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2 years ago

Find the slope of the line that passes through (10, 3) and (7, 11).

Mathematics

1 answer:

Vadim26 [7]2 years ago

8 0

Answer:

Slope of the line is $-\frac{8}{3}$ .

Step-by-step explanation:

Given points are:

(10, 3) and (7, 11)

Here,

x1 = 10 and y1 = 3

x2 = 7 and y2 = 11

Slope of a line is given by

$m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{11-3}{7-10}\\\\m = \frac{8}{-3}$

Therefore,

Slope of the line is $-\frac{8}{3}$ .

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Consider a triangle ABC like the one below. Suppose that a = 31, b = 23, and c = 20. (The figure is not drawn to scale.) Solve t

krok68 [10]

The solution to the triangle is A = 92.0, B = 47.9 and C = 40.1

<h3>How to solve the triangle?</h3>

The figure is not given;

However, the question can still be solved without it

The given parameters are:

a = 31, b = 23, and c = 20

Calculate angle A using the following law of cosine

a² = b² + c² - 2bc * cos(A)

So, we have:

31² = 23² + 20² - 2 * 23 * 20 * cos(A)

Evaluate

961 = 929 - 920 * cos(A)

Subtract 929 from both sides

32 =- 920 * cos(A)

Divide both sides by -920

cos(A) = -0.0348

Take the arc cos of both sides

A = 92.0

Calculate angle B using the following law of sine

a/sin(A) = b/sin(B)

So, we have:

31/sin(92) = 23/sin(B)

This gives

31.0189 = 23/sin(B)

Rewrite as:

sin(B) =23/31.0189

Evaluate

sin(B) =0.7415

Take arc sin of both sides

B = 47.9

Calculate angle C using:

C = 180 - 92.0 - 47.9

Evaluate

C = 40.1

Hence, the solution to the triangle is A = 92.0, B = 47.9 and C = 40.1

Read more about triangles at:

brainly.com/question/2217700

#SPJ1

6 0

1 year ago

Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle

dem82 [27]

Answer:

229.23 feet.

Step-by-step explanation:

The pictorial representation of the problem is attached herewith.

Our goal is to determine the height, h of the tree in the right triangle given.

In Triangle BOH

$Tan 60^0=\dfrac{h}{x}\\h=xTan 60^0$

Similarly, In Triangle BOL

$Tan 50^0=\dfrac{h}{x+60}\\h=(x+60)Tan 50^0$

Equating the Value of h

$xTan 60^0=(x+60)Tan 50^0\\xTan 60^0=xTan 50^0+60Tan 50^0\\xTan 60^0-xTan 50^0=60Tan 50^0\\x(Tan 60^0-Tan 50^0)=60Tan 50^0\\x=\dfrac{60Tan 50^0}{Tan 60^0-Tan 50^0} ft$

Since we have found the value of x, we can now determine the height, h of the tree.

$h=\left(\dfrac{60Tan 50^0}{Tan 60^0-Tan 50^0}\right)\cdotTan 60^0\\h=229.23 feet$

The height of the tree is 229.23 feet.

5 0

3 years ago

George needs to rent a car for one day. He can rent a Cadillac from Gamma Car Rental for $30.39 per day plus 55 cents per mile.

oksian1 [2.3K]

Call the number of days 'd' and the number of miles 'm'.
(Original, eh ?)

Then the equation for Gamma's price is

   Price-G = 30.39d + 0.55m

and the equation for Delta's price is

Price-D = 50.31d + 0.43m .

We're going to set the prices equal, and find out
what the number of miles is:

   Price-G = Price-D.

      30.39d + 0.55m = 50.31d + 0.43m .

Before we go any farther, I'm going to assume that both cases would be
one-day rentals. My reasons: ==> the solution for the number of miles
depends on how many days each car was rented for; ==> even if both
cars are rented for the same number of days, the solution for the number
of miles depends on what that number of days is.

For 1-day rentals, d=1, and

      30.39 + 0.55m = 50.31 + 0.43m .
Beautiful. Here we go.
Subtract 0.43m
from each side: 30.39 + 0.12m = 50.31

Subtract 30.39
from each side: 0.12m = 19.92

Divide each side by 0.12 : m = 166 .

There it is ! If a car is rented from Gamma for a day, and another car
is rented from Delta for a day, and both cars are driven 166 miles, then
the rental prices for both cars will be the same ... (namely $121.69)

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3 years ago

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Nata [24]

4/5 you’re welcome :)

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3 years ago

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Assoli18 [71]

Answer:

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5 0

3 years ago