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4 years ago

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Let f(x) = 4x – 5 and g(x) = 3x + 7. Find f(x) + g(x) and state its domain.

1 answer:

lesantik [10]4 years ago

8 0

$f(x)=4x-5,\ g(x)=3x+7\\\\f(x)+g(x)=(4x-5)+(3x+7)=4x-5+3x+7\\\\=(4x+3x)+(-5+7)=7x+2\\\\\text{It's a linear function. The domain is the set of all real numbers.}\\\\Answer:\\\\f(x)+g(x)=7x+2\\D=\mathbb{R}$

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Write a solution in Interval Notation - (you don't have to help me on all, 1 or 2 is fine c: )

Gemiola [76]

QUESTION 1

The given inequality is

$|m|-2>0$

We group like terms to get,

$|m|>2$

This implies that,

$-m>2$ or $m>2$ .

We simplify the inequality to get,

$m$ or $m>2$ .

We can write this interval notation to get,

$(-\infty,-2)\cup (2,+\infty)$ .

QUESTION 2

$|x-4|-3\:>\:5$ .

We group like terms to get,

$|x-4|\:>\:5+3$ .

$|x-4|\:>\:8$

We split the absolute value sign to get,

$-(x-4)\:>\:8$ or $x-4\:>\:8$

This implies that,

$x-4\:$ or $x-4\:>\:8$

$x\:$ or $x\:>\:8+4$

$x\:$ or $x\:>\:12$

We can write this interval notation to get,

$(-\infty,-4)\cup (12,+\infty)$ .

QUESTION 3

The given inequality is

$|6+9x|\leq 24$

We split the absolute value sign to obtain,

$-(6+9x)\leq 24$ or $(6+9x)\leq 24$

This simplifies to

$6+9x\ge -24$ and $6+9x\leq 24$

$9x\ge -24-6$ and $9x\leq 24-6$

$9x\ge -30$ and $9x\leq 18$

$x\ge -\frac{10}{3}$ and $x\leq 2$

$-\frac{10}{3}\leq x\leq2$

We write this in interval form to get,

$[-\frac{10}{3},2]$

QUESTION 4

The given inequality is

$|1-5a|>29$

We split the absolute value sign to get,

$-(1-5a)>29$ or $1-5a>29$

This simplifies to,

$1-5a\:$ or $1-5a\:>\:29$

This implies that,

$-5a\:$ or $-5a\:>\:29-1$

$-5a\:$ or $-5a\:>\:28$

$a\:>\:6$ or $a\:$

We write this in interval notation to get,

$(-\infty,-\frac{28}{5})\cup (6,+\infty)$

7 0

3 years ago

33x-21x=-24+12 <br> I need help on this math problem. Thanks

lions [1.4K]

X=3. 33x-21x equals 12x. 24+12=36. 12x divided by 36 equals 3

8 0

3 years ago

Help the question is the picture

nikdorinn [45]

Answer:

a>-21(1/3)

Step-by-step explanation:

3/4a>-16

first thing is to divide both sides by 3/4 to isolate the variable.

Since it is not negative, the sign stays the same.

-16/0.75=-21.3 repeating or just 1/3

5 0

3 years ago

Help please me with these two questions. Thank you

arlik [135]

9514 1404 393

Answer:

1. 9/20 hours doing math for 1 hour reading

2. 3 1/3 cups water to 1 cup concentrate

Step-by-step explanation:

1. You have done the math. Copy your answer into the blanks that are waiting for it.

9/20 hours on math for 1 hour reading

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2. 1 2/3 ÷ 1/2 = 5/3 × 2/1 = 10/3 = 3 1/3

3 1/3 cups of water to 1 cup of juice concentrate

4 0

3 years ago

Study the following frequency distribution table.

m_a_m_a [10]

Answer:

Option C is correct.

f = 2

Step-by-step explanation:

The mean is the sum of variables divided by the number of variables

Mean = (Σfx)/(Σf)

xi | 15 | 17 | 20 | 30 | 10 + f

fi | 4 | 4 | 6 | 5 | 6

Σfx = (15×4) + (17×4) + (20×6) + (30×5) + [(10+f)×6] = 60 + 68 + 120 + 150 + 60 + 6f = (458 + 6f)

Σf = 4 + 4 + 6 + 5 + 6 = 25

Mean = 18.8

18.8 = (458+6f) ÷ 25

458 + 6f = 25 × 18.8 = 470

6f = 470 - 458 = 12

f = (12/6) = 2

Hope this Helps!!!

6 0

3 years ago