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Gnom [1K]
3 years ago
9

Graph the solution set of: 2x - 4 ≤ 8 and x + 5 ≥ 7​

Mathematics
2 answers:
Alex17521 [72]3 years ago
8 0

Answer:

x ≤ 6 and x ≥ 2

Step-by-step explanation:

For now, we will start with doing each problem at a time. Here is your equation:

2x - 4 ≤ 8

First, you want to get the variable by itself. So, you add 4 to both sides. It will look like this:

2x - 4 ≤ 8

+ 4 + 4

The four being added on the left side cancels out, and you add 4 to 8. Now, it should look like this:

2x ≤ 12

Next, you want the x by itself. So, you would divide both sides by 2.

2x ≤ 12

/2 /2

2 divided by 2 cancels out, and 12 divided by 2 equals 6. Now, you have a final answer of:

x ≤ 6

But, you now have to do the other one!

Here is what you start off with:

x + 5 ≥ 7

First, you want the variable side by itself. So, you subtract 5 from both sides.

x + 5 ≥ 7

- 5 -5

Now, you have this:

x ≥ 2

Because the variable is already by itself, you don't need to do any more division and this is you final answer. Now put both answers you got together which equals:

x ≤ 6 and x ≥ 2

Tresset [83]3 years ago
4 0

First of all, we have to solve both inequalities: for the first one we have

2x-4\leq 8

Add 4 to both sides

2x\leq 12

Divide both sides by 2:

x\leq 6

For the second one we have

x+5\geq 7

Subtract 5 from both sides

x\geq 2

So, our solution set is composed by all numbers that are less than 6 (included) and more than 2 (included). Using all possible notations, we have

[2,6],\quad 2\leq x \leq 6,\quad \{x \in \mathbb{R}: 2\leq x \leq 6\}

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Solve -9-8(1+4h)=-17
Mariulka [41]
-9-8(1+4h) = -17. We need to solve for h.
First, use the distributive property for 8(1+4h):
8(1+4h) = 8*1 + 8*4h = 8 + 32h

So -9-8(1+4h) = -17
-9 - (8+32h) = -17
-9 - 8 - 32h = -17
-17 - 32h = - 17
Add 17 on both sides to have the variables on a side and the numbers on the other:
-17 - 32h + 17 = -17 + 17
-32h = 0
divide both sides by -32 to get the variable h alone and its value on the other side:
(-32h)/-32 = 0/-32
h = 0.

So -9-8(1+4h) = -17 for h = 0.

You can recheck your answer (very important):
-9 - 8(1+4h) = -9 -8(1+4*0) = -9 - 8(1+0) = -9-8*1 = -9-8 = -17
The answer has been approved.

Hope this Helps! :)
5 0
3 years ago
Read 2 more answers
Jorge is asked to build a box in the shape of a rectangular prism. The maximum girth of the box is 20 cm. What is the width of t
MariettaO [177]

Answer:

The width of the box is 6.7 cm

The maximum volume is 148.1 cm³

Step-by-step explanation:

The given parameters of the box Jorge is asked to build are;

The maximum girth of the box = 20 cm

The nature of the sides of the box = 2 square sides and 4 rectangular sides

The side length of square side of the box = w

The length of the rectangular side of the box = l

Therefore, we have;

The girth = 2·w + 2·l = 20 cm

∴ w + l = 20/2 = 10

w + l = 10

l = 10 - w

The volume of the box, V = Area of square side × Length of rectangular side

∴ V = w × w × l = w × w × (10 - w)

V = 10·w² - w³

At the maximum volume, we have;

dV/dw = d(10·w² - w³)/dw = 0

∴ d(10·w² - w³)/dw = 2×10·w - 3·w² = 0

2×10·w - 3·w² = 20·w - 3·w² = 0

20·w - 3·w² = 0 at the maximum volume

w·(20 - 3·w) = 0

∴ w = 0 or w = 20/3 = 6.\overline 6

Given that 6.\overline 6 > 0, we have;

At the maximum volume, the width of the block, w = 6.\overline 6 cm ≈ 6.7 cm

The maximum volume, V_{max}, is therefore given when w = 6.\overline 6 cm = 20/3 cm  as follows;

V = 10·w² - w³

V_{max} = 10·(20/3)² - (20/3)³ = 4000/27 = 148.\overline {148}

The maximum volume, V_{max} = 148.\overline {148} cm³ ≈ 148.1 cm³

Using a graphing calculator, also, we have by finding the extremum of the function V = 10·w² - w³, the coordinate of the maximum point is (20/3, 4000/27)

The width of the box is;

6.7 cm

The maximum volume is;

148.1 cm³

5 0
3 years ago
Which expressions represents twelve diminished by six times a number:. 12-6n; 6n-12; 12n-6
Ede4ka [16]
12-6n
.......................
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Draw a line representing the rise and a line representing the run of the line State the slope of the line in simplest form
amid [387]
Slope is -5/3
I hope this helps :)

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A ball is thrown upwards and it’s height h m,at time t s,is given by h=7t-4.9t2.How long does the ball spend more than 1.5m abov
Allushta [10]

Answer:  From what you wrote the I think the ball is drop

At time 0 you are 7 meters above ground

You basically just need to solve for

1.5 =7t-4.9t^2

by rearrange the equation you get

4.9t^2-7t+1.5=0

by using Quadratic Formula

t=1.166s

4 0
3 years ago
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