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Solving equations: (a) 5x - 9 = 3x + 3 (b) x + 6 = 34 - x

Jet001 [13]

Answer:

a) 5x - 9 = 3x + 3

5x - 3x = 3 + 9

2x = 12

x = 12 / 2

x = 6

b) x + 6 = 34 - x

x + x = 34 - 6

2x = 28

x = 28 / 2

x = 14

8 0

3 years ago

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How do you turn 9 and 3 5s as a decimal???

Zarrin [17]

Answer:

9.6

Step-by-step explanation:

As 9 and 3/5s, the 9 is whole so you do not change it. To make 3/5th into a decimal you increase the denominator into x/10. To make 5 into 10 you multiply 5x2=10. And since you changed the bottom you have to change the top and multiply it by 2. 3x2=6. So the 9 stays the same and since the first place beind the decimal is tenths, and youre fraction is now 6/10 you put it as 9.6.

Hope it helps!

8 0

3 years ago

When 8 is subtracted from Ollie’s age, the result is the same as subtracting 16 from 3 times his age.

Scilla [17]

X - Ollie's age

8 is subtracted from Ollie's age = x-8
the result is the same as
subtracting 16 from 3 times his age = 3x-16

$x-8=3x-16 \\
x-3x=-16+8 \\
-2x=-8 \\
x=4$

Ollie is 4 years old.

5 0

3 years ago

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Problem PageQuestion An automobile manufacturing plant produced 34 vehicles today: 16 were motorcycles, 9 were trucks, and 9 wer

8_murik_8 [283]

Answer:

Probability that the first vehicle selected is a motorcycle and the second vehicle is a van is (24/187) or 0.1283.

Step-by-step explanation:

We are given that an automobile manufacturing plant produced 34 vehicles today: 16 were motorcycles, 9 were trucks, and 9 were vans.

Plant managers are going to select two of these vehicles for a thorough inspection. The first vehicle will be selected at random, and then the second vehicle will be selected at random from the remaining vehicles.

As we know that, Probability of any event = $\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}$

Now, Probability that the first vehicle selected is a motorcycle is given by;

= $\frac{\text{Number of motorcycles}}{\text{Total number of vehicles}}$

Here, Number of motorcycles = 16

Total number of vehicles = 16 + 9 + 9 = 34

So, Probability that the first vehicle selected is a motorcycle = $\frac{16}{34}$

Similarly, Probability that the second vehicle is a van is given by;

= $\frac{\text{Number of vans}}{\text{Total number of remaining vehicles}}$

Here, Number of vans = 9

And Total number of remaining vehicles after selecting one motorcycle = 34 - 1 = 33

So, Probability that the second vehicle selected is a van = $\frac{9}{33}$

Therefore, the probability that the first vehicle selected is a motorcycle and the second vehicle is a van = $\frac{16}{34}\times \frac{9}{33}$

= $\frac{24}{187}$ = 0.1283

5 0

3 years ago

Given the functions: f(x) = x^2-9 and g(x) = 3 what is (f/g)(x)? A. x-3 B. x-9 C. x+3 D. x+9

uysha [10]

Answer:

f + g)(x) = f (x) + g(x)

= [3x + 2] + [4 – 5x]

= 3x + 2 + 4 – 5x

= 3x – 5x + 2 + 4

= –2x + 6

(f – g)(x) = f (x) – g(x)

= [3x + 2] – [4 – 5x]

= 3x + 2 – 4 + 5x

= 3x + 5x + 2 – 4

= 8x – 2

(f × g)(x) = [f (x)][g(x)]

= (3x + 2)(4 – 5x)

= 12x + 8 – 15x2 – 10x

= –15x2 + 2x + 8

\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(

g

f

)(x)=

g(x)

f(x)

= \small{\dfrac{3x+2}{4-5x}}=

4−5x

3x+2

My answer is the neat listing of each of my results, clearly labelled as to which is which.

( f + g ) (x) = –2x + 6

( f – g ) (x) = 8x – 2

( f × g ) (x) = –15x2 + 2x + 8

\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}

3 0

3 years ago