All categories

3 years ago

Decide whether 0 is a solution of the inequality: a.) 2x – 1 9 c.) x – 3 > 1

Mathematics

1 answer:

marin [14]3 years ago

5 0

Step-by-step explanation:

How to check a solution: Just as you can check the solution to an equation, you can check a solution to an inequality. First, you check the end point by substituting it in the related equation. Then you check to see if the inequality is correct by substituting any other solution to see if it is one of the solutions.

How to tell if its true or false: An inequality is a statement that shows the relationship between two (or more) expressions with one of the following five signs: <, ≤, >, ≥, ≠. Like an equation, an inequality can be true or false. 34 - 12 > 5 + 2 is a true statement. 1 + 3 < 6 - 2 is a false statement.

You might be interested in

Bill Ding plans to build a new hardware store. He buys a rectangular lot that is 50 ft by 200 ft, the 50-ft dimension being alon

enot [183]

Answer:

Length a = 59.62

Width b = 67.09

Cost = $10,734.4

Step-by-step explanation:

Solution:

Let a be the length and b be the width.

Area of the rectangle = a x b

a x b = 4000

Cost of the construction:

Cost = 100a + 80(a + 2b)

Cost = 100a + 80a + 160b

Cost = 180a + 160b Equation of the Cost of the construction.

Now, we need a and b to calculate the minimum cost required to build a lot.

From the area = a x b

we have,

a x b = 4000

b = 4000/a

Putting this equation into the cost of the construction.

We get:

Cost = 180a + 160 x (4000/a)

Cost = 180a + 640000/a

Differentiating with respect to a, we get

$C^{'}$ = 180 - 640000/ $a^{2}$

Putting $C^{'}$ = 0

180 - 640000/ $a^{2}$ = 0

Taking LCM

180 $a^{2}$ - 640000 = 0

Solving for a

180 $a^{2}$ = 640000

$a^{2}$ = 640000/180

$a^{2}$ = 3555.55

Taking square root

a = 59.62

As we know,

b = 4000/a

putting the minimum value of a = 59.62

b = 4000/59.62

b = 67.09

So, now we have both the dimensions a and b

Putting the values of a and b we will get the cost of the construction.

Cost = 180a + 160b

Cost = 180(59.62) + 160(67.09)

Cost = $10,734.4

Hence, $10,734.4 will be the minimum cost of the construction for Bill Ding.

5 0

3 years ago

12% profit on a computer is Rs.540.

Savatey [412]

Answer:

the cost price is Rs. 4500 and the sale price is Rs. 5040.

Step-by-step explanation:

Let the cost price of the compute be Rs. x.

The profit earned is, Rs. 540.

The profit percentage is, 12%.

The formula to compute profit is:

Profit = SP - CP

\begin{gathered}540=x[1+\frac{12}{100}]-x\\540=1.12x-x\\540=0.12x\\x=\frac{540}{0.12}\\x=4500\end{gathered}540=x[1+10012]−x540=1.12x−x540=0.12xx=0.12540x=4500

Compute the selling price as follows:

SP = CP + profit

= 4500 + 540

= 5040

Thus, the cost price is Rs. 4500 and the sale price is Rs. 5040.

8 0

2 years ago

50 POINTSSS

leonid [27]

Answer:

After 2 minutes the temperature of the hot chocolate will be 149.46 degrees Fahrenheit.

Step-by-step explanation:

We are going to use the Newton's law of cooling to solve this exercise. The Newton's law of cooling states that the amount of heat lost by a body is proportional to the difference of temperature between the body and the enviroment. We are going to use the following function :

T(t)=T_{0}+(T_{i}-T_{0}).e^{-kt}T(t)=T

+(T

−T

).e

−kt

Where ''T(t)'' is the temperature of the body that depends of the variable ''t'' which is time.

Where T_{0}T

is the temperature of the surroundings

In this case T_{0}T

is the temperature of the freezer

Where T_{i}T

is the initial temperature of the body which is cooling. In this case, T_{i}T

is the temperature of the hot chocolate

And where ''k'' is a constant. In this case, k=0.12k=0.12 is a data of the exercise

If we replace all the values in the equation and replacing t=2minutest=2minutes

⇒

T(2minutes)=0+(190-0).e^{-(0.12).(2)}T(2minutes)=0+(190−0).e

−(0.12).(2)

T(2minutes)=(190).(e^{-0.24})=149.46T(2minutes)=(190).(e

−0.24

)=149.46

We find that the temperature of the hot chocolate after 2 minutes is 149.46 degrees Fahrenheit

8 0

3 years ago

A video game arcade offers a yearly membership with reduced rates for game play. A single membership costs $60 per year. Game to

Elina [12.6K]

Answer:

2. The y-intercept of the function is $60

3. The function can be represented by the equation y = (1/10)x +60.

5. The range is y ≥ 60

Step-by-step explanation:

The function of the yearly cost in dollars, y, based on x, the number of game tokens is:

$y=\frac{1.00}{10}x+60\\ y=0.10x+60$

1. The slope of the function is $1.00.

The slope of the function is the cost per token, if 10 tokens cost $1.00, than the slope of the function is $0.10. This statement is incorrect.

2. The y-intercept of the function is $60

The y-intercept is the value of y for which x = 0 (If no tokens are bought). In this case, that would be the single membership cost, which is $60. This statement is correct.

3. The function can be represented by the equation y = (1/10)x +60.

As previously mentioned, this equation is correct since it represents the membership cost plus the cost of each token multiplied by the number of tokens bought.

4. The domain is all real numbers

Real numbers include fractions and negative values, which cannot be a possible value for x. Therefore, the actual domain is all natural numbers (non-negative integers). This statement is incorrect.

5. The range is y ≥ 60

The range is all of the possible values of y. The minimum value is the cost of membership with no tokens ($60), and there is no maximum value since infinite tokens could be bought theoretically. This statement is correct.

7 0

4 years ago

Read 2 more answers

The solids are similar. Find the missing dimensions.

DedPeter [7]

Answer:

b = 18 m

c = 19.5 m

h = 9 m

Step-by-step explanation:

Call the smaller solid the original one, and call the larger solid the scaled one.

1. Find the scale factor

scale factor = length in scaled one / corresponding length in original one

scale factor = 7.5/5 = 1.5

The scale factor is 1.5

That means if you multiply any linear dimension of the original one by 1.5, you get the corresponding dimension of the scaled one.

Let's check our scale factor to make sure it's correct.

We see that the 5 m side corresponds to the 7.5 m side.

5 m * 1.5 = 7.5 m

Multiplying an original length by the scale factor of 1.5 gives us the scaled up length, so our scale factor of 1.5 is correct. Now we apply the scale factor of 1.5 to find b, c, and h.

b corresponds to 12 m

b = 12 m * 1.5 = 18 m

c corresponds to 13 m

c = 13 m * 1.5 = 19.5 m

h corresponds to 6 m

h = 6 m * 1.5 = 9 m

Answer:

b = 18 m

c = 19.5 m

h = 9 m

8 0

3 years ago