All categories

2 years ago

Expand then fully factorise 9(f + 3) +36f - 3)

Mathematics

1 answer:

Ganezh [65]2 years ago

3 0

Answer:

3(15f + 8)

Step-by-step explanation:

9f + 27 + 36f - 3

We can take out 3.

3(3f + 9 + 12f -1)

3(15f + 8)

You might be interested in

A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq . By h

julia-pushkina [17]

Well to get the area of 288 the dimensions would be a couple of things but 16 ft by 18 ft seems to work, so the dimensions increase by 4 ft on each side.

12+4=16
14+4=18

18*16=288

6 0

3 years ago

Read 2 more answers

The population, P(t), of China, in billions, can be approximated by1 P(t)=1.394(1.006)t, where t is the number of years since th

vitfil [10]

Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

At the start of 2015, the population was growing at 8.39 million people per year.

Step-by-step explanation:

To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

We know that the population, P(t), of China, in billions, can be approximated by $P(t)=1.394(1.006)^t$

To find the derivative you need to:

$\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t$

To find the population growing at the start of 2014 we say t = 0

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year$

To find the population growing at the start of 2015 we say t = 1

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year$

To convert billion to million you multiple by 1000

$P(0)' = 0.00833901 \:Billion/year \cdot 1000 = 8.34 \:Million/year \\P(1)' = 0.00838904 \:Billion/year \cdot 1000 = 8.39 \:Million/year$

6 0

3 years ago

Can someone please help me check my answers ***Mark Brainliest***

lozanna [386]

I believe the answer for 17 is C. 18 I am not sure how to do. For 19, however, the answer is B. Hope I help, and sorry I can't answer 18.

3 0

4 years ago

Gianna is preparing for the upcoming tennis season. According to her schedule, she can complete at most 10 workouts this week. I

Strike441 [17]

The whole number of minutes that Gianna complete each week as a function of x and y:
$45x+30y$
Since the above number is greater than 450 minutes, we get the inequality:
$45x+30y\geq450$
Also, "she can complete at most 10 workouts this week" so we deduce the inequality:
$\\x+y\leq10$
Therefore, the system of inequalities is the following:
$45x+30y\geq450$
$\\x+y\leq10$
The above system has many solutions, for example :

4 0

3 years ago

I need help with this one .

skelet666 [1.2K]

Answer:

32/9

Step-by-step explanation:

2 to the fifth power is 32. 3 to the second power is 9.

3 0

3 years ago