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3 years ago

Why is it helpful to rewrite inequalities

Mathematics

1 answer:

mr_godi [17]3 years ago

7 0

Answer:

that puts the solution in the form ...

variable is ...

Step-by-step explanation:

It isn't always.

Often, we like to have a solution be in the form ...

variable is ...

So, for an inequality, that puts the variable on the left:

x > 3

y < 27

Personally, I like to see the answer in a form that has the variable and its values in the same relation as on a number line. This means, my preferred inequality symbols are < or ≤, since those have the smaller numbers on the left. I would write the first example above as ...

3 < x

showing that the shaded portion of the number line (representing possible values of the variable) is to the right of the open circle at 3. For me, it is more mental effort to translate x > 3 to the same image.

The forms we choose to use are all about making communication as easy as possible.

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A bird traveled 4 miles north before stopping to rest. The bird then flew 2,640 yards south in search of food. Finally, it flew

ra1l [238]

7 and 1/2 mile because 2,640=1.5 miles
4-1.5=2.5+5=7.5

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3 years ago

Write the following percentages as a fraction in simplest form

alisha [4.7K]

Answer: 241/4%
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3 years ago

What is the answer to this question please explain (picture included)

Yakvenalex [24]

Easy peasy
just use PEMDAS and some exonential laws

$(x^{m})(x^{n})=x^{m+n}$
$(x^{m})^{n}=x^{mn}$
$(ab)^{m}=(a^{m})(b^{m})$

also another is $x^{\frac{m}{n}}=\sqrt[n]{x^{m}}$

so

$[3(2a)^{\frac{3}{2}}]^{2}$ =
$(3^{2})((2a)^{\frac{3}{2}}^{2})$ =
$(9)((2a)^{\frac{3}{2}}^{2})$ =
$(9)((2a)^{\frac{6}{2})$ =
$(9)((2a)^{3})$ =
$(9)(8a^{3})$ =
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3 0

3 years ago

Solve system by elimination y=x^2 y=x+2 SHOW YOUR WORK

Dimas [21]

We have that
y=x²----> equation 1
y=x+2-----> equation 2

multiply equation 1 by -1
-y=-x²

add equation 1 and equation 2
-y=-x²
y=x+2
------------
0=-x²+x+2-------------> -x²+x+2=0-----> x²-x-2=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(x²-x)=2
Complete the square. Remember to balance the equation by adding the same constants to each side
(x²-x+0.5²)=2+0.5²

Rewrite as perfect squares

(x-0.5)²=2+0.5²
(x-0.5)²=2.25-----> (x-0.5)=(+/-)√2.25-----> (x-0.5)=(+/-)1.5
x1=1.5+0.5-----> x1=2
x2=-1.5+0.5---- > x2=-1

for x=2
y=x²----> y=2²----> y=4
the point is (2,4)

for x=-1
y=x²----> y=(-1)²---> y=1
the point is (-1,1)

the answer is
the solution of the system are the points
(2,4) and (-1,1)

3 0

3 years ago

Please answer circle theorem question. Many thx.

pogonyaev

Answer:

x = 125

Step-by-step explanation:

Tangents from an external point to a circle are congruent , that is

CA = CB

Then Δ ABC is isosceles with base angles being congruent

∠ BAC = ∠ ABC = $\frac{180-70}{2}$ = $\frac{110}{2}$ = 55°

∠ ABC and x are adjacent angles on a straight line and sum to 180° , so

x = 180° - 55° = 125°

Then x = 125

3 0

2 years ago