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3 years ago

Explain why graphing the solutions of an inequality is more efficient than listing all the solutions of the inequality.

2 answers:

6 0

The saying "A picture is worth a thousand words" comes to mind here. You can list all of the possible points in a solution region, or you can list a few points to give the general pattern. Though this method requires a bit more work than simply graphing and showing the solution shaded region. A visual is often more efficient at conveying a message especially to those who aren't proficient with algebra. I'm sure there are other reasons why graphs are the better choice, but that's all I could think of really.

prisoha [69]3 years ago

4 0

The number of solutions to an inequality is infinite. You couldn't possibly list them. That's why a graph or set notation has to be used.

examples:

x ≥ 5
The solution set is [5, infinity) in set notation or a graph showing the shaded area above x = 5

two variable ...

y > 2x+1
solution set must be graphed because it's every point above the line y = 2x+1 all the way to infinity.

you can't possibly list all the solutions. Not even for a system of inequalities where the solution set is defined by boundaries can you list all the solutions because there are still an infinite number of points within the bounds.

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1. To the nearest degree, find the measure of angle A.

Assoli18 [71]

Answer:

(1) Option A is correct , The measure of angle A = 26°

(2) Option D is correct, The measure of angle B =70°

Step-by-step explanation:

(1)

In a right angle triangle figure-1 ,

* Hypotenuse(H) is always opposite the right angle and it is always the longest side of the triangle.

* Adjacent side (B) is the non-hypotenuse side that is next to a given angle A.

* Opposite side(P) is across from a given angle A.

To find the Angle A we use the Cosine ratio:

Cosine ratio states that the ratio of the adjacent side of a right triangle to the hypotenuse.

By definition of cosine ratio we have;

$\cos A = \frac{B}{H}$ ....[1]

In the figure - 1 we have B = 18 in and H = 20 in

substitute these in [1] to find angle A

$\cos A =\frac{18}{20} =\frac{9}{10} = 0.9$

$A = cos^{-1} (0.9)$

⇒ $A \approx 26^{\circ}$

therefore, the measure of angle A is, $26^{\circ}$

(2)P

In figure -2

Find the measure of angle B.

First find the side BC, using Pythagoras theorem;

Pythagoras theorem states that in the right angle triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Apply Pythagoras theorem in rt. angle ABC;

$AB^2 = AC^2+BC^2$

Substitute the values of AB = 5.1 cm and AC =4.8 cm to solve for BC

$(5.1)^2=(4.8)^2 +BC^2$

$26.01 = 23.04+BC^2$

Simplify:

$BC^2 = 2.97$ or

$BC = \sqrt{2.97} =1.723 cm$

Now, find the angle B, using tangent ratio;

Tangent ratio states that the ratio of the Opposite side of a right triangle to the adjacent side.

$\tan B = \frac{AC}{BC} =\frac{4.8}{1.732} =2.772$

$B = \tan^{-1} (2.772) \approx 70^{\circ}$

Therefore, the measure of angle B is; $70^{\circ}$ .

4 0

3 years ago

Read 2 more answers

Marcy is taking part in a summer movie club. She will earn 3 points for each movie she attends throughout the summer. Which equa

lawyer [7]

The answer is a \large y=3x

5 0

3 years ago

Have to find volume and surface area but idk how

Setler [38]

Answer:

volume 1050 $in^{3}$

surface area 859 $in^{2}$

Step-by-step explanation:

volume is length times width times height (7*25*12)/2

surface area is area of all the sides added together

2(25*12)+(12*7)+ 2( $\frac{7*25}{2}$ )

4 0

3 years ago

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Evelyn has $524.96 in her checking account. She must maintain a $500 balance to avoid a fee. She wrote a check for $32.50 today.

cupoosta [38]

A linear inequality to represent the algebraic expression is given as 492.46 - x ≥ 500

<h3>Linear Inequality</h3>

Linear inequalities are inequalities that involve at least one linear algebraic expression, that is, a polynomial of degree 1 is compared with another algebraic expression of degree less than or equal to 1.

In this problem, her minimum balance must not decrease beyond $500 or she will pay a fee.

where

x = withdrawals

The inequality to represent this can be written as

524.96 - 32.50 - x ≥ 500

Simplifying this;

492.46 - x ≥ 500

The linear inequality is 492.46 - x ≥ 500

Learn more on linear inequality here;

brainly.com/question/23093488

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4 0

1 year ago

Select the solution for the system of linear equations y=3x+4 and y=x+2

Oduvanchick [21]

Answer:

(- 1, 1 )

Step-by-step explanation:

Given the 2 equations

y = 3x + 4 → (1)

y = x + 2 → (2)

Substitute y = 3x + 4 into (2)

3x + 4 = x + 2 ( subtract x from both sides )

2x + 4 = 2 ( subtract 4 from both sides )

2x = - 2 ( divide both sides by 2 )

x = - 1

Substitute x = - 1 into either of the 2 equations and evaluate for y

Substituting x = - 1 into (2)

y = - 1 + 2 = 1

Solution is (- 1, 1 )

3 0

3 years ago

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