All categories

3 years ago

Solve the following equations for ????. Write your answer in set notation.

Mathematics

1 answer:

ddd [48]3 years ago

7 0

Answer:

a. x=7

b. x=4

c. x=5

d. x=4

e. equation b and d have same solution set.

Step-by-step explanation:

3x=21

x=21/3

x=7.

3x+9-5=16

3x+4=16

3x=12

x=12/3

x=4

6x-9-5=16

6x-14=16

6x=30

x=30/6

x=5

6x+18-10=32

6x+8=32

6x=32-8

6x=24

x=24/6

x=4

e. Equation b and d have the same solution set.

The expression on both sides of the equal in the equation d is are twice of the expression in equation b. So, if (right side)=(left side) is true for some values of x, then 2(right side) = 2(left side) will be true for the same values of x.So we can find the solution without finding the solution set of both the equations.

You might be interested in

What are the solutions of the equation (x-3)^2 + 2(x-3) -8 = 0

Mariulka [41]

Expand and simplify
(x-3) (x-3) +2(x-3) -8=0
(x-3+2)(x-3)-8=0
(x-1)(x-3)-8=0
x^2 -4x +3-8=0
x^2 - 4x -5=0
x^2 -5x +x-5=0
x(x-5)+x-5=0
(x+1)(x-5)=0
x= - 1, 5

6 0

3 years ago

Read 2 more answers

Find the vertex for each equation:

tamaranim1 [39]

1. (−3,−1)

2. (3,−5)

3. (−3,−4)

5 0

2 years ago

Consider this figure of a hexagon.

notsponge [240]

A)
It looks like the [irregular] hexagon has 3 rectangles and 2 triangles within it.
So let's exclude the triangular corners on bottom left and top right for now.
First we have a large rectangle covering most of the upper left of the polygon. 20 ft × 7 ft = 140 sq.ft.
Now we have a rectangle on the bottom right. The width is 11 ft, so take the 7 away from that, 4 ft. × 14 ft. on bottom. 4 ft × 14 ft = 56 sq.ft.
The last small rectangle fits on the right between the 2 other rectangles. It is 24-20 on top/bottom × 7-6 right/left. 4 ft × 1 ft = 4 sq.ft.
Now for the triangles: bottom left is 11-7 × 24-14 = 4 ft × 10 ft. 1/2bh = 1/2×10×4 = 20 sq.ft.
Top right is 24-20 × 11-5 = 4 ft × 6 ft. 1/2bh = 1/2×4×6 = 12 sq.ft.

B)
Add them all together for the total area (A):
A = 140 + 56 + 4 + 20 + 12 = 140+60+32
= 232 sq.ft.

Hope that explains it well enough! ;)

6 0

2 years ago

Read 2 more answers

Bogdan [553]

Answer:

3 gallons of orange juice

8 0

2 years ago

Read 2 more answers

Nando is on a rehabilitation program following a car accident. For the first month, he needs to exercise at most five hours per

emmasim [6.3K]

Answer:

See explanation

Step-by-step explanation:

Let x be the number of hours per week Nando is brisk walking and y be the number of hours per week Nando is biking at a moderate pace.

For the first month, he needs to exercise at most five hours per week, then

$x+y\le 5$

Brisk walking burns about 350 calories per hour, then it burns 350x calories per x hours.

Biking at a moderate pace burns about 700 calories per hour, then it burns 700y calories per y hours.

Nando must burn at least 2,000 calories per week, so

$350x+700y\ge 2,000$

You get the system of two inequalities:

$\left\{\begin{array}{l}x+y\le 5\\ 350x+700y\ge 2,000\end{array}\right.$

The attached graph shows the solution set to this system of inequalities. In this diagram, red region represents the solution set to the first inequality, blue region represents the solution set to the second inequality and their intersection is the solution set to the system of two inequalities.

4 0

3 years ago