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3 years ago

Solving a right triangle (round to the nearest tenth) ‼️‼️‼️

Mathematics

1 answer:

harkovskaia [24]3 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the given angles from 180 for B

B = 180° - (90 + 47)° = 180° - 137° = 43°

-------------------------------------------------------------

tan47° = $\frac{opposite}{adjacent}$ = $\frac{a}{14}$

Multiply both sides by 14

14 × tan47° = a, thus

a ≈ 15.0 (to the nearest tenth )

---------------------------------------------------------------

cos47° = $\frac{adjacent}{hypotenuse}$ = $\frac{14}{c}$

Multiply both sides by c

c × cos47° = 14 ( divide both sides by cos47° )

c = $\frac{14}{cos47}$ ≈ 20.5 ( to the nearest tenth )

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Scientists studying dolphin echolocation simulate the projection of a bottlenose dolphin's clicking sounds using computer

lina2011 [118]

Step-by-step explanation:

The equation of a parabola with focus at (h, k) and the directrix y = p is given by the following formula:

(y - k)^2 = 4 * f * (x - h)

In this case, the focus is at the origin (0, 0) and the directrix is the line y = -1.3, so the equation representing the cross section of the reflector is:

y^2 = 4 * f * x

= 4 * (-1.3) * x

= -5.2x

The depth of the reflector is the distance from the vertex to the directrix. In this case, the vertex is at the origin, so the depth is simply the distance from the origin to the line y = -1.3. Since the directrix is a horizontal line, this distance is simply the absolute value of the y-coordinate of the line, which is 1.3 inches. Therefore, the depth of the reflector is approximately 1.3 inches.

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1 year ago

A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the

maxonik [38]

The students rented 4 small cars and 8 large cars.

Step-by-step explanation:

Given,

Number of people in small car = 4

Number of people in large car = 7

Total people in both type of cars = 72

Let,

x represent the number of small cars rented.

y represent the number of large cars rented.

According to given statement;

4x+7y=72 Eqn 1

y = 2x Eqn 2

Putting value of y from Eqn 2 in Eqn 1

$4x+7(2x)=72\\4x+14x=72\\18x=72$

Dividing both sides by 18

$\frac{18x}{18}=\frac{72}{18}\\x=4$

Putting x=4 in Eqn 2

$y=2(4)\\y=8$

The students rented 4 small cars and 8 large cars.

Keywords: linear equation, substitution method

Learn more about linear equations at:

#LearnwithBrainly

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3 years ago

Use the quadratic formula to solve for x. 4x2 +9x-1=0

insens350 [35]

Answer:

$x=\frac{-9\pm\sqrt{65} }{8}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Standard Form: ax² + bx + c = 0
Quadratic Formula: $x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

Step-by-step explanation:

Step 1: Define

4x² + 9x - 1 = 0

Step 2: Define variables

a = 4

b = 9

c = -1

Step 3: Find roots

Substitute: $x=\frac{-9\pm\sqrt{9^2-4(4)(-1)} }{2(4)}$
Exponents: $x=\frac{-9\pm\sqrt{81-4(4)(-1)} }{2(4)}$
Multiply: $x=\frac{-9\pm\sqrt{81-16} }{8}$
Subtract: $x=\frac{-9\pm\sqrt{65} }{8}$

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3 years ago

You are to paint the globe held aloft by a statue of Atlas. The diameter of the globe is 10.5 in. How much surface area must you

Vera_Pavlovna [14]

Answer:

Step-by-step explanation:

We have been given that we need to paint the globe held aloft by a statue of Atlas. Its diameter is 10.5 in.

First of all we will find the area of globe using area of sphere formula.

, where r represents the radius of sphere.

Since diameter is 2 times the radius, so the radius of our given globe will be:

Since 27 square inches does not need to be painted, so the area we must cover with paint will be:

Upon rounding our answer to nearest hundredth we will get,

Therefore, we must cover 319.36 square inches with paint.

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2 years ago

Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What interest rate did

dolphi86 [110]

Answer:

r = i/pt

r =450/3000*3

r =0.05*100=5%

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3 years ago