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3 years ago

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Which interior angles are possible for a triangle? The measures of the interior angles of a triangle are 90°, 40°, and 50°. The

measures of the interior angles of a triangle are 82°,38°, and 60°. The measures of the interior angles of a triangle are 65°, 25°, and 75°. The measures of the interior angles of a triangle are 57°, 70°, and 33°. The measures of the interior angles of a triangle are 59°, 31°, and 90

1 answer:

seropon [69]3 years ago

3 0

The sum of interior angles of a triangle is always* 180°, so the following triangles are possible:

90°, 40°, 50°
82°, 38°, 60°
59°, 31°, 90°

_____

The following are not possible triangles.

65°, 25°, 75° — add to 165° ≠ 180°
57°, 70°, 33° — add to 160° ≠ 180°

_____

* in plane Euclidean geometry. There are other topologies such that the sum of angles of a triangle differs from 180°.

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3 years ago

A devastating freeze in California's Central Valley in January 2007 wiped out approximately 75% of the state's citrus crop. It t

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The relationship between the percentage of frozen citrus crop, and the cost of box of oranges is an illustration of a linear function.

<em>The linear equation of the function is: </em> $g(P) = 22.9P+7$ <em>.</em>
<em>The inverse function is: </em> $g^{-1}(c) = \frac{1}{22.9}(c - 7)$ <em> .</em>
<em>A practical domain is from 0% to 100%</em>
<em>A practical range is from 7 to 29.9 </em>

<u>A. Input quantity</u>

The input quantity is the percentage of frozen citrus crop

<u />

<u>B. Output quantity </u>

The output quantity is the cost of box of oranges

<u>C. The linear function</u>

We have:

$(P_1,c_1) = (20\%,11.58)\\(P_2,c_2) = (80\%,25.32)$

<em>Calculate the slope of the function</em>

$m = \frac{c_2 - c_1}{P_2 - P_1}$

$m = \frac{25.32 - 11.58}{80\%-20\%}$

$m = \frac{13.74}{60\%}$

$m = 22.9$

<em>The linear equation is calculated as follows:</em>

$c -c_1 = m(P-P_1)$

$c -11.58= 22.9(P-20\%)$

$c-11.58 = 22.9P-4.58$

<u>D. Rewrite as y = mx + b</u>

We have:

$c-11.58 = 22.9P-4.58$

Collect like terms

$c = 22.9P - 4.58 + 11.58$

$c = 22.9P+7$

<em>The function is:</em>

$g(P) = 22.9P+7$

<u>E. A practical domain</u>

The domain is the possible values of P. Because P is a percentage, its possible values are 0% to 100%.

The domain of the function is: $[0\%,100\%]$

<u>F. A practical range</u>

When P = 0%

$c = 22.9 \times 0\% + 7 = 7$

When P = 100%

$c = 22.9 \times 100\% + 7 = 29.9$

Hence, the range of the function is: $[7,29.9]$

G. The meaning of $g^{-1}(12)$

The inverse function of g(P) is $g^{-1}(P)$

So:

$g^{-1}(12)$ is the percentage of frozen citrus crop, when the cost is $12.

<u>H. The inverse formula</u>

We have:

$c = 22.9P+7$

Subtract 7 from both sides

$c - 7 = 22.9P$

Make P the subject

$P = \frac{1}{22.9}(c - 7)$

So, the inverse formula is:

$g^{-1}(c) = \frac{1}{22.9}(c - 7)$

Substitute 12 for c

$g^{-1}(12) = \frac{1}{22.9}(12 - 7)$

$g^{-1}(12) = \frac{1}{22.9} \times 5$

$g^{-1}(12) = 22\%$

Read more about linear equations at:

brainly.com/question/19770987

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3 years ago

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Romashka-Z-Leto [24]

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Step-by-step explanation:

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$\dfrac{dV}{dt}=5\:\text{cm}^3\text{/min}$

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Solving for $\frac{dr}{dt}$ , we get

$\dfrac{dr}{dt} = \left(\dfrac{1}{\pi D^2}\right)\dfrac{dV}{dt} = \dfrac{1}{\pi(20\:\text{cm}^2)}(5\:\text{cm}^3\text{/min})$

$\:\:\:\:\:\:\:= 0.08\:\text{cm/min}$

3 0

3 years ago