Mathematics, 12.07.2019 06:00, lisnel

The sum of the measures of the interior angles of a triangle is 180 °. the measure of the 1st angle is 15 ° less than the 2nd. the measure of the 3rd angle is 45 ° more than half of the second. find the measure of e/ interior angle of the triangle.

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answered: mrsqueenbabe516

1st angle (x): x - 15

2nd angle (y): x

3rd angle (z): $\frac{1}{2}$ x + 45

The sum of the interior angles of a triangle equals 180°

1st angle + 2nd angle + 3rd angle = 180

x - 15 + x + $\frac{1}{2}$ x + 45 = 180

2x + 30 + $\frac{1}{2}$ x = 180 (added like terms on left side)

2x + $\frac{1}{2}$ x = 150 (subtracted 30 from both sides)

4x + x = 300 (multiplied all terms by 2 to eliminate the denominator)

5x = 300 (added like terms on left side)

x = 60 (divided by 5 on both sides)

1st angle (x): x - 15 → (60) - 15 = 45

3rd angle (z): $\frac{1}{2}$ x + 45 → $\frac{1}{2}$ (60) + 45 → 30 + 45 = 75

45°, 60°, 75°

answered: Guest

Hello!

the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

$\frac{a^{m} }{a^{n} }=a^{m-n}$

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

$\frac{3^{4} }{3^{1}}$

then, calculating we have:

$\frac{3^{4} }{3^{1}}=3^{4-1}=3^{3}$

hence, the answer is:

$\frac{3^{4} }{3^{1}}=3^{3}$

have a nice day!

answered: Guest

1. sometimes

2. never

3 .08c = 7.50+.05c 250 pages

step-by-step explanation:

1. sometimes

the theoretical probability of rolling a 1 is 1/6. perhaps you got really lucky and never rolled a 1 in those 60 times. your experimental probability is 0. or perhaps you rolled a 1 20 times. your experimental probability is 20/60 is 1/3. it really just depends on how you rolled in that experiment.

2. never

the probability of the event occurring is 1. that is being 100 % sure it will happen. that is the maximum amount of confidence we have.

3. no customer card cost: .08 times number of pages

customer card cost: 7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03