What is the slope of the line that passes through (1,-4) and (-4,-6)

Solve the oblique triangle where side a has length 10 cm, side c has length 12 cm, and angle beta has measure thirty degrees. Ro

Ugo [173]

Answer:

$Side\ B = 6.0$

$\alpha = 56.3$

$\theta = 93.7$

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with $\alpha, \beta, \theta$

[See Attachment for Triangle]

$A = 10cm$

$C = 12cm$

$\beta = 30$

What the question is to calculate the third length (Side B) and the other 2 angles ( $\alpha\ and\ \theta$ )

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

$B^2 = A^2 + C^2 - 2ABCos\beta$

Substitute: $A = 10$ , $C =12$ ; $\beta = 30$

$B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30$

$B^2 = 100 + 144 - 240*0.86602540378$

$B^2 = 100 + 144 - 207.846096907$

$B^2 = 36.153903093$

Take Square root of both sides

$\sqrt{B^2} = \sqrt{36.153903093}$

$B = \sqrt{36.153903093}$

$B = 6.0128115797$

$B = 6.0$ <em>(Approximated)</em>

Calculating Angle $\alpha$

$A^2 = B^2 + C^2 - 2BCCos\alpha$

Substitute: $A = 10$ , $C =12$ ; $B = 6$

$10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha$

$100 = 36 + 144 - 144 *Cos\alpha$

$100 = 180 - 144 *Cos\alpha$

Subtract 180 from both sides

$100 - 180 = 180 - 180 - 144 *Cos\alpha$

$-80 = - 144 *Cos\alpha$

Divide both sides by -144

$\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}$

$\frac{-80}{-144} = Cos\alpha$

$0.5555556 = Cos\alpha$

Take arccos of both sides

$Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)$

$Cos^{-1}(0.5555556) = \alpha$

$56.25098078 = \alpha$

$\alpha = 56.3$ <em>(Approximated)</em>

Calculating $\theta$

Sum of angles in a triangle = 180

Hence;

$\alpha + \beta + \theta = 180$

$30 + 56.3 + \theta = 180$

$86.3 + \theta = 180$

Make $\theta$ the subject of formula

$\theta = 180 - 86.3$

$\theta = 93.7$

5 0

2 years ago

Transformation !! Photos up above!

dlinn [17]

360 brainliest? Have a nice day

7 0

2 years ago

A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken 5 years ag

Katyanochek1 [597]

Answer:

At 5% significance level, it is statistically evident that there is nodifference in the proportion of college students who consider themselves overweight between the two poll

Step-by-step explanation:

Given that a poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken 5 years ago.

Let five years ago be group I X and as of now be group II Y

$H_0: p_x =p_y\\H_a: p_x \neq p_y$

(Two tailed test at 5% level of significance)

Group I Group II combined p

n 270 300 570

favor 120 140 260

p 0.4444 0.4667 0.4561

Std error for differene = $\sqrt{\frac{0.4561(1-0.4561)}{570} } \\=0.0209$

p difference = -0.0223

Z statistic = p diff/std error = -1.066

p value =0.2864

Since p value >0.05, we accept null hypothesis.

At 5% significance level, it is statistically evident that there is nodifference in the proportion of college students who consider themselves overweight between the two poll

7 0

2 years ago

If n is even, which represents the first consecutive even integer after n?

kow [346]

Answer: $n+2$

Step-by-step explanation:

1. By definition, an even number is that number that can be divided by two.

2. Therefore, keeping this definition on mind, if you have an even number $n$ , the next consecutive even integer after it can be obtained by adding 2.

3. Then, you can conclude the expression that represents the first consecutive even integer after $n$ is:

$n+2$

3 0

3 years ago

Read 2 more answers

The third angle in an isosceles triangle is 32 more than 2 times as large as each of the two base angles. Find the measure of ea

DIA [1.3K]

Answer: the third angle is 106 degrees.

The base angles are 37 degrees each.

Step-by-step explanation:

In an isosceles triangle, the base angles are equal.

Let x represent the measure of each of the base angles.

The third angle in an isosceles triangle is 32 more than 2 times as large as each of the two base angles. It means that the measure of the third angle would be

(2x + 32) degrees

The sum of the angles inna triangle is 180 degrees. It means that

x + x + 2x + 32 = 180

4x = 180 - 32

4x = 148

x = 37

The third angle is

2x = 32 = (2 × 37) + 32

= 74 + 32 = 106

5 0

2 years ago

What is the slope of the line that passes through (1,-4) and (-4,-6)​

What is the slope of the line that passes through (1,-4) and (-4,-6)