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3 years ago

Solve the inequality. Graph the solution.2(5 – 3x) < x-4(3 - x)

Mathematics

1 answer:

VashaNatasha [74]3 years ago

3 0

Answer:

x>2

Step-by-step explanation:

The first thing you need to do is distribute.

2 time 5 and 2 time -3x; -4 times 3 and -4 times -x.

After that you would get 10-6x < x-12+4x.

Now combine like terms. The only like terms are on the right side: x and 4x.

Now it's 10-6x < 5x-12.

Now put x on one side. I prefer to work with a positive x so I would move it to the right.

Now it's 10 < 11x-12.

Isolate the x. Move the -12 first

Now it's 22<11x.

Divide by 11 next.

Now it's 11<x.

Switch it around so it's easier to interpret for the graph.

Final written inequality is x>11.

Graph the line x= 11 but with a dotted line because it is not equal to 11.

Color in everything to the right of the line because everything greater than x is to the right.

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When building a house, the number of days required to build varies inversely with with the number of workers. One house was buil

Helga [31]

Let d represent number of days and n represent number of workers.

We have been given that when building a house, the number of days required to build varies inversely with with the number of workers.

We know that the equation $y=\frac{k}{x}$ represents the relation where y is inversely proportional to x and k is the constant of proportionality.

So our required equation would be $d=\frac{k}{n}$

Upon substituting our given values, we will get:

$19=\frac{k}{35}$

$k=19\cdot 35$

$k=665$

Since constant of proportionality is 665, so our equation would be $d=\frac{665}{n}$ .

To find the number of days it will take to build a similar house with 5 workers, we will substitute $n=5$ in our equation as:

$d=\frac{665}{5}$

$d=133$

Therefore, it will take 133 days for 5 workers to build a similar house.

5 0

3 years ago

PLZZZZ HELP WITH THIS QUESTION

Sauron [17]

A. 1/5 fish

We know that 2/5 of Mike's fish are clownfish. Therefore, 3/5 are not clownish as 5/5 – 2/5 = 3/5. Also, if you look at the model, there are five pieces. If we assume that model represents the whole of Mike's fish and you take away two pieces, you are left with 3/5. So we know that the remaining fish is 3/5

Next, we know that of these 3/5 fish, 1/3 is damselfish, so we need to find 1/3 of 3/5. To do this, we must multiply 1/3 by 3/5 as "of" means multiply in Math.

So: 1/3 • 3/5 = 1 • 3/3 • 5 = 3/15 3 ÷ 3 = 1 and 15 ÷ 3 = 5 3/15 = 1/5

1/5 of Mike's fish are damsel fish

B. 2/5 fish

Now we know that 1/5 of Mike's fish is damselfish, and 2/5 is clownfish. To find the fraction of his fish that are neither, therefore, we must subtract their sum from the whole.

First, we add 1/5 and 2/5 together. Adding the numerators, 1 and 2, we get 1/5 + 2/5 = 3/5

Next, we subtract: 5/5 – 3/5 = 2/5, so 2/5 of his fish are neither clownfish or damselfish

And if you look at the model again, you can see that if you cross out 1 piece for the damselfish, and 2 pieces for the clownfish, you are left with 2/5

8 0

3 years ago

Which expresion is equivalent to 30(1/2x-2)+40(3/4y-4)

Dafna11 [192]

Answer:

15x +30y -220

steps:

30(1/2x-2)+40(3/4y-4)

= 15x-60 +30y-160

= 15x +30y -220

6 0

3 years ago

The base of a rectangle is 6cm longer than its height. The area of a rectangle is 91cm squared. What is the perimeter of the rec

r-ruslan [8.4K]

Width = 7cm

Length = 13cm

Explanation:

Area of rectangle = $91cm^{2}$

Let width of the rectangle = b ,

So, length = b+6

Area of rectangle = (length X width) - eqn 1

Putting the value of length and width in above equation 1,

$91cm^{2} = b (b+6)\\91 = b^{2}+6b\\b^{2} + 6b-91 = 0\\$

On solving the quadratic equation we get,

b = 7cm

So, width (b) = 7cm

and length = 7+6

l = 13cm

Hence,

Width = 7cm

Length = 13cm

6 0

3 years ago

6x + 12 + 2x - 4 Can u help me pls

Ray Of Light [21]

Answer:

8x+8

Step-by-step explanation:

6x+2x=8x 12-4=8

3 0

3 years ago

Solve the inequality. Graph the solution.2(5 – 3x) < x-4(3 - x)​

Solve the inequality. Graph the solution.2(5 – 3x) < x-4(3 - x)