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4 years ago

PLEASE HELP ME :(

Mathematics

1 answer:

arsen [322]4 years ago

6 0

Answer:

2x² + 5x + 3 = (2x + 3)(x + 1)

Step-by-step explanation:

* Lets explain how to factor a trinomial in the form ax² ± bx ± c:

- Look at the last term c

# If the c term is a positive number, then its factors r , s will both

be positive or both be negative

# a has two factors h and k

# The brackets are (hx ± r)(kx ± s) where a = hk , c = rs and b = rk + hs

# If the c term is a negative number, then either r or s will be negative,

but not both.

# a has two factors h and k

# The brackets are (hx + r)(kx - s) <em>or</em> (hx - r)(kx + s)where a = hk ,

c = rs and b = rk - hs

* Lets solve the problem

∵ The equation is 2x² + 5x + 3 = 0

∵ The general form of the equation is ax² + bx + c = 0

∴ a = 2 , b = 5 , c = 3

∵ c is positive

∴ Its factors r and s have same sign

∵ c = 3

∵ 3 = 3 × 1

∴ r = 3 and s = 1

∵ a = 2

∵ The factors of a are h , k

∵ 2 = 2 × 1

∴ h = 2 and k = 1

∵ The brackets are (hx + r)(kx + s)

∴ 2x² + 5x + 3 = (2x + 3)(x + 1)

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Two opposite sides of a square with length x are increased by 3 units each and the other two opposite sides are decreased by 3 u

SCORPION-xisa [38]

All four sides of the original square have length s.

Adding 3 to s results in s+3, the length of the resulting rectangle.
Subtracting 3 from s results in s-3, the width of the rectangle.

The area of the rectangle is (s+3)(s-3) = s^2 - 9 = 27,

and therefore s^2 = 36, and s = 6 square units.

5 0

3 years ago

The port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge, is the largest

Ksenya-84 [330]

Answer:

a) 0.7287

b) 0.9663

c) 0.237

d) 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4.5 million tons of cargo per week

Standard Deviation, σ = 0 .82 million tons

We are given that the distribution of number of tons of cargo handled per week is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P( port handles less than 5 million tons of cargo per week)

P(x < 5)

$P( x < 5) = P( z < \displaystyle\frac{5 - 4.5}{0.82}) = P(z < 0.609)$

Calculation the value from standard normal z table, we have,

$P(x < 5) =0.7287= 72.87\%$

b) P( port handles 3 or more million tons of cargo per week)

$P(x \geq 3) = P(z \geq \displaystyle\frac{3-4.5}{0.82}) = P(z \geq −1.82926)\\\\P( z \geq −1.82926) = 1 - P(z < -1.829)$

Calculating the value from the standard normal table we have,

$1 - 0.0337 = 0.9663 = 96.63\%\\P( x \geq 3) = 96.63\%$

c)P( port handles between 3 million and 4 million tons of cargo per week)

$P(3 \leq x \leq 4) = P(\displaystyle\frac{3 - 4.5}{0.82} \leq z \leq \displaystyle\frac{4-4.5}{0.82}) = P(-1.829 \leq z \leq -0.609)\\\\= P(z \leq -0.609) - P(z < -1.829)\\= 0.271-0.034 = 0.237= 23.7\%$

$P(3 \leq x \leq 4) = 23.7\%$

d) P(X=x) = 0.85

We have to find the value of x such that the probability is 0.85.

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 4.5}{0.82})=0.85$

$= 1 -P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.85$

$=P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.15$

Calculation the value from standard normal z table, we have,

$P( z \leq -1.036) = 0.15$

$\displaystyle\frac{x - 4.5}{0.82} = -1.036\\x = 3.65$

Thus, 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

8 0

3 years ago

Can someone teach me how to do this pleasseeee!

Ludmilka [50]

So the equation is 5-x3
x^3=x*x*x
so you have x=-2
That means y=5-(-2*-2*-2)
y=5-(-8) which gives y=13
Do this for every x and get the y

7 0

3 years ago

Read 2 more answers

Rotate the rectangle 90° clockwise about the origin.

WINSTONCH [101]

The coordinates of the new rectangle formed after transformation are; A'(3, -1); B'(6, -1); C'(6, 4); D'(3, 4)

<h3>How to carry out rotational transformation?</h3>

We are told that the original rectangle which I labelled ABCD in the attached image is rotated 90° clockwise about the origin.

Now, from the translation of Rectangle ABCD into A'B'C'D' using the transformation rule in the question, the new coordinates are;

A'(3, -1)

B'(6, -1)

C'(6, 4)

D'(3, 4)

Read more about Rotational Transformation at; brainly.com/question/4289712

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3 0

2 years ago

Pls answer 17 and 18 I will give brainist

Nataly_w [17]

Answers:

Step-by-step explanation:

17. We need to understand what an indirect proof is. In an indirect proof, you prove a statement by showing that the negation of the statement is false.

The "then" part of the conditional is the "to prove" statement.

In an indirect proof, we assume the opposite of what we want to prove, this is also called proof by contradiction.

So if we need to prove angle A is not an obtuse angle, we will assume it is and then use the proof format to show that angle A cannot be obtuse.

<h2>The answer is B: Assume angle A is an obtuse angle</h2>

18. This question is asking us to use an indirect proof again. The "then" part of the statement is "KL > JK" and is the "to prove" statement.

We need the opposite of this, which would be assuming that KL <u><</u> JK.

<h2>The answer is B: Assume that KL <u><</u> JK</h2><h2>I'm always happy to help :)</h2>

4 0

3 years ago

Read 2 more answers