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2 years ago

Given the function f(X)= |3x-7|, find the values of X that satisfy the equation f(X) = 4

Mathematics

1 answer:

Kay [80]2 years ago

5 0

Answer:

x = 1 or x = $\frac{11}{3}$

Step-by-step explanation:

The expression inside the absolute value function can be positive or negative

That is 3x - 7 = ± 4

There are 2 equations to solve

(1)

3x - 7 = 4 ( add 7 to both sides )

3x = 11 ( divide both sides by 3 )

x = $\frac{11}{3}$

(2)

3x - 7 = - 4 ( add 7 to both sides )

3x = 3 ( divide both sides by 3 )

x = 1

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A restaurant can seat 100 people. It has booths that seat 4 people and tables that seat 6 people. So far, 5 of the booths are fu

lubasha [3.4K]

Okay, lets say
B=booths
T=tables
P=people
without the numbers in your equation would look like this
B(P)+T(P)=100
So with everything plugged in your equation is
5(4)+T(6)=100

7 0

3 years ago

Match each function to its corresponding sequence.

givi [52]

The sequence and their functions are:

f(n) = f(n - 1) + 7 ⇒ 3, 10, 17, 24, 31.....
f(n) = f(n - 1) + 4n - 2 ⇒ 3, 9, 19, 33, 51.....
f(n) = 2[f(n - 1)] ⇒ 3, 6, 12, 24, 48.....

<h3>How to match the functions?</h3>

To do this, we simply set values for n and calculate the function values using the current value of n.

So, we have:

Function 1: f(n) = f(n - 1) + 6n - 5 where f(1) = 3

Let n = 2

f(2) = f(1) + 6(2) - 5 = 3 + 12 - 5 = 10

Let n = 3

f(3) = f(2) + 6(3) - 5 = 10 + 18 - 5 = 23

None of the sequence follows the pattern 3, 10, 23....

Function 2: f(n) = f(n - 1) + 2n - 1 where f(1) = 3

Let n = 2

f(2) = f(1) + 2(2) - 1 = 3 + 4 - 1 = 6

Let n = 3

f(3) = f(2) + 2(3) - 1 = 6 + 6 - 1 = 11

None of the sequence follows the pattern 3, 6, 11....

Function 3: f(n) = f(n - 1) + 6 where f(1) = 3

Let n = 2

f(2) = f(1) + 6 = 3 + 6 = 9

Let n = 3

f(3) = f(2) + 6 = 9 + 6 = 15

None of the sequence follows the pattern 3, 9, 15....

Function 4: f(n) = f(n - 1) + 7 where f(1) = 3

Let n = 2

f(2) = f(1) + 7 = 3 + 7 = 10

Let n = 3, 4 and 5

f(3) = f(2) + 7 = 10 + 7 = 17

f(4) = f(3) + 7 = 17 + 7 = 24

f(5) = f(4) + 7 = 24 + 7 = 31

So, we have:

f(n) = f(n - 1) + 7 ⇒ 3, 10, 17, 24, 31.....

Function 5: f(n) = f(n - 1) + 4n - 2 where f(1) = 3

Let n = 2

f(2) = f(1) + 4(2) - 2 = 3 + 8 - 2 = 9

Let n = 3, 4 and 5

f(3) = f(2) + 4(3) - 2 = 9 + 12 - 2 = 19

f(4) = f(3) + 4(4) - 2 = 19 + 16 - 2 = 33

f(5) = f(4) + 4(5) - 2 = 33 + 20 - 2 = 51

So, we have:

f(n) = f(n - 1) + 4n - 2 ⇒ 3, 9, 19, 33, 51.....

Function 6: f(n) = 2[f(n - 1)] where f(1) = 3

Let n = 2

f(2) = 2 * f(1) = 2 * 3 = 6

Let n = 3, 4 and 5

f(3) = 2 * f(2) = 2 * 6 = 12

f(4) = 2 * f(3) = 2 * 12 = 24

f(5) = 2 * f(4) = 2 * 24 = 48

So, we have:

f(n) = 2[f(n - 1)] ⇒ 3, 6, 12, 24, 48.....

Read more about sequence at:

brainly.com/question/6561461

#SPJ1

7 0

2 years ago

Solve for x. (5x - 24) (8x + 9)

Stella [2.4K]

Answer:

40 $x^{2}$ - 147x - 216

Step-by-step explanation:

(5x - 24) (8x + 9)

First start with multiplying 5x to 8x and 9

40 $x^{2}$ +45x

then multiply -24 by 8x and 9

-192 x -216

40 $x^{2}$ +45x

-192 x -216

________________

40 $x^{2}$ - 147x - 216

7 0

3 years ago

Stainless steels are frequently used in chemical plants to handle corrosive fluids, however, these steels are especially suscept

Ira Lisetskai [31]

Answer: 95% confidence interval would be (0.344,0.456).

Step-by-step explanation:

Since we have given that

n = 295

x = 118

so, $\hat{p}=\dfrac{x}{n}=\dfrac{118}{295}=0.4$

At 95% confidence, z = 1.96

So, margin of error would be

$z\times \sqrt{\dfrac{p(1-p)}{n}}\\\\=1.96\times \sqrt{\dfrac{0.4\times 0.6}{295}}\\\\=0.056$

so, 95% confidence interval would be

$\hat{p}\pm \text{margin of error}\\\\=0.4\pm 0.056\\\\=(0.4-0.056,0.4+0.056)\\\\ =(0.344,0.456)$

Hence, 95% confidence interval would be (0.344,0.456).

6 0

3 years ago

Read 2 more answers

Lucy earns 52 dollars each week working part-time at a bookstore. She earns one additional dollar for each book that she sells.

Misha Larkins [42]

Answer:

A = B + 52

Step-by-step explanation:

A is the total amount each week. 52 is the initial amount that she earns each week. Then, B represents the amount of books she sells. So, 15 books can be represented by

A = 15 + 52 = 67

5 0

2 years ago

Read 2 more answers