MATHEMATICS HIGH SCHOOL

Simplify 6.4a - 4.7a

Answers

Answer 1

Answer:

4.7a+8.2a-6.5a=0

We simplify the equation to the form, which is simple to understand

4.7a+8.2a-6.5a=0

We move all terms containing a to the left and all other terms to the right.

+4.7a+8.2a-6.5a=0

We simplify left and right side of the equation.

+6.4a=0

We divide both sides of the equation by 6.4 to get a.

a=0

Answer 2

Answer:

Answer is 1.7a

Hope it helped.

-Charlie

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What is f(x) = 7x2 + 42x written in vertex form?

Answers

Answer:

$\boxed{\boxed{y = 7(x+3)^2-63}}$

Step-by-step explanation:

The general vertex form of parabola is,

$y=a(x-h)+k$

where,

(h, k) is the vertex of the parabola.

The given function is,

$\Rightarrow f(x) = 7x^2 + 42x$

$\Rightarrow y = 7x^2 + 42x$

$\Rightarrow y = 7(x^2 + 6x)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3-3^2)$

$\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3)-7\cdot 3^2$

$\Rightarrow y = 7(x+3)^2-7\cdot 9$

$\Rightarrow y = 7(x+3)^2-63$

This is vertex form the given function.

Hello,

y=7x²+42x
==>y=7(x²+2*3*x+9)-63
==>y=7(x+3)²-63

Olga buys tickets to a concert. She pays $27.75 for each ticket, plus handling fee of $5.50 for The order. The total cost is $144.25. Right and solve an equation to find out how many tickets,n,Olga bought

Answers

Answer: the number of tickets that Olga bought is 5

Step-by-step explanation:

Let x represent the number of tickets that Olga bought.

Olga buys tickets to a concert. She pays $27.75 for each ticket, plus handling fee of $5.50 for The order. This means that the total amount that Olga paid for x tickets would be

27.75x + 5.5

If the total cost is $144.25, the equation representing the situation would be expressed as

27.75x + 5.5 = 144.25

27.75x = 144.25 - 5.5

27.75x = 138.75

x = 138.75/27.75

x = 5

The function below shows the number of car owners f(t), in thousands, in a city in different years t:f(t) = 0.25t2 − 0.5t + 3.5

The average rate of change of f(t) from t = 2 to t = 6 is ______ thousand owners per year.

Answers

Answer:

1.5 thousand owners per year.

Step-by-step explanation:

Number of car owners is represented by the function as

f(t) = 0.25t² - 0.5t + 3.5

Where 't' is time in years.

Now we have to find the rate of change of f(t) from t = 2 to t = 6

or $(f(6)-f(2))/(6-2)$

f(6) = 0.25 × 36 - 0.5 × 6 + 3.5

= 9 - 3 + 3.5

= 9.5

f(2) = 0.25 × 4 - 0.5 × 2 + 3.5

= 1 - 1 + 3.5

= 3.5

Now average rate of change $(f(6)-f(2))/(6-2)$ = $(9.5-3.5)/(6-2)$

$=(6)/(4)$

= 1.5 thousand owners per year.

The scoop of an excavator holds 27 ft3 of sand. If the capacity of a freight car is 40 tons of sand and we know that 1 ft3 of sand weighs 0.5 tons, how many freight cars can be filled with 120 loads?

Answers

27ft³=x tons
1ft³=0.5 tons

$(27cubicfeet)/(x_t_o_n_s) = (1cubic foot)/(0.5 tons)$

Cross multiply
1x=13.5tons
x=13.5tons

So one scoop/load carries 13.5 tons of sand. Lets see how many 120 loads can carry.

13.5tons*120loads=1620 tons of sand

Now lets see how freight cars it would take to hold 1620 tons of sand

1620/40=40.5 freight cars

Since you can't have .5 of a freight car, lets round 40.5 up to 41

Answer=41 freight cars

Answer:

40.5

Step-by-step explanation:

Simplify the following expression: 35 + (–13) + (+8) – (–6).