Which statement regarding the interior and exterior angles of a triangle is true?

Mathematics

1 answer:

Elena L [17]3 years ago

3 0

Sum of opp. interior angles = ext. angle
sum of all interior angle in a trangle = 180 deg

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What is the difference of the expression below? (12f- 8g+ 3h) - (4f - g+ 5h)

kirill [66]

The answer to $(12f- 8g+ 3h) - (4f - g+ 5h)$ is $8f-7g-2h$

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3 years ago

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Write four consecutive numbers with a mean and medium of 14.5

Ivanshal [37]

Answer:

13, 14, 15, 16

Step-by-step explanation:

Call the first number n. Then the next three consecutive numbers (assuming integers) are n + 1, n + 2, n + 3.

The mean is the total of the numbers divided by how many there are.

$\frac{n+(n+1)+(n+2)+(n+3)}{4}=14.5$

Simplify and multiply by 4.

$4n+6=58\\4n=52\\n=13$

The first number is 13.

The median is 14.5, halfway between the "middle" numbers 14 and 15. This is just a check; no additional equation is necessary.

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3 years ago

A circular oil slick is expanding at a rate of 3m/min. How fast is the area of the oil slick changing when the diameter is 48 me

olga55 [171]

Answer:

$48\pi \:m/min$

Step-by-step explanation:

Diameter = 48 m

Therefore radius r = 48/2 = 24 m

$Area \: of \: circular \: oil \: slick \\ A = \pi {r}^{2} \\ differentiating \: w \: r \: to \: t \: on \: \\ both \: sides \\ \\ \frac{dA}{dt} = \frac{d}{dt} (\pi {r}^{2} )\\ \\ \frac{dA}{dt} =\pi \frac{d}{dt} {r}^{2} \\ \\ \frac{dA}{dt} =\pi \times 2{r}\\ \\ \frac{dA}{dt} =2\pi {r} \\ \\ \bigg(\frac{dA}{dt} \bigg)_{r=24} =2\pi \times {24} \\ \\ \bigg(\frac{dA}{dt} \bigg)_{r=24} =48\pi \: m \: per \: min$