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3 years ago

Consider the system of inequalities.

Mathematics

1 answer:

Ugo [173]3 years ago

7 0

Answer:

The point is (-1,5) and (0,0) also satisfies the given inequalities

The solution of the given inequalities

(x, y) = (4 , -2 )

Step-by-step explanation:

Step(i):-

Given system of equations are

3x + 2y < 8

-5x - 9y > -2

The solution of the given equations are

3x + 2y = 8 multiply '5'

-5x - 9y = -2 multiply '3'

15 x + 10 y = 40 ...(i)

-15x - 27 y = -6.....(ii)

Adding (i) and (ii) , we get

- 17 y = 34

y = -2

Substitute y = -2 in equation 3x + 2y =8

3x - 4 =8

3x = 12

x =4

The solution of the given system of inequalities

(x, y) = (4 , -2 )

Step(ii):-

3x + 2y < 8

-5x - 9y > -2

The point is (-1,5)

-3 + 10 < 8

7 < 8

5 - 45 > -2

-40 > -2

The point (0,0) also satisfies the given inequalities

Final answer :-

The point is (-1,5) and (0,0) also satisfies the given inequalities

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Carmen has a $350 gift card to spent at Modell's. She wants to buy 2 pairs of sneakers that cost $100 each. She wants to find th

tatyana61 [14]

Answer:

The inequality is $200 + x*$8≤ $350

Step-by-step explanation:

An inequality is an inequality between letters (unknowns) and numbers related by arithmetic operations. Its solution set is the set of real numbers that satisfy it. In other words, an algebraic inequality in which its members are linked by the signs <(less than), ≤ (less than or equal to),> (greater than) or ≥ (greater than or equal to) is called an inequality.

Solving an inequality is to find the values of the unknown for which the inequality holds. The solution of an inequality is an interval or a union of intervals of real numbers.

In this case, you know that Carmen wants to buy 2 pairs of sneakers that cost $ 100 each.So the 2 pairs of sneakers will cost Carmen:

2 * $ 100 = $ 200

On the other hand, Carmen wants to find the possible amount of socks that she can buy, knowing that a pair costs $ 8. Being x the amount of socks that she can buy, then Carmen spends on socks:

x*$8

Knowing that Carmen has a $ 350 gift card to spend at Modell's, then what she spent on sneakers and socks cannot be more than $ 350. That is to say, the sum of what was spent on sneakers and socks must be less than or equal to $ 350, because Carmen cannot spend more than she has. This is expressed by the following inequality:

$200 + x*$8≤ $350

Solving for x:

x*$8 ≤ $350 - $200

x*$8≤ $150

x≤ $\frac{150}{8}$

x≤ 18.75

Carmen can buy 2 sneakers and 18 or fewer socks with the $ 350 gift card.

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3 years ago

Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

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4 years ago

when the whole is the same why does it take 4 copies of one tenth to equal 2 copies of one fifth draw a model to support your an

bonufazy [111]

Well 4 copies of one tenth will equal 4 tenths. so when u simplify 4 over ten (4/10 )and divide the top and bottom by the common factor which is 2 then you will get 2 fifths because 4 divided by 2 is 2 and 10 divided by 2 is 5.

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4 years ago

A triangle has sides with lengths of 6 meters, 12 meters, and 16 meters. Is it a right triangle?

Yuki888 [10]

Answer:

i'd say so

Step-by-step explanation: none of the sides are the same length as another

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3 years ago

ach light bulb at Hotel California is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent

Trava [24]

Answer:

10%

Step-by-step explanation:

The computation of the percentage of bulbs that switched on incandescent is as follows;

Let us assume the incandescent be I

And, the fluorescent be F

Now the equation is

0.4I + 0.9F = 0.8 (I+F)

0.41I + 0.9F = 0.8I + 0.8F

So here

0.4I = 0.1F

Now the percentage would be for incandescent in the case of switched on is

= 0.4I ÷ 0.8(I+F) × 100

= 0.1F ÷ 1F

= 10%

6 0

4 years ago