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3 years ago

G(n) = 10n - 10 g(x) = 90 x =?

Mathematics

2 answers:

katen-ka-za [31]3 years ago

7 0

<h2>♪Answer : </h2>

»g(n) = 10n - 10

»g(x) = 90

n = x

»g(x) = 10x - 10

»90 = 10x - 10

»90 + 10 = 10x

»10x = 100

»x = 100/10

»x = 10✅

dybincka [34]3 years ago

4 0

Answer:

x = 10

Step-by-step explanation:

g(n) = 10n - 10

g(x) = 90

Equate to find value of x.

10x - 10 = 90

10x = 100

x = 10

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In triangle ABC, AB = 7, AC = 15, and the length of median AM is 10. Find the area of triangle ABC.

steposvetlana [31]

Answer:

Step-by-step explanation:

We can make use of Heron's formula for the area of the triangle. Let x represent half the length of BC:

MB = MC = x

Then the perimeter of ΔAMB is ...

p1 = 7 + 10 + x

and the value used in Heron's formula, the semi-perimeter is ...

s1 = (17+x)/2

The square of the area of ΔAMB is then ...

A1² = s1·(s1 -x)·(s1 -10)·(s1 -7) = (-1/16)(x^4 -298x^2 +2601)

Similarly, the square of the area of ΔABC is ...

A2² = s2·(s2 -x)·(s2 -10)·(s2 -15) = (-1/16)(x^4 -650x^2 +15625)

We want these two triangle areas to be the same, so we can solve for the value of x that makes it so.

A1² - A2² = 0 = (-1/16)((x^4 -298x^2 +2601) -(x^4 -650x^2 +15625))

352x^2 -13024 = 0 . . . . multiply by -16 and collect terms

x^2 -37 = 0 . . . . . . . . . . . divide by 352

x^2 = 37 . . . . . this is as far as we need to take it in order to find the area.

Substituting the value for x^2 into the expression for A1², we get ...

A1² = (-1/16)((x^2 -298)x^2 +2601) = (-1/16)((37 -298)37 +2601) = 441

So, the area of ΔAMB is √441 = 21 square units. The area of ΔAMC is the same, so the area of ΔABC is ...

area(ΔABC) = 2×area(ΔAMB) = 2×21 units²

area(ΔABC) = 42 units²

_____

<em>Addendum to the answer</em>

After thinking about this a little more, I realized the area is that of half a parallelogram with AB and AC as two sides and AM as half the diagonal. In other words, the area is the same as that of a triangle with sides 7, 15, and 2×10=20. A single straightforward application of Heron's formula gives the area as ...

A = √(21(21-7)(21-15)(21-20)) = √(21(14)(6)) = 42

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3 years ago

A pillow that usually costs $18 is marked down 25%. Which expressions can be used to find the new price of the pillow? CHECK ALL

NARA [144]

The expression 18 - 0.25(18) can be used to find the new price of pillow.

Step-by-step explanation:

Given,

Cost of pillow = $18

Mark down = 25% = $\frac{25}{100} = 0.25$

To find the amount of mark down, we will multiply it with cost of pillow;

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The new price of pillow can be determined by subtracting amount of mark down from the original cost of pillow.

New price = Original Cost of pillow - Amount of mark down

New price = 18 - 0.25(18)

The expression 18 - 0.25(18) can be used to find the new price of pillow.

Keywords: percentage, subtraction

Learn more about percentages at:

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G(n) = 10n - 10 g(x) = 90 x =? ​

G(n) = 10n - 10 g(x) = 90 x =?