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dem82 [27]
2 years ago
5

If f(x) = x + 8 and g(x) = –4x – 3, find (f + g)(x).

Mathematics
2 answers:
Soloha48 [4]2 years ago
6 0

Answer:

\huge\boxed{\sf (f + g)(x) = -3x + 5}

Step-by-step explanation:

<h3><u>Given functions:</u></h3>
  • f(x) = x + 8
  • g(x) = -4x - 3
<h3><u>Solution:</u></h3>

Add both functions

(f + g)(x) = x + 8 + (-4x - 3)

(f + g)(x) = x + 8 - 4x - 3

(f + g)(x) = x - 4x + 8 - 3

(f + g)(x) = -3x + 5

\rule[225]{225}{2}

Alecsey [184]2 years ago
5 0

Answer:

B

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= x + 8 - 4x - 3 ← collect like terms

= - 3x + 5

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What is 3y mean in a math problem
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3 years ago
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What is the average rate of change of f(x), represented by the table of values, over the interval [-3,4]
77julia77 [94]

Answer:

Average rate of change = 3

Step-by-step explanation:

  • We know that the average rate of change is basically a measure of the slope of the  secant line  in the closed interval [a, b].

here   a = -3 and b = 4

  • f(b) = f(4) = 27
  • f(a) = f(-3) = 6

⇒ Average rate of change = f(b) - f(a)  / b - a

                                            = (27 - 6) / (4 - (-3))

                                            = 21 / 7

                                            = 3

Therefore, Average rate of change = 3

6 0
3 years ago
Mrs. Jones is building wooden picture frames. She has 1 5/8 of wood and needs 3/4 for each frame. How many frames can she make w
jonny [76]

Answer:

2\frac{1}{6}\ frames

Step-by-step explanation:

we know that

To find out how many frames she can  make with the exiting material, divide 1 5/8 by 3/4

so

1\frac{5}{8}:\frac{3}{4}

Convert mixed number to an improper fraction

1\frac{5}{8}=\frac{1*8+5}{8}=\frac{13}{8}

substitute

\frac{13}{8}:\frac{3}{4}=\frac{52}{24}\ frames

Simplify

\frac{13}{6}\ frames

Convert to mixed number

\frac{13}{6}\ frames=\frac{12}{6}+\frac{1}{6}=2\frac{1}{6}\ frames

6 0
3 years ago
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airp
beks73 [17]

Answer:

(5.4582 ; 6.8618)

Step-by-step explanation:

Given the data:

6 10 2 6 3 3 3 6 6 6 6 5 8 9 10 10 7 9 3 6 5 10 9 9 10 3 8 6 6 3 3 6 6 5 4 10 9 3 5 7 10 6 3 8 6 8 3 3 5 5

Sample mean, xbar = Σx / n

n = sample size = 50

ΣX = 308

xbar = 308 / 50 = 6.16

Using a Calculator :

The sample standard deviation, s = 2.469

Confidence interval = xbar ± margin of error

Margin of Error = Tcritical * s/sqrt(n)

Tcritical at 95% ; df = 50 - 1 = 49

Tcritical = 2.010

Hence,

Margin of Error= 2.010 * (2.469/sqrt(50)) = 0.7018

Lower boundary : (6.16 - 0.7018) = 5.4582

Upper boundary : (6.16 + 0.7018) = 6.8618

(5.4582 ; 6.8618)

4 0
3 years ago
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