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3 years ago

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

Mathematics

2 answers:

yawa3891 [41]3 years ago

3 0

Step-by-step explanation:

number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

babunello [35]3 years ago

3 0

Solve the inequality:

3(8 – 4x) < 6(x – 5)
8 - 4x < 2(x - 5)
8 - 4x < 2x - 10
8 + 10 < 4x + 2x
18 < 6x
3 < x
x > 3

The solution set is the space to the right from 3, where 3 is given by an open circle.

Correct choice reflecting the answer is B:

A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

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section of a pipe's length and weight are in proportion. If 2.5 m of pipe weighs 10 kg, then A) 5 m of pipe weighs 30 kg. B) 5 m

motikmotik

We will proceed to resolve each case to determine the solution.

we know that

$2.5$ m of pipe weighs $10$ kg

by proportion

Find the weighs of each case

case A) $5$ m of pipe weighs $30$ kg

$\frac{10}{2.5}\frac{kg}{m}=\frac{x}{5}\frac{kg}{m}\\ \\2.5*x=5*10\\ \\x=50/2.5\\x=20\ kg$

$20\ kg\neq30\ kg$

therefore

The statement case A) is False

case B) $5$ m of pipe weighs $40$ kg

$\frac{10}{2.5}\frac{kg}{m}=\frac{x}{5}\frac{kg}{m}\\ \\2.5*x=5*10\\ \\x=50/2.5\\x=20\ kg$

$20\ kg\neq40\ kg$

therefore

The statement case B) is False

case C) $10$ m of pipe weighs $40$ kg

$\frac{10}{2.5}\frac{kg}{m}=\frac{x}{10}\frac{kg}{m}\\ \\2.5*x=10*10\\ \\x=100/2.5\\x=40\ kg$

$40\ kg=40\ kg$

therefore

The statement case C) is True

case D) $10$ m of pipe weighs $80$ kg

$\frac{10}{2.5}\frac{kg}{m}=\frac{x}{10}\frac{kg}{m}\\ \\2.5*x=10*10\\ \\x=100/2.5\\x=40\ kg$

$40\ kg\neq80\ kg$

therefore

The statement case D) is False

therefore

the answer is

$10$ m of pipe weighs $40$ kg

3 0

3 years ago

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If sin x equal to a/b what is sin(90-x)

Slav-nsk [51]

Answer:

(a/b √b^2 – a^2}}{b})

Step-by-step explanation:

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3 years ago

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aniked [119]

It would be A because the r is being distributed to both the a and the b

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3 years ago

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Darcie wants to crochet a minimum of 3 blankets blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a

bearhunter [10]

Answer:

The inequality to determine the number of days, $s$ , Darcie can skip crocheting and still meet her goal is:

$s\leq 15$

Thus, Darcie can skip a maximum of 15 days.

Step-by-step explanation:

Question

Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways. Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.

Given:

Darcie has a target to crochet a minimum of 3 blankets.

Rate at which Darcie crochets = $\frac{1}{15}$ of a blanket per day.

Darcie has 60 days to crochet the blankets

To write an inequality to determine the number of days, $s$ , Darcie can skip crocheting and still meet her goal.

Solution:

The number of days Darcie can skip crocheting is represented by $s$

So, number of days left for Darcie to crochet = $60-s$

In 1 day Darcie crochets $\frac{1}{15}$ of a blanket.

So, in $(60-s)$ days she will crochet = $\frac{1}{15}(60-s)$ blankets.

Her aim is to crochet at least 3 blankets.

Thus, the inequality can be given as:

$\frac{1}{15}(60-s)\geq 3$

Solving for $s$

Multiplying both sides by 15 to remove fractions.

$15\times\frac{1}{15}(60-s)\geq 3\times 15$

$60-s\geq 45$

Subtracting both sides by 60.

$60-60-s\geq 45-60$

$-s\geq -15$

Dividing both sides by -1.

$\frac{-s}{-1}\leq \frac{-15}{-1}$ [ On dividing by negative number the sign of the inequality is reversed]

∴ $s\leq 15$

Thus, Darcie can skip a maximum of 15 days.

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3 years ago

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Determined if the graph represents a polynomial function if it does determine the number of turning points and the least degree

skelet666 [1.2K]

The graph of f is a polynomial function
There are two turning points, namely, x = 0 and x = -2

<h2>Explanation:</h2>

A polynomial function in one variable is given by the form:

$f(x)=a_{n}x^n+a_{n-1}x^{n-1}+\cdots +a_{2}x^2+a_{1}x+a_{0}$

Since you haven't provided any expression, I'll choose the following function:

$f(x)=x^{3}+3x^{2}+3$

So this is indeed a polynomial function. A turning point is an x-value where we have either a local maximum or local minimum. So we need to take the derivative of this functions:

$f'(x)=3x^2+6x \\ \\ Finding \ turning \ points: \\ \\ 3x^2+6x=0 \\ \\ x(3x+6)=0 \\ \\ \\ So: \\ \\ x=0 \\ \\ and \\ \\ \ 3x+6=0 \therefore \ \boxed{x=-2}$

Conclusion:

The graph of f is a polynomial function
There are two turning points, namely, x = 0 and x = -2

<h2>Learn more:</h2>

Polynomial function: brainly.com/question/13729121

#LearnWithBrainly

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