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3 years ago

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The smallest angle of a triangle is measure x degrees. The second angle is 45 degrees more than the smallest angle. The third an

gle is three times larger as the smallest angle. Write algebraic expression to express measures of the second and third angles of the triangle.

1 answer:

Masja [62]3 years ago

6 0

Answer:

Step-by-step explanation:

The sum of the angles is 180°

x+(x+45)+(3x) = 180

5x = 135

First angle = x = 27°

Second angle = x+45 = 72°

Third angle = 3x = 81°

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Answer:

13

Step-by-step explanation:

Put n as 4

$3(4)+1=12+1=13$

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Find S12 for geometric series: (-7.5) + 15 + (-30) + ...

kolezko [41]

Answer:

S12 for geometric series: (-7.5) + 15 + (-30) + ... would be: 10237.5

Step-by-step explanation:

Given the sequence to find the sum up-to 12 terms

$(-7.5) + 15 + (-30) + ...$

As we know that

A geometric sequence has a constant ratio 'r' and is defined by

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$\frac{15}{\left(-7.5\right)}=-2,\:\quad \frac{\left(-30\right)}{15}=-2$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=-2$

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$a_1=\left(-7.5\right)$

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$a_n=\left(-7.5\right)\left(-2\right)^{n-1}$

$a_n=-\left(-2\right)^{n-1}\cdot \:7.5$

$\mathrm{Geometric\:sequence\:sum\:formula:}$

$a_1\frac{1-r^n}{1-r}$

$\mathrm{Plug\:in\:the\:values:}$

$n=12,\:\spacea_1=\left(-7.5\right),\:\spacer=-2$

$=\left(-7.5\right)\frac{1-\left(-2\right)^{12}}{1-\left(-2\right)}$

$=-7.5\cdot \frac{1-\left(-2\right)^{12}}{1+2}$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=-\frac{-30712.5}{1+2}$ ∵ $\left(1-\left(-2\right)^{12}\right)\cdot \:7.5=-30712.5$

$=-\frac{-30712.5}{3}$

$=\frac{30712.5}{3}$

$=10237.5$

Thus, S12 for geometric series: (-7.5) + 15 + (-30) + ... would be: 10237.5

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4 years ago

280.5-240.9 how do I solve this subtraction

SpyIntel [72]

Answer:

39.6 is the answer.

Step-by-step explanation:

280.5 - 240.9

Subtract :

280.5 - 240.9

= 39.6

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4 years ago

p is inversely proportional to 3q-1. The difference in the values of p when q = 1 and q=2 respectively is 3. Find the value of p

Vsevolod [243]

Step-by-step explanation:

3q - 1 = 3(1) - 1 = 2

3q -1 = 3(2)- 1= 5

10/p = 2 10/p = 5

p= 5 p= 2 (5-2=3, so 10/p is correct)

q=5, 3(5) -1 = 14

10/p = 14

p = 0.71??

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