Archive for the ‘Algebra’ Category

Problem 2033

What is the slope of the line that is perpendicular to y = 4x – 3?

 

Solution:-

 

The slope is represented by m in y = mx + b. Perpendicular lines have opposite reciprocal slopes.

m = \frac{-1}{4}

 

Problem 3032

Find the slope of the line through the points (5, -2) and (0, 2)

 

Solution:-

 

m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}.

m = \frac{-4}{5}

 

Problem 2031

A truck and a car leave a service station at the same time and travel in the same direction. The truck travels at 60 mps and the car travels at 52 mph. They can maintain radio contact within a range of 12 miles. When will they lose contact?

 

Solution:-

 

Let t = number of hours before the vehicles lose contact. The first step is to write two equations using the formula d = rt.

Remember that since the vehicles started at the same time, their times are equal.

First, use d = rt to represent the distance driven by the trunk.

trunk distance = 60t

Now use d = rt to r represent the distance driven by the car.

car distance = 52t

Since the radios have a range of 12 miles, the vehicles will loss contact when they are 12 miles apart, that is, when the difference of the distance is 12 miles .

Simplify

60t – 52t = 12

8t = 12

Solve for t and reduce

t = 1.5

the vehicle will lose contact after 1.5 hours

Problem 2026

Fill in the blank with an appropriate word.

When two straight lines intersect, the nonadjacent angles formed are________________ angels.

 

Solution:-

 

When two straight lines intersect, the nonadjacent angles formed are called vertical angles.

 

Problem 2025

Unscramble the word to make a metric unit of measurement.

greseed sulesic

 

Solution:-

 

Unscramble greseed sulesic to make a metric unit of measurement.

degress celsius

 

Problem 2024

Five hundred ticket were sold for a school play, which generated 3560 in revenue. The price of the tickets were 5 for children, 7 for students, and 10 for adults. There were 180 more student tickets sold than adult tickets. Let x be the number of children tickets sold, let y be the number of student tickets sold, and let z be the number of adult tickets sold. Find the number of each type of ticket sold.

 

Solution:-

 

X = 120

Y = 280

Z = 100

 

Problem 2023

One type of lawn fertilizer consists of a mixture of nitrogen, phosphorus, and potassium. An 80 lb sample contains 8 more lb of nitrogen and phosphorus than potassium. There is 16 lb more potassium than 5 times the amount of phosphorus. Let x be the amount of nitrogen, let y be the amount of phosphorus, and let z be tge amount of potassium in the sample.

Find the amount of each of the chemicals in the sample.

 

Solution:-

 

Write a 3 by 3 system of equation to solve the problem stated above. Do not solve the system.

Equation 1: x + y +z =80

Equation 2: x + y – x = 8

Equation 3: -5y +z = 16.

 

Problem 2022

If possible, solve the system of linear equations and check your answer.

3x + 7y = 9

x + 5y = 11

 

Solution:-

 

The solution is (-4,3).

 

Problem 2016

Solve the logarithmic equation.

7log x = -14

 

Solution:-

 

First divide both of the equation by the common factor.

log x = -2

now write an equivalent exponential equation.

10-2 = x

Calculate the value of x as a decimal.

x = 0.01

check your solution in the equation.

Since this value makes the equation true, the solution is x = 0.01.

 

Problem 2015

Solve the exponential equation.

2.4 e-1.2x = 1

 

Solution:-

 

The solution is x = .7296