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3 years ago

Complete the equation so that it has infinitely many solutions. 8x - 14 = 8x -

Mathematics

2 answers:

kati45 [8]3 years ago

6 0

Answer:

8x-14=8x-14

Step-by-step explanation:

So if both the equations are the same, that means that any value of x put in the equation will equal itself, so that means that there are infinite solutions to the equation

If you try to solve this equation, this happens

8x-14=8x-14

add 14 to both sides

8x=8x

divide by 8 both sides

x=x

This means that there are infinite solutions because any number could be x and it would still work

omeli [17]3 years ago

6 0

Take fourteen and put it on the other side so it’s 8x-14=8x-14 it’s the same on both side so it’s infinitely or many solutions.

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Answer:

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Step-by-step explanation:

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3 years ago

A car travels 42 miles for every 2 gallons of gasoline. What is the unit rate?

svetoff [14.1K]

Answer:

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Step-by-step explanation:

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2 years ago

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pav-90 [236]

Answer:

Step-by-step explanation:

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2 years ago

Christina wants to compute the cost of tiling the floor in her bathroom. The floor measures 7 feet 6 inches by 8 feet 10 inches.

ArbitrLikvidat [17]

Answer:

Two boxes will cost $\$35.95\cdot 2=\$71.9.$ The cost of one tile is approximately $\dfrac{\$71.9}{67}\approx \$1.08.$

Step-by-step explanation:

Note that 1 ft = 12 in, then

$7\ ft\ 6\ in=7\cdot 12+6\ in =90\ in,\\ \\8\ ft\ 10\ in=8\cdot 12+10\ in=106\ in.$

The area of the floor is

$90\cdot 106=9540\ in^2.$

Now

$1\ ft^2=144\ in^2,$

then

144 sq. in - 1 tile,

9540 sq. in - x tiles.

Mathematically,

$\dfrac{144}{9540}=\dfrac{1}{x},\\ \\x=\dfrac{9540}{144}=66.25$

tiles is needed to cover the floor (67 full tiles).

Each box of tiles contains 45 tiles, so Cristina has to buy 2 boxes. These two boxes will cost $\$35.95\cdot 2=\$71.9.$ The cost of one tile is approximately $\dfrac{\$71.9}{67}\approx \$1.08.$

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2 years ago

Find the logarithmic function y = logbx that passes through the points

katovenus [111]

$b\in(0,\ 1)\ \cup\ (1,\ \infty)\\x > 0\\y\in\mathbb{R}\\--------------------------\\\\y=\log_bx\\\\For\ (1,\ 0)\to x=1,\ y=0.\ Substitute:\\\\\log_b1=0\to b^0=1\to b\in(0,\ 1)\ \cup\ (1,\ \infty)\\\\For\ (116,\ 2)\to x=116,\ y=2.\ Substitute:\\\\\log_b116=2\to b^2=116\to b=\sqrt{116}\\\to b=\sqrt{4\cdot29}\to b=\sqrt4\cdot\sqrt{29}\to b=2\sqrt{29}\\\\For\ (4,\ -1)\to x=4,\ y=-1.\ Substitute:\\\\\log_b4=-1\to b^{-1}=4\to b=\dfrac{1}{4}$

Different values of b.

<h3>Answer: There is no logarithmic function whose graph goes through given points.</h3><h3 />

Maybe the second point is $\left(\dfrac{1}{16},\ 2\right)$

Substitute:

$\log_b\dfrac{1}{16}=2\to b^2=\dfrac{1}{16}\to b=\sqrt{\dfrac{1}{16}}\to b=\dfrac{1}{4}$

<h3>Then we have the answer:</h3>

$\boxed{y=\log_{\frac{1}{4}}x}$

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3 years ago