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3 years ago

ASAP Please.What is the perimeter of triangle ABC? Round each step to the nearest tenth. Enter your answer in the box.

Mathematics

1 answer:

Digiron [165]3 years ago

5 0

Answer:

The perimeter of triangle ABC is 15.8 units

Step-by-step explanation:

we know that

The perimeter of a triangle is equal to the sum of its three length sides

$P=AB+BC+AC$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have the coordinates

$A(5,-1),B(-1,1),C(0,-3)$

step 1

Find the distance AB

we have

$A(5,-1),B(-1,1)$

substitute in the formula

$d=\sqrt{(1+1)^{2}+(-1-5)^{2}}$

$d=\sqrt{(2)^{2}+(-6)^{2}}$

$d_A_B=\sqrt{40}\ units$

$d_A_B=6.3\ units$

step 2

Find the distance BC

we have

$B(-1,1),C(0,-3)$

substitute in the formula

$d=\sqrt{(-3-1)^{2}+(0+1)^{2}}$

$d=\sqrt{(-4)^{2}+(1)^{2}}$

$d_B_C=\sqrt{17}\ units$

$d_B_C=4.1\ units$

step 3

Find the distance AC

we have

$A(5,-1),C(0,-3)$

substitute in the formula

$d=\sqrt{(-3+1)^{2}+(0-5)^{2}}$

$d=\sqrt{(-2)^{2}+(-5)^{2}}$

$d_A_C=\sqrt{29}\ units$

$d_A_C=5.4\ units$

step 4

Find the perimeter

$P=AB+BC+AC$

substitute the values

$P=6.3+4.1+5.4$

$P=15.8\ units$

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lesantik [10]

Answer:

$\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}$

Step-by-step explanation:

We are given the equation:

$4\sin^2(x)+6\sin(x)+2=0$

First, we can divide everything by 2:

$2\sin^2(x)+3\sin(x)+1=0$

Notice that we have an equation in quadratic form. Namely, if we make a substitution where u = sin(x), we acquire:

$2u^2+3u+1=0$

Solve for u. Factor:

$(2u+1)(u+1)=0$

Zero Product Property:

$2u+1=0\text{ or } u+1=0$

Solving for both cases:

$\displaystyle u=-\frac{1}{2}\text{ or } u=-1$

And by substitution:

$\displaystyle \sin(x)=-\frac{1}{2}\text{ or } \sin(x)=-1$

For the first case, recall that sin(x) is -1/2 for every 7π/6 and every 11π/6. Hence, for the first case, our solutions are:

$\displaystyle x=\frac{7\pi}{6}+2n\pi \text{ and } x=\frac{11\pi}{6}+2n\pi, n\in\mathbb{Z}$

Where n is an integer.

For the second case, sin(x) is -1 for every 3π/2. Thus:

$\displaystyle x=\frac{3\pi}{2}+2n\pi$

All together, our solutions are:

$\displaystyle x=\Big\{\frac{7\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi, \frac{11\pi}{6}+2n\pi}\Big\}, n\in\mathbb{Z}$

4 0

3 years ago

7. For the equation y = -1/4X 8 state<br> the slope and the y-intercept.

SVETLANKA909090 [29]

Answer:

slope = -1/4

y-intercept = 8

Step-by-step explanation:

In the equation y = -1/4 x + 8

The slope is -1/4 and the y-intercept is 8.

Linear equations are written like "y=mx + b"

"m" stands for slope.

"b" stands for y-intercept.

8 0

3 years ago

In a capture-recapture study, 97 grizzly bears were tagged and released back into the wild. A month later, 200 bears were captur

3241004551 [841]

Answer:

539

Step-by-step explanation:

Let the total population of grizzly bears=x

In the first capture, 97 were tagged.

Therefore, ratio of the total population to the tagged=x:97

A month later, when 200 bears were captured, 36 were tagged.

Ratio of the sample to the tagged=200:36

Since a sample is representative of the population, the ratios are the same. We therefore have:

x:97=200:36

$\dfrac{x}{97} =\dfrac{200}{36}\\ $Cross multiply\\36x=200 X 97\\x=200 X 97 \div 36\\x=538.9 \approx 539$

There are about 539 grizzly bears in the population

7 0

3 years ago

__x4=12<br> 12÷4 =__ <br> The Number in the blanks represents :

Rama09 [41]

The number in the blanks is 3

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3 years ago

The manager of a fast-food restaurant determines that the average time that her customers wait for service is 3.5 minutes.The ma

Lana71 [14]

Answer:

The advertisement should use 16 minutes.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

The manager of a fast-food restaurant determines that the average time that her customers wait for service is 3.5 minutes.

This means that $m = 3.5, \mu = \frac{1}{3.5} = 0.2857$

What number of minutes should the advertisement use?

The values of x for which:

$P(X > x) = 0.01$

$e^{-\mu x} = 0.01$

$e^{-0.2857x} = 0.01$

$\ln{e^{-0.2857x}} = \ln{0.01}$

$-0.2857x = \ln{0.01}$

$x = -\frac{\ln{0.01}}{0.2857}$

$x = 16.12$

Rounding to the nearest number, the advertisement should use 16 minutes.

5 0

3 years ago