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3 years ago

6|6-4x|=8x+4 Need help solving the equation. I need help checking the extraneous solutions too.

1 answer:

8 0

$6|6-4x|=8x+4\\\\Formula\ for\ absolute\ value\\\\
|a|=a,\ for\ a \geq 0\\ or\\|a|=-a,\ for\ a \ \ -4x \geq -6\ \ -->\ \ \ x \leq \frac{3}{2}\\\\
6(6-4x)=8x+4\\
36-24x=8x+4\ \ |subtract\ 4\\
32-24x=8x\ \ | add\ 24x\\
32=32x\ \ | divide\ by\ 32\\
x=1\ \ \ and\ 1 \leq \frac{3}{2}\\\\
II\\
for\ 6-4x \ \ -4x < -6\ \ -->\ \ \ x > \frac{3}{2}\\\\
6(-6+4x)=8x+4\\
-36+24x=8x+4\ \ | subtract4\\
-40+24x=8x\ \ \ | subtract\ 24x\\
-40=-16x\ \ | divide\ by\ -16$ $x=2,5\ \ and\ 2,5>\frac{3}{2}\\\\Solutions:\\
x\in \{1;2,5\}$

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If pentagon OPQRS is dilated by a scale factor of seven over four from the origin to create O'P'Q'R'S', what is the ordered pair

GrogVix [38]

Answer:

The order pair of point Q' is (-21/4 , -7/2)

Step-by-step explanation:

* Lets explain the dilation

- A dilation is a transformation that changes the size of a figure.

- The figure can become larger or smaller, but the shape of the

figure does not change.

- The scale factor, measures how much the image will be larger

or smaller

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

- The center of dilation is a fixed point in the plane about which all

points are expanded or contracted

* Lets solve the problem

- The pentagon OPQRS is dilated by a scale factor 7/4

- The center of dilation is the origin

- The image of the pentagon after the dilation is O'P'Q'R'S'

∵ The coordinates of the vertices of the pentagon OPQRS are

O (-1 , 2) , P (-5 , 3) , Q (-3 , -2) , R (2 , 1) , S (2 , 5)

- To find the image of each point after the dilation multiply each

coordinates of the points by the scale factor of dilation

∵ The scale factor is 7/4

∵ The coordinates of point Q are (-3 , -2)

∴ The image of point Q after dilation is (-3 × 7/4 , -2 × 7/4)

∴ The image of point Q after dilation is (-21/4 , -7/2)

∵ Q' is the image of Q

∴ Q' = (-21/4 , -7/2)

* The order pair of point Q' is (-21/4 , -7/2)

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4 years ago

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3 years ago

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For a package to qualify for a certain postage rate, the sum of its length and girth cannot exceed 85 inches. If the girth is 63

tester [92]

Answer:

Length of package can be = 22 inches

Step-by-step explanation:

Given:

For a package to qualify for a certain postage rate, the sum of its length and girth cannot exceed 85 inches

To find length of package when girth of package is = 63 inches

Solution:

Let length of package be = $l$ inches

Let girth length of package be = $g$ inches

Sum of length and girth of package = $(l+g)$ inches

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Thus, the inequality representing the situation can be given as:

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