y = \frac{\sqrt {10}}{2}$

Hence:

$(x,y) = (\frac{5}{2},\frac{\sqrt{10}}{2}})$

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3 years ago

What is the mode of the following data values?

lozanna [386]

The mode of the following data values would be 21.
mode is usually a number that is repeated more than once, and in this case, 21 appears twice.
your answer is c

7 0

3 years ago

Read 2 more answers