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3 years ago

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Mathematics

1 answer:

Katena32 [7]3 years ago

3 0

Answer:
B. Yes, because it touches the y-axis exactly one time
C. Yes, because each x-value has exactly on corresponding y-value

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kramer

Inequalities are used to express unequal expressions.

The inequalities from the word problems are:

$\mathbf{m - 3.5 \le -2}$ .
$\mathbf{0 \ge 2x + 1}$ .
$\mathbf{-\frac 12 \ge 2k - 4}$

The statements from the inequalities are:

-4 is not a solution to $\mathbf{x + 8 < -3}$
-6 is not a solution to $\mathbf{10 \le 3 - m}$
-1 is not a solution to $\mathbf{-3x \le -12.5}$

Graph b represents $\mathbf{x > -7}$

<h3>The word problems</h3>

<u>1. A number minus 3.5 is less than or equal to -2</u>

The statement can be broken down into the following expressions

$\mathbf{A\ number\ minus\ 3.5 \to m - 3.5}$

$\mathbf{less\ than\ or\ equal\ to\ -2 \to \le -2}$

So, when the expressions are brought together, we have:

$\mathbf{m - 3.5 \le -2}$

<u>2. Zero is greater than or equal to twice a number x plus 1</u>

The statement can be broken down into the following expressions

$\mathbf{Zero\ is\ greater\ than\ or\ equal\ to \to 0 \ge }$

$\mathbf{twice\ a\ number\ x\ plus\ 1\ \to 2x + 1}$

So, when the expressions are brought together, we have:

$\mathbf{0 \ge 2x + 1}$

<u />

<u>3. -1/2 is at least twice a number k minus 4</u>

The statement can be broken down into the following expressions

$\mathbf{-\frac 12\ is\ at\ least \to -\frac 12 \ge }$

$\mathbf{twice\ a\ number\ k\ minus\ 4\ \to 2k - 4}$

So, when the expressions are brought together, we have:

$\mathbf{-\frac12 \ge 2k - 4}$

None of the options is correct

<h3>The solutions</h3>

<u>4. Tell whether -4 is a solution to x + 8 < -3</u>

We have:

$\mathbf{x + 8$

Subtract 8 from both sides

$\mathbf{x + 8 - 8$

$\mathbf{x$

The above inequality means that:

-4 is not a solution, because -4 is greater than -11

<u>5. Tell whether -6 is a solution to 10 <= 3 - m</u>

We have:

$\mathbf{10 \le 3 - m}$

Subtract 3 from both sides

$\mathbf{10 -3\le 3 - 3 - m}$

$\mathbf{7 \le - m}$

Multiply both sides by -1 (the inequality sign changes)

$\mathbf{-7 \ge m}$

Make m the subject

$\mathbf{m \le -7}$

The above inequality means that:

-6 is not a solution, because -6 is greater than -7

<u>6. Tell whether -1 is a solution to -3x <= -12.5</u>

We have:

$\mathbf{-3x \le -12.5}$

Divide both sides by -3 (the inequality sign changes)

$\mathbf{x \ge 4\frac16}$

The above inequality means that:

<em>x is greater than or equal to </em> $\mathbf{4\frac16}$ <em />

-1 is not a solution, because -1 is less than $\mathbf{4\frac16}$ <em />

<h3>The graph</h3>

The inequality is given as: $\mathbf{x > -7}$

The less than sign (>) means that:

The graph would use an open circle
The arrow must point to the right

Only graph b satisfies this condition

Hence, the graph of $\mathbf{x > -7}$ is graph b

Read more about inequalities at:

brainly.com/question/15137133

4 0

2 years ago

Are they inverse ? please hurry

ddd [48]

Answer:

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Which equation has no solution?

Blababa [14]

C is the answer. Adding all the "x" values would give 0, therefore, no solution

6 0

3 years ago

A shipping container shaped like a rectangular prism must have a maximum volume of 10 cubic yards. If the container is 2 1/2 yar

denpristay [2]

Answer:

$1\frac{1}{7} yards$

Step-by-step explanation:

The maximum volume the shipping container can have is 10 cubic yards.

The volume of a rectangular prism is given as:

V = L * W * H

where L is length, W is width and H is height.

To find the maximum height of the container, make H the subject of formula:

$H = \frac{V}{L * W}$

We have been given the length and width of the container as 2 1/2 yards and 3 1/2 yards respectively.

Hence, the maximum height is:

$H = \frac{10}{2\frac{1}{2} * 3\frac{1}{2} } \\\\H = \frac{10}{\frac{5}{2} * \frac{7}{2} }$

$H = \frac{10}{\frac{35}{4} } \\\\H = \frac{10 * 4}{35} \\\\H = \frac{40}{35} = \frac{8}{7} = 1\frac{1}{7}$

The maximum height of the container is $1\frac{1}{7} yards$ .

7 0

3 years ago

a bakery has 4 trays with 16 muffins on each tray the bakery has 3 trays of cupcakes for 24 cupcakes on each tray if 15 cupcakes

stira [4]

64 muffins and 57 cupcakes. Since no muffins were sold, the amount of muffins wouldn't change. Since 15 cupcakes were sold, you just subtract 15 from the total amount of cupcakes (3 * 24 = 72; 72 - 15 = 57).

7 0

3 years ago

Read 2 more answers