Q2 - With decimals
Work these simultaneous equations out
on paper and write down your answers.
The cost of 8 CDs and 7 DVDs is
$113.50.
The cost of 12 CDs and 8 DVDs is
$153.
a =
10a + 3b = 31
15a + 4b = 45
b =
m =
4m + 10n = 83
9m + 6 = 96
n =
p =
8p + 59 = 27
12p + 40 = 51
All the CDs are the same price and
all the DVDs are the same price.
q=
Find the cost of one of each.
6S + 7t = 42
S =
1 CD is $
8s + 3t = -1
t =
[8]
[4]
1 DVD is $

Answer:

Simplify the following algebraic expressions.

- 6x + 5 + 12x -6

2(x - 9) + 6(-x + 2) + 4x

3x2 + 12 + 9x - 20 + 6x2 - x

(x + 2)(x + 4) + (x + 5)(-x - 1)

1.2(x - 9) - 2.3(x + 4)

(x2y)(xy2)

(-x2y2)(xy2)

Solution

Group like terms and simplify.

- 6x + 5 + 12x -6 = (- 6x + 12x) + (5 - by

Solution

Use rules of exponential to simplify the numerator first.

(a b2)(a3 b) / (a2 b3) = (a4 b3) / (a2 b3)

Rewrite as follows.

(a4 / a2) (b3 / b3)

Use rule of quotient of exponentials to simplify.

= a2

Rewrite as follows.

(21 x5) / (3 x4) = (21 / 3)(x5 / x4)

Simplify.

= 7 x

(6 x4)(4 y2) / [ (3 x2)(16 y) ]

Multiply terms in numerator and denominator and simplify.

(6 x4)(4 y2) / [ (3 x2)(16 y) ] = (24 x4 y2) / (48 x2 y)

Rewrite as follows.

= (24 / 48)(x4 / x2)(y2 / y)

Simplify.

= (1 / 2) x2 y

Factor 4 out in the numerator.

(4x - 12) / 4 = 4(x - 3) / 4

Simplify.

= x - 3

Factor -5 out in the numerator.

(-5x - 10) / (x + 2) = - 5 (x + 2) / (x + 2)

Simplify.

= - 5

Factor numerator and denominator as follows.

(x2 - 4x - 12) / (x2 - 2x - 24) = [(x - 6)(x + 2)] / [(x - 6)(x + 4)]

Simplify.

= (x + 2) / (x + 4) , for all x not equal to 6

Solve for x the following linear equations.

2x = 6

6x - 8 = 4x + 4

4(x - 2) = 2(x + 3) + 7

0.1 x - 1.6 = 0.2 x + 2.3

- x / 5 = 2

(x - 4) / (- 6) = 3

(-3x + 1) / (x - 2) = -3

x / 5 + (x - 1) / 3 = 1/5

Solution

Divide both sides of the equation by 2 and simplify.

2x / 2 = 6 / 2

x = 3

Add 8 to both sides and group like terms.

6x - 8 + 8 = 4x + 4 + 8

6x = 4x + 12

Add - 4x to both sides and group like terms.

6x - 4x = 4x + 12 - 4x

2x = 12

Divide both sides by 2 and simplify.

x = 6

Expand brackets.

4x - 8 = 2x + 6 + 7

Add 8 to both sides and group like terms.

4x - 8 + 8 = 2x + 6 + 7 + 8

4x = 2x + 21

Add - 2x to both sides and group like terms.

4x - 2x = 2x + 21 - 2x

2x = 21

Divide both sides by 2.

x = 21 / 2

Add 1.6 to both sides and simplify.

0.1 x - 1.6 = 0.2 x + 2.3

0.1 x - 1.6 + 1.6 = 0.2 x + 2.3 + 1.6

0.1 x = 0.2 x + 3.9

Add - 0.2 x to both sides and simplify.

0.1 x - 0.2 x = 0.2 x + 3.9 - 0.2 x

- 0.1 x = 3.9

Divide both sides by - 0.1 and simplify.

x = - 39

Multiply both sides by - 5 and simplify.

- 5(- x / 5) = - 5(2

What is the y intercept of the line - 4 x + 6 y = - 12?

Solution

Set x = 0 in the equation and solve for y.

- 4 (0) + 6 y = - 12

6 y = - 12

y = - 2

y intercept: (0 , - 2)

What is the x intercept of the line - 3 x + y = 3?

Solution

Set y = 0 in the equation and solve for x.

- 3 x + 0 = 3

x = -1

x intercept: (-1 , 0)

What is point of intersection of the lines x - y = 3 and - 5 x - 2 y = - 22?

Solution

A point of intersection of two lines is solution to the equations of both lines. To find the point of intersection of the two lines, we need to solve the system of equations x - y = 3 and -5 x - 2 y = -22 simultaneously. Equation x - y = 3 can be solved for x to give

x = 3 + y

Substitute x by 3 + y in the equation - 5 x - 2 y = -22 and solve for y

-5 (3 + y) - 2 y = - 22

-15 - 5 y - 2 y = - 22

-7 y = - 22 + 15

-7 y = - 7

y = 1

Substitute x by 3 + y in the equation -5 x - 2 y = - 22 and solve for y

x = 3 + y = 3 + 1 = 4

Point of intersection: (4 , 1)

For what value of the constant k does the line - 4 x + k y = 2 pass through the point (2,-3)?

Solution

For the line to pass through the point (2,-3), the ordered pair (2,-3) must be a solution to the equation of the line. We substitute x by 2 abd y by - 3 in the equation.

- 4(2) + k(-3) = 2

Solve the for k to obtain

k = - 10 / 3

What is the slope of the line with equation y - 4 = 10?

Solution

Write the given equation in slope intercept form y = m x + b and identify the slope m.

y = 14

It is a horizontal line and therefore the slope is equal to 0.

What is the slope of the line with equation 2 x = -8?

Solution

The above equation may be written as

x = - 4

It is a vertical line and therefore the slope is undefined.

Find the x and y intercepts of the line with equation x = - 3?

Solution

The above is a vertical line with x intercept only given by

(-3 , 0)

Find the x and y intercepts of the line with equation 3 y - 6 = 3?

Solution

The given equation may be written as

y = 3

The above is a horizontal line with y intercept only given by

(0 , 3)

What is the slope of a line parallel to the x axis?

Solution

A line parallel to the x axis is a horizontal line and its slope is equal to 0.

What is the slope of a line perpendicular to the x axis?

Solution

A line perpendicular to the x axis is a vertical line and its slope is undefined

Step-by-step explanation:

y = -22 and solve for y

-5 (3 + y) - 2 y = - 22

-15 - 5 y - 2 y = - 22

-7 y = - 22 + 15

-7 y = - 7

y = 1

the Johnson family went out to dinner and spent a total of $68.32 before tax. if tax is 6% of the total meal, how much will the family pay in total?​

PLZ HELP!!!! WILL GIVE BRAINLIEST IF CORRECT! The social studies teacher wants to know whether the students in the entire school prefer a model United Nations activity or a student government activity. The teacher draws a random sample from the following groups:

All teachers in the school
All boys in each grade
All students in each grade
All students in the social studies club
Which group best represents the population he should take a random sample from to get the best results for his survey? (5 points)

Question 1 options:

1)

All teachers in the school

2)

All boys in each grade

3)

All students in each grade

4)

All students in the social studies club

Round to the nearest ten thousand.

758,928

What is the perimeter?

PLEASE HELP!! I need it asap tysm

Someone please help :( ?????

Can anyone please help me with this!!! :(

hi what is 24/30 simplified to
​

Which expression is equivalent to -5(8x+9) -7x?

A. -33x+9
B. -47x-45
C. -33x - 45
D. 33x - 45

the numerical coefficient in the expression -3×y² is​

The measure of the second angle is 15 degrees more than the measure of the first angle the measure of the third angle is 45 degrees more than the measure of the first angle tine the measures of the interior angles in the triangle

asap pleaseeeee!!!!!

Find the value of x and the value of the given angle using the picture below?

Mrs. Beads grouped her students two different waysFirst, she students into groups with the same number of students in each group No students were leftover. Then she put students into 6 group with the same number of students in each group with none leftover
A) 14
B) 16
C) 18
D) 24
E) 30

HELP ASAP!!!
Use Pythagorean Theorem to solve. Round to the nearest tenth •
33 cm
х
55 cm

You want to put a 3 inch thick layer of topsoil for a new 23 ft by 24 ft garden. The dirt store sells by the
cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic
yards.
cubic yards

- 5x + 9y = - 32
-5x - 3y = 4

Identify the y-intercept for the line 4x – 2y = 4
Give your answer as a coordinate.
PLEASE HELP ASAP

Nancy bought a package of 4 spiral notebooks for a total cost of $18.25. Which equation represents p, the cost, in dollars, of each notebook?

In fact, weather on consecutive days depends on similar atmospheric conditions and therefore consecutive days are not independent events.With the weather forecast of the previous exercise, the probability that it rains over the weekend (either Saturday or Sunday) isA. 0.7516B. 0.3758 C. 0.2484D. Because consecutive days are not independent, we cannot compute P(rain both days) with the information given.

The ratio of the number of girls to the number of boys in a classroom 6:5. After 16 girls left the room, the ratio became 2:3. How many girls were there at first?

can anyone help with this?

A small plane took 3 hours to fly 960 km from Ottawa to Halifax with a tail wind. On the return trip, flying into the wind, the plane took 4 hours. Find the wind speed and the speed of the plane in still air. (5 marks)

If you spend $400 on a new phone and it is depreciating about 50% per year , how much will it be worth by its third year?

The area of a rectangle 320in^2. The ratio of the length to the width is 5:4. Find the length and the width

When a number is decreased by 8.3%, the result is 50. What is the original number to the nearest tenth?

The probability that Brian buys a sandwich is 0.1. The probability that Brian gets the bus is 0.6. Assuming the events are independent, what is the probability that Brian buys a sandwich and gets the bus?

1
Suppose f(x) = x2 - x - 12, g(x) = x + 3, and h(x) = 6x - 1. Which of the following function operations are
three that apply.
A (g x h)(x) = 6x2 + 17x-3
B (n + 1)(x) = x2 + 5x - 13
C (f = g)(x) = x - 4
D (f - h)(x) = x2 - 7x-13
E (g- h)(x) = 5x - 4
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Ill give you brainliest and 5 stars help plz

Can someone help me with this?