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3 years ago

Find all solutions in the integers of the equation ||x−3|−5| = 10, where the bars indicate absolute value.

Mathematics

1 answer:

Helga [31]3 years ago

3 0

Answer:

x = 18 or x = -12.

Step-by-step explanation:

||x-3|-5| = 10 only if |x-3|-5 = 10 or |x-3|-5 = -10, i.e., if |x-3|=15 or |x-3|=-5; but |x-3| cannot be equal to -5, because |x-3| should be a non-negative value. Therefore, the first equation is true only if |x-3|=15. |x-3| = 15 only if x-3 = 15 or x-3 = -15, i.e., x = 18 or x = -12. We can verify this in the following way: ||18-3|-5|=||15|-5|=|10|=10 and ||-12-3|-5|=||-15|-5|=|15-5|=|10|=10. This verify that our solution is correct.

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The top and bottom ends of a windshield wiper blade are R = 24 in. and r = 14 in., respectively, from the pivot point. While in

Orlov [11]

Answer:

Area swept by the blade = 448 $in^{2}$

Step-by-step explanation:

The arc the wiper wipes is for 135 degrees angle.

So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.

Then subtract the area of sector with 14 inches from area of sector with radius as 24 inches.

So, area of sector with r=24 in = $\frac{135}{360} *\pi *24^{2}$

Simplify it,

=216 $\pi$

Now, let's find area of sector with radius 14 inches

Area of sector with r=14 in = $\frac{135}{360} *\pi *14^{2}$

Simplify it

=73.5 $\pi$

So, area swept by the blade = 216 $\pi$ -73.5 $\pi$

Simplify it and use pi as 3.14.....

Area of swept =678.584 - 230.907

=447.6769

Round to nearest whole number

So, area swept by the blade = 448 $in^{2}$

3 0

3 years ago

What is the difference quotient of the function g(x) = 4^x

lidiya [134]

Answer:

First choice

Step-by-step explanation:

The difference quotient in general is $\frac{g(x+h)-g(x)}{h}$ . To get an expression for $g(x+h)$ , replace x with x + h.

For this question,

$\frac{4^{x+h}-4^x}{h}=\frac{4^x\cdot4^h-4^x}{h}$

Factor $4^x$ out of the numerator.

$\frac{4^x(4^h-1)}{h}$

8 0

3 years ago

The jars of peanut butter that I buy cost $7.20 each and normally contain 500 grams. At present, however, each jar contains an e

Alex_Xolod [135]

Answer:

$0.54

Step-by-step explanation:

Given:

The jars of peanut butter that I buy cost $7.20 each and normally contain 500 grams.

At present, however, each jar contains an extra 20% free.

And additionally, the supermarket has a "buy 3 jars get another one free''.

Question asked:

By how much is the cost per 100 grams of peanut butter less than it normally is if I take full advantage of the supermarket's offer today?

Solution:

Cost of a jars of peanut = $7.20

Normally, weight of peanut butter in one packet = 500 gram

At supermarket offer, each jar contains an extra 20% free, means a packet of peanut butter contains = 500 + 20% of 500 $=500+500\times \frac{20}{100} =500+100=600\ gram$

And extra benefit = buy 3 jars get another one free, means we will get 4 jars by just giving price of only 3 jars.

That means, total weight of peanut butter you are getting by giving 3 packet's price = Each jar weigh $\times$ number of jars

= 600 $\times$ 4 = 2400 gram

Cost of each packet will be same as previously as during the offer; $7.20

Cost of 3 packet's peanut (2400 gram) = $7.20\times3=\$21.6$

Now, we will calculate cost per 100 grams of peanut butter :

During offer:

Cost of 2400 grams of peanut butter = $21.6

Cost of 1 gram of peanut butter = $\frac{21.6}{2400}$

Cost of 100 gram of peanut butter = $\frac{21.6}{2400}\times100=\frac{2160}{2400} =\$0.9$

Normal day:

Cost of 500 grams of peanut butter = $7.20

Cost of 1 gram of peanut butter = $\frac{7.20}{500}$

Cost of 100 gram of peanut butter = $\frac{7.20}{500}\times100=\frac{720}{500} =\$1.44$

We found that cost of 100 gram of peanut butter in normal day is $1.44 while cost of 100 gram of peanut butter during offer is $0.9 means cost per 100 gram during offer is ($1.44 - $0.9 = )$0.54 less than cost during normal day.

Conclusion:

Therefore, cost per 100 grams of peanut butter is $0.54 less than it is normally if you take full advantage of the supermarket's offer today.

7 0

3 years ago

What is the mean of the numbers?

velikii [3]

Answer:

1.6666666666666...

Step-by-step explanation:

10/6=5/3=1.6666666...

6 0

3 years ago

Answer this. I will giveBRAINLIEST

sweet [91]

Answer:

Multiply both sides by 3, then subtract 6 from both sides

Step-by-step explanation:

d + 6 / 3 = 6 (multiply both sides by 3)

d + 6 = 18 (subtract 6 from both sides)

d = 12

6 0

3 years ago

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