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3 years ago

|2x + 1| - 4 < 5 solve and graph

Mathematics

2 answers:

NeX [460]3 years ago

7 0

Answer:

The value of x could be 3

Step-by-step explanation:

2 x 3 = 6 + 1 - 4 = 3 which is less than 5

Illusion [34]3 years ago

4 0

Answer:

Step-by-step explanation:

Can you give brainliest please

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Solve the equation uding the most direct method: 3x(x+6)=-10?

Tanzania [10]

To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

<h3>Distribute</h3>

Use the distributive property to distribute 3x into the term (x + 6):

$3x(x+6)=-10$

$3x^2+18x=-10$

<h3>Rearrange</h3>

To create a quadratic equation, add 10 to both sides of the equation:

$3x^2+18x+10=-10+10$

$3x^2+18x+10=0$

<h3>Use the Quadratic Formula</h3>

The quadratic formula is defined as:

$\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

a = 3
b = 18
c = 10

Set up the quadratic formula:

$\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}$

Simplify by using BPEMDAS, which is an acronym for the order of operations:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Use BPEMDAS:

$\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}$

Simplify the radicand:

$\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}$

Create a factor tree for 204:

204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.

The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

$\sqrt{4\times51}$

Then, using the Product Property of Square Roots, break this into two radicands:

$\sqrt{4} \times \sqrt{51}$

Since 4 is a perfect square, it can be evaluated:

$2 \times \sqrt{51}$

To simplify further for easier reading, remove the multiplication symbol:

$2\sqrt{51}$

Then, substitute for the quadratic formula:

$\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}$

This gives us a combined root, which we should separate to make things easier on ourselves.

<h3>Separate the Roots</h3>

Separate the roots at the plus-minus symbol:

$\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}$

$\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}$

Then, simplify the numerator of the roots by factoring 2 out:

$\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}$

$\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}$

Then, simplify the fraction by reducing 2/6 to 1/3:

$\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}$

$\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}$

The final answer to this problem is:

$\displaystyle x=\frac{-9 + \sqrt{51}}{3}$

$\displaystyle x=\frac{-9 - \sqrt{51}}{3}$

3 0

2 years ago

Pls help due today!!!!!!

Agata [3.3K]

Answer: A

Step-by-step explanation:

For a line to be perpendicular, the slope should be the opposite reciprocal. The intercept doesn't matter, so we automatically know that it's A.

6 0

3 years ago

A sociologist surveyed 300 people about their level of anxiety on a scale of 1 to 100. Unfortunately, the person inputting the d

Lerok [7]

Answer:

non sampling error

Step-by-step explanation:

Sampling error in a statistical analysis arising from the unrepresentativeness of the sample taken.

Non Sampling error is a term used in statistics that refers to an error that occurs during data collection, causing the data to differ from the true values.

4 0

3 years ago

Read 2 more answers

Is the statement (3 to the 5th power) to the 4th power = (3 to the 4th power) to the 5th power true? pls explain your reasoning

dezoksy [38]

Answer:

Step-by-step explanation:

It is due because you multiply the powers

5*4=20 4*5 =20

the result in both cases is 3 to the 20th power

4 0

3 years ago

A refrigerator is priced at 525.50 there is a 7% sales tax rate

Evgesh-ka [11]

Answer:

562.29

Step-by-step explanation:

you would just multiply 525.50 by 7 which is 3678.5 and divide that by 100 which is 36.785 and add that to 525.50 which is 562.285 which can be rounded to 562.29

6 0

4 years ago