Multiply (3x-7)(2x^2-8x+3)

An equation of a circle is given as (x + 6)2 + (y − 7)2 = 81. Find the center and radius of the circle.

choli [55]

The equation of a circle is written as (x – h)^2 + (y – k)^2 = r^2

h and k are the center point and r is the radius.

In the given equation h = -6 and k = 7 and r would be the square root of 81, which is 9.

Center (-6,7)

Radius = 9

8 0

3 years ago

A pharmacy claims that the average medication costs $32 but it could differ as much as $8. Write and solve an absolute value ine

gogolik [260]

It looks like you're supposed to pick a combination of two answers:
an absolute-value inequality, and
a sentence describing the meaning of that inequality.

We've got two choices for each, and therefore four possible combinations of choices.

First, let's tackle the sentence description. We're told that
"it [the cost] could differ [from the average of $32] as much as $8."
That sets a maximum value for the difference; it's UP TO $8.
If the cost is less than average, it could be as little as
$32 - $8 = $24
and if the cost is more than average, it could be as much as
$32 + $8 = $40.
So the medication costs range from $24 to $40, and we want an answer that states that.

Now for the inequalities:
|x - 32| describes the SIZE of the difference. Using the absolute-value function means we don't distinguish between
x - 32
and
32 - x
as far as our interests are concerned; we eliminate the sign from the subtraction and just look at the size of the difference.

But in the case we're looking at, we've got a MAXIMUM value for the difference; it can't be more than 8. The inequality
|x - 32| ≥ 8
says the difference is 8 or MORE, so we don't want that. Instead, we want
|x - 32| ≤ 8
which says the difference is anywhere from 0 to 8.

Combining these conclusions, we see we're looking for this answer:
|x - 32| ≤ 8; The medication costs range from $24 to $40
which is the third one listed.

4 0

4 years ago

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ᗩ 10 OᑌᑎᑕE ᗷᗩG Oᖴ ᑭOᑭᑕOᖇᑎ ᑕOᔕT $2.45 ᗩT TᕼE ᗰOᐯIEᔕ. ᗯᕼᗩT Iᔕ TᕼE ᑕOᔕT Oᖴ 4 ᗷᗩGᔕ

Tems11 [23]

the cost of 4 bags of popcorn is $9.80 ( 2.45 x 4 )

the total weight of the popcorn would be 40 ounces ( 4 x 10 )

3 0

3 years ago

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How do I solve this using the Pythagorean theorem and leaving it in radical form ?

scoray [572]

If the legs of a right triangle are a and b and the hypotnuse is c then
a²+b²=c²

so we are given
the legs are x and √7
and the hypotnuse is √19
so

x²+(√7)²=(√19)²
x²+7=19
minus 7 both sides
x²=12
sqrt both sides
x=√12
x=√(4*3)
x=(√4)(√3)
x=2√3

7 0

4 years ago

] Monica Geller, head chef at Allesandro's and is looking to update the commercial equipment in her kitchen and bar that will al

liubo4ka [24]

Answer:

The maximum amount that should be spent on the upgrade is $38,298,000.

Step-by-step explanation:

Let the initial purchase be x.

The ROI = 15% of x = 0.15x

At the end of 4 years, salvage value = 10% of x = 0.1x

Current income per day = $16 × 230 = $3680

Expected income per day = $21 × 245 = $5145

Increase in income per day = $5145 - $3680 = $1465

For 4 years (assuming a year is 365 days),

Increase in income = $1465 × 365 × 4 = $2138900

Maintenance and utility cost for 4 years = 4 × $56000 = $224000

At the end of 4 years,

ROI = $2138900 + salvage value = $2138900 + 0.1x - $224000

0.15x = $1914900 + 0.1x

0.05x = $1914900

x = $38298000

5 0

3 years ago

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