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3 years ago

13

10 the sides of a triangle are 17ft., 19ft., and 15 ft. find the measure of the angle opposite the longest side. round your answ

er to the nearest degree

1 answer:

nalin [4]3 years ago

4 0

The law of cosines is used for this purpose. It tells you
c² = a² + b² - 2ab×cos(C)
Solving for the angle C gives
C = arccos((a² + b² - c²)/(2ab))
C = arccos(( 17² + 15² - 19²)/(2×17×15))
C = arccos(153/510)
C ≈ 72.5424°

The measure of the angle opposite the longest side is about 73°.

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5 0

3 years ago

The line $y = 3$ intersects the graph of $y = 4x^2 + x - 1$ at the points $A$ and $B$. The distance between $A$ and $B$ can be w

raketka [301]

Answer:

61

Step-by-step explanation:

Let's find the points $A$ and $B$ .

We know that the $y$ -coordinates of both are $3$ .

So let's first solve:

$3=4x^2+x-1$

Subtract 3 on both sides:

$0=4x^2+x-1-3$

Simplify:

$0=4x^2+x-4$

I'm going to use the quadratic formula, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ , to solve.

We must first compare to the quadratic equation, $ax^2+bx+c=0$ .

$a=4$

$b=1$

$c=-4$

$\frac{-1 \pm \sqrt{1^2-4(4)(-4)}}{2(4)}$

$\frac{-1 \pm \sqrt{1+64}}{8}$

$\frac{-1 \pm \sqrt{65}}{8}$

Since the distance between the points $A$ and $B$ is horizontal. We know this because they share the same $y-coordinate$ .This means we just need to find the positive difference between the $x$ -values we found for the points of $A$ and $B$ .

So that is, the distance between $A$ and $B$ is:

$\frac{-1+\sqrt{65}}{8}-\frac{-1-\sqrt{65}}{8}$

$\frac{-1+\sqrt{65}+1+\sqrt{65}}{8}$

$\frac{2\sqrt{65}}{8}$

$\frac{\sqrt{65}}{4}$

If we compare this to $\frac{\sqrt{m}}{n}$ , we should see that:

$m=65 \text{ and } n=4$ .

So $m-n=65-4=61$ .

5 0

3 years ago

Read 2 more answers

A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 5 grams and the amo

krok68 [10]

Answer:

The jeweler made 9 necklaces.

The jeweler made 8 bracelets.

Step-by-step explanation:

x = number of bracelets

y = number of necklaces

17 = x + y

238 = 5x + 22y

Make one of the coefficients, x, the same.

17 = x + y

Multiply this equation by 5.

85 = 5x + 5y

Subtract the equations to get rid of x.

(238 = 5x + 22y) - (85 = 5x + 5y)

(5x - 5x) + (22y - 5y) = 238 - 85

22y - 5y = 238 - 85

17y = 153

y = 153/17 = 9

The jeweler made 9 necklaces. Substitute this back into one of the equations to find x.

17 = x + y

17 = x + 9

17 - 9 = x

x = 8

238 = 5x + 22y

238 = 5x + 22(9)

238 = 5x + 198

238 - 198 = 5x

40 = 5x

x = 40/5

x = 8

The jeweler made 8 bracelets.

8 0

3 years ago

The pair of linear equations 2x-3y = 14 and 3x - 2y = 4 has solution(s).<br><br>answer plz....

Lesechka [4]

Answer:

2x -3y =1 and 3x-2y= 4 has

Step-by-step explanation:

The pair of linear equations 2x-3y=1 and 3x-2y=4 has one unique solution. , then it has a unique solution other wise not. Since , , it means the pair of linear equations has only one unique solution. Hence, the pair of linear equations 2x-3y=1 and 3x-2y=4 has only one unique solution.

a1/a2= 2/3

b1/b2= 3/-2 (-) cancle so it remains

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a1/a2 = b1/b2 not equal to c1/c2 as no solution

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3 years ago

Ivan rented a truck for the day. There is a base fee of $17.95, and there was an additional charge of 91 cents for each mile dri

lozanna [386]

Answer:

293 miles

Step-by-step explanation:

284.58-17.95=266.63

266.63/0.91=293

293 miles

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2 years ago