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3 years ago

4. (07.04 MC)

Mathematics

1 answer:

timofeeve [1]3 years ago

6 0

Answer:

11779 ft

Step-by-step explanation:

We are given that

$\theta=23^{\circ}$

Distance between tower and plane,d=5000 ft

We have to find the distance between the plane and bird.

Let x be the distance between bird and plane

We know that

$tan\theta=\frac{perpendicular\;side}{Base}$

Using the formula

$tan23=\frac{5000}{x}$

$x=\frac{5000}{tan23}=11779.3 \approx 11779ft$

Hence, the distance between the plane and bird=11779 ft

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10. Mark ran 3 miles everyday for 2 weeks. How far did mark run in all?

Alexxandr [17]

14 days = 2 weeks so

14 times 3 = 42

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Round 0.311 to the nearest tenth

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0.3 because it’s less than 5

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Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together the

klasskru [66]

The rate charged per hour by each mechanic was: x = 75 $ / hr and y = 115 $ / hr.

<h3>What is a system of equations?</h3>

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given;

The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours.

Together they charged a total of $3225.

For this case we have the following variables:

x be the amount of $ / hr that the mechanic obtains 1.

y be the amount of $ / hr obtained by mechanic 2.

An equation to express this would be:

x + y = 190

20x + 15y = 3225

Solving the system of equations we have:

20x + 15(190 -x) = 3225

20x + 2850 - 15x = 3225

5x = 375

x = 75

simililary

y = 190 - x

y = 115

Hence, the rate charged per hour by each mechanic was:

x = 75 $ / hr

y = 115 $ / hr

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1 year ago

Divide. Enter the answer in simplest form. 6 2/3 divided by 2 1/2

Roman55 [17]

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2 years ago

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Just number 3 is fine please but if you could also 4

PIT_PIT [208]

Answer:

3. r = -8

4. x = -5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define equation

2(-5r + 2) = 84

Step 2: Solve for r

Divide 2 on both sides: -5r + 2 = 42
Subtract 2 on both sides: -5r = 40
Divide -5 on both sides: r = -8

Step 3: Check

Plug in r into the original equation to verify it's a solution.

Substitute in r: 2(-5(-8) + 2) = 84
Multiply: 2(40 + 2) = 84
Add: 2(42) = 84
Multiply: 84 = 84

Here we see that 84 does indeed equal 84.

∴ r = -8 is a solution of the equation.

Step 4: Define equation

264 = -8(-8 + 5x)

Step 5: Solve for x

Divide both sides by -8: -33 = -8 + 5x
Add 8 to both sides: -25 = 5x
Divide 5 on both sides: -5 = x
Rewrite: x = -5

Step 6: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x: 264 = -8(-8 + 5(-5))
Multiply: 264 = -8(-8 - 25)
Subtract: 264 = -8(-33)
Multiply: 264 = 264

Here we see that 264 does indeed equal 264.

∴ x = -5 is a solution of the equation.

8 0

2 years ago